i) Inverted Yield Curve Indicates Recession: The shape of the yield curve, particularly when inverted, serves as a significant indicator of an impending recession.

2) Expectation Theory

3) Interest Rate Breakdown

i) Breaking down interest rates involves considering various components:

Real Interest Rate

Inflation Premium:

Default Premium:

Liquidity Premium:

Maturity Premium:

Part 1 - Who Wants to Chair the Fed? Quiz 1

Game: https://lewis500.github.io/macro/

The Federal Reserve (Fed) often faces the challenging dilemma of balancing economic growth with price stability - commonly referred to as the trade-off between controlling inflation and minimizing unemployment.

1. Inflation vs. Unemployment

Raising Interest Rates: Helps control inflation by slowing down spending and investment. However, this can increase unemployment as businesses cut back on hiring or production.
Lowering Interest Rates: Boosts economic growth and reduces unemployment by encouraging spending and investment. However, it can lead to rising inflation if demand outpaces supply.

2. Long-term Stability vs. Short-term Relief

The Fed must make decisions that sometimes prioritize long-term economic health (e.g., curbing inflation) over short-term relief for the economy (e.g., reducing unemployment), or vice versa.

3. Uncertainty and Lag Effects

Monetary policy decisions take time to affect the economy, making it hard to predict their full impact.
External factors, such as global economic conditions or supply shocks, add to the complexity.

In the game, you play as the Fed chair and must make interest rate decisions to strike this delicate balance while keeping inflation and unemployment within acceptable ranges. Success depends on how well you manage these competing goals over time.

Factors to Consider:

1. Current Inflation Rate:

Is inflation above or below the Fed’s target (usually 2%)?
Lowering interest rates could worsen inflation if it's already too high.

2. Unemployment Rate:

Is unemployment high? If so, a rate cut might stimulate job creation and economic activity.

3. Economic Growth:

Is the economy slowing down? If GDP growth is sluggish or negative, lowering interest rates can help boost investment and spending.

4. Consumer and Business Confidence:

Are businesses and consumers optimistic about the future? A rate cut might encourage more borrowing and spending if confidence is low.

5. Financial Market Conditions:

Are financial markets signaling distress? A lower interest rate could stabilize markets by making borrowing cheaper.

6. Global Economic Trends:

Are there external pressures, such as a global slowdown or trade disruptions, that might justify lowering rates to cushion the economy?

7. Lag Effects of Monetary Policy:

How quickly will the rate cut affect the economy? Policy changes take time, so we should consider the timing of their decision.

8. Federal Reserve’s Dual Mandate:

The Fed is tasked with promoting maximum employment and stable prices. Which goal is more at risk currently?

In-Class Debate: Should the Fed Reduce Interest Rates Soon, or Is It Better to Wait?

Support your decision with evidence based on the factors above.
Play the game to help decide.

The next Federal Open Market Committee (FOMC) meeting is scheduled for January 28–29, 2025. Let’s wait and see what unfolds leading up to this critical decision.

Part II – Who Determines Interest Rates?

Market data website:

http://finra-markets.morningstar.com/BondCenter/Default.jsp (FINRA bond market data)

Market watch on Wall Street Journal has daily yield curve and interest rate information.

http://www.marketwatch.com/tools/pftools/

In class Exercise: Draw the yield curve as of January 16, 2025.

Use current data on interest rates across various maturities (e.g., 3-month, 1-year, 10-year Treasury yields).
Analyze the shape of the curve to assess market expectations about future economic growth and interest rates.

Part III: Shapes of Yield Curve

For class discussion: What factors contributed to the shifts in yield curve shapes in 2023?

https://www.jufinance.com/fin435_25s/yield_curve_1_15_2025.html

Data:

Date	1 Mo	3 Mo	6 Mo	1 Yr	2 Yr	3 Yr	5 Yr	7 Yr	10 Yr	20 Yr	30 Yr
1/6/2020	1.54	1.56	1.56	1.54	1.54	1.56	1.61	1.72	1.81	2.13	2.28
1/6/2021	0.09	0.09	0.09	0.11	0.14	0.2	0.43	0.74	1.04	1.6	1.81
1/6/2022	0.04	0.1	0.23	0.45	0.88	1.15	1.47	1.66	1.73	2.12	2.09
1/6/2023	4.32	4.67	4.79	4.71	4.24	3.96	3.69	3.63	3.55	3.84	3.67
1/5/2024	5.54	5.47	5.24	4.84	4.4	4.17	4.02	4.04	4.05	4.37	4.21
1/15/2025	4.40	4.35	4.26	4.19	4.27	4.34	4.45	4.70	4.66	5.06	4.88

In Class Exercise

Create your own yield curve by visiting https://www.jufinance.com/game/yield_curve.html.

Year	Key Observations	Implications
2020	· The curve slopes upward.	· Indicates expectations of steady economic growth.
	· Short-term rates (~1.54% for 1-month) are lower than long-term rates (~2.28% for 30-year).	· Investors demand higher yields for longer maturities due to the risk of inflation and uncertainty over time.
		· Typical of a healthy economy.
2021	o Rates are near zero for short-term maturities (~0.09% for 1-month) and remain low for long-term maturities (~1.81% for 30-year).	o Reflects the Federal Reserve’s accommodative monetary policy in response to the COVID-19 pandemic.
	o The curve remains upward-sloping but is relatively flat.	o Low rates aimed to stimulate borrowing, investment, and consumption.
		o Suggests muted growth.
2022	· Short-term rates rise slightly (~0.04% for 1-month to ~0.10% for 3-month), but long-term rates remain subdued (~2.09% for 30-year).	· Indicates modest economic recovery as the pandemic's impact wanes.
2022	· The curve steepens slightly compared to 2021.	· Rising yields for longer maturities suggest improving growth expectations.
2023	o Short-term rates (~4.32% for 1-month) and long-term rates (~3.67% for 30-year) increase sharply.	o Reflects aggressive Federal Reserve rate hikes to combat high inflation.
2023	o The curve inverts for intermediate maturities (e.g., 2-year yield at 4.24% > 10-year yield at 3.55%).	o The inversion of the curve signals potential recession risks, as short-term borrowing costs exceed long-term borrowing costs.
2024	· Rates peak at short maturities (~5.54% for 1-month), with long-term rates slightly lower (~4.21% for 30-year).	· Suggests that the Federal Reserve may pause rate hikes as inflation shows signs of slowing.
2024	· The curve flattens across all maturities.	· A flat curve reflects uncertainty about future growth and potential recession risks.
2025	o Short-term rates decrease slightly (~4.40% for 1-month), while long-term rates increase slightly (~4.88% for 30-year).	o Reflects that inflation is moderating, and the Fed may consider lowering rates in the future.
2025	o The curve shows a mild upward slope, indicating normalization.	o Investors are cautious but anticipate moderate economic growth over the long term.

General Observations

1. Shifts in Monetary Policy:

The Fed's aggressive rate hikes in 2022–2023 are evident in the steep rise in short-term rates.
The slight decline in short-term rates in 2025 suggests that the Fed may be nearing the end of its tightening cycle.

2. Inversions and Recession Signals:

The inverted curve in 2023 is a classic recession indicator, suggesting economic slowdown concerns.
The normalization in 2025 reflects improved market confidence but still warrants caution.

3. Market Expectations:

The long-term rates have remained relatively stable compared to short-term rates, reflecting subdued inflation expectations over the long term.

Conclusion

The yield curves highlight the economic shifts from pre-pandemic growth (2020) to pandemic-driven lows (2021), recovery (2022), inflation-driven tightening (2023), and cautious normalization (2025). The curve as of 2025 suggests that while economic pressures are easing, uncertainties around growth and inflation persist.

`Understanding the yield curve (video)`

`Introduction to the yield curve (khan academy)`

Summary of Yield Curve Shapes and Explanations

Normal Yield Curve
When bond investors expect the economy to hum along at normal rates of growth without significant changes in inflation rates or available capital, the yield curve slopes gently upward. In the absence of economic disruptions, investors who risk their money for longer periods expect to get a bigger reward — in the form of higher interest — than those who risk their money for shorter time periods. Thus, as maturities lengthen, interest rates get progressively higher and the curve goes up.

Steep Curve – Economy is improving
Typically the yield on 30-year Treasury bonds is three percentage points above the yield on three-month Treasury bills. When it gets wider than that — and the slope of the yield curve increases sharply — long-term bond holders are sending a message that they think the economy will improve quickly in the future.

Inverted Curve – Recession is coming
At first glance an inverted yield curve seems like a paradox. Why would long-term investors settle for lower yields while short-term investors take so much less risk? The answer is that long-term investors will settle for lower yields now if they think rates — and the economy — are going even lower in the future. They're betting that this is their last chance to lock in rates before the bottom falls out.

Flat or Humped Curve

To become inverted, the yield curve must pass through a period where long-term yields are the same as short-term rates. When that happens the shape will appear to be flat or, more commonly, a little raised in the middle.

Unfortunately, not all flat or humped curves turn into fully inverted curves. Otherwise we'd all get rich plunking our savings down on 30-year bonds the second we saw their yields start falling toward short-term levels.

On the other hand, you shouldn't discount a flat or humped curve just because it doesn't guarantee a coming recession. The odds are still pretty good that economic slowdown and lower interest rates will follow a period of flattening yields.

https://www.finra.org/finra-data/fixed-income/corp-and-agency

Who Determines Interest Rates?

`https://www.investopedia.com/ask/answers/who-determines-interest-rates/`

By NICK K. LIOUDIS Updated Aug 15, 2019

Interest rates are the cost of borrowing money. They represent what creditors earn for lending you money. These rates are constantly changing, and differ based on the lender, as well as your creditworthiness. Interest rates not only keep the economy functioning, but they also keep people borrowing, spending, and lending. But most of us don't really stop to think about how they are implemented or who determines them. This article summarizes the three main forces that control and determine interest rates.

KEY TAKEAWAYS

Interest rates are the cost of borrowing money and represent what creditors earn for lending money.
Central banks raise or lower short-term interest rates to ensure stability and liquidity in the economy.
Long-term interest rates are affected by demand for 10- and 30-year U.S. Treasury notes.
Low demand for long-term notes leads to higher rates, while higher demand leads to lower rates.
Retail banks also control rates based on the market, their business needs, and individual customers.

Short-Term Interest Rates: Central Banks

In countries using a centralized banking model, short-term interest rates are determined by central banks. A government's economic observers create a policy that helps ensure stable prices and liquidity. This policy is routinely checked so the supply of money within the economy is neither too large, which causes prices to increase, nor too small, which can lead to a drop in prices.

In the U.S., interest rates are determined by the Federal Open Market Committee (FOMC), which consists of seven governors of the Federal Reserve Board and five Federal Reserve Bank presidents. The FOMC meets eight times a year to determine the near-term direction of monetary policy and interest rates. The actions of central banks like the Fed affect short-term and variable interest rates.

If the monetary policymakers wish to decrease the money supply, they will raise the interest rate, making it more attractive to deposit funds and reduce borrowing from the central bank. Conversely, if the central bank wishes to increase the money supply, they will decrease the interest rate, which makes it more attractive to borrow and spend money.

The Fed funds rate affects the prime rate—the rate banks charge their best customers, many of whom have the highest credit rating possible. It's also the rate banks charge each other for overnight loans.

The U.S. prime rate remained at 3.25% between Dec. 16, 2008 and Dec. 17, 2015, when it was raised to 3.5%.

Long-Term Interest Rates: Demand for Treasury Notes

Many of these rates are independent of the Fed funds rate, and, instead, follow 10- or 30-year Treasury note yields. These yields depend on demand after the U.S. Treasury Department auctions them off on the market. Lower demand tends to result in high interest rates. But when there is a high demand for these notes, it can push rates down lower.

If you have a long-term fixed-rate mortgage, car loan, student loan, or any similar non-revolving consumer credit product, this is where it falls. Some credit card annual percentage rates are also affected by these notes.

These rates are generally lower than most revolving credit products but are higher than the prime rate.

Many savings account rates are also determined by long-term Treasury notes.

Other Rates: Retail Banks

Retail banks are also partly responsible for controlling interest rates. Loans and mortgages they offer may have rates that change based on several factors including their needs, the market, and the individual consumer.

For example, someone with a lower credit score may be at a higher risk of default, so they pay a higher interest rate. The same applies to credit cards. Banks will offer different rates to different customers, and will also increase the rate if there is a missed payment, bounced payment, or for other services like balance transfers and foreign exchange.

Summary: Who Determines Interest Rates?

Key Influences on Interest Rates

1. Short-Term Interest Rates: Central Banks

Central banks, like the Federal Reserve in the U.S., set short-term interest rates to manage the money supply and ensure price stability.
The Federal Open Market Committee (FOMC) meets eight times a year to adjust monetary policy and set the Federal Funds Rate, influencing rates like the prime rate (the rate banks charge their best customers).
Higher rates reduce borrowing and spending, while lower rates encourage borrowing and stimulate the economy.

2. Long-Term Interest Rates: Treasury Notes

Long-term rates are tied to the yields on 10- and 30-year U.S. Treasury notes, determined by demand during Treasury auctions.
Higher demand for Treasury notes lowers their interest rates, while lower demand increases them.
Fixed-rate loans like mortgages, car loans, and student loans, as well as savings account rates, are influenced by these yields.

3. Other Rates: Retail Banks

Retail banks determine rates for consumer loans and mortgages based on factors like market conditions, their business needs, and individual customer creditworthiness.
Borrowers with lower credit scores face higher rates due to increased default risk.
Rates may also change due to missed payments or specific services, such as balance transfers.

Part IV – Breaking Down of Interest Rates of Treasury and Corporate Bonds

Quiz 2 Game - Interest Rate Explorer

1. Compare Treasury and Corporate Bonds:

Feature	Treasury Bonds	Corporate Bonds (e.g., Microsoft)
Issuer	U.S. Government	Corporations (e.g., Microsoft)
Risk Level	Risk-free (backed by the U.S. government)	Some risk (default and liquidity risk)
Return/Yield	Lower returns	Higher returns to compensate for risks
Liquidity	Highly liquid	Less liquid compared to Treasuries
Default Risk	None	Depends on the company’s credit rating
Purpose	Fund government operations	Fund corporate projects or operations

2. Breaking Down of Interest Rates: Play this game bond_yield_breakdown game! ( https://www.jufinance.com/game/bond_yield_break_down.html)

Component	Definition	Explanation (Simple Analogy)
Real Rate	The true return after removing inflation.	"It’s like growing your savings without losing purchasing power."
Inflation Premium	Compensation for the rise in prices over time.	"If inflation is 3%, lenders want at least 3% to break even."
Default Risk Premium	The chance the borrower won’t pay back.	"Treasuries have 0% default risk. Corporate bonds have some, even for Microsoft."
Liquidity Premium	Compensation for the ease of selling the bond.	"Treasuries are highly liquid, but corporate bonds may take time to sell."
Maturity Premium	The added risk for lending over a long period.	"Longer bonds mean more uncertainty, so investors demand higher yields."

Formula --- Break down of interest rate

r = r* + IP + DRP + LP + MRP

r = required return on a debt security

r* = real risk-free rate of interest

IP = inflation premium

DRP = default risk premium

LP = liquidity premium

MRP = maturity risk premium

MRP_t = 0.1% (t – 1)

DRP_t + LP_t = Corporate spread * (1.02)^(t−1)

Interest Rate	Short-Term	Long-Term	Short-Term	Long-Term
Parameter	Treasuries	Treasuries	Corporate	Corporate
r*	X	X	X	X
IP	X	X	X	X
MRP		X		X
DRP			X	X
LP			X	X

Maturity

Treasury Security Yield (%)

Microsoft Bond Yield (%)

Corporate Spread

1 Month	4.43	N/A	N/A
3 Month	4.34	N/A	N/A
6 Month	4.28	N/A	N/A

2 Year	4.27	4.01	-0.26
5 Year	4.42	4.44	0.02
10 Year	4.61	4.48	-0.13
20 Year	4.91	5.08	0.17
30 Year	4.84	5.3	0.46

https://www.finra.org/finra-data/fixed-income/corp-and-agency (corporate bonds)

https://www.finra.org/finra-data/fixed-income/treasuries (Treasury Securities)

Maturity	Treasury Yield (%)	Microsoft Yield (%)	Corporate Spread (%)	Real Rate (%)	Inflation Premium (%)	Maturity Premium (%)	Corporate Spread (Default + Liquidity) (%)
2 Year	4.27	4.01	-0.26	1	3.17	0.100	-0.26
5 Year	4.42	4.44	0.02	1	3.02	0.400	0.02
10 Year	4.61	4.48	-0.13	1	2.71	0.900	-0.13
20 Year	4.91	5.08	0.17	1	2.01	1.900	0.17
30 Year	4.84	5.3	0.46	1	0.94	2.900	0.46

Note:

Microsoft Yields > Treasury Yields:

Corporate bonds compensate for default and liquidity risks.

Longer-Term Yields are Higher:

Reflects maturity risk for both Treasuries and Microsoft bonds.

3. Visualize the Yield Curves

4. Simplify the Yield Spread Formula

Objective: Break down the difference between Treasury and corporate bonds.

· Formula:
Corporate Yield – Treasury Yield = Default Risk Premium + Liquidity Premium.

· Example for 30-Year Bond:

Microsoft: 5.30%
Treasury: 4.84%
Spread: 0.46% = DRP + LP.

Concept	Real-Life Analogy	Explanation
Treasury Bond	Lending to Your Parents	Safe and reliable; you know they will always pay you back.
Corporate Bond	Lending to a Business Friend	Trustworthy, but there’s a small chance they might not repay you.
Yield Spread	Extra Payment for Taking the Risk	"Would you charge your business friend a bit more for the risk? That’s the spread."

In Class Exercise

Activity 1: Create Your Own Yield Curve

Find yield data (Treasury and Intel).
Graph both curves on paper or a digital tool.

Activity 2: Calculate the Spread

Give specific bond yields and ask students to calculate spreads.

Activity 3: Group Debate

"Why do corporate bonds pay more than Treasuries?"

Key Takeaways

Treasuries are risk-free and more liquid, so they pay lower yields.
Corporate bonds offer higher yields to compensate for risks like default and liquidity.
The spread shows the extra compensation investors demand for corporate bonds.

Part V – Expectation Theory Quiz

Scenario: "Which Investment Should You Choose?"

You have $10,000 to invest and three simple options:

· Option 1: Invest for 1 year at 5%, then reinvest each year for the next 4 years at the rates below:

· Option 2: Lock your money in for 3 years at a fixed rate of 4.5% per year.

Option 3: Lock your money in for 5 years at a fixed rate of 4% per year.

Based on your results, which option is better if you plan to use the money after 5 years?

Online Calculator

Question for discussion: If a% and b% are both known to investors, such as the bank rates, how much is the future interest rate, such as c%?

(1+a)^N = (1+b)^m *(1+c)^(N-M)

Either earning a% of interest rate for N years,

or b% of interest rate for M years, and then c% of interest rate for (N-M) years,

investors should be indifferent. Right?

Then,

(1+a)^N = (1+b)^m *(1+c)^(N-M)è c = ((1+a)^N / (1+b)^m)^(1/(N-M))-1

Or approximately,

N*a = M*b +(N-M)*(c)è c = (N*a – M*b) /(N-M)

What Is Expectations Theory

Expectations theory attempts to predict what short-term interest rates will be in the future based on current long-term interest rates. The theory suggests that an investor earns the same amount of interest by investing in two consecutive one-year bond investments versus investing in one two-year bond today. The theory is also known as the "unbiased expectations theory.”

Understanding Expectations Theory

The expectations theory aims to help investors make decisions based upon a forecast of future interest rates. The theory uses long-term rates, typically from government bonds, to forecast the rate for short-term bonds. In theory, long-term rates can be used to indicate where rates of short-term bonds will trade in the future (https://www.investopedia.com/terms/e/expectationstheory.asp)

Example: Given that the current 2-year rate is 4.1% and the 1-year rate is 4.3%, what is the expected 1-year rate one year from now? (Answer: 3.9%. Why?)

Chapter 6 In class exercise

Interest Rate	Short-Term	Long-Term	Short-Term	Long-Term
Parameter	Treasuries	Treasuries	Corporate	Corporate
r*	X	X	X	X
IP	X	X	X	X
MRP		X		X
DRP			X	X
LP			X	X

1 You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.5%. Your brother-in-law, a broker at Safe and Sound Securities, has given you the following estimates of current interest rate premiums:

Inflation premium = 3.25%
Liquidity premium = 0.6%
Maturity risk premium = 1.8%
Default risk premium = 2.15%

On the basis of these data, what is the real risk-free rate of return? (answer: 2.25%)

Solution:

General equation: Rate = r* + Inflation + Default + liquidity + maturity

30-day T-bills = short term Treasury Security è Default = liquidity = maturity = 0

So 30-day T-bills = 5.5% = r* + inflation =r* + 3.25%

2 The real risk-free rate is 3%. Inflation is expected to be 2% this year and 4% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?(answer: 6%, 6.33%)

Solution:

General equation: Rate = r* + Inflation + Default + liquidity + maturity

2-year T-notes = intermediate term Treasury Security è Default = liquidity = 0, maturity=0 as given

Inflation = average of inflations from year 1 to year 2 = (2% + 4%)/2 = 3%

So 2-year T-notes = r* + inflation = 3% + 3% = 6%

3-year T-notes = short term Treasury Security è Default = liquidity = 0, maturity=0 as given

Inflation = average of inflations from year 1 to year 2 = (2% + 4% +4%)/3 = 3.33%

So 2-year T-notes = r* + inflation = 3% + 3.33% = 6.33%

3 A Treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield of 8%. Assume that the liquidity premium on the corporate bond is 0.5%. What is the default risk premium on the corporate bond? (answer: 1.5%)

Solution:

General equation: Rate = r* + Inflation + Default + liquidity + maturity

10 year T-notes = intermediate term Treasury Security è Default = liquidity = 0, maturity is not zero

So 10-year T-notes = r* + inflation + maturity = 6%

10 year corporate bond rate = r* + Inflation + Default + liquidity + maturity = 8%

Its liquidity = 0.5%, its maturity = 10-year-notes’ maturity.

Comparing 10 year T-notes and 10 year corporate bonds, we get default = 8%-6%-0.5%=1.5%

	r*	inflation	default	liquity	maturity
10 - year- T-notes = 6%	Same	same	0	0	same
10 year corp bonds = 8%	Same	same	?	1.50%	same

4 The real risk-free rate is 3%, and inflation is expected to be 3% for the next 2 years. A 2-year Treasury security yields 6.2%. What is the maturity risk premium for the 2-year security? (answer: 0.2%)

General equation: Rate = r* + Inflation + Default + liquidity + maturity

2-year T-notes = intermediate term Treasury Security è Default = liquidity = 0, maturity=?

2-year T-notes = 6.2% = r* + inflation + maturity = 3% + 3% + maturity

5 One-year Treasury securities yield 5%. The market anticipates that 1 year from now, 1-year Treasury securities will yield 6%. If the pure expectations theory is correct, what is the yield today for 2-year Treasury securities? (answer: 5.5%)

Or,

Swiss franc carry trade comes fraught with safe-haven rally risk (FYI)

By Harry Robertson

September 2, 20241:03 AM EDTUpdated 5 months ago

https://www.reuters.com/markets/currencies/swiss-franc-carry-trade-comes-fraught-with-safe-haven-rally-risk-2024-09-02/

LONDON, Sept 2 (Reuters) - As investors turn to the Swiss franc as an alternative to Japan's yen to fund carry trades, the risk of the currency staging one of its rapid rallies remains ever present.

The Swiss franc has long been used in the popular strategy where traders borrow currencies with low interest rates then swap them into others to buy higher-yielding assets.

Its appeal has brightened further as the yen's has dimmed. Yen carry trades imploded in August after the currency rallied hard on weak U.S. economic data and a surprise Bank of Japan rate hike, helping spark global market turmoil.

The Swiss National Bank (SNB) was the first major central bank to kick off an easing cycle earlier this year and its key interest rate stands at 1.25%, allowing investors to borrow francs cheaply to invest elsewhere.

By comparison, interest rates are in a 5.25%-5.50% range in the United States, 5% in Britain, and 3.75% in the euro zone.

"The Swiss franc is back as a funding currency," said Benjamin Dubois, global head of overlay management at Edmond de Rothschild

STABILITY

The franc is near its highest in eight months against the dollar and in nine years against the euro , reflecting its status as a safe-haven currency and expectations for European and U.S. rate cuts.

But investors hope for a gradual decline in the currency's value that could boost the returns on carry trades.

Speculators have held on to a $3.8 billion short position against the Swiss franc even as they have abruptly moved to a $2 billion long position on the yen , U.S. Commodity Futures Trading Commission data shows.

"There is more two-way risk now in the yen than there has been for quite some time," said Bank of America senior G10 FX strategist Kamal Sharma. "The Swiss franc looks the more logical funding currency of choice."

BofA recommends investors buy sterling against the franc , arguing the pound can rally due to the large interest rate gap between Switzerland and Britain, in a call echoed by Goldman Sachs.

The SNB appears set to cut rates further in the coming months as inflation dwindles. That would lower franc borrowing costs and could weigh on the currency, making it cheaper to pay back for those already borrowing it.

Central bankers also appear reluctant to see the currency strengthen further, partly because of the pain it can cause exporters. BofA and Goldman Sachs say they believe the SNB stepped in to weaken the currency in August.

"The SNB will likely guard against currency appreciation through intervention or rate cuts as required," said Goldman's G10 currency strategist Michael Cahill.

'INHERENTLY RISKY'

Yet the Swissie, as it is known in currency markets, can be an unreliable friend.

Investors are prone to pile into the currency when they get nervous, thanks to its long-standing safe-haven reputation.

Cahill said the franc is best used as a funding currency at moments when investors are feeling optimistic.

A quick rally in the currency used to fund carry trades can wipe out gains and cause investors to rapidly unwind their positions, as the yen drama showed. High levels of volatility or a drop in the higher-yielding currency can have the same effect.

The SNB and Swiss regulator Finma declined to comment when asked by Reuters about the impact of carry trades on the Swiss currency.

As stock markets tumbled in early August, the Swiss franc jumped as much as 3.5% over two days. The franc-dollar pair has proven sensitive to the U.S. economy, often rallying hard on weak data that causes U.S. Treasury yields to fall.

"Any carry trade is inherently risky and this is particularly true for those funded with safe-haven currencies," said Michael Puempel, FX strategist at Deutsche Bank.

"The main risk is that when yields move lower in a risk-off environment, yield differentials compress and the Swiss franc can rally," Puempel added.

A gauge of how much investors expect the Swiss currency to move , derived from options prices, is currently at around its highest since March 2023.

"Considering the central banks, you can see how there may be more sentiment for some carry players to prefer the franc over the yen," said Nathan Vurgest, head of trading at Record Currency Management.

"The ultimate success of this carry trade might still be dependent on how quickly it can be closed in a risk-off scenario," Vurgest said, referring to a moment where investors cut their riskier trades to focus on protecting their cash.

Get the latest news and expert analysis about the state of the global economy with the Reuters Econ World newsletter. Sign up here.

Reporting by Harry Robertson; Editing by Dhara Ranasinghe and Alexander Smith

Key Insights from the Article:

1. Swiss Franc as a Funding Currency:

The Swiss franc has gained popularity as a funding currency for carry trades due to its low-interest rate (1.25%), particularly as the yen has become less favorable after recent volatility and a surprise rate hike by the Bank of Japan.

2. Carry Trade Dynamics:

Investors borrow currencies with low interest rates (e.g., the Swiss franc) and invest in higher-yielding currencies like the British pound or U.S. dollar.
The attractiveness of the Swiss franc is tied to its low borrowing costs and the potential for a gradual decline in its value.

3. Safe-Haven Risks:

The Swiss franc's safe-haven status introduces risk for carry trades. In times of market stress, investors flock to the franc, causing it to rally and potentially wiping out carry trade gains.
This was evident when the franc jumped 3.5% over two days in early August during stock market turmoil.

4. Central Bank Influence:

The Swiss National Bank (SNB) is expected to cut rates further, which could lower borrowing costs for the franc and make it cheaper for carry trades.
The SNB appears to actively intervene in the currency market to prevent excessive appreciation, supporting exporters and stabilizing the economy.

5. Strategist Views:

Bank of America and Goldman Sachs favor the Swiss franc as a funding currency over the yen due to reduced volatility and predictability.
BofA and Goldman Sachs recommend buying higher-yielding currencies like sterling against the franc to benefit from interest rate differentials.

6. Risks of Swiss Franc Carry Trades:

Sudden rallies in the franc (often triggered by safe-haven demand or weak U.S. data) pose significant risks to carry trades.
Yield compression in risk-off scenarios can amplify losses for traders.

7. Investor Sentiment:

The success of Swiss franc carry trades depends on investor optimism and the ability to close trades quickly during market stress.
Volatility expectations for the franc are currently elevated, reflecting concerns about market risks.

This analysis highlights the opportunities

Chapter 6 – Assignments

· Chapter six case study (due with first mid term exam) Part1 Video Part2 Video Part3 Video

Optional: Are there any arbitrage opportunities based on the information provided below? Why or why not?

Currency	Interest Rate (%)	Exchange Rate (1 Currency to USD)
Euro (EUR)	2.36	1.04
British Pound (GBP)	4.75	1.23
Norwegian Krone (NOK)	4.5	0.088
Swiss Franc (CHF)	0.5	1.10

Chapter 7 Bond Valuation

ppt Bond_CFO_Decision_Game

https://www.morningstar.com/portfolios/experts-forecast-stock-bond-returns-2025-edition

For discussion: https://jufinance.com/risk_tolerance.html Quiz

Bond Type	Characteristics	Suitability	Risk
Short-Term Bonds	Quick maturity, Low risk, Lower returns	Conservative, Need liquidity	Reinvestment Risk
Long-Term Bonds	Higher returns, High risk	Long-term, High risk tolerance	Default Risk; Market interest rate risk
Corporate Bonds	Higher yields, Higher risk, Company influence	Seeking returns, Accepting higher risk	Default Risk; Market interest rate risk (assuming long maturity)
Treasury Securities	Low risk, Steady income, Different maturities	Conservative, Stable income requirement	Market interest rate risk (assuming long maturity)
Municipal Bonds	Tax advantages, Credit risk	Tax-efficient income, Higher tax bracket	Default Risk; Market interest rate risk (assuming long maturity)

· Among the aforementioned bonds, do you have a preference? If so, what factors influence your choice?

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Where to Invest in 2025: Key Takeaways: (self-developed video on youtube)

https://www.morningstar.com/markets/where-investors-can-find-highest-bond-yields-2025-2

1. Cash is No Longer King:

· Why? Cash yields peaked in 2024 (5.5%) and are now dropping (4.3%-4.4%). Yields on cash reset daily, so returns are no longer guaranteed.

· Risk: Hoarding cash means missing out on higher returns from other investments, like bonds or stocks.

2. Interest Rates are Expected to Drop:

· Forecast: Interest rates may fall to 3% by the end of 2025.

· The yield curve is flattening, meaning long-term bonds now offer better opportunities.

3. Move Out of Cash and Into Bonds:

· Long-Term Bonds: Offer both price appreciation (when rates fall) and steady income. Ideal for a declining interest-rate environment.

· Short-Term Bonds: Less attractive as their income potential fades with falling rates.

4. Corporate Bonds are Less Appealing in 2025:

· High-yield bonds (like “junk bonds”) now have low yield spreads, meaning the extra return over Treasuries is not enough to justify the risk.

· Example: High-yield bonds yield 7.2%, but the risk premium is only 2.6%—historically very low.

5. Emerging Market Bonds Offer Higher Yields:

· Countries like Brazil (14%) and Mexico (10%) offer attractive “real yields” (returns after inflation).

· Risks: Currency fluctuations, political instability, and lower liquidity compared to US bonds.

6. Why Bonds are Important in Portfolios:

· Treasuries provide stability and hedge against market volatility.

· Today’s bond yields (~4%) offer positive real returns, which weren’t possible in past years.

7. Tips for Investing:

Avoid chasing yield blindly—assess risks like creditworthiness and economic conditions.
Maintain a diversified portfolio to balance risk and opportunity.
Keep a long-term perspective amid potential volatility in 2025 (e.g., geopolitical conflicts, Fed policy changes).

Market data website:

FINRA: https://www.finra.org/finra-data/fixed-income (FINRA bond market data)

Relationship between bond prices and interest rates (Khan academy)

Reading material:

· Interest rate risk — When Interest rates Go up, Prices of Fixed-rate Bonds Fall, issued by SEC at https://www.sec.gov/files/ib_interestraterisk.pdf

· Higher market interest rates è lower fixed-rate bond prices è higher fixed-rate bond yields

· Lower fixed-rate bond coupon rates è higher interest rate risk

· Higher fixed-rate bond coupon rates è lower interest rate risk

· Lower market interest rates è higher fixed-rate bond prices è lower fixed-rate bond yields èhigher interest rate risk to rising market interest rates

· Longer maturity è higher interest rate risk è higher coupon rate

· Shorter maturity è lower interest rate risk è lower coupon rate

From https://www.sec.gov/files/ib_interestraterisk.pdf

Bond Pricing Excel Formula

To calculate bond price in EXCEL (annual coupon bond):

Price=abs(pv(yield to maturity, years left to maturity, coupon rate*1000, 1000)

To calculate yield to maturity (annual coupon bond)::

Yield to maturity = rate(years left to maturity, coupon rate *1000, -price, 1000)

To calculate bond price (semi-annual coupon bond):

Price=abs(pv(yield to maturity/2, years left to maturity*2, coupon rate*1000/2, 1000)

To calculate yield to maturity (semi-annual coupon bond):

Yield to maturity = rate(years left to maturity*2, coupon rate *1000/2, -price, 1000)*2

To calculate duration:

DURATION=DURATION(DATE(2025,2,4),DATE(2035,2,4),5%,7%,2,0)=7.80

Interpretation:

· A duration of 7.80 means that for every 1% increase in interest rates, the bond’s price is expected to decrease by approximately 7.8%. Conversely, if interest rates fall by 1%, the bond’s price would increase by 7.8%.

In Class Exercise (could be used to prepare for the first midterm exam)

Excel Solution

1. AAA firm’ bonds will mature in eight years, and coupon is $65. YTM is 8.2%. Bond’s market value? ($903.04, abs(pv(8.2%, 8, 65, 1000))

· Rate 8.2%

· Nper 8

· Pmt 65

· Pv ?

· FV 1000

2. AAA firm’s bonds’ market value is $1,120, with 15 years maturity and coupon of $85. What is YTM? (7.17%, rate(15, 85, -1120, 1000))

· Rate ?

· Nper 15

· Pmt 85

· Pv -1120

· FV 1000

3. Sadik Inc.'s bonds currently sell for $1,180 and have a par value of $1,000. They pay a $105 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to call (YTC)? (7.74%, rate(5, 105, -1180, 1100)) What is their yield to maturity (YTM)? (8.35%, rate(15, 105, -1180, 1000))

· Rate ?

· Nper 15

· Pmt 105

· Pv -1180

· FV 1000

4. Malko Enterprises’ bonds currently sell for $1,050. They have a 6-year maturity, an annual coupon of $75, and a par value of $1,000. What is their current yield? (7.14%, 75/1050)

5. Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of $1,000, and it makes semiannual interest payments. If you require an 8.4% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond? ($1,105.69, abs(pv(8.4%/2, 20*2, 9.5%*1000/2, 1000)) )

· Rate 8.4%/2

· Nper 20*2

· Pmt 95/2

· Pv ?

· FV 1000

6. Grossnickle Corporation issued 20-year, non-callable, 7.5% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 5.5%. What is the current price of the bonds, given that they now have 19 years to maturity? ($1,232.15, abs(pv(5.5%, 19, 75, 1000)))

· Rate 7.5%/2

· Nper 19

· Pmt 75

· Pv ?

· FV 1000

7. McCue Inc.'s bonds currently sell for $1,250. They pay a $90 annual coupon, have a 25-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bond's YTM and its YTC? (Subtract the YTC from the YTM; it is possible to get a negative answer.) (2.62%, YTM = rate(25, 90, -1250, 1000), YTC = rate(5, 90, -1250, 1050))

· Rate ? ------------ ?

· Nper 25 ------------- 5

· Pmt 90 ------------ 90

· Pv -1250 ------------ -1250

· FV 1000 ------------ 1000

8. Taussig Corp.'s bonds currently sell for $1,150. They have a 6.35% annual coupon rate and a 20-year maturity, but they can be called in 5 years at $1,067.50. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. Under these conditions, what rate of return should an investor expect to earn if he or she purchases these bonds? (4.2%, rate(5, 63.5, -1150, 1067.5))

9. A 25-year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $925. If the yield to maturity remains at its current rate, what will the price be 5 years from now? ($930.11, rate(25, 85, -925, 1000), abs(pv( rate(25, 85, -925, 1000), 20, 85, 1000))

Fixed Income Investor's Reference Guide (FYI) Quiz

(This guide is based on principles and insights from trusted financial resources, including Investopedia, Morningstar, Bloomberg, and FINRA.)

Key Metrics for Bond Analysis

1) Yield to Maturity (YTM):

· The total return earned by holding a bond until maturity. Essential for comparing bond values.

2) Duration:

· A measure of price sensitivity to interest rate changes. Longer duration = higher sensitivity.

3) Convexity:

· Enhances duration analysis by accounting for large interest rate shifts.

4) Credit Ratings:

· Assess bond risk via agencies like Moody’s, S&P, and Fitch. Higher ratings = lower risk.

5) Spread Analysis:

· Compare bond yields against benchmarks (e.g., Treasuries) to gauge risk and reward.

Types of Bonds

1. Government Bonds:

· Low risk, used as market benchmarks (e.g., U.S. Treasuries).

· Risk: Interest rate risk for long maturities.

2. Corporate Bonds:

· Higher yields but increased risk. Categories include investment-grade and junk bonds.

· Risk: Default and liquidity risks.

3. Municipal Bonds:

· Tax-exempt income for high-tax-bracket investors.

· Risk: Default and interest rate risks.

4. TIPS (Inflation-Protected Securities):

· Inflation-adjusted principal protects against rising prices.

5. Emerging Market Bonds:

· High yields, but risks include currency fluctuations and political instability.

Key Risks in Fixed Income

1) Interest Rate Risk: Bond prices drop when rates rise; longer maturities are most affected.

2) Credit Risk: The possibility of the bond issuer defaulting on payments.

3) Liquidity Risk: Difficulty in selling bonds quickly at fair prices.

4) Reinvestment Risk: Falling rates reduce income when reinvesting proceeds.

5) Inflation Risk: Fixed payments lose purchasing power as inflation increases.

Tools for Bond Investors

1) Bond Screeners: Platforms like Bloomberg, FINRA, and Morningstar for research and filtering.

2) Excel: Use Excel to model YTM, duration, and portfolio returns.

3) Bond Indices: Benchmarks like Bloomberg Barclays Aggregate Index track bond market performance.

4) Economic Indicators: Stay updated with Fed decisions, inflation rates, and employment reports.

Portfolio Strategies

1) Laddering: Divide investments across maturities to manage reinvestment and interest rate risks.

2) Barbell Strategy: Combine short-term and long-term bonds for flexibility and yield.

3) Core-Satellite Approach: Base your portfolio on stable bonds while adding high-yield options for growth.

Monitoring the Market

1) Yield Curve Analysis: A normal curve signals growth, while an inverted one predicts economic slowdown.

2) Credit Spreads: Wider spreads indicate higher risk; narrower spreads suggest stability.

3) Central Bank Policies: Interest rate changes by the Fed affect bond yields and prices significantly.

Practical Exercises

1) Bond Trading Simulation: Platforms like Investopedia allow practice in a risk-free environment.

2) Case Studies: Analyze market events like the 2008 financial crisis to understand bond behavior.

3) Portfolio Construction: Create mock portfolios tailored to specific investment goals.

Inspirational Stories and Role-Playing

1. Learn from bond market legends like Bill Gross and their strategies.

2. Simulate decision-making as a CFO or bond trader to understand market dynamics (Play a simple simulation game here)

Key Takeaways

1) Always analyze YTM, duration, and credit ratings to make informed decisions.

2) Diversify with a mix of government, corporate, and municipal bonds to balance risk.

3) Leverage tools like bond screeners and economic data for insights.

4) Track the yield curve, credit spreads, and Fed policies to anticipate market trends.

5) Practice with simulations and real-world scenarios to refine your skills.

2025 Global Fixed Income Outlook (FYI)

https://www.morganstanley.com/im/en-us/individual-investor/insights/articles/2025-global-fixed-income-outlook.html

Category	Key Insights
Macroeconomic Landscape	High inflation (except China), low growth (except U.S.), loose fiscal and tight monetary policy.
U.S. Economic Strength	Strong growth driven by AI, productivity, and consumer spending.
Fed Policy	Fed rate cuts to be smaller than in 2024; ECB expected to cut more.
Bond Market Outlook	U.S. Treasury yields range-bound (4% to 4.75%), favor curve steepening strategies.
Credit Markets	Tight credit spreads but strong fundamentals; preference for securitized credit over corporate credit.
Emerging Markets	Headwinds from strong U.S. dollar and trade uncertainty, but selective opportunities exist.
Currency Trends	U.S. dollar remains strong due to fiscal policy, higher yields, and trade policies.
Major Risks	Risks include geopolitical tensions, inflation resurgence, and aggressive corporate leverage.
Investment Strategy	Favor high-quality credit, shorter-duration bonds, and securitized credit while maintaining flexibility.

Reference Websites for Spreads and Metrics (FYI)

Spread/Metric	Website	Details
10-Year vs. 2-Year Treasury Spread	https://fred.stlouisfed.org/series/T10Y2Y	Daily yield curve rates for U.S. Treasuries.
	FRED (Federal Reserve Economic Data)	Historical yield curve data and economic indicators.
Credit Spreads (Investment-Grade/High-Yield vs. Treasury)	FINRA Bond Center	Provides credit spread data and bond ratings.
	Bloomberg	Industry-standard for corporate bond spreads and high-yield bond data (subscription required).
Sector Spreads (e.g., Technology, Energy)	Bloomberg	Sector-specific bond spreads and analysis (subscription required).
	Morningstar	Offers detailed credit ratings and sector-specific bond analysis.
Emerging Market Bond Spread vs. Treasury	J.P. Morgan EMBI: https://etfdb.com/etf/EMB/	Tracks spreads and yields for emerging market debt (access via Bloomberg or financial platforms).
	MarketWatch: https://www.marketwatch.com/investing/fund/emb	Provides updates on emerging market bond spreads and performance.
Municipal Bond Spread (Muni-Treasury Ratio)	Municipal Securities Rulemaking Board (MSRB)	Tools and educational resources on municipal bond spreads and yields.
	FINRA Bond Center	Includes municipal bond data and comparisons to Treasuries.
Inflation-Linked Spreads (Breakeven Inflation Rate)	FRED (Federal Reserve Economic Data): https://fred.stlouisfed.org/series/DFII10	Provides breakeven inflation data derived from TIPS and nominal Treasuries.
	Bureau of Labor Statistics (BLS)	Publishes inflation data, critical for understanding breakeven rates.
International Yield Spreads	Bloomberg	Tracks spreads between U.S. Treasuries and foreign government bonds (subscription required).
	Yahoo Finance	Offers international bond rates and basic comparisons.

Assignments of Chapter 7 – Due with the first midterm exam:

1) Chapter 7 Case Study Case study video part 1 part 2

2) Critical Thinking Challenge (Choose one of the two options)

Option 1: As the CFO of a growing corporation, you need to secure funding for a major expansion project. You can issue short-term bonds with lower interest rates but higher refinancing risk, or long-term bonds with higher interest rates but more stability. Considering factors like interest rate trends, economic conditions, and the company’s cash flow stability, which type of bond would you choose? How would changes in the economy (e.g., inflation, a credit downgrade, or a financial crisis) impact your decision? Defend your choice with financial reasoning – refer to https://www.jufinance.com/game/bond_cfo_game.html

3) Option 2: The 10-year and 2-year Treasury yield spread is a widely followed indicator of economic expectations and potential recessions. If the spread is negative (inverted yield curve), it historically signals a potential economic downturn, while a positive and widening spread suggests economic growth and rising interest rates (https://fred.stlouisfed.org/series/T10Y2Y)

Looking at the current 10-year vs. 2-year yield spread, what conclusions can you draw about the bond market in the coming year? Based on this, would you recommend investing in short-term or long-term bonds? Consider factors such as recession risk, interest rate expectations, and Federal Reserve policy in your response.

Bond Pricing Formula (FYI)

Bond Pricing Excel Formula

To calculate bond price in EXCEL (annual coupon bond):

Price=abs(pv(yield to maturity, years left to maturity, coupon rate*1000, 1000)

To calculate yield to maturity (annual coupon bond)::

Yield to maturity = rate(years left to maturity, coupon rate *1000, -price, 1000)

To calculate bond price (semi-annual coupon bond):

Price=abs(pv(yield to maturity/2, years left to maturity*2, coupon rate*1000/2, 1000)

To calculate yield to maturity (semi-annual coupon bond):

Yield to maturity = rate(years left to maturity*2, coupon rate *1000/2, -price, 1000)*2

Bond Calculator

Bond Duration Calculator (FYI)

https://exploringfinance.com/bond-duration-calculator/

Experts Forecast Stock and Bond Returns: 2025 Edition (FYI)

https://www.morningstar.com/portfolios/experts-forecast-stock-bond-returns-2025-edition

Long-term return expectations drop across major asset classes, and some firms are now forecasting higher returns for bonds than US stocks over the next decade.

Christine Benz Jan 13, 2025

Investors, it’s time to tone down your expectations.

That’s a key takeaway from my nonannual roundup of investment providers’ capital markets assumptions for the next decade. In their most recent release, nearly every firm in my roundup had reduced their return expectations for US stocks. Meanwhile, every firm in my survey is expecting higher returns from non-US stocks than domestic over the next 10 years, and some firms’ 10-year bond market forecasts are higher than their return expectations for US stocks.

How to Use the Forecasts

Although it’s reasonable to be skeptical about predicting the market’s direction, especially over the short term, the fact is that you need to have some type of return expectation in mind when you’re creating a financial plan. If you can’t plug in a long-term return assumption, it’s tough to figure out how much to save and what sort of withdrawal rate to use once you retire. Long-term historical returns are one option. But at certain points in time—like 2000—they might lead to overly rosy planning assumptions, which in turn might lead you to save too little or overspend in retirement.

To draw some conclusions about what sorts of return assumptions might be reasonable for planning, I have been amalgamating investment firms’ capital markets assumptions at least once a year. Firms use different methodologies to arrive at their capital markets assumptions, but most employ some combination of current dividend yields, valuation, and earnings-growth expectations to guide their equity forecasts. Fixed-income return assumptions are more straightforward given the tight historical correlation between starting yields and returns over the next decade. That explains why you see more uniformity among firms’ fixed-income return expectations, with variations driven largely by time-period differences.

Before you take these or any other return forecasts and run with them, it’s important to bear in mind that these return estimates are more intermediate-term than they are long-term. The firms I’ve included below all prepare capital markets forecasts for the next seven to 10 years, not the next 30. (BlackRock and Vanguard do provide 30-year forecasts as well as 10-year, and Fidelity’s capital markets assumptions apply to a 20-year horizon. But those are outliers in terms of making such far-reaching forecasts available to the public.) As such, these forecasts will have the most relevance for investors whose time horizons are in that ballpark, or for new retirees who face sequence-of-return risk in the next decade.

Expert Forecasts for Long-Term Asset-Class Returns

Vanguard’s latest US equity market return forecast is down meaningfully from where it was a year ago. (The firm presents its forecasts in a range.) The new forecast calls for US equity gains of 2.8%-4.8% over the next decade, down from a range of 4.2%-6.2% in late 2023. Its non-US equity return forecast (6.9%-8.9%) is roughly unchanged from a year ago and substantially higher than the US return expectation. Vanguard provides subasset-class forecasts, too. In its most recent run, its 10-year return forecast for value stocks (4.2%-6.2%) was substantially higher than its outlook for growth names (negative 0.4% to positive 1.6%). The firm also expects small-cap stocks to best large-cap stocks: The range for the former was 4.2%-6.2% versus 2.8%-4.8% for the latter.

Vanguard’s return expectations for US aggregate bonds are slightly lower than they were a year ago: a range of 4.3%-5.3% today versus 4.8%-5.8% in 2023. The firm is expecting better returns—albeit with higher volatility—from lower-quality bonds: a range of 5.3%-6.3% for US high-yield bonds and 5%-6% for emerging-markets sovereign bonds.

BlackRock

Highlights: 6.2% 10-year expected nominal return for US equities; 3.7% for US aggregate bonds (as of Sept. 30, 2024).

Despite US stocks’ strong gains in 2024, BlackRock was a rare firm in that it increased its US equity return expectations a bit from the year prior. The firm’s 10-year US equity return was just over 5% in September 2023, but that number jumped to 6.2% a year later. Meanwhile, the firm’s forecasts for non-US equities over the next decade were a bit lower than in the previous year: It was expecting gains of roughly 8% for non-US stocks broadly as well as emerging markets and European equities; those estimates were 9%-10% a year ago.

Fixed-income returns dipped slightly, too, as of September 2024. BlackRock’s models call for a 3.7% expected 10-year return from US aggregate bonds versus 5% in 2023.

Fidelity

Fidelity’s capital markets assumptions employ a 20-year horizon (2024-43) and therefore can’t be stacked up neatly against the 10-year returns from other firms in our survey.

The firm is forecasting a 5.7% nominal and a 3.1% real return for US equities over the next 20 years, less than half of US stocks’ 7.4% annualized real return over the period from 2004 to 2023 and well below US stocks’ 7% real return since 1926. Fidelity cites elevated equity valuations as the main constraint on US equity gains relative to their gains over the past 20 years. The firm expects the 20-year returns on non-US stocks to be a bit higher than US stocks over the next two decades: 6.8% nominally. The firm is most sanguine about the prospects for emerging-markets equities: 8.6% nominally.

On the fixed-income side, the firm was forecasting a 5.2% nominal 20-year return (2.6% real) for the Bloomberg US Aggregate Bond Index as of April 2024.

J.P. Morgan

Highlights: 6.7% nominal returns for U.S. large-cap equities over a 10- to 15-year horizon; 4.6% nominal returns for US aggregate bonds (as of September 2024).

J.P. Morgan’s expectations for equities’ returns over the next 10-15 years were higher than most of the firms in our survey, but they declined from the firm’s September 2023 numbers. Owing to higher valuations, its forecast for US large caps dropped to 6.7% from 7% a year ago. The firm’s outlook for non-US equities generally declined, too: Its 10- to 15-year outlook for developed-markets equities was 8.1%, down from 9.2% in late 2023, and for emerging-markets equities it was 7.2%, down from 8.9% in 2023.

On the fixed-income side, the firm reduced return expectations slightly relative to the year-ago period. It’s expecting a 4.6% return from US aggregate bonds, down from 5.1% a year ago. The firm’s return expectations for high-risk bond types also declined slightly. The firm’s 10- to 15-year forecast for high-yield bonds is 6.1%, down from 6.5% last year, and its forecast for emerging-markets sovereign bonds dropped to 5.8% from 6.8%.

Schwab

Highlights: 6.0% nominal returns for US large caps during the next 10 years; 4.9% nominal returns for US aggregate bonds (as of Oct. 31, 2024).

Schwab modestly lowered its 10-year return expectations for US stocks to 6.0% from 6.2% a year ago. The firm’s outlook for non-US developed-markets large caps was also a bit lower than last year’s forecast: 7.1% versus 7.6% in 2023.

In line with the outlook from other investment providers, the firm is forecasting a 4.9% gain for US aggregate bonds versus 5.7% last year. (All figures are nominal.)

Research Affiliates

Highlights: 3.4% nominal returns for US large caps during the next 10 years; 5.1% nominal returns for US aggregate bonds (as of Dec. 31, 2024; valuation-dependent model).

Research Affiliates’ 10-year US market return expectations declined, from a 4% nominal return projection for US large caps at the end of 2023 to 3.4% at year-end 2024. The firm is expecting US aggregate bonds to outperform stocks over the next decade, and its expected volatility for bonds is also substantially lower. The firm accords a return edge to US small-cap stocks versus large-cap stocks: a 7.4% 10-year annualized return assumption for small caps. Consistent with past forecasts, the firm is expecting better things from non-US stocks: a 9.5% 10-year annualized return for developed-markets large-cap stocks outside the US and 9% for emerging-markets equities.

Grantham Mayo Van Otterloo

Highlights: Negative 6.3% real returns for US large caps over the next seven years; 1.5% real returns for US bonds (as of November 2024).

They’re getting worse! Not only were GMO’s return expectations for core US asset classes lower than they were a year ago, they were the lowest of any firm in our survey. The firm is expecting negative 6.3% real returns for US large caps over the next seven years, down from its negative 2.6% real return forecast in November 2023. Consistent with previous forecasts, the firm’s outlook for non-US stocks is brighter than its expectation for US names: The seven-year real return forecast for international large caps is 0.4%; 2.5% for international small-caps; 2.4% for emerging-markets equities; and a whopping (for GMO) 5.7% real return for emerging-markets value stocks. All of those numbers are lower than they were a year ago.

The firm’s outlook for bonds also looks worse than its late-2023 number: a 1.5% real return for US bonds (down from 1.9% in 2023) and a 2.5% real return forecast from emerging-markets bonds.

Morningstar Multi-Asset Research (MAR) (not public-facing)

Highlights: 5.6% 10-year nominal returns for US stocks; 4.9% 10-year nominal returns for US aggregate bonds (as of Dec. 31, 2024).

MAR’s outlook for non-US stocks is substantially better than its case for US stocks. While the 10-year return expectation for US stocks is just 5.6%, it’s 9.6% for non-US developed-markets stocks and 11% for emerging-markets equities. Note that Morningstar changed its methodology for these forecasts between last year’s installment and this year’s: The forecast now blends Morningstar’s bottom-up equity research with top-down considerations. (Previously, the assumptions were top-down only.) In general, that change pushes up the return forecast for equities. The methodology for fixed-income return assumptions stayed the same.

2025 Global Fixed Income Outlook (FYI)

https://www.morganstanley.com/im/en-us/individual-investor/insights/articles/2025-global-fixed-income-outlook.html

As we enter 2025, the fixed income landscape presents a complex interplay of macroeconomic conditions, sector-specific dynamics, and geopolitical uncertainties. The post-pandemic world is markedly different: inflation (excluding China) remains generally high, while economic growth (excluding the US) is relatively low. Monetary policy is tighter than pre-pandemic levels, while fiscal policy is easy—perhaps even too easy. Additionally, politics has gained prominence; the election of Donald Trump in the US caps off a series of leadership changes in the Western world, with every G7 nation having changed leadership except Italy, which did so during the pandemic. This new landscape will influence bond market behavior in the coming year.

Throughout this outlook, we aim to provide a comprehensive analysis of anticipated trends in fixed income markets, highlighting key areas of opportunity and caution for investors. We will discuss our views on economic conditions, bond yields, credit markets, currencies, and the major risks we believe may arise in the year ahead.

Economic Conditions and Bond Yields:

We expect the U.S. economy to experience solid growth in 2025, primarily driven by the current productivity boom and resilient consumer spending, while Europe is likely to face more subdued economic conditions. The AI boom and the associated investment requirements in both the tech and energy sectors should not be underestimated. Emerging markets present a heterogeneous landscape, offering both opportunities and challenges, particularly in light of potential U.S. trade policies under the Trump administration.

In the U.S., we anticipate growth to remain robust. One of the biggest uncertainties for 2025 is how aggressive the incoming U.S. President Trump will be. Tariff increases, depending on their size and comprehensiveness, are likely to be inflationary and detrimental to growth (as observed in 2018/2019), as will reduced immigration. The market currently does not expect a full implementation, which justifies the positive reaction to his election. The negative impact of tariffs and immigration restrictions (which can be seen as a negative supply shock) may be offset, at least to some degree, by other policies expected to benefit the economy. For instance, we anticipate that supportive fiscal policy, which is currently driving investment and contributing to a productivity boom, will continue to promote strong non-inflationary growth. Market deregulation, including in the energy sector, could also prove disinflationary. Furthermore, household, and corporate balance sheets should remain robust, and a strong labor market will support consumption. Overall, we believe medium-term growth is likely to be strong, but the sequencing of policies and the response of other countries will be crucial in understanding the dynamic interplay of growth, inflation, and Fed policy responses. With growth in 2025 expected to be solid, Fed rate cuts are likely to be smaller (market pricing has correctly adjusted in the last few days of the year) than in 2024.

In Europe, we expect more subdued growth; 2025 should see growth centered around 1%, a meaningful improvement over 2022 and 2023. The manufacturing sector is likely to remain a drag on fixed investment, but a strong services sector will help compensate, supported by a rebound in household consumption that is unlikely to be robust enough to drive significant economic upswing. Additionally, the threat of U.S. tariffs, the ongoing implications of the Russia-Ukraine war, and the China’s economic slowdown have led markets to increase the cumulative easing expected from the ECB. This contrasts sharply with the U.S. bond market, which has significantly reduced the amount of easing anticipated from the Fed moving forward. We expect the ECB to cut rates at least as much, if not more than, the Fed in 2025.

Globally, economic growth is projected to be solid, with estimates between 3.0% and 3.3%. We believe China’s economic growth will stabilize, if not improve, in 2025, supporting a positive global economic outlook. Despite facing trade uncertainties and geopolitical tensions, the global economy is expected to benefit from coordinated monetary policies and improved consumer sentiment across various regions. All central banks, except for Japan and Brazil, are easing policy, which bolsters the economic outlook. This backdrop will significantly impact managing inflationary pressures worldwide.

Regarding interest rates, we believe U.S. yields are likely to remain range-bound in the coming year as markets attempt to decipher the true state of the economy—considering solid growth, a stable unemployment rate, and gently declining inflation—as well as the likely scale of the incoming administration’s policies. Some central banks, like the ECB and the Bank of Canada, may accelerate rate cuts, while others, such as the Bank of Mexico and various emerging market central banks, may pause or slow their rate-cutting in response to ongoing uncertainty and dollar strength. One of the biggest risks to this benign outlook is how firmly the market holds onto it.

We remain agnostic about the near-term outlook for U.S. yields, anticipating a range of 4% to 4.75% for the U.S. Treasury 10-year, with rate cuts unlikely to exceed those currently priced into the markets. Given that and lack of term premium in the U.S. yield curve we continue to avoid longer-duration bonds. Aside from Japan, we are neutral on duration in developed markets overalland retain curve steepening exposures, particularly in the U.S. Cross-market, we remain underweight U.S. duration compared to New Zealand, based on economic and monetary policy outlook differentials. We also maintain an underweight position in Japanese government bonds and are long Japanese inflation breakevens, as we believe Japanese inflation is structurally moving higher, prompting the BoJ to raise interest rates more than the market currently anticipates. At this time, we do not believe portfolio risks should tilt toward taking on above-normal interest rate risk, as credit sectors appear more rewarding. However, from a longer-term perspective, nominal and real yields in most countries are high by historical standards, suggesting that investors with a longer-than-one-year horizon may find that even a buy-and-hold strategy can yield rewarding returns if executed correctly with the appropriate fixed income sectors.

Credit Markets:

Our base case remains constructive for credit, supported by expectations of a “soft landing,” fiscal policy that remains conducive to growth, employment, and consumption, and strong corporate fundamentals (both at the investment-grade and high-yield levels). Assuming our forecast that the Republican administration’s agenda is implemented to some degree (we are more confident about deregulation and tax cuts than about trade), U.S. corporate performance should remain solid, benefiting credit spreads.

However, the longer-term impact of Republican policies is less clear. Greater opportunities and more regulatory leeway typically lead to riskier behavior and increased leverage, which is not usually positive for creditors. With credit spreads on the tighter side (tight by historical standards but not expensive), opportunities remain attractive; however, we do not expect high excess returns. Security selection will remain key given current valuations. The absolute level of yields appears satisfactory, even amidst significant uncertainty surrounding the Trump administration, particularly from a medium-term perspective. While spreads look historically tight, yields (when combining spreads with the risk-free U.S. Treasury or German government bond yields) appear compelling by historical comparison. Regarding risks, there is little reason to expect spreads to widen materially when economic growth is decent and central banks are cutting interest rates. On a positive note, yield-focused buying should help contain spread widening. We remain modestly overweight in credit within our portfolios, with a slight bias toward financials.

Amid the current noise and uncertainty, we continue to believe that the most attractive opportunities lie in securitized credit, particularly in U.S. mortgage-backed securities. U.S. households with prime credit ratings maintain strong balance sheets, which should continue to support consumer credit and ancillary structures, especially as housing prices remain firm and the unemployment rate stays low. Changes in U.S. tax policy should also be supportive. Higher coupon U.S. agency mortgage securities continue to be attractive compared to investment-grade corporates, and we believe they are likely to outperform U.S. Treasury securities. Similar to our corporate credit positioning, we aim to enhance our securitized credit exposures by moving up in credit quality and out of non-U.S. structures, given tighter spreads and increased macroeconomic risks in Europe. One area within securitized credit that may be vulnerable to potential shifts in Fed policy is office backed commercial mortgage-backed securities (CMBS). If interest rates do not fall as much as expected, refinancing many U.S. office-backed deals could become problematic, prompting us to generally avoid this sector. However, transparency in this sector has significantly improved, allowing investors to identify solid collateral (office buildings) versus problematic investments that should be avoided. It is quite possible that we will increase our exposure to CMBS in 2025 as opportunities arise.

Emerging Markets:

Emerging market bonds are likely to face headwinds under a Republican-led administration. Stronger U.S. growth, coupled with higher rates for an extended period and weaker global trade linkages, is typically not conducive to strong EM performance. Some of Trump’s comments regarding the BRIC countries suggest a potentially volatile environment that these nations will need to navigate in the coming years. Nevertheless, we believe that countries with solid economic outlooks, decent growth, declining inflation, and central banks willing and able to cut interest rates—despite policy changes in the U.S.—are likely to perform well. Potential U.S. trade policies will not impact all countries equally, making it essential to focus on individual country fundamentals, as specific nations may still offer investment opportunities amid broader uncertainties. Indeed, in the years following Trump's first administration, countries like Vietnam benefitted from trade diversions from heavily tariffed nations. This pattern is likely to continue during and after the second Trump administration.

Currency Markets:

In currency markets, the outlook for the U.S. dollar remains strong following the U.S. election. While the dollar appears stretched compared to its historical levels, its fundamental support remains robust. Easier fiscal policy, tighter monetary policy (relative to prior expectations), trade wars, and stronger U.S. growth all bode well for the dollar. Economic fundamentals in most countries remain inferior to those in the U.S. concerning the growth/inflation nexus. However, one caveat to this optimistic narrative could be a deterioration in the labor market and signs that the Fed may become more aggressive in cutting rates. Further deterioration would provide the Fed with room to continue cutting interest rates, as long as the Trump agenda does not disrupt the inflation outlook. The U.S. economy continues to excel regarding its growth trajectory, productivity performance, profit results, and yield levels. It will be challenging for other countries to generate the kind of fundamental support that the U.S. dollar enjoys, especially with a Republican administration focused on implementing a higher tariff strategy. This presents a high hurdle for other currencies to overcome in terms of fundamentals. That said, much of this good news is already reflected in the price, reducing the upside potential for the dollar.

Major Risks:

The fixed income market faces several risks in 2025, including geopolitical tensions that could disrupt supply chains and market confidence. Furthermore, aggressive corporate behavior, driven by strong profits, may lead to increased leverage and asset quality concerns, although it may also result in stronger economic growth and higher inflation. Importantly, a resurgence in inflation could restrict the Fed’s ability to maintain accommodative policies, while volatility in equity and interest rates might undermine investor confidence in carry trades and hinder the growth agenda of the Trump administration. Indeed, as mentioned earlier, a curtailment of monetary easing and rising yields could pose significant risks for economies in 2025, though this remains a risk rather than a high-probability outcome—at least for now.

Summary:

The fixed income outlook for 2025 presents a mix of opportunities and challenges across various sectors. As investors navigate this complex landscape, a careful and strategic approach is essential. Staying informed about macroeconomic indicators and sector-specific developments will be critical for making informed investment decisions. With a focus on high-quality credits, securitized products, and selective exposure to emerging markets, investors can position themselves to capitalize on potential growth while mitigating risks associated with the evolving economic environment.

Category	Key Insight
Macroeconomic Landscape	High inflation (except China), low growth (except U.S.), loose fiscal and tight monetary policy.
U.S. Economic Strength	Strong growth driven by AI, productivity, and consumer spending.
Fed Policy	Fed rate cuts to be smaller than in 2024; ECB expected to cut more.
Bond Market Outlook	U.S. Treasury yields range-bound (4% to 4.75%), favor curve steepening strategies.
Credit Markets	Tight credit spreads but strong fundamentals; preference for securitized credit over corporate credit.
Emerging Markets	Headwinds from strong U.S. dollar and trade uncertainty, but selective opportunities exist.
Currency Trends	U.S. dollar remains strong due to fiscal policy, higher yields, and trade policies.
Major Risks	Risks include geopolitical tensions, inflation resurgence, and aggressive corporate leverage.
Investment Strategy	Favor high-quality credit, shorter-duration bonds, and securitized credit while maintaining flexibility.

Chapter 8 Risk and Return

ppt Game (CAPM, FF3, FF5)

Steps to Build an Optimal Stock Portfolio for a Client: https://www.investopedia.com/terms/p/portfolio.asp

As a broker, my goal is to create an optimal stock portfolio that aligns with my client’s risk tolerance, investment goals, and market outlook. Below are the key steps to follow:

Step 1: Know Your Client ("Know Yourself")

Before making any investment recommendations, I need to understand my client’s financial profile and investment preferences. This includes:

Investment Goals – What is the client investing for? (Retirement, income generation, wealth growth, etc.)
Risk Tolerance – Are they risk-averse, risk-neutral, or risk-seeking?
Investment Horizon – Short-term (1-3 years), medium-term (3-7 years), or long-term (7+ years)?
Liquidity Needs – Do they need access to cash frequently?
Market Knowledge & Experience – Are they a beginner, intermediate, or expert investor?
Ethical or Sector Preferences – Any preference for ESG investing, tech stocks, dividend stocks, etc.?

Step 2: Define Investment Strategy

Once I understand my client’s preferences, I decide on an appropriate strategy:

Growth Investing: Focus on high-growth stocks (e.g., tech, biotech).
Value Investing: Look for undervalued stocks with strong fundamentals.
Dividend Investing: Prioritize stocks with consistent dividends.
Sector Rotation: Invest in different sectors based on economic cycles.
Index vs. Active Management: Decide between passive index investing or actively managed portfolios.

Step 3: Conduct Market Research & Stock Selection

Using fundamental and technical analysis, I identify potential stocks:

· Fundamental Analysis:

Revenue, earnings growth, and profit margins
P/E Ratio, PEG Ratio, and Price-to-Book Ratio
Debt levels and financial stability
Industry trends and competitive positioning

· Technical Analysis: (For short-term trades)

Moving Averages (SMA, EMA)
Relative Strength Index (RSI)
Volume trends and chart patterns

I also consider macroeconomic factors like interest rates, inflation, and market cycles.

Step 4: Build the Optimal Portfolio Using Modern Portfolio Theory (MPT)

To construct an optimal portfolio, I follow Harry Markowitz's MPT approach:

1. Diversification:

Select stocks across multiple sectors (e.g., Tech, Healthcare, Consumer Goods, Energy, Financials).
Include a mix of large-cap, mid-cap, and small-cap stocks.

2. Risk-Return Optimization:

Calculate expected returns for each stock.
Assess correlation between stocks to minimize volatility.
Use Efficient Frontier analysis to determine the best risk-adjusted return.

3. Portfolio Allocation:

Conservative Portfolio: 60% Bonds, 30% Large-Cap Stocks, 10% Cash
Balanced Portfolio: 50% Stocks, 30% Bonds, 20% Alternative Investments
Aggressive Portfolio: 80% Stocks, 15% Bonds, 5% Cash

Step 5: Execute the Investment Plan

Once the portfolio is set, I help my client with:

Opening a brokerage account (if they don’t have one).
Placing trades at the right market conditions.
Using stop-loss orders to limit downside risk.
Considering tax-efficient strategies (tax-loss harvesting, dividend reinvestment).

Step 6: Monitor and Rebalance the Portfolio

Markets change, and so do investment goals. I regularly:

Review performance (quarterly or annually).
Rebalance portfolio to maintain the target allocation.
Adjust strategy based on market conditions, interest rates, or life events.

Conclusion

Setting up an optimal portfolio requires a deep understanding of my client’s goals and risk tolerance, followed by a strategic approach to stock selection, diversification, and risk management. By continuously monitoring and rebalancing, I ensure the portfolio stays aligned with my client’s financial objectives.

Key Insights from Modern Portfolio Theory (MPT) Quiz

https://www.investopedia.com/terms/m/modernportfoliotheory.asp

1. Definition and Purpose

MPT is a mathematical framework for constructing investment portfolios to maximize returns for a given level of risk.
It helps investors diversify their holdings to achieve an optimal risk-return balance.
Developed by Harry Markowitz in 1952.

2. Core Concept: Diversification

Investments are either high-risk, high-return or low-risk, low-return.
MPT suggests that investors can achieve better results by mixing assets with different risk profiles.
The goal is to reduce overall portfolio risk rather than evaluating each asset in isolation.

3. Risk and Return Trade-off

Expected portfolio return is calculated as the weighted sum of individual asset returns.
Risk (variance/standard deviation) is not simply the sum of individual risks—correlations between assets matter.
Low or negatively correlated assets can significantly reduce portfolio volatility.

4. Efficient Frontier

Every possible portfolio can be plotted on a risk-return graph.
The "Efficient Frontier" is the set of optimal portfolios that offer the highest return for the lowest risk.
Investors should aim to build portfolios on this frontier.

5. Application in Portfolio Construction

MPT is widely used in ETF-based portfolio strategies.
Example: Combining stocks and government bonds to reduce risk due to negative correlation.
Example: Adding small-cap stocks to a Treasury portfolio to balance risk and improve returns during inflation.

6. Criticism of MPT

MPT uses variance as a measure of risk, treating all fluctuations (up and down) as equally undesirable.
In reality, investors care more about downside risk (losing money) than upside volatility (gaining money).
Post-Modern Portfolio Theory (PMPT) improves on MPT by focusing on downside risk instead of variance.

Key Takeaway

MPT remains a fundamental concept in finance, emphasizing diversification to manage risk. However, its limitations, particularly in measuring risk, have led to refinements like PMPT, which better aligns with investor preferences.

Homework Assignment Template (excel)

Solutions:

· 2stocks

· 3stocks

· 4stocks

Select your own stocks or refer to the provided list for stock selections. Construct four different portfolios containing 2, 3, 4, and 5 stocks each. For each portfolio:

Calculate risk and return using historical data.
Draw graphs to visualize the risk-return relationship.

Be sure to analyze how diversification impacts portfolio risk and return as the number of stocks increases.

Step	Stocks	Sectors	Reason	Risk-Return Analysis
1	AAPL, JNJ	Tech, Healthcare	Growth + Stability	2-Stock Risk-Return Simulator
2	AAPL, JNJ, NVDA	Tech, Healthcare, Semiconductors	High-Growth Addition	3-Stock Risk-Return Simulator
3	AAPL, JNJ, NVDA, JPM	Tech, Healthcare, Semiconductors, Financials	Financial Sector Diversification	4-Stock Risk-Return Simulator
4	AAPL, JNJ, NVDA, JPM, XOM	Tech, Healthcare, Semiconductors, Financials, Energy	Energy Exposure for Inflation Hedge	5-Stock Risk-Return Simulator
5	AAPL, JNJ, NVDA, JPM, XOM, PG	Tech, Healthcare, Semiconductors, Financials, Energy, Consumer Staples	Defensive Stock Addition	6-Stock Risk-Return Simulator
6	AAPL, JNJ, NVDA, JPM, XOM, PG, CAT	Tech, Healthcare, Semiconductors, Financials, Energy, Consumer Staples, Industrials	Infrastructure & Cyclical Exposure	7-Stock Risk-Return Simulator
7	AAPL, JNJ, NVDA, JPM, XOM, PG, CAT, BABA	Tech, Healthcare, Semiconductors, Financials, Energy, Consumer Staples, Industrials, International	International Diversification	8-Stock Risk-Return Simulator

Note: Manually calculate risk-return metrics using mathematical formulas and then verify their results using the simulators on jufinance.com/game.

Hint:

3 Stock Portfolio Return = w₁*r₁ + w₂*r₂ + w₃*r₃

where: w₁, w₂, w₃, are the weights of each stock in the portfolio, and r₁, r₂, r₃, are the returns of each stock in the portfolio.

3 Stock Portfolio Standard Deviation:

Portfolio Standard Deviation = sqrt(w₁²*σ₁²+ w₂²*σ₂²+ w₃²*σ₃² + 2*w₁*w₂*ρ₁₂*σ₁*σ₂ + 2*w₁*w₃*ρ₁₃*σ₁*σ₃ + 2*w₂*w₃*ρ₂₃*σ₂*σ₃ )

4 Stock Portfolio Return = w₁*r₁ + w₂*r₂ + w₃*r₃ + w₄*r₄

4 Stock Portfolio Standard Deviation:

Portfolio Standard Deviation = sqrt(w₁²*σ₁²+ w₂²*σ₂²+ w₃²*σ₃² + w₄²*σ₄²+ 2*w₁*w₂*ρ₁₂*σ₁*σ₂ + 2*w₁*w₃*ρ₁₃*σ₁*σ₃ + 2*w₁*w₄*ρ₁₄*σ₁*σ₄ + 2*w₂*w₃*ρ₂₃*σ₂*σ₃ + 2*w₂*w₄*ρ₂₄*σ₂*σ₄ + 2*w₃*w₄*ρ₃₄*σ₃*σ₄ )

5 Stock Portfolio Return = w₁*r₁ + w₂*r₂ + w₃*r₃ + w₄*r₄ + w₅*r₅

where: w₁, w₂, w₃, w₄, w₅, w₆, w₇, w₈ are the weights of each stock in the portfolio, and r₁, r₂, r₃, r₄, r₅, r₆, r₇, r₈are the returns of each stock in the portfolio.

5 Stcok Portfolio Standard Deviation:

Portfolio Standard Deviation = sqrt(w₁²*σ₁²+ w₂²*σ₂²+ w₃²*σ₃² + w₄²*σ₄²+ w₅²*σ₅²+ 2*w₁*w₂*ρ₁₂*σ₁*σ₂ + 2*w₁*w₃*ρ₁₃*σ₁*σ₃ + 2*w₁*w₄*ρ₁₄*σ₁*σ₄ + 2*w₁*w₅*ρ₁₅*σ₁*σ₅ + 2*w₁*w₈*ρ₁₈*σ₁*σ₈ + 2*w₂*w₃*ρ₂₃*σ₂*σ₃ + 2*w₂*w₄*ρ₂₄*σ₂*σ₄ + 2*w₂*w₅*ρ₂₅*σ₂*σ₅ + 2*w₃*w₄*ρ₃₄*σ₃*σ₄ + 2*w₃*w₅*ρ₃₅*σ₃σ₅ + 2*w₄*w₅*ρ₄₅*σ₄σ₅)

where: σ_1,σ_2,σ_3,σ_4,σ_5,are the standard deviations of each stock in the portfolio. ρ_12,ρ_13,ρ_14,ρ_15,ρ_23,ρ_24,ρ_25,ρ_34,ρ_35,ρ_45,are correlation coefficients between the stock returns. They represent the pairwise correlations between the stocks in the portfolio.

Equations

1. Expected return and standard deviation

Calculator

Given a probability distribution of returns, the expected return can be calculated using the following equation:

where

E[R] = the expected return on the stock,
N = the number of states,
p_i = the probability of state i, and
R_i = the return on the stock in state i.

Given an asset's expected return, its variance can be calculated using the following equation:

where

N = the number of states,
p_i = the probability of state i,
R_i = the return on the stock in state i, and
E[R] = the expected return on the stock.

The standard deviation is calculated as the positive square root of the variance.

http://www.zenwealth.com/businessfinanceonline/RR/MeasuresOfRisk.html

2. Two stock portfolio equations:

Calculator

W1 and W2 are the percentage of each stock in the portfolio.

Portfolio Variance Part 1 (youtube)

r₁₂ = the correlation coefficient between the returns on stocks 1 and 2,
s₁₂ = the covariance between the returns on stocks 1 and 2,
s₁ = the standard deviation on stock 1, and
s₂ = the standard deviation on stock 2.

s₁₂ = the covariance between the returns on stocks 1 and 2,
N = the number of states,
p_i = the probability of state i,
R_1i = the return on stock 1 in state i,
E[R₁] = the expected return on stock 1,
R_2i = the return on stock 2 in state i, and
E[R₂] = the expected return on stock 2.

3.. Historical returns

Holding period return (HPR) = (Selling price – Purchasing price + dividend)/ Purchasing price

HPR calculator

4. CAPM model

· What Is the Capital Asset Pricing Model?

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for pricing risky securities and generating expected returns for assets given the risk of those assets and cost of capital.

R_i = R_f + β_i *( R_m - R_f) ------ CAPM model

R_i = Expected return of investment

R_f = Risk-free rate

β_i = Beta of the investment

R_m = Expected return of market

(R_m - R_f) = Market risk premium

CAPM calculator

· What is Beta? Where to find Beta?

· SML – Security Market Line

RISK and Return General Template

In Class Exercise Video

1. How to achieve the best investment results (low risk, high return) (SOLUTION, updated FYI)
- Modern Portfolio Theory
Three stock portfolio: A, B, C
Year	A	B	C
1	10%	4%	12%
2	5%	6%	5%
3	4%	8%	7%
4	7%	10%	8%
5	1%	5%	14%

Assuming you have $10,000, how should you allocate funds among the three stocks to create an optimal portfolio with the highest return and lowest risk?

Steps

1. Mean, risk for each stock

2. Correlation between stocks: 3 correlations

3. Set it up as a portfolio and get portfolio's mean and risk

Portfolio Return = w₁*r₁ + w₂*r₂ + w₃*r₃

where: w₁, w₂, w₃ are the weights of each stock in the portfolio, and r₁, r₂, r₃ are the returns of each stock in the portfolio.

Portfolio Standard Deviation:

Portfolio Standard Deviation = sqrt(w₁²*σ₁²+ w₂²*σ₂²+ w₃²*σ₃² + 2*w₁*w₂*ρ₁₂*σ₁*σ₂ + 2*w₁*w₃*ρ₁₃*σ₁*σ₃ + 2*w₂*w₃*ρ₂₃*σ₂*σ₃)

where: σ_1,σ_2,σ₃are the standard deviations of each stock in the portfolio. ρ_12,ρ_13,ρ₂₃are correlation coefficients between the stock returns. They represent the pairwise correlations between the stocks in the portfolio.

For example, ρ₁₂ represents the correlation coefficient between the returns of stock 1 and stock 2, ρ₂₃ represents the correlation coefficient between the returns of stock 2 and stock.

4. Use solver to find lowest risk (standard deviation) for any given return.

2. An investor currently holds the following portfolio: He invested 30% of the fund in Apple with Beta equal 1.1. He also invested 40% in GE with Beta equal 1.6. The rest of his fund goes to Ford, with Beta equal 2.2. Use the above information to answer the following questions.

1) The beta for the portfolio is? (1.63)

Solution:

0.3*1.1+0.4*1.6+(1-0.3-0.4)*2.2=1.63(weighted average of beta)

3. The three month Treasury bill rate (this is risk free rate) is 2%. S&P500 index return is 10% (this is market return). Now calculate the portfolio’s return. 15.04%

Solution:

0.3*1.1+0.4*1.6+(1-0.3-0.4)*2.2=1.63--- This is beta and then plug into the CAPM.

Return = 2% + 1.63*(10%-2%) = 15.04%

Refer to the following graph. The three month Treasury bill rate (this is risk free rate) is 2%. S&P500 index return is 10% (this is market return).

1. What is the value of A? 2%

Solution: This is the intercept of the SML

2. What is the value of B? 10%

Solution:

B is the market return, so 10%, since Beta =1

3. How much is the slope of the above security market line? 8%

Solution:

Slope = rise/run = (10%-2%)/(1-0), just compare risk free rate (Beta=0) and market return (beta=1)

4. Your uncle bought Apple in January, year 2000 for $30. The current price of Apple is $480 per share. Assume there are no dividend ever paid. Calculate your uncle’s holding period return. 15 times

Solution:

Holding period return = (480-30)/30 =1500%=15 times

5. Your current portfolio’s BETA is about 1.2. Your total investment is worth around $200,000. You uncle just gave you $100,000 to invest for him. With this $100,000 extra funds in hand, you plan to invest the whole $100,000 in additional stocks to increase your whole portfolio’s BETA to 1.5 (Your portfolio now worth $200,000 plus $100,000). What is the average BETA of the new stocks to achieve your goal? (hint: write down the equation of the portfolio’s Beta first) 2.10

Solution:

Total amount = 200000 + 100000=300000

New portfolio beta = 1.2*200000/300000 + X*(100000/300000) = 1.5 è X=2.1

Years Market r Stock A Stock B

1 3% 16% 5%

2 -5% 20% 5%

3 1% 18% 5%

4 -10% 25% 5%

5 6% 14% 5%

· Calculate the average returns of the market r and stock A and stock B. (Answer: -1%, 18.6%, 5%)

· Calculate the standard deviations of the market, stock A, & stock B (Answer: 6.44%, 4.21%; 0 )

· Calculate the correlation of stock market r and stock a. (Answer: -0.98)

· Assume you invest 50% in stock A and 50% in stock B. Calculate the average return and the standard deviation of the portfolio. (Answer: 11.8%; 2.11%)

Calculate beta of stock A and beta of stock B, respectively (Answer: -0.64, 0)

Solution of Question 7, or refer to https://www.jufinance.com/portfolio/

What Is the Capital Asset Pricing Model?

R_i = R_f + β_i *( R_m - R_f) ------ CAPM model

R_i = Expected return of investment

R_f = Risk-free rate

β_i = Beta of the investment

R_m = Expected return of market

(R_m - R_f) = Market risk premium

Investors expect to be compensated for risk and the time value of money. The risk-free rate in the CAPM formula accounts for the time value of money. The other components of the CAPM formula account for the investor taking on additional risk.

The beta of a potential investment is a measure of how much risk the investment will add to a portfolio that looks like the market. If a stock is riskier than the market, it will have a beta greater than one. If a stock has a beta of less than one, the formula assumes it will reduce the risk of a portfolio.

A stock’s beta is then multiplied by the market risk premium, which is the return expected from the market above the risk-free rate. The risk-free rate is then added to the product of the stock’s beta and the market risk premium. The result should give an investor the required return or discount rate they can use to find the value of an asset.

The goal of the CAPM formula is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared to its expected return.

For example, imagine an investor is contemplating a stock worth $100 per share today that pays a 3% annual dividend. The stock has a beta compared to the market of 1.3, which means it is riskier than a market portfolio. Also, assume that the risk-free rate is 3% and this investor expects the market to rise in value by 8% per year.

The expected return of the stock based on the CAPM formula is 9.5%.

The expected return of the CAPM formula is used to discount the expected dividends and capital appreciation of the stock over the expected holding period. If the discounted value of those future cash flows is equal to $100 then the CAPM formula indicates the stock is fairly valued relative to risk.

(https://www.investopedia.com/terms/c/capm.asp)

Finding Beta Value (https://finance.zacks.com/stock-beta-value-8004.html)

The current beta value of a company stock is provided for free by many online financial news services, including Morningstar, Google Finance and Yahoo Finance. Online brokerage services provide more extensive tracking of a company's beta measurements, including historical trends. Beta is sometimes listed under "market data" or other similar headings, as it describes past market performance. A stock with a beta of 1.0 has the same price volatility as the market index, meaning if the market gains, the stock makes gains at the same rate. A stock with a beta of greater than 1.0 is riskier and has greater price fluctuations, while stocks with beta values of less than 1.0 are steadier and generally larger companies.

Examples of Beta

Beta is often measured against the S&P 500 index. An S&P 500 stock with a beta of 2.0 produced a 20 percent increase in returns during a period of time when the S&P 500 Index grew only 10 percent. This same measurement also means the stock would lose 20 percent when the market dropped by only 10 percent. High beta values, including those more than 1.0, are volatile and carry more risk along with greater potential returns. The measurement doesn't distinguish between upward and downward movements. Investing Daily notes that investors try to use stocks with high beta values to quickly recoup their investments after sharp market losses.

Small-Cap Stocks

Beta values are useful to evaluate stock prices of smaller companies. These small-capitalization stocks are attractive to investors because their price volatility can promise greater returns, but Market Watch recommends only buying small-cap stocks with beta values of less than 1.0. The beta value is also a component of the Capital Asset Pricing Model, which helps investors analyze the risk of an investment and the returns needed to make it profitable.

The Importance of Diversification

`http://www.youtube.com/watch?v=RoqAcdTFVFY`

Understanding Diversification in Stock Trading to Avoid Losses

`http://www.youtube.com/watch?v=FrmoXog9zig`

How to Build a Portfolio | by Wall Street Survivor

`http://www.youtube.com/watch?v=V48NECmT3Ns`

Understanding the Fama and French Three Factor Model (FYI)

https://www.investopedia.com/terms/f/famaandfrenchthreefactormodel.asp

Nobel Laureate Eugene Fama and researcher Kenneth French, former professors at the University of Chicago Booth School of Business, attempted to better measure

market returns and, through research, found that value stocks outperform growth stocks. Similarly, small-cap stocks tend to outperform large-cap stocks. As an

evaluation tool, the performance of portfolios with a large number of small-cap or value stocks would be lower than the CAPM result, as the Three-Factor Model

adjusts downward for observed small-cap and value stock outperformance.

The Fama and French model has three factors: the size of firms, book-to-market values, and excess return on the market. In other words, the three factors used

are small minus big (SMB), high minus low (HML), and the portfolio's return less the risk-free rate of return. SMB accounts for publicly traded companies

with small market caps that generate higher returns, while HML accounts for value stocks with high book-to-market ratios that generate higher returns

in comparison to the market.

Fama and French’s Five Factor Model

Researchers have expanded the Three-Factor model in recent years to include other factors. These include "momentum," "quality," and "low volatility,"

among others. In 2014, Fama and French adapted their model to include five factors. Along with the original three factors, the new model adds the concept that

companies reporting higher future earnings have higher returns in the stock market, a factor referred to as profitability.

The fifth factor, referred to as "investment", relates the concept of internal investment and returns, suggesting that companies directing profit towards

major growth projects are likely to experience losses in the stock market.

Small Minus Big (SMB): Definition and Role in Fama/French Model (FYI)

By WILL KENTON Updated November 30, 2020 Reviewed by DAVID KINDNESS

https://www.investopedia.com/terms/s/small_minus_big.asp

What Does Small Minus Big Mean?

Small minus big (SMB) is one of the three factors in the Fama/French stock pricing model. Along with other factors, SMB is used to explain portfolio returns.

This factor is also referred to as the "small firm effect," or the "size effect," where size is based on a company's market capitalization.

KEY TAKEAWAYS

· Small minus big (SMB) is a factor in the Fama/French stock pricing model that says smaller companies outperform larger ones over the long-term.

· High minus low (HML) is another factor in the model that says value stocks tend to outperform growth stocks.

· Beyond the original three factors in the Fama/French model—the SMB, HML, and market factors—the model has been expanded to include other factors, such as momentum, quality, and low volatility.

Understanding Small Minus Big (SMB)

Small minus big is the excess return that smaller market capitalization companies return versus larger companies. The Fama/French Three-Factor Model is an extension of the Capital Asset Pricing Model (CAPM). CAPM is a one-factor model, and that factor is the performance of the market as a whole. This factor is known as

the market factor. CAPM explains a portfolio's returns in terms of the amount of risk it contains relative to the market. In other words, according to CAPM, the

primary explanation for the performance of a portfolio is the performance of the market as a whole.

The Fama/Three-Factor model adds two factors to CAPM. The model essentially says there are two other factors in addition to market performance

that consistently contribute to a portfolio's performance. One is SMB, where if a portfolio has more small-cap companies in it, it should outperform the market

over the long run.

Small Minus Big (SMB) vs. High Minus Low (HML)

The third factor in the Three-Factor model is High Minus Low (HML). "High" refers to companies with a high book value-to-market value ratio. "Low'"

refers to companies with a low book value-to-market value ratio. This factor is also referred to as the "value factor" or the "value versus growth factor"

because companies with a high book to market ratio are typically considered "value stocks."

Companies with a low market-to-book value are typically "growth stocks." And research has demonstrated that value stocks outperform growth stocks in the long

run. So, in the long run, a portfolio with a large proportion of value stocks should outperform one with a large proportion of growth stocks.

Special Considerations

The Fama/French model can be used to evaluate a portfolio manager's returns. Essentially, if the portfolio's performance can be attributed to the three factors, then the portfolio manager has not added any value or demonstrated any skill.

This is because if the three factors can completely explain the portfolio's performance, then none of the performance can be attributed to the manager's ability.

A good portfolio manager should add to a performance by picking good stocks. This outperformance is also known as "alpha."

Application of the Fama French 5 factor model (FYI only)

https://blog.quantinsti.com/fama-french-five-factor-asset-pricing-model/

Five Factor Investing with ETFs (youtube)

The theoretical starting point for the Fama-French five-factor model is the dividend discount model as the model states that the value of a stock today is dependent

upon future dividends. Fama and French use the dividend discount model to get two new factors from it, investment and profitability (Fama and French, 2014).

The empirical tests of the Fama French models aim to explain average returns on portfolios formed to produce large spreads in Size, B/M, profitability and investment.

Firstly, the model is applied to portfolios formed on size, B/M, profitability and investment. The portfolio returns to be explained are from improved versions of the

sorts that produce the factor.

Secondly, the five-factor model’s performance is compared to the three-factor model’s performance with regards to explaining average returns associated with

major anomalies not targeted by the model (Fama and French, 2014).

With the addition of profitability and investment factors, the five-factor model time series regression has the equation below:

R_it - RF_t = a_i + b_i(RM_t — RF_t) + s_iSMB_t+ h_iHML_t + r_iRMW_t + c_iCMA_t + e_it

Where:

R_it is the return in month t of one of the portfolios

RF_t is the riskfree rate

Rm - Rf is the return spread between the capitalization-weighted stock market and cash

SMB is the return spread of small minus large stocks (i.e. the size effect)

HML is the return spread of cheap minus expensive stocks (i.e. the value effect)

RMW is the return spread of the most profitable firms minus the least profitable

CMA is the return spread of firms that invest conservatively minus aggressively (AQR, 2014)

The purpose of the regression test is to observe whether the five-factor model captures average returns on the variables and to see which variables are positively

or negatively correlated to each other and additionally identifying the size of the regression slopes and how all these factors are related to and affect average

returns of stocks values.

The tests done by Fama and French (2014) show that the value factor HML is redundant for describing average returns when profitability and investment factors

have been added into the equation and that for applications were sole interest is abnormal returns, a four or five-factor model can be used but if portfolio tilts are

also of interest in addition to abnormal returns then the five-factor model is best to use.

The results also show that the Fama-French five-factor model explains between 71% and 94% of the cross-section variance of expected returns for the size,

value, profitability and investment portfolios.

It has been proven that a five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns performs better than

the three-factor model in that it lessens the anomaly average returns left unexplained.

The new model shows that the highest expected returns are attained by companies that are small, profitable and value companies with no major growth prospects

(Fama and French, 2014).

The Fama-French five-factor model’s main setback, however, is its failure to capture the low average returns on small stocks whose returns perform like those of firms

that invest a lot in spite of low profitability as well as the model’s performance being indifferent to the way its factors are defined (Fama and French, 2015).

Modern Portfolio Theory: What MPT Is and How Investors Use It

By The Investopedia Team Updated August 29, 2023 Reviewed by Gordon Scott Fact checked by Suzanne Kvilhaug

https://www.investopedia.com/terms/m/modernportfoliotheory.asp

What Is the Modern Portfolio Theory (MPT)?

The modern portfolio theory (MPT) is a practical method for selecting investments in order to maximize their overall returns within an acceptable level of risk. This mathematical framework is used to build a portfolio of investments that maximize the amount of expected return for the collective given level of risk.

American economist Harry Markowitz pioneered this theory in his paper "Portfolio Selection," which was published in the Journal of Finance in 1952.

A key component of the MPT theory is diversification. Most investments are either high risk and high return or low risk and low return. Markowitz argued that investors could achieve their best results by choosing an optimal mix of the two based on an assessment of their individual tolerance to risk.

Key Takeaways

· The modern portfolio theory (MPT) is a method that can be used by risk-averse investors to construct diversified portfolios that maximize their returns without unacceptable levels of risk.

· The modern portfolio theory can be useful to investors trying to construct efficient and diversified portfolios using ETFs.

· Investors who are more concerned with downside risk might prefer the post-modern portfolio theory (PMPT) to MPT.

· Modern Portfolio Theory

· Investopedia / Matthew Collins

Understanding the Modern Portfolio Theory (MPT)

The modern portfolio theory argues that any given investment's risk and return characteristics should not be viewed alone but should be evaluated by how it affects the overall portfolio's risk and return. That is, an investor can construct a portfolio of multiple assets that will result in greater returns without a higher level of risk.

As an alternative, starting with a desired level of expected return, the investor can construct a portfolio with the lowest possible risk that is capable of producing that return.

Based on statistical measures such as variance and correlation, a single investment's performance is less important than how it impacts the entire portfolio.

Acceptable Risk

The MPT assumes that investors are risk-averse, meaning they prefer a less risky portfolio to a riskier one for a given level of return. As a practical matter, risk aversion implies that most people should invest in multiple asset classes.

The expected return of the portfolio is calculated as a weighted sum of the returns of the individual assets. If a portfolio contained four equally weighted assets with expected returns of 4%, 6%, 10%, and 14%, the portfolio's expected return would be:

(4% x 25%) + (6% x 25%) + (10% x 25%) + (14% x 25%) = 8.5%

The portfolio's risk is a function of the variances of each asset and the correlations of each pair of assets. To calculate the risk of a four-asset portfolio, an investor needs each of the four assets' variances and six correlation values, since there are six possible two-asset combinations with four assets. Because of the asset correlations, the total portfolio risk, or standard deviation, is lower than what would be calculated by a weighted sum.

Benefits of the MPT

The MPT is a useful tool for investors who are trying to build diversified portfolios. In fact, the growth of exchange-traded funds (ETFs) made the MPT more relevant by giving investors easier access to a broader range of asset classes.

For example, stock investors can reduce risk by putting a portion of their portfolios in government bond ETFs. The variance of the portfolio will be significantly lower because government bonds have a negative correlation with stocks. Adding a small investment in Treasuries to a stock portfolio will not have a large impact on expected returns because of this loss-reducing effect.

Looking for Negative Correlation

Similarly, the MPT can be used to reduce the volatility of a U.S. Treasury portfolio by putting 10% in a small-cap value index fund or ETF. Although small-cap value stocks are far riskier than Treasuries on their own, they often do well during periods of high inflation when bonds do poorly. As a result, the portfolio's overall volatility is lower than it would be if it consisted entirely of government bonds. Moreover, the expected returns are higher.

The modern portfolio theory allows investors to construct more efficient portfolios. Every possible combination of assets can be plotted on a graph, with the portfolio's risk on the X-axis and the expected return on the Y-axis. This plot reveals the most desirable combinations for a portfolio.

For example, suppose Portfolio A has an expected return of 8.5% and a standard deviation of 8%. Assume that Portfolio B has an expected return of 8.5% and a standard deviation of 9.5%. Portfolio A would be deemed more efficient because it has the same expected return but lower risk.

It is possible to draw an upward sloping curve to connect all of the most efficient portfolios. This curve is called the efficient frontier.

Investing in a portfolio underneath the curve is not desirable because it does not maximize returns for a given level of risk.

Criticism of the MPT

Perhaps the most serious criticism of the MPT is that it evaluates portfolios based on variance rather than downside risk.

That is, two portfolios that have the same level of variance and returns are considered equally desirable under modern portfolio theory. One portfolio may have that variance because of frequent small losses. Another could have that variance because of rare but spectacular declines. Most investors would prefer frequent small losses, which would be easier to endure.

The post-modern portfolio theory (PMPT) attempts to improve modern portfolio theory by minimizing downside risk instead of variance.

Term project – efficient frontier (group project, due with final)

Quiz Game – For Demonstration

· Term project word file Graph Video

· Sample outcome (from 2023) In class exercise 2-14-2024 (Excel)

· Efficient Frontier template (FYI) (based on Modern Portfolio Theory, or Markowitz Portfolio Theory)

· Efficient Frontier Sample Report (word file)

Note:

· The efficient frontier is a fundamental concept in modern portfolio theory, representing a set of optimal portfolios that offer the highest expected return for a given level of risk.

· Visualizing this frontier helps investors understand the trade-off between risk and return, enabling them to make informed investment decisions.

· If the solver generates no results, try adding more constraints. For example: each stock's weight should be greater than 5% but less than 30% to ensure the investment is spread across all stocks.

(based on 2/24/2024 in class exercise data)

Key Findings:

1. Max Sharpe Ratio Portfolio (Optimal Risk-Adjusted Return)

1) Expected Return: 4.19%

2) Volatility (Risk): 12.85%

3) Sharpe Ratio: 0.326

2. Min Volatility Portfolio (Lowest Risk Portfolio)

1) Expected Return: 1.14%

2) Volatility (Risk): 6.70%

3) Sharpe Ratio: 0.170

Takeaways:

The Efficient Frontier shows the best possible portfolios at different risk levels.
Higher returns require accepting more risk. The Max Sharpe Ratio portfolio provides the best balance of return per unit of risk.
The Minimum Volatility Portfolio is safest, but returns are lower.
The Sharpe Ratio helps compare risk-adjusted returns - higher is better.

Summary

Data Collection:

· Gather monthly closing prices for eight securities (CSG, HD, C, LUV, TXN, JNJ, IBM, BA) from January 31, 2019, to January 31, 2024, from Yahoo Finance.

· Calculate monthly returns for each security using the formula:

Statistical Analysis:

· Calculate the average monthly return and standard deviation for each security.

· Annualize the average monthly return and standard deviation.

Correlation Analysis:

· Use the correlation function in Excel to calculate pairwise correlation coefficients between the eight securities.

· Construct a correlation matrix.

Covariance Matrix:

· Calculate the covariance matrix for the securities using the correlation coefficients and standard deviations.

Equally Weighted Portfolio:

· Formulate an equally weighted portfolio with 1/8th investment in each security.

· Calculate the bordered covariance matrix for the equally weighted portfolio.

· Determine the variance of the portfolio and its expected return.

Solver Analysis:

· Use Excel Solver to find optimal portfolio weights that minimize the portfolio's standard deviation.

· Define constraints for the weights and the portfolio's expected return.

· Iterate the solver process to obtain solutions for various target portfolio returns.

Efficient Frontier:

· Graph the portfolio expected returns and standard deviations along with those of individual securities and the equally weighted portfolio.

· Plot the efficient frontier, showing the trade-off between expected return and risk for different portfolio compositions.

By following these steps, you can construct the efficient frontier and determine optimal portfolio allocations based on the risk-return trade-off.

Explanation:

The goal of the efficient frontier is to help investors identify the optimal portfolio that provides the maximum return for a given level of risk, or the minimum risk for a given level of return. The efficient frontier is a graph that shows the different possible combinations of risk and return for a given set of investments or assets. It represents the set of portfolios that offer the highest expected return for a given level of risk, or the lowest risk for a given level of return.

By plotting different portfolios on the efficient frontier, investors can evaluate the risk-return trade-offs of different investment options and choose the portfolio that best meets their investment objectives. The efficient frontier provides a way to quantify the trade-offs between risk and return and to help investors make informed decisions about their investment strategies.

Portfolio Return:

Portfolio Return = w₁*r₁ + w₂*r₂ + w₃*r₃ + w₄*r₄ + w₅*r₅ + w₆*r₆ + w₇*r₇ + w₈*r₈

Portfolio Standard Deviation:

Portfolio Standard Deviation = sqrt(w₁²*σ₁²+ w₂²*σ₂²+ w₃²*σ₃² + w₄²*σ₄²+ w₅²*σ₅²+ w₆²*σ₆²+ w₇²*σ₇²+ w₈²*σ₈²+ 2*w₁*w₂*ρ₁₂*σ₁*σ₂ + 2*w₁*w₃*ρ₁₃*σ₁*σ₃ + 2*w₁*w₄*ρ₁₄*σ₁*σ₄ + 2*w₁*w₅*ρ₁₅*σ₁*σ₅ + 2*w₁*w₆*ρ₁₆*σ₁*σ₆ + 2*w₁*w₇*ρ₁₇*σ₁*σ₇ + 2*w₁*w₈*ρ₁₈*σ₁*σ₈ + 2*w₂*w₃*ρ₂₃*σ₂*σ₃ + 2*w₂*w₄*ρ₂₄*σ₂*σ₄ + 2*w₂*w₅*ρ₂₅*σ₂*σ₅ + 2*w₂*w₆*ρ₂₆*σ₂*σ₆ + 2*w₂*w₇*ρ₂₇*σ₂*σ₇ + 2*w₂*w₈*ρ₂₈*σ₂*σ₈ + 2*w₃*w₄*ρ₃₄*σ₃*σ₄ + 2*w₃*w₅*ρ₃₅*σ₃σ₅ + 2*w₃*w₆*ρ₃₆*σ₃*σ₆ + 2*w₃*w₇*ρ₃₇*σ₃*σ₇ + 2*w₃*w₈*ρ₃₈*σ₃*σ₈ + 2*w₄*w₅*ρ₄₅*σ₄σ₅ + 2*w₄*w₆*ρ₄₆*σ₄*σ₆ + 2*w₄*w₇*ρ₄₇*σ₄*σ₇ + 2*w₄*w₈*ρ₄₈*σ₄*σ₈ + 2*w₅*w₆*ρ₅₆*σ₅*σ₆ + 2*w₅*w₇*ρ₅₇*σ₅*σ₇ + 2*w₅*w₈*ρ₅₈*σ₅*σ₈ + 2*w₆*w₇*ρ₆₇*σ₆*σ₇ + 2*w₆*w₈*ρ₆₈*σ₆*σ₈ + 2*w₇*w₈*ρ₇₈*σ₇*σ₈ )

where: σ_1,σ_2,σ_3,σ_4,σ_5,σ_6,σ_7,σ₈are the standard deviations of each stock in the portfolio. ρ_12,ρ_13,ρ_14,ρ_15,ρ_16,ρ_17,ρ_18,ρ_23,ρ_24,ρ_25,ρ_26,ρ_27,ρ_28,ρ_34,ρ_35,ρ_36,ρ_37,ρ_38,ρ_45,ρ_46,ρ_75,ρ_48,ρ_56,ρ_57,ρ_58,ρ_67,ρ_68,ρ₇₈are correlation coefficients between the stock returns. They represent the pairwise correlations between the stocks in the portfolio.

For example, ρ₁₂ represents the correlation coefficient between the returns of stock 1 and stock 2, ρ₂₃ represents the correlation coefficient between the returns of stock 2 and stock.

About the CML (Capital market line, optional)

To draw a tangent line from the risk-free rate to the efficient frontier, follow these steps:

· Determine the risk-free rate: The risk-free rate is the rate of return an investor can earn with zero risk. It is typically represented by the yield on a short-term U.S. Treasury bill.

· Find the portfolio with the highest Sharpe ratio: The Sharpe ratio is a measure of risk-adjusted return that takes into account the portfolio's expected return and standard deviation. The portfolio with the highest Sharpe ratio is the portfolio that offers the best risk-adjusted return.

· Calculate the slope of the tangent line: The slope of the tangent line is equal to the Sharpe ratio of the portfolio with the highest Sharpe ratio.

· Draw the tangent line: The tangent line starts at the risk-free rate on the y-axis and has a slope equal to the Sharpe ratio of the portfolio with the highest Sharpe ratio. The tangent line intersects the efficient frontier at the point where the portfolio with the highest Sharpe ratio is located.

The tangent line represents the optimal portfolio for an investor who wants to maximize their risk-adjusted return. Any portfolio on the tangent line is a combination of the risk-free asset and the portfolio with the highest Sharpe ratio.

The tangent line drawn from the risk-free rate to the efficient frontier is called the Capital Market Line (CML). The CML is a graphical representation of the concept of the Capital Asset Pricing Model (CAPM), which is a widely used model in finance that describes the relationship between the risk and expected return of an asset or a portfolio.

The CML is the straight line that connects the risk-free rate to the point of tangency with the efficient frontier, which represents the optimal portfolio for an investor who wants to maximize their risk-adjusted return. The slope of the CML is the market risk premium, which is the excess return that investors require to invest in a risky asset rather than a risk-free asset. The CML can be used to determine the required return for any level of risk, and it provides a benchmark for evaluating the performance of different investment portfolios.

FYI only:

https://homepage.divms.uiowa.edu/~mbognar/applets/normal.html

FYI:

Develop a Stock Data Fetcher in Google Sheets

https://script.google.com/macros/s/AKfycby5vZhxEOed7AcET57IfRwkanirTqOszZ8Wtfs9OEM42vFb6As_cQaJL9wOWPF170xn/exec (example)

Step 1: Create a New Google Sheet

Open Your Web Browser: Go to Google Sheets.
Sign In: If you aren’t signed in already, use your Google account to sign in.
Create a New Sheet: Click on the “Blank” option to create a new, empty Google Sheet.

Step 2: Set Up the Google Apps Script

Open the Script Editor:

In your new Google Sheet, click on Extensions in the top menu.
Select Apps Script from the dropdown menu. This will open the Apps Script editor in a new tab.

Clear Any Default Code:

If there is any default code in the editor, delete it to start with a blank script.

Paste the Script:

Copy the following script and paste it into the editor:

// Function to serve the HTML file

function doGet() {

return HtmlService.createHtmlOutputFromFile('index');

}

function fetchStockData(ticker, startDateStr) {

var sheet = SpreadsheetApp.getActiveSpreadsheet().getActiveSheet();

// Clear previous data

sheet.getRange("A1:F1000").clearContent();

// Set the header row for daily data

sheet.getRange("A1").setValue("Date");

sheet.getRange("B1").setValue("Closing Price");

sheet.getRange("C1").setValue("Stock Name");

// Fetch and display the stock name using GOOGLEFINANCE

var stockNameFormula = `=GOOGLEFINANCE("${ticker}", "name")`;

sheet.getRange("C2").setFormula(stockNameFormula);

// Set up the formula to fetch daily data using GOOGLEFINANCE

var formula = `=GOOGLEFINANCE("${ticker}", "close", "${startDateStr}", TODAY(), "daily")`;

sheet.getRange("A2").setFormula(formula);

// Wait for the data to populate

SpreadsheetApp.flush();

// Copy the daily data into an array

var dataRange = sheet.getRange("A2:B1000").getValues();

var validData = dataRange.filter(row => row[0] && row[1]); // Remove empty rows and invalid data

if (validData.length === 0) {

return "No data available. Please check the stock ticker and date range.";

}

// Set the header row for monthly data in columns D, E, and F

sheet.getRange("D1").setValue("Month");

sheet.getRange("E1").setValue("Closing Price");

sheet.getRange("F1").setValue("Monthly Return");

// Process data to calculate the last trading day of each month

var monthlyData = {};

validData.forEach(row => {

var date = new Date(row[0]);

var price = row[1];

var monthKey = `${date.getFullYear()}-${(date.getMonth() + 1).toString().padStart(2, '0')}`;

// Keep updating to get the last price of the month

monthlyData[monthKey] = price;

});

// Write the monthly data and calculate returns

var previousPrice = null;

var rowIndex = 2;

for (var month in monthlyData) {

var price = monthlyData[month];

sheet.getRange(rowIndex, 4).setValue(month); // Write month in column D

sheet.getRange(rowIndex, 5).setValue(price); // Write price in column E

if (previousPrice !== null) {

var monthlyReturn = ((price - previousPrice) / previousPrice) * 100;

sheet.getRange(rowIndex, 6).setValue(monthlyReturn.toFixed(2) + "%"); // Write return in column F

}

previousPrice = price;

rowIndex++;

}

return "Data fetched and returns calculated successfully!";

}

Save the Script:

Click on the Save icon (or press Ctrl + S).
Name Your Project: Give it a simple name like "Stock Data Fetcher."

Step 3: Authorize and Run the Script

Authorize the Script:

Click on the Run button (the ▶ icon).
A dialog box will appear asking for permission. Click Review Permissions.
Choose your Google account and click Allow to grant the necessary permissions.

Run the Script:

After authorizing, click Run again to execute the script.

Step 4: Create the HTML File

1. In the Apps Script editor, click on the + button next to "Files" and select HTML.

2. Name the new file Index.html.

3. Paste the following HTML code into the Index.html file:

<!DOCTYPE html>

<html>

<head>

<title>Stock Data Fetcher</title>

<style>

body {

font-family: Arial, sans-serif;

margin: 20px;

}

h2 {

color: #333;

}

label {

display: block;

margin-top: 10px;

}

input, button {

margin-top: 5px;

}

.footer {

margin-top: 20px;

font-size: 12px;

color: #666;

text-align: center;

}

</style>

</head>

<body>

<h2>Stock Data Fetcher</h2>

<label for="ticker">Stock Ticker:</label>

<label for="startDate">Start Date:</label>

<button onclick="fetchData()">Fetch Data</button>

<button onclick="openGoogleSheet()">Open Google Sheet</button>

function fetchData() {

var ticker = document.getElementById('ticker').value;

var startDate = document.getElementById('startDate').value;

// Call the Apps Script function

google.script.run.withSuccessHandler(function(response) {

document.getElementById('status').innerText = response;

}).fetchStockData(ticker, startDate);

}

function openGoogleSheet() {

// Replace with the URL of your Google Sheet

var sheetUrl = "YOUR_GOOGLE_SHEET_URL"; // Replace with your actual Google Sheet URL

window.open(sheetUrl, "_blank");

}

</script>

</body>

</html>

Step 5: Deploy Your Web App

In the Apps Script editor, click on Deploy > New deployment.
Choose Web app.
Set the following options:

Description: Enter a name like "Stock Data Fetcher Deployment."
Execute as: Select Me.
Who has access: Choose Anyone (if you want others to use it) or Only myself for private use.

Click Deploy and follow the instructions to authorize the app.
Copy the web app URL provided after deployment.

Step 6: Access and Use the Web App

Open the web app using the URL you copied.
Enter the stock ticker and start date.
Click Fetch Data to retrieve and display the data in your Google Sheet.
Share the URL so that others can use your app to fetch stock data.

Troubleshooting Tips:

1. Ensure You Have the Correct Google Sheet URL:

o Make sure to replace "YOUR_GOOGLE_SHEET_URL" in the HTML script with the correct URL of your Google Sheet.

o To copy the URL:

§ Open your Google Sheet.

§ Click on the address bar and copy the full URL.

§ Paste this URL into the sheetUrl variable in the HTML file.

2. Set Google Sheet Share Settings:

o Open your Google Sheet.

o Click the “Share” button in the top right corner.

o In the sharing settings, select "Anyone with the link" and choose the appropriate permissions (view, comment, or edit).

o Click "Copy link" and use this link as your Google Sheet URL in the script.

3. Update the HTML Code:

o Replace the placeholder in the openGoogleSheet function with your actual Google Sheet URL:

function openGoogleSheet() {

  var sheetUrl = "YOUR_GOOGLE_SHEET_URL"; // Replace with your actual Google Sheet URL

  window.open(sheetUrl, "_blank");

Key Points to Remember:

Correct URL: Ensure you copy and paste the full Google Sheet URL correctly.
Sharing Settings: Double-check that the Google Sheet is set to "Anyone with the link" for access.

First Midterm Exam (2/27/2025, Closed book Closed notes)

Solutions T/F Calculations

Study Guide Calculation Sample Questions

30 T/F questions

1. Yield Curve & Interest Rates

1) Yield Curve Shapes: Understand what an inverted, steep, and flat yield curve indicate about market expectations and the economy.

2) Yield Spreads: Know how the difference between corporate bonds and Treasury yields reflects default and liquidity risks.

3) Maturity Risk Premium: Recognize that longer maturities typically carry a higher premium.

4) Demand Effects: Higher demand for long-term Treasuries generally lowers their yields.

2. Monetary Policy & Risk-Free Assets

1) Fed Actions: Be aware of how accommodative monetary policy (e.g., near-zero short-term rates during COVID) works.

2) Risk-Free Rate Concepts: Know that Treasury bonds are considered “risk-free” (backed by the U.S. government) and that the real risk-free rate isn’t solely set by central banks.

3) Interest Rate Components: Familiarize yourself with the formula (r = r* + IP + DRP + LP + MRP) and what each term generally represents.

3. Bond Characteristics & Analysis

1) Bond Duration: Understand duration as a measure of a bond’s sensitivity to a 1% change in interest rates.

2) Coupon Impact: Remember that higher coupons tend to reduce interest rate risk.

3) Tools & Functions: Know that Excel functions like DURATION and Solver are used in bond analysis.

4) Credit Ratings: Review why credit ratings (from Moody’s, S&P, etc.) are important for assessing risk.

4. Portfolio & Investment Strategies

1) Diversification: Modern Portfolio Theory (MPT) emphasizes that combining different assets reduces overall risk.

2) Efficient Frontier: Know that this curve represents portfolios with the highest return for a given risk.

3) Calculating Returns & Risk: Portfolio return is the weighted sum of individual returns; however, overall risk (standard deviation) involves correlations between assets.

4) Risk Tolerance: Understand that a client’s risk tolerance is crucial to portfolio construction (it is not irrelevant).

5. Investment Styles & Risk Measures

1) Growth vs. Value Investing: Be able to distinguish between investing in high-growth (tech, biotech) versus undervalued companies.

2) Small-Cap Stocks: Recognize that while these can boost returns, they also increase risk.

3) Sharpe Ratio: This metric measures risk-adjusted return; higher values indicate better performance per unit of risk.

4) Reinvestment Risk: Know that short-term bonds carry the risk of having to reinvest at lower yields.

Nine Calculation Questions (on Interest rate breakdown, and expectation theory)

The nominal interest rate on a security can be expressed as:

r = r* + IP + DRP + LP + MRP

· r*: Real risk-free rate – the return required in an environment without inflation.

· IP: Inflation premium – compensation for expected inflation.

· DRP: Default risk premium – additional yield for the possibility of default (zero for Treasuries).

· LP: Liquidity premium – extra yield for bonds that are less liquid (zero for Treasuries).

· MRP: Maturity risk premium – increases with the bond’s term to maturity to compensate for uncertainty over time.

Note: Treasury bonds generally have no DRP or LP, whereas corporate bonds include these additional risk premiums.

For example, if a one-year Treasury yield is 7% and expected inflation is 2%, then r* ≈ 7% – 2% = 5%.

Expectations Theory & Forward Rates

Pure expectations theory states that long-term yields are determined by the market’s expectation of future short-term rates. In simple terms, the yield on a long-term bond is roughly the average of current and expected future short-term yields.

· For instance, if you know the current one-year yield and the two-year yield, you can solve for the expected one-year forward rate using:

· (Current one-year yield + Forward rate) / 2 = Two-year yield

Corporate vs. Treasury Bond Yield Breakdown

Understanding the differences in yield components is crucial:

· Treasury Bonds: Their yield comprises the real risk-free rate (r*), the inflation premium (IP), and the maturity risk premium (MRP). They have no default risk premium (DRP) or liquidity premium (LP) because they are considered risk-free and highly liquid.

· Corporate Bonds: In addition to r*, IP, and MRP, their yield includes a default risk premium (DRP) and a liquidity premium (LP) to compensate for additional risks.

Example:

· Consider a corporate bond where:

o r* = 2%, IP = 1%, MRP = 0.5%, and DRP = 1.5%, LP =?

o The yield on a Treasury bond with the same term would be:

o 2% + 1% + 0.5% = 3.5%.

o If the corporate bond yields 7%, then the liquidity premium (LP) is:

o LP = 7% – (2% + 1% + 0.5% + 1.5%) = 7% – 5% = 2%.

· Similarly, for a Treasury bond with r* = 3% and MRP = 0.4% yielding 5%, the inflation premium (IP) is:

o IP = 5% – (3% + 0.4%) = 1.6%.

Calculation Techniques

· Treasury Yield: Sum r*, IP, and (if applicable) MRP.

· Corporate Yield: Add DRP and LP to the Treasury components.

· Forward Rates: Use the compound relationship between yields.

Chapter 10 WACC

ppt Game_WACC Quiz_WACC-1 Quiz_WACC_2

One option (if beta is given)

Another option (if dividend is given):

WACC Formula

WACC calculator (annual coupon bond)

(www.jufinance.com/wacc)

WACC calculator (semi-annual coupon bond)

(www.jufinance.com/wacc_1)

WACC Calculator help videos FYI

Summary of Equations

Discount rate to figure out the value of projects is called WACC (weighted average cost of capital)

WACC = weight of debt * cost of debt + weight of equity *( cost of equity)

· Wd= total debt / Total capital = total borrowed / total capital

· We= total equity/ Total capital

· Cost of debt = rate(nper, coupon, -(price – flotation costs), 1000)*(1-tax rate)

· Cost of Equity = D1/(Po – Flotation Cost) + g

· D1: Next period dividend; Po: Current stock price; g: dividend growth rate

· Note: flotation costs = flotation percentage * price

· Or if beta is given, use CAPM model

1. Cost of equity = risk free rate + beta *(market return – risk free rate)

2. Cost of equity = risk free rate + beta * market risk premium

(FYI: Hertz Global Holdings Inc (NYSE:HTZ) WACC %:5.43% As of 3/3/2025

As of today (2025-03-03), Hertz Global Holdings's weighted average cost of capital is 5.43%%. Hertz Global Holdings's ROIC % is

-4.70% (calculated using TTM income statement data). Hertz Global Holdings generates higher returns on investment than it costs the company to raise the capital needed for that investment. It is earning excess returns. A firm that expects to continue generating positive excess returns on new investments in the future will see its value increase as growth increases.

*Note: The beta of this company cannot be obtained because it has a price history shorter than 3 years. It will thus be set to 1 as default to calculate WACC. https://www.gurufocus.com/term/wacc/HTZ/WACC/Hertz+Global+Holdings+Inc

Hertz Global Holdings WACC % Calculation

The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's cost of capital. Generally speaking, a company's assets are financed by debt and equity. WACC is the average of the costs of these sources of financing, each of which is weighted by its respective use in the given situation. By taking a weighted average, we can see how much interest the company has to pay for every dollar it finances.

WACC

(E + D)

Cost of Equity

(E + D)

Cost of Debt

(1 - Tax Rate)

1. Weights:
Generally speaking, a company's assets are financed by debt and equity. We need to calculate the weight of equity and the weight of debt.
The market value of equity (E) is also called "Market Cap". As of today, Hertz Global Holdings's market capitalization (E) is $1238.074 Mil.
The market value of debt is typically difficult to calculate, therefore, GuruFocus uses book value of debt (D) to do the calculation. It is simplified by adding the latest one-year quarterly average Short-Term Debt & Capital Lease Obligation and Long-Term Debt & Capital Lease Obligation together. As of Dec. 2024, Hertz Global Holdings's latest one-year quarterly average Book Value of Debt (D) is $18507.8 Mil.
a) weight of equity = E / (E + D) = 1238.074 / (1238.074 + 18507.8) = 0.0627
b) weight of debt = D / (E + D) = 18507.8 / (1238.074 + 18507.8) = 0.9373

2. Cost of Equity:
GuruFocus uses Capital Asset Pricing Model (CAPM) to calculate the required rate of return. The formula is:
Cost of Equity = Risk-Free Rate of Return + Beta of Asset * (Expected Return of the Market - Risk-Free Rate of Return)
a) GuruFocus uses 10-Year Treasury Constant Maturity Rate as the risk-free rate. It is updated daily. The current risk-free rate is 4.157%. Please go to Economic Indicators page for more information. Please note that we use the 10-Year Treasury Constant Maturity Rate of the country/region where the company is headquartered. If the data for that country/region is not available, then we will use the 10-Year Treasury Constant Maturity Rate of the United States as default.
b) Beta is the sensitivity of the expected excess asset returns to the expected excess market returns. Hertz Global Holdings's beta is 2.33.
c) (Expected Return of the Market - Risk-Free Rate of Return) is also called market premium. GuruFocus requires market premium to be 6%.
Cost of Equity = 4.157% + 2.33 * 6% = 18.137%

3. Cost of Debt:
GuruFocus uses latest TTM Interest Expense divided by the latest one-year quarterly average debt to get the simplified cost of debt.
As of Dec. 2024, Hertz Global Holdings's interest expense (positive number) was $959 Mil. Its total Book Value of Debt (D) is $18507.8 Mil.
Cost of Debt = 959 / 18507.8 = 5.1816%.

4. Multiply by one minus TTM Tax Rate:
GuruFocus uses the most recent TTM Tax Expense divided by the most recent TTM Pre-Tax Income to calculate the tax rate. The calculated TTM tax rate is limited to between 0% and 100%. If the calculated tax rate is higher than 100%, it is set to 100%. If the calculated tax rate is less than 0%, it is set to 0%.
The latest calculated TTM Tax Rate = -375 / -3237 = 11.58%.

Hertz Global Holdings's Weighted Average Cost Of Capital (WACC) for Today is calculated as:

WACC	=	E / (E + D)	*	Cost of Equity	+	D / (E + D)	*	Cost of Debt	*	(1 - Tax Rate)
	=	0.0627	*	18.137%	+	0.9373	*	5.1816%	*	(1 - 11.58%)
	=	5.43%

HERTZ WACC in 2017

Excel file is here. Thanks to Chris, Brian and Hanna, the CFA competition team of 2017.

In Class Exercise (https://www.jufinance.com/fin435_24s/wacc_in_class_exercise.html)

1. IBM financed 10m via debt coupon 5%, 10 year, price is $950 and flotation is 7% of the price, tax 40%.

IBM financed 20m via equity. D1=$5. Po=50, g is 5%. Flotation cost =0. So WACC?

Answer:

· Wd=1/3. We=2/3.

· Kd = rate(10, 5%*1000, -(950-950*7%), 1000)*(1-40%) = 3.98%------ after tax cost of debt

· Ke = 5/(50 – 0) + 5% =15% -------- cost of equity

· WACC = Wd*Kd +We*Ke = (1/3)*3.98% + (2/3)*15% =11.33%

2. Firm AAA sold a noncallable bond now has 20 years to maturity. 9.25% annual coupon rate, paid semiannually, sells at a price = $1,075, par = $1,000. Tax rate = 40%, calculate after tax cost of debt (5.08%)

Answer:

· after tax cost of debt = rate(nper, coupon, -(price-flotation), 1000)*(1-tax rate)

· After tax of debt = rate(20*2, 9.25%*1000/2, -(1075-0), 1000)*(1-40%)=5.08%

2. Firm AAA’s equity condition is as follows. D₁ = $1.25; P₀ = $27.50; g = 5.00%; and Flotation = 6.00% of price. Calculate cost of equity (9.84%)

Answer:

· Cost of equity = D1/(Po-flotation) + g= 1.25/(27.5-6%*27.5) + 5% = 9.84%

3. Continue from above. Firm AAA raised 10m from the capital market. In it, 3m is from the debt market and the rest from the equity market. Calculate WACC.

Answer:

· WACC = Wd*Kd +We*Ke =

· WACC = (3/10)*5.08% + (7/10)*9.84%

4. Common stock currently sells = $45.00 / share; and earn $2.75 /share this year, payout ratio is 70%, and its constant growth rate = 6.00%. New stock can be sold at the current price, a flotation cost =8%. How much would the cost of new stock beyond the cost of retained earnings?

Answer:

Expected EPS₁ $2.75

Payout ratio 70%

Current stk price $45.00

g 6.00%

F 8.00%

D₁ $1.925

r_s = D₁/P₀ + g 10.28%

r_e =D₁/(P₀ × (1 − F)) + g 10.65%

Difference = r_e – r_s 0.37%

5. (1) The firm's noncallable bonds mature in 20 years, an 8.00% annual coupon, a market price of $1,050.00. (2) tax rate = 40%. (3) The risk-free rate=4.50%, the market risk premium = 5.50%, stock’s beta =1.20. (4) capital structure consists of 35% debt and 65% common equity. What is its WACC?

Answer:

Coupon rate 8.00%

Maturity 20

Bond price $1,050.00

Par value $1,000

Tax rate 40%

r_RF 4.50%

RP_M 5.50%

b 1.20

Weight debt 35%

Weight equity 65%

Bond yield 7.51% (=rate(20, 8%*1000, -1050, 1000)

A-T cost of debt 4.51% (= rate(20, 8%*1000, -1050, 1000)*(1-40%)

Cost of equity, r_s= r_RF + b(RP_M) 11.10% (=4.5% + 1.2*5.5%)

WACC = w_d(r_d)(1 – T) + w_c(r_s) = 8.79% (=35%*4.51% + 65% * 11.1%)

· WACC Case study (due with the 2^nd midterm exam)

· Case video just in case

https://jufinance.com/video/chapter10_case_2024.mp4

Hint:

Corporate Bond Data is available at FINRA.ORG: https://www.finra.org/finra-data/fixed-income/corp-and-agency

Muni Bond Data is available at EMMA: https://emma.msrb.org/

Treasury Securities Data is available at Treasury Direct: https://www.treasurydirect.gov/

FYI: WACC calculator https://fairness-finance.com/fairness-finance/finance/calculator/wacc.dhtml

Cost of Capital by Sector (US)

https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/wacc.html

*Industry Name*	*Number of Firms*	*Beta*	*Cost of Equity*	*E/(D+E)*	*Std Dev in Stock*	*Cost of Debt*	*Tax Rate*	*After-tax Cost of Debt*	*D/(D+E)*	*Cost of Capital*
Advertising	58	1.63	13.57%	68.97%	52.72%	5.88%	6.39%	4.41%	31.03%	10.73%
Aerospace/Defense	77	1.41	12.28%	79.33%	37.56%	5.50%	8.60%	4.13%	20.67%	10.59%
Air Transport	21	1.42	12.29%	34.92%	37.73%	5.50%	10.47%	4.13%	65.08%	6.98%
Apparel	39	1.32	11.75%	65.98%	38.51%	5.50%	12.04%	4.13%	34.02%	9.15%
Auto & Truck	31	1.54	13.03%	66.58%	52.61%	5.88%	3.00%	4.41%	33.42%	10.15%
Auto Parts	37	1.47	12.64%	70.10%	39.52%	5.50%	9.30%	4.13%	29.90%	10.09%
Bank (Money Center)	7	1.08	10.30%	31.61%	19.59%	4.73%	16.25%	3.55%	68.39%	5.68%
Banks (Regional)	557	0.5	6.88%	60.75%	16.76%	4.73%	18.84%	3.55%	39.25%	5.57%
Beverage (Alcoholic)	23	1.01	9.90%	81.36%	49.87%	5.50%	9.39%	4.13%	18.64%	8.82%
Beverage (Soft)	31	1.3	11.62%	86.75%	41.72%	5.50%	6.42%	4.13%	13.25%	10.63%
Broadcasting	26	1.32	11.73%	40.51%	46.90%	5.50%	15.76%	4.13%	59.49%	7.21%
Brokerage & Investment Banking	30	1.2	11.04%	33.21%	28.00%	5.50%	15.32%	4.13%	66.79%	6.42%
Building Materials	45	1.28	11.47%	77.56%	29.19%	5.50%	16.71%	4.13%	22.44%	9.82%
Business & Consumer Services	164	1.17	10.84%	78.45%	45.78%	5.50%	9.43%	4.13%	21.55%	9.39%
Cable TV	10	1.26	11.34%	48.25%	25.41%	5.50%	21.95%	4.13%	51.75%	7.60%
Chemical (Basic)	38	1.25	11.29%	67.43%	46.58%	5.50%	9.83%	4.13%	32.57%	8.95%
Chemical (Diversified)	4	1.41	12.27%	63.19%	39.49%	5.50%	12.02%	4.13%	36.81%	9.27%
Chemical (Specialty)	76	1.28	11.47%	78.49%	42.32%	5.50%	10.75%	4.13%	21.51%	9.89%
Coal & Related Energy	19	1.45	12.51%	82.16%	61.96%	5.88%	2.28%	4.41%	17.84%	11.06%
Computer Services	80	1.17	10.84%	75.44%	47.78%	5.50%	6.47%	4.13%	24.56%	9.19%
Computers/Peripherals	42	1.29	11.55%	91.31%	48.73%	5.50%	9.13%	4.13%	8.69%	10.90%
Construction Supplies	49	1.26	11.39%	76.85%	35.11%	5.50%	10.52%	4.13%	23.15%	9.71%
Diversified	23	1.04	10.05%	82.48%	57.84%	5.88%	2.98%	4.41%	17.52%	9.06%
Drugs (Biotechnology)	598	1.24	11.26%	86.71%	58.41%	5.88%	0.94%	4.41%	13.29%	10.35%
Drugs (Pharmaceutical)	281	1.27	11.41%	88.02%	64.88%	5.88%	2.37%	4.41%	11.98%	10.57%
Education	33	1.1	10.42%	76.56%	41.81%	5.50%	7.10%	4.13%	23.44%	8.94%
Electrical Equipment	110	1.59	13.32%	81.62%	58.55%	5.88%	4.47%	4.41%	18.38%	11.68%
Electronics (Consumer & Office)	16	1.54	13.02%	85.87%	39.56%	5.50%	3.98%	4.13%	14.13%	11.76%
Electronics (General)	138	1.2	11.02%	84.16%	44.94%	5.50%	6.29%	4.13%	15.84%	9.92%
Engineering/Construction	43	1.2	10.99%	75.99%	35.17%	5.50%	13.30%	4.13%	24.01%	9.34%
Entertainment	110	1.45	12.49%	75.03%	57.81%	5.88%	3.45%	4.41%	24.97%	10.47%
Environmental & Waste Services	62	1.02	9.91%	79.66%	48.09%	5.50%	5.42%	4.13%	20.34%	8.73%
Farming/Agriculture	39	1.14	10.65%	74.70%	54.43%	5.88%	6.64%	4.41%	25.30%	9.07%
Financial Svcs. (Non-bank & Insurance)	223	0.89	9.14%	9.05%	27.15%	5.50%	14.61%	4.13%	90.95%	4.58%
Food Processing	92	0.92	9.33%	77.60%	34.23%	5.50%	7.74%	4.13%	22.40%	8.16%
Food Wholesalers	14	1.12	10.55%	68.42%	32.42%	5.50%	11.94%	4.13%	31.58%	8.52%
Furn/Home Furnishings	32	1.27	11.43%	64.13%	41.91%	5.50%	12.67%	4.13%	35.87%	8.81%
Green & Renewable Energy	19	1.6	13.39%	45.23%	67.60%	7.01%	6.73%	5.26%	54.77%	8.93%
Healthcare Products	254	1.16	10.78%	88.81%	50.94%	5.88%	3.70%	4.41%	11.19%	10.07%
Healthcare Support Services	131	1.16	10.77%	80.90%	47.79%	5.50%	6.74%	4.13%	19.10%	9.50%
Heathcare Information and Technology	138	1.47	12.62%	87.56%	53.87%	5.88%	4.30%	4.41%	12.44%	11.60%
Homebuilding	32	1.5	12.80%	75.57%	33.33%	5.50%	17.81%	4.13%	24.43%	10.68%
Hospitals/Healthcare Facilities	34	1.17	10.85%	53.41%	51.19%	5.88%	9.56%	4.41%	46.59%	7.85%
Hotel/Gaming	69	1.46	12.55%	60.03%	38.05%	5.50%	8.14%	4.13%	39.97%	9.18%
Household Products	127	1.16	10.74%	86.56%	56.83%	5.88%	6.73%	4.41%	13.44%	9.89%
Information Services	73	1.4	12.22%	88.45%	45.11%	5.50%	12.45%	4.13%	11.55%	11.29%
Insurance (General)	21	1.23	11.17%	76.63%	43.76%	5.50%	10.26%	4.13%	23.37%	9.53%
Insurance (Life)	27	0.94	9.46%	51.97%	28.89%	5.50%	11.41%	4.13%	48.03%	6.90%
Insurance (Prop/Cas.)	51	0.8	8.65%	82.33%	27.67%	5.50%	10.92%	4.13%	17.67%	7.85%
Investments & Asset Management	600	0.62	7.58%	72.28%	9.91%	4.73%	4.01%	3.55%	27.72%	6.47%
Machinery	116	1.22	11.16%	82.75%	32.36%	5.50%	10.37%	4.13%	17.25%	9.94%
Metals & Mining	68	1.29	11.54%	82.27%	70.06%	7.01%	4.15%	5.26%	17.73%	10.43%
Office Equipment & Services	16	1.18	10.87%	59.95%	35.22%	5.50%	19.53%	4.13%	40.05%	8.17%
Oil/Gas (Integrated)	4	0.98	9.69%	89.68%	30.55%	5.50%	14.22%	4.13%	10.32%	9.11%
Oil/Gas (Production and Exploration)	174	1.26	11.35%	83.28%	56.98%	5.88%	4.60%	4.41%	16.72%	10.19%
Oil/Gas Distribution	23	0.99	9.77%	58.34%	33.55%	5.50%	6.90%	4.13%	41.66%	7.42%
Oilfield Svcs/Equip.	101	1.38	12.05%	75.41%	46.90%	5.50%	7.07%	4.13%	24.59%	10.10%
Packaging & Container	25	0.95	9.54%	61.74%	24.43%	4.73%	14.66%	3.55%	38.26%	7.25%
Paper/Forest Products	7	1.38	12.10%	69.51%	42.84%	5.50%	12.76%	4.13%	30.49%	9.66%
Power	48	0.73	8.19%	56.45%	17.18%	4.73%	12.30%	3.55%	43.55%	6.17%
Precious Metals	74	1.23	11.21%	85.97%	72.54%	7.01%	2.87%	5.26%	14.03%	10.37%
Publishing & Newspapers	20	1.11	10.50%	70.34%	30.92%	5.50%	9.67%	4.13%	29.66%	8.61%
R.E.I.T.	223	1.06	10.20%	56.39%	21.54%	4.73%	3.38%	3.55%	43.61%	7.30%
Real Estate (Development)	18	1.52	12.89%	47.05%	51.25%	5.88%	6.66%	4.41%	52.95%	8.40%
Real Estate (General/Diversified)	12	0.79	8.57%	71.52%	28.66%	5.50%	9.37%	4.13%	28.48%	7.31%
Real Estate (Operations & Services)	60	1.35	11.87%	47.79%	44.43%	5.50%	5.47%	4.13%	52.21%	7.83%
Recreation	57	1.42	12.30%	65.76%	42.13%	5.50%	9.49%	4.13%	34.24%	9.50%
Reinsurance	1	0.83	8.81%	68.92%	19.37%	4.73%	6.48%	3.55%	31.08%	7.17%
Restaurant/Dining	70	1.41	12.26%	76.47%	41.15%	5.50%	8.54%	4.13%	23.53%	10.34%
Retail (Automotive)	30	1.52	12.91%	63.50%	35.71%	5.50%	15.84%	4.13%	36.50%	9.70%
Retail (Building Supply)	15	1.79	14.51%	82.50%	37.55%	5.50%	13.39%	4.13%	17.50%	12.69%
Retail (Distributors)	69	1.28	11.45%	71.65%	37.08%	5.50%	13.59%	4.13%	28.35%	9.38%
Retail (General)	15	1.36	11.98%	83.35%	31.53%	5.50%	21.26%	4.13%	16.65%	10.67%
Retail (Grocery and Food)	13	0.67	7.85%	60.31%	28.26%	5.50%	16.45%	4.13%	39.69%	6.37%
Retail (Online)	63	1.49	12.71%	83.91%	59.41%	5.88%	4.09%	4.41%	16.09%	11.38%
Retail (Special Lines)	78	1.48	12.64%	71.86%	38.59%	5.50%	15.02%	4.13%	28.14%	10.25%
Rubber& Tires	3	0.84	8.86%	23.24%	39.79%	5.50%	0.00%	4.13%	76.76%	5.22%
Semiconductor	68	1.61	13.43%	89.88%	38.40%	5.50%	8.18%	4.13%	10.12%	12.49%
Semiconductor Equip	30	1.76	14.32%	89.46%	41.57%	5.50%	10.94%	4.13%	10.54%	13.24%
Shipbuilding & Marine	8	0.94	9.49%	71.93%	41.16%	5.50%	6.23%	4.13%	28.07%	7.98%
Shoe	13	1.33	11.77%	91.73%	39.37%	5.50%	10.70%	4.13%	8.27%	11.13%
Software (Entertainment)	91	1.36	11.98%	95.42%	58.71%	5.88%	3.82%	4.41%	4.58%	11.63%
Software (Internet)	33	1.55	13.09%	84.99%	55.24%	5.88%	2.37%	4.41%	15.01%	11.79%
Software (System & Application)	390	1.47	12.61%	91.44%	52.11%	5.88%	3.40%	4.41%	8.56%	11.91%
Steel	28	1.34	11.85%	77.76%	38.30%	5.50%	14.95%	4.13%	22.24%	10.14%
Telecom (Wireless)	16	1.03	10.00%	60.55%	51.92%	5.88%	3.83%	4.41%	39.45%	7.80%
Telecom. Equipment	79	1.23	11.20%	89.54%	41.35%	5.50%	4.06%	4.13%	10.46%	10.46%
Telecom. Services	49	0.88	9.12%	45.93%	55.37%	5.88%	6.54%	4.41%	54.07%	6.57%
Tobacco	15	2	15.76%	80.61%	44.06%	5.50%	9.83%	4.13%	19.39%	13.51%
Transportation	18	1.06	10.17%	77.21%	28.05%	5.50%	16.39%	4.13%	22.79%	8.79%
Transportation (Railroads)	4	1.11	10.46%	78.46%	16.34%	4.73%	16.57%	3.55%	21.54%	8.97%
Trucking	35	1.55	13.06%	69.49%	41.17%	5.50%	14.79%	4.13%	30.51%	10.33%
Utility (General)	15	0.64	7.65%	57.41%	14.97%	4.73%	13.20%	3.55%	42.59%	5.90%
Utility (Water)	16	1.15	10.73%	69.74%	27.96%	5.50%	8.45%	4.13%	30.26%	8.73%
Total Market	7165	1.16	10.75%	65.14%	41.37%	5.50%	7.52%	4.13%	34.86%	8.44%
Total Market (without financials)	5649	1.29	11.56%	79.11%	47.98%	5.50%	6.38%	4.13%	20.89%	10.01%

***** How much does Amazon worth in 2019?”

FYI: Amazon.com Inc. (AMZN) https://www.stock-analysis-on.net/NASDAQ/Company/Amazoncom-Inc/DCF/Present-Value-of-FCFF

Present Value of Free Cash Flow to the Firm (FCFF)

In discounted cash flow (DCF) valuation techniques the value of the stock is estimated based upon present value of some measure of cash flow. Free cash flow to the firm (FCFF) is generally described as cash flows after direct costs and before any payments to capital suppliers.

Intrinsic Stock Value (Valuation Summary)

Amazon.com Inc., free cash flow to the firm (FCFF) forecast

Year	Value	FCFF_t or Terminal value (TV_t)	Calculation	Present value at 16.17%
0¹	FCFF₀	(4,286)
1	FCFF₁	–	= (4,286) × (1 + 0.00%)	–
2	FCFF₂	–	= – × (1 + 0.00%)	–
3	FCFF₃	–	= – × (1 + 0.00%)	–
4	FCFF₄	–	= – × (1 + 0.00%)	–
5	FCFF₅	–	= – × (1 + 0.00%)	–
5	Terminal value (TV₅)	–	= – × (1 + 0.00%) ÷ (16.17% – 0.00%)	–
Intrinsic value of Amazon.com's capital				–
Less: Debt (fair value)				45,696
Intrinsic value of Amazon.com's common stock				–

Intrinsic value of Amazon.com's common stock (per share)				$–
Current share price				$1,642.81

Weighted Average Cost of Capital (WACC)

Amazon.com Inc., cost of capital

	Value¹	Weight	Required rate of return²	Calculation
Equity (fair value)	803,283	0.95	16.97%
Debt (fair value)	45,696	0.05	2.10%	= 2.99% × (1 – 29.84%)

¹ USD $ in millions

Equity (fair value) = No. shares of common stock outstanding × Current share price
= 488,968,628 × $1,642.81 = $803,282,551,764.68

Debt (fair value). See Details »

² Required rate of return on equity is estimated by using CAPM. See Details »

Required rate of return on debt. See Details »

Required rate of return on debt is after tax.

Estimated (average) effective income tax rate
= (20.20% + 36.61% + 60.59% + 0.00% + 31.80%) ÷ 5 = 29.84%

WACC = 16.17%

FCFF Growth Rate (g)

FCFF growth rate (g) implied by PRAT model

Amazon.com Inc., PRAT model

	Average	Dec 31, 2017	Dec 31, 2016	Dec 31, 2015	Dec 31, 2014	Dec 31, 2013
*Selected Financial Data (USD $ in millions)*
Interest expense		848	484	459	210	141
Net income (loss)		3,033	2,371	596	(241)	274

Effective income tax rate (EITR)¹		20.20%	36.61%	60.59%	0.00%	31.80%

Interest expense, after tax²		677	307	181	210	96
Interest expense (after tax) and dividends		677	307	181	210	96

EBIT(1 – EITR)³		3,710	2,678	777	(31)	370

Current portion of long-term debt		100	1,056	238	1,520	753
Current portion of capital lease obligation		5,839	3,997	3,027	2,013	955
Current portion of finance lease obligations		282	144	99	67	28
Long-term debt, excluding current portion		24,743	7,694	8,235	8,265	3,191
Long-term capital lease obligations, excluding current portion		8,438	5,080	4,212	3,026	1,435
Long-term finance lease obligations, excluding current portion		4,745	2,439	1,736	1,198	555
Total stockholders' equity		27,709	19,285	13,384	10,741	9,746
Total capital		71,856	39,695	30,931	26,830	16,663
*Ratios*
Retention rate (RR)⁴		0.82	0.89	0.77	–	0.74
Return on invested capital (ROIC)⁵		5.16%	6.75%	2.51%	-0.12%	2.22%
*Averages*
RR	0.80
ROIC	3.31%

Growth rate of FCFF (g)⁶	0.00%

¹ See Details »

2017 Calculations

² Interest expense, after tax = Interest expense × (1 – EITR)
= 848 × (1 – 20.20%) = 677

³ EBIT(1 – EITR) = Net income (loss) + Interest expense, after tax
= 3,033 + 677 = 3,710

⁴ RR = [EBIT(1 – EITR) – Interest expense (after tax) and dividends] ÷ EBIT(1 – EITR)
= [3,710 – 677] ÷ 3,710 = 0.82

⁵ ROIC = 100 × EBIT(1 – EITR) ÷ Total capital
= 100 × 3,710 ÷ 71,856 = 5.16%

⁶ g = RR × ROIC
= 0.80 × 3.31% = 0.00%

FCFF growth rate (g) forecast

Amazon.com Inc., H-model

Year	Value	g_t
1	g₁	0.00%
2	g₂	0.00%
3	g₃	0.00%
4	g₄	0.00%
5 and thereafter	g₅	0.00%

where:
g₁ is implied by PRAT model
g₅ is implied by single-stage model
g₂, g₃ and g₄ are calculated using linear interpoltion between g₁ and g₅

Calculations

g₂ = g₁ + (g₅ – g₁) × (2 – 1) ÷ (5 – 1)
= 0.00% + (0.00% – 0.00%) × (2 – 1) ÷ (5 – 1) = 0.00%

g₃ = g₁ + (g₅ – g₁) × (3 – 1) ÷ (5 – 1)
= 0.00% + (0.00% – 0.00%) × (3 – 1) ÷ (5 – 1) = 0.00%

g₄ = g₁ + (g₅ – g₁) × (4 – 1) ÷ (5 – 1)
= 0.00% + (0.00% – 0.00%) × (4 – 1) ÷ (5 – 1) = 0.00%

Summary and Key Insights

Step 1: Understanding Free Cash Flow to the Firm (FCFF)

· FCFF represents the cash generated by a company before paying investors (equity holders and debt holders).

· The first FCFF value (initial year) is usually taken from financial reports (income statement, cash flow statement).

· If it's negative, it means the company spent more than it generated.

Step 2: Forecasting Future FCFF

· The future FCFF values are estimated based on growth assumptions (historical trends, industry expectations).

· A common approach is to assume a constant growth rate or use detailed business projections.

· If growth is 0%, future cash flows stay the same as the first value.

Step 3: Discounting Future Cash Flows

· Because money today is worth more than money in the future, we apply a discount rate to adjust future cash flows.

· The discount rate is based on the company’s Weighted Average Cost of Capital (WACC) (a mix of how much it costs to borrow money and how much investors expect in return).

· A higher WACC means the company’s future cash flows are worth less today.

Step 4: Determining the Final (Terminal) Value

· Instead of forecasting cash flows forever, we calculate a final lump sum value called the terminal value.

· This represents how much the business will be worth at a point in the future based on expected stability.

Step 5: Calculating the Company’s Value

· The sum of all discounted FCFF values (including terminal value) gives the intrinsic value of the firm.

· Subtract total debt from this value to get the intrinsic value of the company’s stock.

· Divide by total shares outstanding to get the value per share.

Key Insights

1. FCFF tells us how much cash a company actually makes for its investors.

· If negative, the company is burning cash.

· If positive, it's generating real value.

2. Future FCFF is estimated based on expected growth.

· No growth? The company isn’t expected to expand much.

3. The discount rate (WACC) determines how much today’s investors care about future cash.

· Higher WACC = More risk = Future cash is worth less today.

4. Terminal value represents the long-term worth of the company.

· If a company is expected to last, this is a big portion of its value.

5. Subtract debt to find out what the company’s stock is worth.

· A company can have great cash flow but still owe too much money!

6. If the stock market price is higher than intrinsic value → Overvalued.

· If lower → Undervalued.

Recommended websites for WACC

Hertz

· https://valueinvesting.io/HTZGQ/valuation/wacc

https://www.gurufocus.com/term/wacc/HTZ/WACC/Hertz+Global+Holdings+Inc

Tesla

· https://www.gurufocus.com/term/wacc/TSLA/WACC-Percentage/Tesla

· https://valueinvesting.io/TSLA/valuation/wacc // cost of equity = long term bond rate + premium

Wal-Mart

· https://www.gurufocus.com/term/wacc/WMT/WACC-Percentage/Walmart#:~:text=As%20of%20today%20(2023%2D03,cost%20of%20capital%20is%206.42%25.

· https://valueinvesting.io/WMT/valuation/wacc

Amazon

· https://valueinvesting.io/AMZN/valuation/wacc

· https://www.gurufocus.com/term/wacc/AMZN/WACC-Percentage/Amazon.com

Apple

· https://www.gurufocus.com/term/wacc/AAPL/WACC-Percentage/Apple

· https://valueinvesting.io/AAPL/valuation/wacc

What is DCF? DCF Quiz A simple game to show how DCF works

Video – Amazon – DCF Example (self-made video in spring 2023)

Evaluation of Amazon based on DCF – ChatGPT done in Spring 2023

DCF (Discounted Cash Flow) analysis is a commonly used method for evaluating the intrinsic value of a company. It is based on the idea that the value of a company is determined by the present value of its expected future cash flows.

Here are the steps to evaluate Amazon using DCF:

Step 1: Estimate Amazon's Free Cash Flow (FCF)

FCF is the cash generated by a company after accounting for all capital expenditures needed to maintain or grow the business. To calculate Amazon's FCF, we can start with its operating cash flow and subtract its capital expenditures.

Operating cash flow for the last 12 months (as of September 2021) was $92.5 billion, and capital expenditures were $24.5 billion. Therefore, Amazon's FCF is:

FCF = Operating cash flow - Capital expenditures

FCF = $92.5 billion - $24.5 billion

FCF = $68 billion

Step 2: Estimate Amazon's growth rate

Next, we need to estimate the rate at which Amazon's FCF is likely to grow in the future. One way to do this is to look at the historical growth rates and make an educated guess about future growth.

Amazon's FCF has grown at an average rate of 25% over the past five years. Assuming a conservative growth rate of 15% for the next five years, and then a terminal growth rate of 3% after that, we can estimate Amazon's future FCF as follows:

Year 1 FCF = $68 billion x (1 + 15%) = $78.2 billion

Year 2 FCF = $78.2 billion x (1 + 15%) = $89.9 billion

Year 3 FCF = $89.9 billion x (1 + 15%) = $103.4 billion

Year 4 FCF = $103.4 billion x (1 + 15%) = $119 billion

Year 5 FCF = $119 billion x (1 + 15%) = $137 billion

Terminal FCF = $137 billion x (1 + 3%) / (11% - 3%) = $1760.94 billion (11% is the WACC)

Step 3: Determine Amazon's Discount Rate

The discount rate is the rate of return required by investors to compensate for the risk of investing in a company. A higher discount rate indicates a higher level of risk. To determine Amazon's discount rate, we can use the CAPM (Capital Asset Pricing Model), which takes into account the risk-free rate, market risk premium, and Amazon's beta.

Assuming a risk-free rate of 2%, a market risk premium of 6%, and Amazon's beta of 1.5, we can calculate Amazon's discount rate as follows:

Discount rate = Risk-free rate + Beta x Market risk premium

Discount rate = 2% + 1.5 x 6%

Discount rate = 11%

Step 4: Calculate Amazon's Intrinsic Value

Finally, we can calculate Amazon's intrinsic value using the discounted cash flow formula, which is the sum of the present value of all future cash flows.

Intrinsic value = (Year 1 FCF / (1 + Discount rate)^1) + (Year 2 FCF / (1 + Discount rate)^2) + ... + (Terminal FCF / (1 + Discount rate)^5)

Intrinsic value = ($78.2 billion / (1 + 11%)^1) + ($89.9 billion / (1 + 11%)^2) + ($103.4 billion / (1 + 11%)^3) + ($119 billion / (1 + 11%)^4) + ($137 billion / (1 +11%)^5) + ($1.76 trillion / (1 + 11%)^5)

Intrinsic value = $1,423 billion

We made the assumption that AMAZON's cost of equity is roughly equivalent to its WACC for the purpose of simplifying the calculation. However, according to gurufocus.com, as of the end of March 2023, AMAZON's WACC is 9.65%.

Step 5: Compare Intrinsic Value with Market Value

The last step is to compare the intrinsic value we calculated with the current market value of Amazon. As of March 2023, Amazon's market capitalization is around $2.4 trillion.

Comparing the intrinsic value of $1,423 billion with the market capitalization of $2.4 trillion, we can see that the market value is higher than the intrinsic value, which suggests that the stock may be overvalued. However, it's important to keep in mind that the DCF analysis is based on various assumptions and estimates, and the actual value of a company may differ from the calculated intrinsic value.

Therefore, it's important to use multiple valuation methods and take into account other factors such as industry trends, competitive landscape, and management quality to make an informed investment decision.

To calculate the estimated per-share stock price based on the DCF analysis, we can divide the intrinsic value by the total number of shares outstanding. As of December 2021, Amazon had around 500 million shares outstanding.

Estimated Per-Share Stock Price = Intrinsic Value / Shares Outstanding

Estimated Per-Share Stock Price = $1,423 billion / 500 million

Estimated Per-Share Stock Price = $2,847

Therefore, based on this DCF analysis, the estimated per-share stock price for Amazon is $2,847. However, it's important to note that this is just an estimate based on certain assumptions and estimates, and the actual stock price may differ based on various factors such as market sentiment, company performance, and global economic conditions.

Step one of DCF: FCF - Chapter 3 Financial Statement

ppt

Balance Sheet Template https://www.jufinance.com/10k/bs

Income Statement Template https://www.jufinance.com/10k/is

Cash flow template https://www.jufinance.com/10k/cf

Note: All companies, foreign and domestic, are required to file registration statements, periodic reports, and other forms electronically through EDGAR.

************ What is Free Cash Flow **************

What is free cash flow (video)

What is free cash flow (FCF)? Why is it important?

• FCF is the amount of cash available from operations for distribution to all investors (including stockholders and debt holders) after making the necessary investments to support operations.

• A company’s value depends on the amount of FCF it can generate.

What are the five uses of FCF?

o Pay interest on debt.

o Pay back principal on debt.

o Pay dividends.

o Buy back stock.

o Buy non-operating assets (e.g., marketable securities, investments in other companies, etc.)

FCF calculator

https://www.jufinance.com/fcf

In class exercise

Firm AAA has EBIT (operating income) of $3 million, depreciation of $1 million. Firm AAA’s expenditures on fixed assets = $1 million. Its net operating working capital = $0.6 million. Calculate for free cash flow. Imagine that the tax rate =40%.

FCF = EBIT(1 – T) + Deprec. – (Capex + NOWC)

answer:

EBIT $3

Tax rate 40%

Depreciation $1

Capex + NOWC $1.60

So, FCF = 3*(1-40%) + 1 –(1+0.6) = 1.2

Case study of chapter 3 on Cash Flow Statement and FCF only (due with the second midterm exam)

Case video on 3/11/2024

A review of Cash Flow Statement (FIN301): https://www.jufinance.com/10k/cf/

Excel Template

Cash Flow Statement		Notes
Cash at the beginning of the year		Cash, last year's balance sheet; "=Cash in 2022"
Cash From operation
net income		Income statement of 2023
plus depreciation		Income statement of 2023
-/+ AR		Changes of AR between this year and last year - balance sheet. CHANGE SIGN! use 2023 - 2022
-/+ Inventory		Changes of Inventory between this year and last year /// balance sheet. CHANGE SIGN! use 2023 - 2022
+/- AP		Changes of AP between this year and last year /// balance sheet. use 2023 - 2022
net change in cash from operation	--
Cash From investment
-/+ (NFA+depreciation)		Changes of NFA between this year & last year, add back depreciation//balance sheet. CHANGE SIGN!
net change in cash from investment	--
Cash From Financing
+/- long term debt		Changes of LD between this year and last year /// balance sheet. use 2023 - 2022
Common stock		Changes of CS between this year and last year /// balance sheet. use 2023 - 2022
- dividend		Income statement of 2023; Do not add negative sign to subtract dividend
net change in cash from financing	--

Total net change of cash	--

Cash at the end of the year	--	Should match Cash on current year's balance sheet; if not, go back and check; "=2023's cash"

Step 2 of DCF - Chapter 12: Cash Flow Estimation and Monte Carlo Method in Excel

· Monte Carlo quiz

· DCF Game 1

· DCF Game 2 (helpful for the following case study)

ppt

Chapter 12 case study (due with the second midterm exam. Monte Carol is required. And refer to https://www.jufinance.com/game/dcf_simple_monte_carlo.html)

· Chapter 12 case study in class part i video

· Chapter 12 case study in class part ii – Monte Carlo - video

· Monte Carlo Demonstration Based on Case in Class (FYI, Video)

Monte Carlo Simulation for Bitcoin Price Prediction (FYI)

Model Explanation:

Monte Carlo simulation is used to predict possible future prices of Bitcoin by modeling random fluctuations in the market. The key idea is that Bitcoin prices follow a stochastic (random) process influenced by daily returns and volatility.

Initial Price (S0): $65,000 (starting Bitcoin price)
Daily Expected Return (µ): 0.1% (assumed daily average increase)
Daily Volatility (σ): 3% (assumed daily price fluctuation)
Time Horizon: 30 days
Number of Simulations: 1,000 (each represents a possible price scenario)

The formula used to simulate the price each day is: S_t= S_t-1*(1+random shock)

where the random shock follows a normal distribution with mean µ and standard deviation σ.

Results & Interpretation:

1. Multiple Possible Price Paths

The simulation generates 1,000 possible futures for Bitcoin’s price.
Each line represents one possible future movement based on random price changes.

2. Sample Test Cases (Final Graph)

To make it easier to understand, I selected 10 different test results from the 1,000 simulations.
Each test represents a possible Bitcoin price movement over 30 days.
Some tests show Bitcoin going up, others show going down, demonstrating market uncertainty.

3. The model I used follows the standard Geometric Brownian Motion (GBM) approach, which is the same technique used by quantitative analysts and traders to price options and assess financial risk. The parameters (daily return, volatility, number of simulations) are typical estimates, and the results are generated from real mathematical calculations.

In Class Exercise - Estimate the Bitcoin price

· using Monte Carlo simulation in Excel, assuming a normal distribution and running the simulation 1,000 times:

Step 1: Set Up Your Data

1. Open Excel and label your columns:

A1: "Current Price"
B1: "Expected Return (%)"
C1: "Volatility (%)"
D1: "Simulated Price"

2. Enter initial values (example):

A2: Enter the current Bitcoin price (e.g., 65000)
B2: Enter expected return (e.g., 5 for 5%)
C2: Enter volatility (e.g., 50 for 50%)

Step 2: Set Up Monte Carlo Formula

1. In D2, enter the following formula to simulate one possible future Bitcoin price:

=A$2 * EXP((B$2/100 - (C$2/100)^2 / 2) + (C$2/100) * NORM.INV(RAND(),0,1))

EXP(...) simulates the Geometric Brownian Motion (GBM).
NORM.INV(RAND(),0,1) generates a random standard normal value.

2. Drag the formula down from D2 to D1001 to generate 1,000 simulated prices.

Step 3: Analyze the Results

1. Compute key statistics:

Mean (Average Price Prediction):

=AVERAGE(D2:D1001)

Standard Deviation of Simulations:

=STDEV(D2:D1001)

Minimum & Maximum Predicted Prices:

=MIN(D2:D1001)

=MAX(D2:D1001)

2. Create a Histogram:

Select D2:D1001, go to Insert > Charts > Histogram.

Step 4: Interpret the Results

The Monte Carlo simulation will give you 1,000 potential future Bitcoin prices based on your assumptions.
The mean will be your best estimate, while the spread (standard deviation) gives insight into volatility.

Note: What is NORM.INV in Excel?

NORM.INV is an Excel function that returns the inverse of the cumulative normal distribution for a given probability, mean, and standard deviation.

Syntax:

NORM.INV(probability, mean, standard_dev)

probability – The probability corresponding to the normal distribution (between 0 and 1).
mean – The expected mean (average) of the normal distribution.
standard_dev – The standard deviation (spread) of the distribution.

Why Use `NORM.INV(RAND(), 0, 1)` in Monte Carlo Simulations?

RAND() generates a random number between 0 and 1 (a uniform distribution).
NORM.INV(RAND(), 0, 1) transforms that uniform random number into a value that follows a standard normal distribution (mean = 0, standard deviation = 1).
This is necessary in Monte Carlo simulations to introduce randomness while maintaining normal distribution properties.

Example Usage

If you want to simulate random returns for Bitcoin using a normal distribution:

=NORM.INV(RAND(), 0, 1)

This gives a random z-score from a normal distribution, which can be used in Monte Carlo models.

Critical thinking challenge (due with the final exam):

· Recalculate 100 times of the NPV based on the Monte Carlo simulation method by randomly changing the tax rate and the WACC (or any two factors)

· Report statistical results: Mean, Standard Deviation, Min, Max of the NPV.

· Report the Histogram of the NPV, or the probability distribution of the NPV, such as the following:

Instructions on Monte Carlo Simulation Process (using Tax Rate and WACC as example):

· Pick two variables, such as tax rate and WACC.

· Parameter Definition:

You defined the parameters for the two variables, such as tax rate and WACC, including their means and standard deviations.

· Random Sample Generation: Using the norminv function, you generated 100 sets of random samples for tax rate and WACC, ensuring they follow normal distributions based on the provided mean and standard deviation.

· NPV Calculation: For each set of randomly generated tax rate and WACC, you calculated the Net Present Value (NPV) using the appropriate formula.

· Statistical Analysis: You reported statistical results including the mean, standard deviation, minimum, and maximum NPV values obtained from the Monte Carlo simulation.

· Histogram Visualization: You visualized the probability distribution of NPV values by creating a histogram.

· Summary of Results:

Mean NPV: The average NPV across the 100 iterations.

Standard Deviation of NPV: The measure of dispersion of NPV values around the mean.

Minimum NPV: The lowest NPV value obtained.

Maximum NPV: The highest NPV value obtained.

Histogram: The histogram provides a visual representation of the distribution of NPV values, showing the frequency of NPV occurrences within different ranges.

· Conclusion:

Your Monte Carlo simulation approach effectively captured the variability and uncertainty in NPV outcomes resulting from fluctuations in tax rates and WACC. The statistical analysis and histogram visualization offer insights into the range of potential NPV values and their likelihood of occurrence, aiding in decision-making processes related to financial planning and investment evaluation.

About norminv function in excel: =norminv(RAND(), mean, standard_deviation)

· RAND() generates a random number between 0 and 1.

· For example, to generate a random tax rate with a mean of 25% and a standard deviation of 2.5%, you can use:

=norminv(RAND(), 25%, 2.5%)

Monte Carlo Simulation Demonstration (FYI， 2023 video)

Introduction to Monte Carlo Simulation in Excel 2016 (youtube)

Structure Try this DCF In class exercise demonstration first

Years

Investment Outlay

Equipment cost

$(----------)

Installation

(--------)

Increase in inventory

(-------)

Increase in A/P

-------

Initial net investment

$(-------)

Operating Cash Flows

Units sales

-------

Price per unit

* $ ---

$ ---

Total revenues

-------

Operating costs (w/o deprn)

-------

Depreciation

-------

Total costs

-------

Operating income

-------

Taxes on operating income

-------

A-T operating income

-------

Depreciation

-------

Operating cash flow

-------

Terminal Year Cash Flows

Recovery of net working capital -------

Salvage value

-------

Tax on salvage value

(-------)

Total termination cash flow

-------

Project Cash Flows

Net cash flows

$(-------)

$ -------

In class exercise (self-study)

1. What is the project's Year 1 cash flow?

Sales revenues $22,250

Depreciation $8,000

Other operating costs $12,000

Tax rate 35.0%

Answer:

Sales revenues $22,250

− Operating costs (excl. deprec.) 12,000

− Depreciation 8,000

Operating income (EBIT) $ 2,250

− Taxes Rate = 35% 788

After-tax EBIT $ 1,463

+ Depreciation 8,000

Cash flow, Year 1 $ 9,463

2. The required equipment has a 3-year tax life, and it will be depreciated by the straight-line method over 3 years. What is the project's Year 1 cash flow?

Equipment cost (depreciable basis) $65,000

Straight-line depreciation rate 33.333%

Sales revenues, each year $60,000

Operating costs (excl. deprec.) $25,000

Tax rate 35.0%

Answer:

Equipment life, years 3

Equipment cost $65,000

Depreciation: rate = 33.333% $21,667

Sales revenues $60,000

− Basis x rate = depreciation 21,667

− Operating costs (excl. deprec.) 25,000

Operating income (EBIT) $13,333

− Taxes Rate = 35.0% 4,667

After-tax EBIT $ 8,667

+ Depreciation 21,667

Cash flow, Year 1 $30,333

3. The equipment that would be used has a 3-year tax life, and the allowed depreciation rates for such property are 33%, 45%, 15%, and 7% for Years 1 through 4. Revenues and other operating costs are expected to be constant over the project's 10-year expected life. What is the Year 1 cash flow?

Equipment cost (depreciable basis) $65,000

Sales revenues, each year $60,000

Operating costs (excl. deprec.) $25,000

Tax rate 35.0%

Answer:

Equipment cost $65,000

Depreciation rate 33.0%

Sales revenues $60,000

− Operating costs (excl. deprec.) 25,000

− Depreciation 21,450

Operating income (EBIT) $13,550

− Taxes Rate = 35% 4,743

After-tax EBIT $ 8,808

+ Depreciation 21,450

Cash flow, Year 1 $30,258

4. The equipment that would be used has a 3-year tax life, would be depreciated by the straight-line method over its 3-year life, and would have a zero salvage value. No new working capital would be required. Revenues and other operating costs are expected to be constant over the project's 3-year life. What is the project's NPV?

Risk-adjusted WACC 10.0%

Net investment cost (depreciable basis) $65,000

Straight-line deprec. rate 33.3333%

Sales revenues, each year $65,500

Operating costs (excl. deprec.), each year $25,000

Tax rate 35.0%

Answer:

WACC 10.0% Years 0 1 2 3

Investment cost -$65,000

Sales revenues $65,500 $65,500 $65,500

− Operating costs (excl. deprec.) 25,000 25,000 25,000

− Depreciation rate = 33.333% 21,667 21,667 21,667

Operating income (EBIT) $18,833 $18,833 $18,833

− Taxes Rate = 35% 6,592 6,592 6,592

After-tax EBIT $12,242 $12,242 $12,242

+ Depreciation 21,667 21,667 21,667

Cash flow -$65,000 $33,908 $33,908 $33,908

NPV $19,325

5. The equipment originally cost $22,500, of which 75% has been depreciated. The firm can sell the used equipment today for $6,000, and its tax rate is 40%. What is the equipment’s after-tax salvage value for use in a capital budgeting analysis? Note that if the equipment's final market value is less than its book value, the firm will receive a tax credit as a result of the sale.

Answer:

% depreciated on equip. 75%

Tax rate 40%

Equipment cost $22,500

− Accumulated deprec. 16,875

Current book value of equipment $ 5,625

Market value of equipment 6,000

Gain (or loss): Market value − Book value $ 375

Taxes paid on gain (−) or credited (+) on loss -150

AT salvage value = market value +/− taxes $ 5,850

The Monte Carlo Simulation: Understanding the Basics (FYI)

By KUSHAL AGARWAL Updated June 19, 2023

https://www.investopedia.com/articles/investing/112514/monte-carlo-simulation-basics.asp#:~:text=Monte%20Carlo%20is%20used%20in,under%20analysis%20and%20its%20volatility.https://www.investopedia.com/articles/investing/112514/monte-carlo-simulation-basics.asp#:~:text=Monte%20Carlo%20is%20used%20in,under%20analysis%20and%20its%20volatility.

What Is a Monte Carlo Simulation?

Analysts can assess possible portfolio returns in many ways. The historical approach, which is the most popular, considers all the possibilities that have already happened. However, investors shouldn't stop at this. The Monte Carlo method is a stochastic (random sampling of inputs) method to solve a statistical problem, and a simulation is a virtual representation of a problem. The Monte Carlo simulation combines the two to give us a powerful tool that allows us to obtain a distribution (array) of results for any statistical problem with numerous inputs sampled over and over again.

KEY TAKEAWAYS

· The Monte Carlo method uses a random sampling of information to solve a statistical problem; while a simulation is a way to virtually demonstrate a strategy.

· Combined, the Monte Carlo simulation enables a user to come up with a bevy of results for a statistical problem with numerous data points sampled repeatedly.

· The Monte Carlo simulation can be used in corporate finance, options pricing, and especially portfolio management and personal finance planning.

· On the downside, the simulation is limited in that it can't account for bear markets, recessions, or any other kind of financial crisis that might impact potential results.

Monte Carlo Simulation Demystified

Monte Carlo simulations can be best understood by thinking about a person throwing dice. A novice gambler who plays craps for the first time will have no clue what the odds are to roll a six in any combination (for example, four and two, three and three, one and five). What are the odds of rolling two threes, also known as a "hard six?" Throwing the dice many times, ideally several million times, would provide a representative distribution of results, which will tell us how likely a roll of six will be a hard six. Ideally, we should run these tests efficiently and quickly, which is exactly what a Monte Carlo simulation offers.

The problem with looking to history alone is that it represents, in effect, just one roll, or probable outcome, which may or may not be applicable in the future. A Monte Carlo simulation considers a wide range of possibilities and helps us reduce uncertainty. A Monte Carlo simulation is very flexible; it allows us to vary risk assumptions under all parameters and thus model a range of possible outcomes. One can compare multiple future outcomes and customize the model to various assets and portfolios under review.

A Monte Carlo simulation can accommodate a variety of risk assumptions in many scenarios and is therefore applicable to all kinds of investments and portfolios.

Applying the Monte Carlo Simulation

The Monte Carlo simulation has numerous applications in finance and other fields. Monte Carlo is used in corporate finance to model components of project cash flow, which are impacted by uncertainty. The result is a range of net present values (NPVs) along with observations on the average NPV of the investment under analysis and its volatility. The investor can, thus, estimate the probability that NPV will be greater than zero. Monte Carlo is used for option pricing where numerous random paths for the price of an underlying asset are generated, each having an associated payoff. These payoffs are then discounted back to the present and averaged to get the option price. It is similarly used for pricing fixed income securities and interest rate derivatives. But the Monte Carlo simulation is used most extensively in portfolio management and personal financial planning.

Uses in Portfolio Management

A Monte Carlo simulation allows an analyst to determine the size of the portfolio a client would need at retirement to support their desired retirement lifestyle and other desired gifts and bequests. She factors into a distribution of reinvestment rates, inflation rates, asset class returns, tax rates, and even possible lifespans. The result is a distribution of portfolio sizes with the probabilities of supporting the client's desired spending needs.

The analyst next uses the Monte Carlo simulation to determine the expected value and distribution of a portfolio at the owner's retirement date. The simulation allows the analyst to take a multi-period view and factor in path dependency; the portfolio value and asset allocation at every period depend on the returns and volatility in the preceding period. The analyst uses various asset allocations with varying degrees of risk, different correlations between assets, and distribution of a large number of factors – including the savings in each period and the retirement date – to arrive at a distribution of portfolios along with the probability of arriving at the desired portfolio value at retirement. The client's different spending rates and lifespan can be factored in to determine the probability that the client will run out of funds (the probability of ruin or longevity risk) before their death.

A client's risk and return profile is the most important factor influencing portfolio management decisions. The client's required returns are a function of her retirement and spending goals; her risk profile is determined by her ability and willingness to take risks. More often than not, the desired return and the risk profile of a client are not in sync with each other. For example, the level of risk acceptable to a client may make it impossible or very difficult to attain the desired return. Moreover, a minimum amount may be needed before retirement to achieve the client's goals, but the client's lifestyle would not allow for the savings or the client may be reluctant to change it.

Monte Carlo Simulation Example

Let's consider an example of a young working couple who works very hard and has a lavish lifestyle including expensive holidays every year. They have a retirement objective of spending $170,000 per year (approx. $14,000/month) and leaving a $1 million estate to their children. An analyst runs a simulation and finds that their savings-per-period is insufficient to build the desired portfolio value at retirement; however, it is achievable if the allocation to small-cap stocks is doubled (up to 50 to 70% from 25 to 35%), which will increase their risk considerably. None of the above alternatives (higher savings or increased risk) are acceptable to the client. Thus, the analyst factors in other adjustments before running the simulation again. the analyst delays their retirement by two years and decreases their monthly spend post-retirement to $12,500. The resulting distribution shows that the desired portfolio value is achievable by increasing allocation to small-cap stock by only 8 percent. With the available insight, the analyst advises the clients to delay retirement and decrease their spending marginally, to which the couple agrees.

The Bottom line

A Monte Carlo simulation allows analysts and advisors to convert investment chances into choices. The advantage of Monte Carlo is its ability to factor in a range of values for various inputs; this is also its greatest disadvantage in the sense that assumptions need to be fair because the output is only as good as the inputs. Another great disadvantage is that the Monte Carlo simulation tends to underestimate the probability of extreme bear events like a financial crisis. In fact, experts argue that a simulation like the Monte Carlo is unable to factor in the behavioral aspects of finance and the irrationality exhibited by market participants. It is, however, a useful tool for advisors.

Second Midterm Exam (closed book closed notes)

· 4/3/2025

· T/F Solution (60 questions)

· Calculation Solution

Study Guide

Part I - WACC (Weighted Average Cost of Capital) – 30 points

Definition: The average rate a firm pays to finance its assets, weighted by proportion of debt and equity.
Use: It’s the discount rate used to evaluate investment projects.
Components:

Weight of Debt (Wd) and Weight of Equity (We)
Cost of Debt (Kd): Interest rate the company pays on its debt, adjusted for taxes.
Cost of Equity (Ke): The return required by equity investors.

Cost of Debt

Represents the effective rate a company pays on borrowed funds.
Affected by:

Interest rate (coupon)
Bond price
Tax savings from interest (tax shield)

Expressed after-tax, since interest is tax-deductible.

Cost of Equity

There are two main ways to estimate it:

Dividend Discount Model (DDM):

Used if dividend info is available.
Reflects return investors expect based on dividends and growth.

Capital Asset Pricing Model (CAPM):

Used if beta is given.
Reflects return based on market risk.

Flotation Costs

Costs of issuing new securities (e.g., underwriting, legal fees).
Reduce the actual funds received by the firm.
Must be subtracted from the price when calculating cost of new capital.

Capital Structure

Mix of debt and equity used to finance operations.
Affects WACC because debt is cheaper (due to tax benefits) but increases financial risk.

WACC Applications

Used as the discount rate in NPV (Net Present Value) and valuation models.
If project’s return > WACC → good investment.
If return < WACC → reject the project.

DCF (Discounted Cash Flow) Concept

A method to estimate the intrinsic value of a company.
Based on present value of future free cash flows (FCF).
FCF = cash available after investments needed to maintain or grow assets.
Involves estimating:

FCF for future years.
Terminal value (long-term value).
Discounting back using WACC.

Summary

WACC is not fixed – it changes with:

Interest rates
Company risk (beta)
Debt/equity proportions
Market conditions

Part II - DCF Step 1 – Free Cash Flow (FCF) – 20 points

(Chapter 3 – Financial Statements & Cash Flow Analysis)

What is Free Cash Flow (FCF)?

FCF = Cash available to investors (both debt and equity holders) after the company reinvests to maintain/grow operations.
Why it matters: It reflects the company’s ability to pay dividends, repay debt, and reinvest.

Common Uses of FCF:

Paying interest on debt
Repaying principal
Paying dividends
Stock repurchase
Buying non-operating assets (investments, securities)

Helpful Tools:

Part III - DCF Step 2 – Cash Flow Estimation & Monte Carlo Simulation - 20 points

(Chapter 12)

What is Monte Carlo Simulation?

A method used to estimate uncertainty in financial forecasts by running many simulations using random variables (e.g., WACC, tax rate, growth).
Helps in understanding range and probability of possible outcomes (e.g., NPVs).

Key Concepts:

Random Sampling: Input variables like tax rate or WACC are randomly sampled from a normal distribution.
Multiple Simulations: Typically 100 or 1,000 iterations.
NPV Calculation: Each simulation generates an NPV based on different inputs.
Results Analyzed Using:

Mean (average NPV)
Standard deviation (volatility)
Minimum & maximum NPV
Histogram to visualize probability distribution

Applications in Capital Budgeting:

Helps decision-making under uncertainty.
Used to test how changes in WACC, tax rates, growth rates, etc. impact valuation outcomes.
Example: Simulating future Bitcoin prices, stock prices, or project NPVs.

Summary:

FCF is central to valuation: A company’s worth is tied to how much FCF it can generate.
Monte Carlo Simulation gives a probabilistic (not just point-estimate) view of value.
Great for showing risk, volatility, and confidence ranges around financial forecasts.

Part IV- Cash Flow Estimation - 30 points

· (refer to https://www.jufinance.com/game/dcf_project_simulator.html

· https://www.jufinance.com/game/dcf_simple_monte_carlo.html)

Project Description: //// Solution

You are evaluating a new beverage kiosk startup.

Initial Equipment Cost: $100,000
Installation Cost: $10,000
Increase in Inventory (Working Capital): $8,000
Increase in Accounts Payable: $3,000
Project Life: 4 years
Salvage Value of Equipment (end of Year 4): $15,000
Tax Rate: 30%
Discount Rate (WACC): 10%
Depreciation Method: Straight-line over 4 years, no salvage value for depreciation purposes
Expected Annual Revenues: $85,000
Annual Operating Costs (excluding depreciation): $45,000

Q1. What is the initial investment outlay for the project?

Q2. What is the annual depreciation expense?

Q3. What is the Year 1 operating cash flow?

Q4. What are the terminal year cash flows, and how are they calculated?

Q5. NPV=?

Q6. Final Decision

Chapter 19 Derivatives

· Chapter 19 PPT

· Self-produced video 1

· Self-produced video 2

· Self-produced video 3

· Game 1 – Call and Put Options - Basic

o Learn how to draw the payoff graphs for call and put options

· Game 2 – Option Strategies (optional – level 1)

· Game 3 – Options Strategies (optional – level 2)

· Straddle Strategy Proactive Put Covered Call Options Profit Analyzer

· Quiz 1 (basic) Quiz 2 (optional, strategy) Quiz3 (call, put, protective put, covered call, straddle)

· Binomial Calculation Demonstration

· Binomial Model Demonstration

· Black-Scholes Model Demonstration

Chapter 19 Case Study Part I - due with final

Chapter 19 Case Study part II – due with final

Case video in class Part I (4.9.2024) – Black-Schools-Merton Option Pricing Model

Case video in class part II (4.11.2024) – Binomial Option Pricing Model

1^st, understand what is call and put option

2^nd, understand the pay off of call and put option

3^rd, can draw payoff profile of call and put option

Call and Put Option Calculator

Call and Put Option Diagram Illustration Excel

(Thanks to Dr. Greence at UAH)

4^th, can calculate call option pricing using binomial model

Binomial Calculator by ChatGPT

Instruction on Binomial model - in class exercise - case study

· In the first step, you are calculating the range of values at expiration by considering the two possible ending stock prices of $30 and $50. You then calculate the ending option and portfolio values for each of these stock prices.

· Next, in step 2, you are equalizing the range of payoffs for the stock and the option by buying 0.75 shares and selling 1 option. This allows you to create a riskless hedged investment in step 3, where you calculate the ending values of the portfolio for the two possible ending stock prices.

· Finally, in step 4, you are pricing the call option by calculating the present value of the portfolio using the risk-free rate of 8%. The calculated present value of the portfolio is $20.83, which can be used to calculate the call option value.

^5th, can calculate call option price using black-scholes model

Black-Scholes-Merton Option Calculator

https://www.mystockoptions.com/black-scholes.cfm

Black-Scholes-Merton Option Calculator by ChatGPT (at jufinance.com)

www.jufinance.com/https://www.jufinance.com/option_chatgpt/

(Just Ask ChatGPT for the Black Scholes Option pricing model code in JavaScript and HTML. Then, copy the code, open Notepad, paste it, and save the file as an HTML file, like option.html. Easy!)

Black-Scholes-Merton Model Illustration Excel

Binomial Option Pricing Model Explained ----

using In Class Case Study as an example (FYI only)

· Binomial Calculation Demonstration

The binomial option pricing model is a mathematical formula that allows us to calculate the fair value of an option by modeling the possible future prices of the underlying asset, and calculating the probability of each price occurring.

The model works by creating a binomial tree that represents the possible future prices of the asset, and then working backward through the tree to calculate the expected value of the option at each node.

Here are the steps to use the binomial option pricing model:

Step 1: Determine the Inputs

The first step is to gather the inputs needed for the model. These include:

· The current price of the underlying asset

· The range of possible future prices of the asset

· The exercise price of the option

· The risk-free rate of interest

· The time until expiration of the option

Let’s try to work on the same question as we did in class. A stock that is currently trading at $40, and two possible future prices at the end of one year are: $30 and $50. The exercise price of the option is $35, the risk-free rate is 8%, and the time until expiration is one year --- our case study example

Step 2: Calculate the Up and Down Factors

The next step is to calculate the up and down factors, which represent the expected percentage increase and decrease in the stock price over one period. These factors are calculated as:

· Up factor (u) = Future price if stock goes up / Current stock price

· Down factor (d) = Future price if stock goes down / Current stock price

In our example, the up factor is $50 / $40 = 1.25, and the down factor is $30 / $40 = 0.75.

Step 3: Create the Binomial Tree

This step involves creating the binomial tree as below.

Binomial Tree

$40

/ \

$50 $30

Step 4: Calculate the Risk-Neutral Probability

The next step is to calculate the probability of each future price occurring, using the risk-neutral probability. The risk-neutral probability is the probability of the stock going up or down, assuming that the market is risk-neutral and the expected return of the stock is equal to the risk-free rate.

The risk-neutral probability is calculated as:

Risk-neutral probability (p) = (1+r*t - d)/(u-d)

where r is the risk-free rate and t is the time until expiration; u is the up factor and d is the down factor.

In our example, the risk-neutral probability is approximately:

Pu = (1+0.08*1 - 0.75)/(1.25-0.75)= 0.66

Or use the more accurate model:

Risk-neutral probability Pu = (e^((r * t)/n) - d) / (u - d)

where r is the risk-free rate and t is the time until expiration, and n is the height of the binomial tree. In our example, n=1.

In our example, the risk-neutral probability is:

Pu = (e^(0.08 * 1) - 0.75) / (1.25 - 0.75) = 0.6666

Step 5: Calculate the Option Value at Each Node of the Tree

To get the value of the option at each node of the tree, we should work backward from the end of the tree to the current price of the stock.

Simply speaking, at the end of the tree, the option value = difference between the stock price and the exercise price, or zero if the stock price is below the exercise price.

For example, we need to calculate the value of the option if the stock price goes up to $50, and if it goes down to $30. The results are as follows.

Vu = Max($50 - $35, 0) = $15

Vd = $0

Working backward up the tree, we can calculate the option value at each node as the discounted expected value of the option at the next period:

Option value = v = (Pu * Vu + Pd * Vd) / (1 + r)^t;

Option Value at $40 = (0.66 x $15 + (1 - 0.66) x $0) / (1 + 0.08)^1 = $9.17

Therefore, the value of the option is approximately $9.17 if the stock price

Black-Scholes-Merton Option Pricing Model Explained ----

using In Class Case Study as an example (FYI only)

C = SN(d1) – X*exp(-r*t)*N(d2)

where:

· S = the current stock price

· X = the option strike price

· r = the risk-free interest rate

· t = time until expiration, expressed as a fraction of a year

V =	P[ N (d₁) ] − Xe^{-rRF t} [ N (d₂) ]
d₁ =	{ ln (P/X) + [r_RF + s² /2) ] t } / s (t^1/2)
d₂ =	d₁ − s (t ^{1 / 2})

d1 = [ln(S/X) + (r + σ^2/2)t] / [σsqrt(t)]

d2 = d1 - σ*sqrt(t)

σ = the annualized standard deviation of stock returns

Using the values used in the case study in class:

· S = X = 21

· r = 0.05

· σ = 0.3

· t = 0.36

First, we calculate d1 and d2:

d1 = ln(21/21)+(0.05+0.3^2/2)*0.36)/(0.3*sqrt(0.36)) =0.19

d2 = 0.19 - 0.3*sqrt(0.36) = 0.01

Next, we calculate the call option price using the Black-Scholes formula:

C = SN(d1) – X*exp(-r*t)*N(d2)

C = 21*normdist(0.19, 0, 1, true) - 21*exp(-0.05*0.36)*normdist(0.01, 0, 1, true) = 1.687 (rounded to three decimal places)

Therefore, the expected result for the call option price using the Black-Scholes formula with the given inputs is approximately 1.687.

By the way, based on Put - Call Parity, the put option price (P) is the following:

P = C - S + Xe^(-rt)

= 1.687 - 21 + 21*exp(-0.05*0.36) = 1.3124

FYI – normdist function in Excel

The normdist function is used in Excel to calculate the probability density function of a normally distributed random variable. This function takes four arguments: x, mean, standard_dev, and cumulative.

Here is a brief explanation of each argument:

· x: This is the value for which you want to calculate the probability density function. It must be a numeric value.

· mean: This is the mean of the distribution. It must be a numeric value.

· standard_dev: This is the standard deviation of the distribution. It must be a numeric value.

· cumulative: This is an optional argument that specifies whether you want to calculate the cumulative distribution function or the probability density function. If this argument is omitted or set to TRUE, the function will calculate the cumulative distribution function. If it is set to FALSE, the function will calculate the probability density function.

To use the normdist function in Excel, follow these steps:

· In a cell, type =NORMDIST(x, mean, standard_dev, cumulative) and replace the values of x, mean, standard_dev, and cumulative with the values you want to use.

· Press Enter. Excel will calculate the probability density function or the cumulative distribution function of the normally distributed random variable, depending on the value of the cumulative argument.

For example,

1) if you want to calculate the probability density function of a normally distributed random variable with a mean of 10 and a standard deviation of 2 at the value of 12, use the following: =NORMDIST(12, 10, 2, FALSE) = probability density at that point.

2) =NORMDIST(12, 10, 2, true) calculates the cumulative distribution function (CDF) of a normally distributed random variable with a mean of 10 and a standard deviation of 2, evaluated at the value of 12.

The true value of the fourth argument - calculate the CDF.

Seminar one – Is it possible for Samsung to Acquire Nvidia?

Chapter 21 Mergers and Divestitures

· watch TV series Succession and gain insights of the dynamics of such corporate fights

· ppt

· Quiz

· Hostile Takeover Mechanism Game

Mergers rules of SEC

Mergers are business combination transactions involving the combination of two or more companies into a single entity. Most state laws require that mergers be approved by at least a majority of a company's shareholders if the merger will have a significant impact on either the acquiring or target company.

If the company you've invested in is involved in a merger and is subject to the SEC disclosure rules, you will receive information about the merger in the form of either a proxy statement on Schedule 14A or an information statement on Schedule 14C.

The proxy or information statement will describe the terms of the merger, including what you will receive if the merger proceeds. If you believe the amount you will receive is not fair, check the statement for information on appraisal or dissenter's rights under state law. You must follow the procedures precisely or your rights may be lost.

You can obtain a copy of a company's proxy or information statement by using the SEC's EDGAR database.

Topic	Description / Key Points
Types of Mergers
Horizontal Merger	Between firms in the same industry (e.g., Pepsi and Coca-Cola)
Vertical Merger	Between firms at different production stages (e.g., car maker and tire supplier)
Conglomerate Merger	Between unrelated businesses (e.g., Amazon buying Whole Foods)
Merger Motives
Synergy	Combined firms are more valuable than separate (cost savings, revenue gains)
Market Power	Increased pricing power and market share
Tax Benefits	Use of tax loss carryforwards, interest deductions
Diversification	Reducing business risk (though not always shareholder value-enhancing)
Valuation Techniques
Comparable Company Analysis	Uses valuation multiples of similar public firms (P/E, EV/EBITDA, etc.)
Precedent Transactions	Uses multiples from similar past M&A deals
DCF (Discounted CF)	Forecast free cash flow, discount with WACC to find intrinsic value
Accretion/Dilution Analysis	Determines whether EPS increases (accretive) or decreases (dilutive) post-merger
Merger Process
Letter of Intent (LOI)	Non-binding agreement to negotiate key terms
Due Diligence	Comprehensive evaluation of target firm’s financials, legal, operations
Definitive Agreement	Final binding contract outlining purchase terms
Regulatory Approval	Subject to antitrust laws (e.g., FTC, DOJ in U.S.)
Hostile Takeover Defense
Poison Pill (Shareholder Rights Plan)	Gives existing shareholders right to buy more shares at a discount to dilute hostile acquirer
White Knight	Target firm seeks a more friendly acquirer to avoid hostile takeover
Staggered Board	Only a portion of the board is elected each year, delaying acquirer’s control
Golden Parachute	Lucrative severance packages for execs to deter hostile bids
Dual-Class Shares	Founders retain voting control through super-voting shares
Pac-Man Defense	Target company attempts to acquire the hostile bidder instead
Greenmail	Target buys back shares from hostile acquirer at a premium to avoid takeover
Regulations
Hart-Scott-Rodino Act	Requires notification of large M&A deals to U.S. antitrust authorities
SEC Filing Requirements	Must file Schedule TO, Schedule 13D/G, Form S-4 depending on deal structure
Recent Trends
SPACs	Special Purpose Acquisition Companies—blank check firms for merging with private firms
ESG in M&A	More focus on environmental, social, and governance factors in deal evaluations
Tech Sector Consolidation	Large tech firms acquiring start-ups to strengthen ecosystems and data control

Whole Foods’ SEC Filing (FYI)

· Whole foods form 8k filed with SEC on 8/23/2017

“As a result of the Merger, each share of common stock……was converted into the right to receive $42.00 in cash, without interest (the “Merger Consideration”).”

· Whole Foods DEFA 14A 8k form with SEC 6/14/2017

· Whole foods DEFA 14A 8k form with SEC 6/16/2017

· Whole foods is providing materials for the upcoming shareholder voting.

· Whole foods DEFA 14A 8k with SEC 7/21/2017

Has law suit documents

· Whole foods DEFA 14A 8k with SEC 7/21/2017

Notifying shareholders for upcoming special shareholder meeting

Amazon’s SEC filing

· Amazon Form 8k with SEC on 6/15/2017

Financing of the Merger

The Company expects to finance the Merger with debt financing ……

· Amazon Whole Foods Merger Agreement on 6/15/2017

For the term project, if you work on this M&A case, you should be able to find most of the information in this agreement.

· Amazon 8k form Completion of acquisition or disposition of assets 8/28/2018

Final Offer from Amazon: $42/share; a total of $13.4 billions

Why does Amazon's Bezos want Whole Foods? (video)

Mergers and Acquisitions Explained: A Crash Course on M&A (youtube, FYI)

Is it possible for Samsung to acquire Nvidia?

· A self produced video on “Is it possible for Samsung to Acquire Nvidia”

What Nvidia could do to scare off Samsung in the event of a hostile takeover attempt?

Defense Tactic	What It Is	How It Scares Off Samsung
Poison Pill	Shareholder rights plan that dilutes Samsung's stake if it crosses a threshold	Makes acquisition expensive and complicated, reducing Samsung's voting power
White Knight	Find a friendly U.S. company to buy Nvidia or form alliance	Blocks Samsung’s bid and aligns Nvidia with a strategic or national-interest partner
Staggered Board	Board members serve staggered terms (e.g. 3-year rotations)	Delays Samsung’s ability to gain full control via board elections
Golden Parachute	Lucrative exit packages for top executives	Increases cost of acquisition and discourages replacement of leadership
Dual-Class Shares	Nvidia could create or reinforce voting-share imbalance	Founders/insiders retain control even if Samsung acquires economic ownership
Legal/Regulatory Play	Trigger U.S. national security or antitrust investigations	U.S. government likely to block deal on national interest grounds (e.g. Committee on CFIUS)
Pac-Man Defense	Nvidia counterattacks and tries to acquire a stake in Samsung	Creates financial and strategic chaos; raises costs and deters Samsung
Crown Jewel Defense	Nvidia threatens to spin off or sell its most valuable assets	Makes Nvidia less attractive and harder to control strategically
Greenmail	Nvidia buys back Samsung’s shares at a premium to end the threat	Stops the takeover, though costly—used to quickly eliminate aggressive acquirers

Deal	Buyer & Target	Deal Value	Key Teaching Points
1	ExxonMobil buys Pioneer Natural Resources	$59.5B (stock deal)	· Largest U.S. energy M&A since Exxon’s 1999 Mobil merger
			· Vertical integration in Permian Basin
			· Use to teach resource-based synergies + strategic reserves
2	Capital One buys Discover Financial	$35.3B (all-stock)	Creates 6th largest U.S. bank by assets
			Strengthens Capital One’s credit card network
			Use to teach horizontal merger, antitrust risk, EPS dilution/accretion
3	Mars Inc. buys Kellanova (Kellogg spinoff)	$35.9B	· Massive CPG deal (snacks focus)
			· Brand consolidation: Pringles, Pop-Tarts, Rice Krispies
			· Use for consumer branding + synergy discussion
4	Cisco buys Splunk	$28B	Cybersecurity + AI + data monitoring
			Strategic shift to software-based revenue
			Use to teach valuation premiums in tech (Splunk had 30% premium)
5	Hewlett Packard Enterprise buys Juniper Networks	$14B	· HPE expanding AI/networking stack
			· Cloud infrastructure competition with Cisco/Arista
			· Useful for tech platform strategy teaching
6	Home Depot buys SRS Distribution	$18.25B	Expands Pro customer base (roofing, siding)
			Construction market targeting
			Good case for channel expansion logic
7	J&J buys Shockwave Medical	$13.1B	· Adds cardiovascular device tech (lithotripsy)
			· Healthcare innovation synergy
			· Use to teach product/tech acquisition strategy
8	Skydance merges with Paramount Global	$8B	Media merger under pressure from streaming wars
			Restructuring via private equity (RedBird Capital)
			Use to teach governance battles, voting rights, legacy firm survival

For your knowledge (FYI):

· You own around 100 shares of the stock of AAA, which is currently being sold for around $120 per share. A 2-for-1 stock split is about to be declared by the company. After the split has taken place, which of the following describes your probable position? You own 200 shares of AAA’s stock. Meanwhile, the AAA stock price will be near $60 per share.

· Alice Gordan and Alex Roy believe that when the dividend payout ratio is lowered, the required return on equity tends to increase. On which of the following assumptions is their argument based? dividends are viewed as less risky than future capital gains.

· A strict residual dividend policy is followed by your firm. Everything remains constant, which of the factors mentioned below are most probably going to result in an increase in the dividend per share of a firm? when a company’s profit (net income) rises

· Horizontal merger would be an example of The Home Depot and Lowe’s getting merged.

· When the merger of two companies in a similar industry takes place in order to develop products that are needed at various stages of the production cycle, it is referred to as: integration vertically

· A rights offering that provides the existing target shareholders with the rights to purchase shares in the acquirer of the target at an extremely discounted price after particular conditions are met is referred to as a: poison pill

(Twitter POISON Pill Explained by a Lawyer (youtube), FYI)

· A scenario where each and every director gets a three-year term to provide their services and the terms are arranged in a staggered manner so that just one-third of the directors are eligible for the election every year is referred to as a: classified board

· In a situation where it becomes inevitable that a hostile takeover may take place, and a target company may at times search for another friendlier company in order to acquire it, is referred to as a: white knight

Can Twitter find a white knight to fend off Elon Musk? (youtube, FYI)

· When a firm is being taken over and the senior managers of that firm are let go, a very lucrative severance package is offered to those senior managers. It is referred to as a: golden parachute

Seminar Two – Which option should NVIDIA choose: paying dividends or engaging in share repurchases?

Chapter 15 Distributions to Shareholders

· Ppt

· Quiz on Dividend Policy

· Game 1: Understanding Dividend Policy Theories

· Game 2: Real-World Dividend Strategies of Major Companies

Major Dividend Policy Theory Explained

Theory one: Indifference theory

Do Dividends even matter? - Dividend Irrelevance theory (video)

n Assuming:

– No transactions costs to buy and sell securities

– No flotation costs on new issues

– No taxes

– Perfect information

– Dividend policy does not affect k_e

n Dividend policy is irrelevant. If dividends are too high, investors may use some of the funds to buy more of the firm’s stock. If dividends are too low, investors may sell off some of the stock to generate additional funds.

Theory two: bird in hand theory – High dividend can increase firm value

Warren Buffett and the first investment primer: a bird in the hand equals two in the bush (Aesop) (video)

Dividends are less risky. Therefore, high dividend payout ratios will lower k_e (reducing the cost of capital), and increase stock price

Theory three: Tax effect theory – Low dividend can increase firm value

Dividend Clienteles | Business Finance (FINC101)

1) Dividends received are taxable in the current period. Taxes on capital gains, however, are deferred into the future when the stock is actually sold.

2) The maximum tax rate on capital gains is usually lower than the tax rate on ordinary income. Therefore, low dividend payout ratios will lower k_e (reducing the cost of capital), raise g, and increase stock price.

Theory Four: Signaling Theory

Core Idea:
Dividends convey information. Managers use dividend changes to signal their confidence or concerns.

Assumptions:

Managers have more information than investors.
Increasing dividends signals strong expected future cash flows.
Cutting dividends may signal trouble, even if needed for reinvestment.

Implication:
Dividend increases can lead to higher stock prices due to positive investor interpretation.

Examples:

General Electric (GE) cutting dividends during crisis signaled distress.
Johnson & Johnson consistently raising dividends signals financial strength.

Which theory is most correct? – again, results are mixed.

1) Some research suggests that high payout companies have high required return on stock, supporting the tax effect hypothesis.

2) But other research using an international sample shows that in countries with poor investor protection (where agency costs are most severe), high payout companies are valued more highly than low payout companies.

Summary:

Theory	Core Idea	Assumptions / Basis	Implication / Effect on Firm Value	Real-World Examples
1. Dividend Irrelevance (Modigliani & Miller)	Dividends don’t affect firm value in perfect markets. Investors can self-manage income by trading shares.	No taxes, no transaction costs, perfect info, no flotation costs. Dividend policy does not affect ke.	Dividend policy is irrelevant; firm value depends only on earnings and investments.	Berkshire Hathaway
2. Bird-in-Hand Theory (Gordon & Lintner)	Investors prefer the certainty of dividends over risky future capital gains.	Investors are risk-averse. Dividends reduce uncertainty and perceived risk.	High payout ratios reduce ke (cost of equity) and increase stock price.	Coca-Cola, Procter & Gamble
3. Tax Preference Theory	Investors prefer capital gains due to lower and deferred taxes.	Dividends are taxed now; capital gains taxed later and often at lower rates.	Lower dividend payouts reduce ke, raise g (growth rate), and increase firm value.	NVIDIA, Apple (buyback focus)
4. Signaling Theory	Dividend changes send signals to investors about future prospects.	Managers have more info than investors. Dividend increases = confidence; cuts = potential trouble.	Dividend changes influence investor expectations and stock prices.	Johnson & Johnson (raises); GE (cut in crisis)

Should NVIDIA Pay Dividends? | Exploring Financial Strategies with Dr. Foley - Made by InVideo.ai

Theory	Explanation	Alignment with NVIDIA
Residual Theory of Dividends	Companies should pay dividends only when they have excess funds after financing all positive NPV projects.	NVIDIA might not align with this theory as it is a high-growth technology company that may prioritize reinvesting profits into research and development, acquisitions, or other growth opportunities over paying dividends.
Bird-in-Hand Theory	Investors prefer dividends because they provide a certain return, while capital gains are uncertain.	NVIDIA might not align with this theory as it might prioritize reinvestment to capitalize on growth opportunities, especially considering its position in the dynamic technology sector.
Clientele Effect	Companies tend to attract investors with similar preferences to their dividend policies.	NVIDIA may align with this theory if it has a significant portion of investors who prefer capital appreciation over dividends and therefore chooses not to pay dividends to maintain this investor base.
Signaling Theory	Paying dividends can signal to investors that a company is financially healthy and confident about its future prospects.	NVIDIA might not align with this theory as it might prefer to reinvest profits rather than signal financial health through dividend payments, especially considering its growth potential and position in the technology sector.
Tax Considerations	Dividends are typically taxed differently than capital gains. Companies might consider the tax implications of paying dividends on their investors and themselves.	NVIDIA might align with this theory as it could consider the tax implications of paying dividends, both for its investors and for the company itself, in making its dividend policy decisions.

NVIDIA Capital Return Policy: Dividend vs. Share Repurchase

Aspect	Details
Dividend Policy	NVIDIA pays a modest quarterly cash dividend of $0.01 per share (post-split), amounting to $0.04 annually. This represents a dividend yield of approximately 0.04% and a payout ratio of about 1.14%, indicating that a minimal portion of earnings is distributed as dividends.
Dividend History	The company increased its quarterly dividend by 150% in May 2024, from $0.04 to $0.10 per share (pre-split), equivalent to $0.01 per share post-split.
Share Repurchase Strategy	NVIDIA actively repurchases its shares, with a significant $50 billion share repurchase authorization announced in August 2024. In the first half of fiscal 2025, the company returned $15.4 billion to shareholders through share repurchases and dividends.
Rationale for Buybacks	The company utilizes share repurchases to return capital to shareholders, aiming to offset dilution from stock-based compensation and to enhance earnings per share (EPS).
Criticism of Buybacks	Some investors question the timing and scale of NVIDIA's buybacks, especially given the high valuation of its stock, suggesting that the funds could be better allocated to research and development or other growth initiatives.
Capital Allocation Focus	NVIDIA prioritizes reinvesting earnings into growth areas such as artificial intelligence and data centers, with dividends and buybacks serving as secondary means of returning capital to shareholders.

What is a Stock Split? Firm increases the number of shares outstanding, say 2:1. Sends shareholders more shares.

Reasons for stock split:

· There’s a widespread belief that the optimal price range for stocks is $20 to $80.

· Stock splits can be used to keep the price in the optimal range.

· Stock splits generally occur when management is confident, so are interpreted as positive signals.

Final Exam (4/29, 11:30-2PM, in class, non-cumulative, closed book closed notes)

T/F Solutions Calculation Session Solutions (unavailable)

You may also arrange to meet and take the final exam at a different time by appointment

Finance Exit Exam (with final, in class, closed book closed notes, 40 multiple choice questions)

Term Project due

Final Exam Study Guide

Chapter 19: Options

Part I – T/F questions

1. Core Concepts – Options Basics

Understand:

What is a call option? What is a put option?
Who are the buyer and seller of an option?
How do payoffs work for buyers vs. sellers?

2. Option Strategies – Conceptual Focus

Know the Purpose of:

Covered Call → Generate income while holding stock
Protective Put → Insurance on stock downside
Straddle → Profit from volatility (up or down)

T/F Practice (sample):

T/F: A covered call limits both upside and downside.
T/F: A straddle profits only when stock prices fall.
T/F: A protective put behaves like a long call.
T/F: A strangle uses the same strike price for call and put.
T/F: A proactive put is purchased before anticipated negative news.

Part II: Quantitative Practice (Short Answer Format)

· (refer to https://www.jufinance.com/game/options.html)

Sample questions (Solutions: https://www.jufinance.com/fin435_25s/call_put_sample_questions_solutions_spring_2025.html)

1. Call and Put Options - Payoff and Profit

Be able to:

Calculate payoff and Profit for:

Long Call
Long Put
Short Call
Short Put

For example:

Calculate the payoff of:

A call option with a $40 strike and $50 underlying price at expiry.
A put option with a $40 strike and $30 underlying price at expiry.

Write the formulas:

Call payoff = max(S - K, 0)
Put payoff = max(K - S, 0)

2. Option Strategy Examples (for extra credits)

Covered call example:

Stock bought at $50, call sold with strike $55 and premium $2. What’s total payoff if stock ends at $60?

· Protective Put

· Straddle

3. Binomial Model (1-step)(refer to class website for details)(open book open notes)

· Refer to https://www.jufinance.com/game/binomial_cal_demonstration.html

Sample Question (Solution: https://www.jufinance.com/fin435_25s/binomial_sample_solutions_spring_2025.html)

Given:

Current stock price $S = 40$
Up factor $u = 1.25$
Down factor $d = 0.75$
Strike price $K = 35$
Risk-free rate $r = 8 %$
Time to maturity $T = 1 year$

Step 1: Calculate Up and Down Final Prices

• **Sup=Su=401.25=50**

• **Sdown=Sd=400.75=30**

Step 2: Calculate Call Option Values at Terminal Nodes

• At S=50:

Call Payoff=max⁡(50−35,0)=15

• At S=30:

Call Payoff=max⁡(30−35,0)=0

Step 3: Calculate Risk-Neutral Probability

We use the formula:

$Pu$ = (1+r*t - d)/(u-d) (1+0.08*1 - 0.75)/(1.25-0.75)= 0.66

Step 4: Calculate Option Price Today

Use the risk-neutral expected value discounted at the risk-free rate:

$v
= (Pu * Vu + Pd * Vd) / (1 + r)^$ t

Option Value at $40 = (0.66 x $15 + (1 - 0.66) x $0) / (1 + 0.08)^1 = $9.17

Final Answer: Call Option Price = $9.17

4. Black-Scholes Model (refer to class website for details) (open book open notes)

· Refer to https://www.jufinance.com/game/black_scholes_option_pricing_demonstration.html

C = SN(d1) – X*exp(-r*t)*N(d2)

where:

· S = the current stock price

· X = the option strike price

· r = the risk-free interest rate

· t = time until expiration, expressed as a fraction of a year

V =	P[ N (d₁) ] − Xe^{-rRF t} [ N (d₂) ]
d₁ =	{ ln (P/X) + [r_RF + s² /2) ] t }/ s (t^1/2)
d₂ =	d₁ − s (t ^{1 / 2})

d1 = [ln(S/X) + (r + σ^2/2)t] / [σsqrt(t)]

d2 = d1 - σ*sqrt(t)

σ = the annualized standard deviation of stock returns

Black-Scholes Sample Question (same as the case study example in class)

(Solutions https://www.jufinance.com/fin435_25s/blackscholes_sample_solutions_spring_2025.html)

· S = X = 21

· r = 0.05

· σ = 0.3

· t = 0.36

First, we calculate d1 and d2:

d1 = ln(21/21)+(0.05+0.3^2/2)*0.36)/(0.3*sqrt(0.36)) =0.19

d2 = 0.19 - 0.3*sqrt(0.36) = 0.01

Next, we calculate the call option price using the Black-Scholes formula:

C = SN(d1) – X*exp(-r*t)*N(d2)

C = 21*normdist(0.19, 0, 1, true) - 21*exp(-0.05*0.36)*normdist(0.01, 0, 1, true) = 1.687 (rounded to three decimal places)

Therefore, the expected result for the call option price using the Black-Scholes formula with the given inputs is approximately 1.687.

Chapter 21 (Merger Acquisition)

T/F questions on the following concepts: Poison pill, white knight, staggered board, golden parachute, green mail.

Sample questions:

Background:
A large tech firm, PantherSoft Inc., has become the target of an aggressive takeover by Predator Corp., known for hostile takeovers and restructuring targets. In response, PantherSoft’s board and executives take several defensive actions.

Details:

The board quickly amends company bylaws to allow only one-third of the directors to be elected each year.
They also approve generous compensation packages for top executives in case they lose their jobs due to a takeover.
A friendly firm, GuardianTech, is approached to make a competing offer.
PantherSoft offers to repurchase a large block of its own stock from Predator Corp. at a premium.
The board adopts a rights plan allowing existing shareholders to buy more stock at a discount if Predator acquires more than 15% of shares.

Student Task (True/False + Explanation):

Q1. Action #1 is an example of a poison pill strategy. (T/F)
Q2. Action #2 represents a golden parachute. (T/F)
Q3. Action #3 is a white knight defense. (T/F)
Q4. Action #4 is referred to as greenmail. (T/F)
Q5. A staggered board makes it easier for hostile acquirers to gain control. (T/F)

Answer Key (M&A Defense Mechanisms)

Q1. Action #1 is an example of a poison pill strategy.
Answer: False
Explanation: This is a staggered board strategy. By allowing only a portion of the board to be elected each year, it delays the hostile bidder’s ability to gain full control, making a takeover harder.

Q2. Action #2 represents a golden parachute.
Answer: True
Explanation: A golden parachute gives lucrative compensation to executives if they’re terminated following a takeover. This makes the acquisition more expensive and protects management.

Q3. Action #3 is a white knight defense.
Answer: True
Explanation: A white knight is a friendly third party that the target firm invites to acquire them instead of the hostile bidder. In this case, GuardianTech plays the white knight.

Q4. Action #4 is referred to as greenmail.
Answer: True
Explanation: Greenmail involves the target company buying back its own stock from the hostile bidder at a premium to make them go away. It’s a legal bribe to stop the takeover attempt.

Q5. A staggered board makes it easier for hostile acquirers to gain control.
Answer: False
Explanation: A staggered board makes it harder, not easier, for a hostile acquirer to gain board control quickly since only a fraction of directors are up for election at a time.

Chapter 16 (Dividend Policies)

I will give you a list of companies, and you will identify which dividend policy each one has chosen and explain your reasoning. And play this game to learn!

Happy Graduation!