FIN435 Class Web Page, Spring '23

Jacksonville University

Instructor: Maggie Foley

The Syllabus

Exit Exam Questions (will be posted in week 10 on blackboard)

FTX PPT Short Selling PPT

 

How to find a good job? (video; Thanks to Dr. Simak)

 

Weekly SCHEDULE, LINKS, FILES and Questions

Week

Coverage, HW, Supplements

-       Required

 

Reading Materials

Week

1

Marketwatch Stock Trading Game (Pass code: havefun)

Use the information and directions below to join the game.

1.     URL for your game: 
https://www.marketwatch.com/game/jufin435-23s    

2.     Password for this private game: havefun.

3.     Click on the 'Join Now' button to get started.

4.     If you are an existing MarketWatch member, login. If you are a new user, follow the link for a Free account - it's easy!

5.     Follow the instructions and start trading!

6. Game will be over on 4/22/2022

 

How to Use Finviz Stock Screener  (youtube, FYI)

 

How To Win The MarketWatch Stock Market Game (youtube, FYI)

 

How Short Selling Works (Short Selling for Beginners) (youtube, FYI)

 

 

Chapter 6 Interest rate

 

 

Part I: Who determines interest rates in the US?

ppt

 

 

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/

http://www.youtube.com/watch?v=yph8TRldW6k

 

The yield curve (Video, Khan academy)

 

 

Treasury Yields (1/10/2023)

NAME

COUPON

PRICE

YIELD

1 MONTH

1 YEAR

TIME (EST)

GB3:GOV

3 Month

0.00

4.42

4.55%

+33

+451

12:31 AM

GB6:GOV

6 Month

0.00

4.59

4.76%

+11

+458

12:31 AM

GB12:GOV

12 Month

0.00

4.41

4.62%

-2

+424

12:31 AM

GT2:GOV

2 Year

4.25

100.07

4.21%

-13

+332

12:31 AM

GT5:GOV

5 Year

3.88

100.93

3.66%

-10

+215

12:31 AM

GT10:GOV

10 Year

4.13

104.89

3.53%

-5

+177

12:31 AM

GT30:GOV

30 Year

4.00

106.22

3.65%

+10

+157

12:31 AM

 

Treasury Inflation Protected Securities (TIPS) (1/10/2023)

NAME

COUPON

PRICE

YIELD

1 MONTH

1 YEAR

TIME (EST)

GTII5:GOV

5 Year

1.63

100.66

1.48%

+5

+280

1/9/2023

GTII10:GOV

10 Year

0.63

93.91

1.31%

+1

+209

1/9/2023

GTII20:GOV

20 Year

0.75

87.82

1.48%

+7

+179

1/9/2023

GTII30:GOV

30 Year

0.13

69.44

1.41%

+14

+160

1/9/2023

 

 

Federal Reserve Rates (1/10/2023)

RATE

CURRENT

1 YEAR PRIOR

FDFD:IND

Fed Funds Rate

 

4.32

0.07

FDTR:IND

Fed Reserve Target

 

4.50

0.25

PRIME:IND

Prime Rate

 

7.50

3.25

 

 

 

Municipal Bonds (1/10/2023)

NAME

YIELD

1 DAY

1 MONTH

1 YEAR

TIME (EST)

BVMB1Y:IND

Muni Bonds 1 Year Yield

 

2.54%

-4

+2

+222

1/9/2023

BVMB2Y:IND

Muni Bonds 2 Year Yield

 

2.38%

-4

-11

+199

1/9/2023

BVMB5Y:IND

Muni Bonds 5 Year Yield

 

2.35%

-5

-15

+159

1/9/2023

BVMB10Y:IND

Muni Bonds 10 Year Yield

 

2.45%

-4

-14

+126

1/9/2023

BVMB30Y:IND

Muni Bonds 30 Year Yield

 

3.42%

-4

-9

+174

1/9/2023

 

https://www.bloomberg.com/markets/rates-bonds/government-bonds/us

 

In Class Exercise:

       Please draw the yield curve based on the above information;

       What can be predicted from the current yield curve?

       What is TIPs? What is municipal bond? What is Fed Fund Rate?

       Why are the TIPS rates negative?

 

 

For Daily Treasury rates such as the following, please visit

https://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/textview.aspx?data=yield

 

 

Date 1 Mo 2 Mo 3 Mo 4 Mo 6 Mo 1 Yr 2 Yr 3 Yr 5 Yr 7 Yr 10 Yr 20 Yr 30 Yr

01/03/2023 4.17 4.42 4.53 4.70 4.77 4.72 4.40 4.18 3.94 3.89 3.79 4.06 3.88

01/04/2023 4.20 4.42 4.55 4.69 4.77 4.71 4.36 4.11 3.85 3.79 3.69 3.97 3.81

01/05/2023 4.30 4.55 4.66 4.75 4.81 4.78 4.45 4.18 3.90 3.82 3.71 3.96 3.78

01/06/2023 4.32 4.55 4.67 4.74 4.79 4.71 4.24 3.96 3.69 3.63 3.55 3.84 3.67

01/09/2023 4.37 4.58 4.70 4.74 4.83 4.69 4.19 3.93 3.66 3.60 3.53 3.83 3.66

 

 

For class discussion: Why do interest rates change daily? Interest rates are determined by whom 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.

 

 

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 ratethe 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.

https://www.gurufocus.com/yield_curve.php

Understanding the yield curve (video)

Introduction to the yield curve (khan academy)

image004.jpg

image068.jpg

image064.jpg

image070.jpg

image072.jpg

Chapter six case study

 

What is interest rates

https://www.youtube.com/watch?v=Pod73wrvdSQ

 

 

Gerald Celente: Low Interest Rates are Building the Biggest Bubble in Modern History - 9/21/14

https://www.youtube.com/watch?v=pTpK6Te6tYI

 

 

 

How interest rates are set

https://www.youtube.com/watch?v=Oz5hNemSdWc

 

 

 

What happens if Fed raise interest rates

https://www.youtube.com/watch?v=4OP-3Ui6K1s

 

 

 

 

What Is the Relationship Between Inflation and Interest Rates?

By JEAN FOLGERdated Dec 6, 2019

 

Inflation and interest rates are often linked and frequently referenced in macroeconomics. Inflation refers to the rate at which prices for goods and services rise. In the United States, the interest rate, or the amount charged by a lender to a borrower, is based on the federal funds rate that is determined by the Federal Reserve (sometimes called "the Fed").

By setting the target for the federal funds rate, the Fed has at its disposal a powerful tool that it uses to influence the rate of inflation. This tool enables the Fed to expand or contract the money supply as needed to achieve target employment rates, stable prices, and stable economic growth.

KEY TAKEAWAYS

  • There is an inverse correlation between interest rates and the rate of inflation.
  • In the U.S, the Federal Reserve is responsible for implementing the country's monetary policy, including setting the federal funds rate which influences the interest rates banks charge borrowers.
  • In general, when interest rates are low, the economy grows and inflation increases.
  • Conversely, when interest rates are high, the economy slows and inflation decreases.

 

The Inverse Correlation Between Interest Rates and Inflation

Under a system of fractional reserve banking, interest rates and inflation tend to be inversely correlated. This relationship forms one of the central tenets of contemporary monetary policy: Central banks manipulate short-term interest rates to affect the rate of inflation in the economy.

The below chart demonstrates the inverse correlation between interest rates and inflation. In the chart, CPI refers to the Consumer Price Index, a measurement that tracks changes in prices. Changes in the CPI are used to identify periods of inflation and deflation.

In general, as interest rates are reduced, more people are able to borrow more money. The result is that consumers have more money to spend, causing the economy to grow and inflation to increase.

The opposite holds true for rising interest rates. As interest rates are increased, consumers tend to save as returns from savings are higher. With less disposable income being spent as a result of the increase in the interest rate, the economy slows and inflation decreases.

To better understand how the relationship between inflation and interest rates works, it's important to understand the banking system, the quantity theory of money, and the role interest rates play.

Fractional Reserve Banking

The world currently uses a fractional reserve banking system. When someone deposits $100 into the bank, they maintain a claim on that $100. The bank, however, can lend out those dollars based on the reserve ratio set by the central bank. If the reserve ratio is 10%, the bank can lend out the other 90%, which is $90 in this case. A 10% fraction of the money stays in the bank vaults.

As long as the subsequent $90 loan is outstanding, there are two claims totaling $190 in the economy. In other words, the supply of money has increased from $100 to $190. This is a simple demonstration of how banking grows the money supply.

Quantity Theory of Money

In economics, the quantity theory of money states that the supply and demand for money determines inflation. If the money supply grows, prices tend to rise, because each individual piece of paper becomes less valuable.

Hyperinflation is an economic term used to describe extreme inflation where price increases are rapid and uncontrolled. While central banks generally target an annual inflation rate of around 2% to 3% as an acceptable rate for a healthy economy, hyperinflation goes well beyond this. Countries that experience hyperinflation have an inflation rate of 50% or more per month.

Interest Rates, Savings, Loans, and Inflation

The interest rate acts as a price for holding or loaning money. Banks pay an interest rate on savings in order to attract depositors. Banks also receive an interest rate for money that is loaned from their deposits.

When interest rates are low, individuals and businesses tend to demand more loans. Each bank loan increases the money supply in a fractional reserve banking system. According to the quantity theory of money, a growing money supply increases inflation. Thus, low interest rates tend to result in more inflation. High interest rates tend to lower inflation.

This is a very simplified version of the relationship, but it highlights why interest rates and inflation tend to be inversely correlated.

The Federal Open Market Committee

The Federal Open Market Committee (FOMC) meets eight times each year to review economic and financial conditions and decide on monetary policy. Monetary policy refers to the actions taken that affect the availability and cost of money and credit. At these meetings, short-term interest rate targets are determined.

Using economic indicators such as the Consumer Price Index (CPI) and the Producer Price Indexes (PPI), the Fed will establish interest rate targets intended to keep the economy in balance. By moving interest rate targets up or down, the Fed attempts to achieve target employment rates, stable prices, and stable economic growth. The Fed will raise interest rates to reduce inflation and decrease rates to spur economic growth.

Investors and traders keep a close eye on the FOMC rate decisions. After each of the eight FOMC meetings, an announcement is made regarding the Fed's decision to increase, decrease, or maintain key interest rates. Certain markets may move in advance of the anticipated interest rate changes and in response to the actual announcements. For example, the U.S. dollar typically rallies in response to an interest rate increase, while the bond market falls in reaction to rate hikes.

Super inverted yield curve doesn't work very well for markets, says Wells Fargo's Schumacher

The yield curve is predicting we've already seen a peak in interest rates, says Ed Yardeni

Chapter 6 Interest rate Part II: Term Structure of Interest rate

 

Calculator

 

image020.jpg

 

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

 

Or approximately,

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

 

 

What Is Expectations Theory (video)

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)

 

 

Expectations Theory

By CHRIS B. MURPHY  Updated Apr 21, 2019

 

Example of Calculating Expectations Theory

Let's say that the present bond market provides investors with a two-year bond that pays an interest rate of 20% while a one-year bond pays an interest rate of 18%. The expectations theory can be used to forecast the interest rate of a future one-year bond.

  • The first step of the calculation is to add one to the two-year bonds interest rate. The result is 1.2.
  • The next step is to square the result or (1.2 * 1.2 = 1.44).
  • Divide the result by the current one-year interest rate and add one or ((1.44 / 1.18) +1 = 1.22).
  • To calculate the forecast one-year bond interest rate for the following year, subtract one from the result or (1.22 -1 = 0.22 or 22%).

In this example, the investor is earning an equivalent return to the present interest rate of a two-year bond. If the investor chooses to invest in a one-year bond at 18% the bond yield for the following years bond would need to increase to 22% for this investment to be advantageous.

  • 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
  • In theory, long-term rates can be used to indicate where rates of short-term bonds will trade in the future

 

Expectations theory aims to help investors make decisions by using long-term rates, typically from government bonds, to forecast the rate for short-term bonds.

 

Disadvantages of Expectations Theory

Investors should be aware that the expectations theory is not always a reliable tool. A common problem with using the expectations theory is that it sometimes overestimates future short-term rates, making it easy for investors to end up with an inaccurate prediction of a bonds yield curve.

Another limitation of the theory is that many factors impact short-term and long-term bond yields. The Federal Reserve adjusts interest rates up or down, which impacts bond yields including short-term bonds. However, long-term yields might not be as impacted because many other factors impact long-term yields including inflation and economic growth expectations. As a result, the expectations theory doesn't take into account the outside forces and fundamental macroeconomic factors that drive interest rates and ultimately bond yields.

Chapter 6 In class exercise

 

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 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 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 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 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 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,

 

 

 

Real Interest rate in the US from 2000-2022

https://fred.stlouisfed.org/series/REAINTRATREARAT1YE

 

 

 

Three Month T-Bill rate (a proxy of the risk free rate)

https://www.cnbc.com/quotes/US3M

 

Chapter 7

 

ppt

 

 

 Market data website:

1.   FINRA

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

2.      WSJ

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

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

http://www.youtube.com/watch?v=yph8TRldW6k

 

 

Simplified Balance Sheet of WalMart

 

Balance Sheet of WalMart    https://www.nasdaq.com/market-activity/stocks/wmt/financials

 

Period Ending:

1/31/2022

1/31/2021

1/31/2020

1/31/2019

Current Assets

Cash and Cash Equivalents

$14,760,000

$17,741,000

$9,465,000

$7,722,000

Short-Term Investments

--

--

--

--

Net Receivables

$8,280,000

$6,516,000

$6,284,000

$6,283,000

Inventory

$56,511,000

$44,949,000

$44,435,000

$44,269,000

Other Current Assets

$1,519,000

$20,861,000

$1,622,000

$3,623,000

Total Current Assets

$81,070,000

$90,067,000

$61,806,000

$61,897,000

Long-Term Assets

Long-Term Investments

--

--

--

--

Fixed Assets

$112,624,000

$109,848,000

$127,049,000

$111,395,000

Goodwill

$29,014,000

$28,983,000

$31,073,000

$31,181,000

Intangible Assets

--

--

--

--

Other Assets

$22,152,000

$23,598,000

$16,567,000

$14,822,000

Deferred Asset Charges

--

--

--

--

Total Assets

$244,860,000

$252,496,000

$236,495,000

$219,295,000

Current Liabilities

Accounts Payable

$82,172,000

$87,349,000

$69,549,000

$69,647,000

Short-Term Debt / Current Portion of Long-Term Debt

$3,724,000

$3,830,000

$6,448,000

$7,830,000

Other Current Liabilities

$1,483,000

$1,466,000

$1,793,000

--

Total Current Liabilities

$87,379,000

$92,645,000

$77,790,000

$77,477,000

Long-Term Debt

$39,107,000

$45,041,000

$48,021,000

$50,203,000

Other Liabilities

$13,009,000

$12,909,000

$16,171,000

--

Deferred Liability Charges

$13,474,000

$14,370,000

$12,961,000

$11,981,000

Misc. Stocks

$8,638,000

$6,606,000

$6,883,000

$7,138,000

Minority Interest

--

--

--

--

Total Liabilities

$161,607,000

$171,571,000

$161,826,000

$146,799,000

Stock Holders Equity

Common Stocks

$276,000

$282,000

$284,000

$288,000

Capital Surplus

$86,904,000

$88,763,000

$83,943,000

$80,785,000

Retained Earnings

--

--

--

--

Treasury Stock

$4,839,000

$3,646,000

$3,247,000

$2,965,000

Other Equity

-$8,766,000

-$11,766,000

-$12,805,000

-$11,542,000

Total Equity

$83,253,000

$80,925,000

$74,669,000

$72,496,000

Total Liabilities & Equity

$244,860,000

$252,496,000

$236,495,000

$219,295,000

 

For discussion:

         What is this long term debt?

         Who is the lender of this long term debt?

So this long term debt is called bond in the financial market. Where can you find the pricing information and other specifications of the bond issued by WMT?

 

image004.jpg 

 

Investing Basics: Bonds(video)

Relationship between bond prices and interest rates (Khan academy)

 

 

FINRA Bond market information

 http://finra-markets.morningstar.com/BondCenter/Default.jsp

 

 

Go to http://finra-markets.morningstar.com/BondCenter/Default.jsp  , the bond market data website of FINRA to find bond information. For example, find bond sponsored by Wal-mart

Or, just go to www.finra.org Investor center  market data  bond  corporate bond

 

https://finra-markets.morningstar.com/BondCenter/Results.jsp 

 

2.     Understand what is coupon, coupon rate, yield, yield to maturity, market price, par value, maturity, annual bond, semi-annual bond, current yield.

 

Refer to the following bond at http://finra-markets.morningstar.com/BondCenter/BondDetail.jsp?ticker=C104227&symbol=WMT.GP

 

 

 

 

 

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

 

Question: What shall investors do as interest rates are expected to rise in March 2022?

 

All Bonds are Subject to Interest Rate RiskEven If the Bonds Are Insured or Government Guaranteed

There is a misconception that, if a bond is insured or is a u.s. government obligation, the bond will not lose value. In fact, the U.S. government does not guarantee the market price or value of the bond if you sell the bond before it matures. This is because the market price or value of the bond can change over time based on several factors, including market interest rates. https://www.sec.gov/files/ib_interestraterisk.pdf

 

Relationship between bond prices and interest rates (Khan academy)

 

Heres how rising interest rates may affect your bond portfolio in retirement

PUBLISHED WED, JAN 19 20228:00 AM EST, Kate Dore, CFP

https://www.cnbc.com/2022/01/19/heres-how-rising-interest-rates-may-affect-your-bond-portfolio-.html

 

KEY POINTS

       Generally, market interest rates and bond prices move in opposite directions, meaning as rates increase, bond values will typically fall.

       Retirees may reduce interest rate risk by choosing bonds with a shorter duration, which are less sensitive to rate hikes.

       However, rising interest rates may still be good for retirees with a longer timeline, experts say.

 

Many retirees rely on bonds for income, lower risk and portfolio growth. However, as the Federal Reserve prepares to raise interest rates, some worry about the effects on their nest egg.

 

The cost of living has swelled for months, with the Consumer Price Index, the key measure of inflation, rising 7% year over year in December, the fastest since 1982, according to the U.S. Department of Labor.

 

Last week, Federal Reserve Chairman Jerome Powell said he expects a series of rate hikes this year, with reduced pandemic support from the central bank, to quell rising inflation.

 

This may alarm investors since market interest rates and bond prices typically move in opposite directions, meaning higher rates generally cause bond values to fall, known as interest rate risk.

 

For example, lets say you have a 10-year $1,000 bond paying a 3% coupon. If market interest rates rise to 4% in one year, the asset will still pay 3%, but the bonds value may drop to $925.

 

The reason for the price dip is new bonds may be issued with the higher 4% coupon, making the original 3% bond less attractive unless someone can buy it at a discount.

 

With higher yields elsewhere, investors tend to sell their current bonds to purchase the higher-paying ones, and heavy selling causes prices to slide, explained certified financial planner Brad Lineberger, president of Carlsbad, California-based Seaside Wealth Management.

 

Why bond duration matters

Another fundamental concept of bond investing is so-called duration, measuring a bonds sensitivity to interest rate changes. Although its expressed in years, its different from the bonds maturity since it factors in the coupon, time to maturity and yield paid through the term.

 

As a rule of thumb, the longer a bonds duration, the more sensitive it will be to interest rate hikes, and the more its price will decline, Lineberger said.

 

Generally, if youre trying to reduce interest rate risk, youll want to consider bonds or bond funds with a shorter duration, said Paul Winter, a CFP and owner of Five Seasons Financial Planning in Salt Lake City.

 

Also, bonds with higher coupon rates and lower credit quality tend to be less sensitive to higher interest rates, other factors being equal, he said.

 

A longer timeline

While rising interest rates will cause bond values to decrease, eventually, the declines will be more than offset as bonds mature and can be reinvested for higher yields, said CFP Anthony Watson, founder and president of Thrive Retirement Specialists in Dearborn, Michigan.

 

Rising interest rates are good for retirees with a longer-term time frame, he said, and thats most people in their retirement years.

 

The best way to manage interest rate risk is with a diversified portfolio, including international bonds, with short to immediate maturities that are less affected by rate hikes and can be reinvested sooner, Watson said.

 

 

For class discussion:

What is duration? How to calculate a bonds duration? a portfolios duration?

 

Bond Portfolio Duration (FYI)

https://analystnotes.com/cfa-study-notes-calculate-the-duration-of-a-portfolio-and-explain-the-limitations-of-portfolio-duration.html

 

There are two ways to calculate the duration of a bond portfolio:

 

1)     The weighted average of the time to receipt of aggregate cash flows. This method is based on the cash flow yield, which is the internal rate of return on the aggregate cash flows.

 

Limitations: This method cannot be used for bonds with embedded options or for floating-rate notes due to uncertain future cash flows. The cash flow yield is not commonly calculated. The change in cash flow yield is not necessarily the same as the change in the yields-to-maturity on the individual bonds. Interest rate risk is not usually expressed as a change in the cash flow yield.

 

2)     The weighted average of the durations of individual bonds that compose the portfolio. The weight is the proportion of the portfolio that a bond comprises.

3)      

Portfolio Duration = w1D1 + w2D2 + w3D3 + ... + wkDk

wi = the market value of bond i / market value of the portfolio

Di = the duration of bond i

k = the number of bonds in the portfolio

 

This method is simpler to use and quite accurate when the yield curve is flat. Its main limitation is that it assumes a parallel shift in the yield curve.

 

In class exercises

 

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

 

 

 

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

 

       Rate 8.2%

       Nper 8

       Pmt 65

       Pv ?

       FV 1000

 

 

 

2.                  AAA firms 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))

 

 

 

Assignment:

Chapter 7 Case Study Due with the first mid term exam

 

     Case video part I did in class on 1/30/2023

 

     Case video part II did in class on 2/1/2023

      

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 are the duration and the convexity of this bond?

       ---- FYI: https://www.youtube.com/watch?v=cjlq08iDlIw

       bond-convexity-calculator

 

 

Bond Pricing Formula (FYI)

 

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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/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Duration (FYI)

By ADAM HAYES Updated August 18, 2021, Reviewed by GORDON SCOTT,

Fact checked by KIRSTEN ROHRS SCHMITT

https://www.investopedia.com/terms/d/duration.asp

What Is Duration?

Duration is a measure of the sensitivity of the price of a bond or other debt instrument to a change in interest rates. A bond's duration is easily confused with its term or time to maturity because certain types of duration measurements are also calculated in years.

 

However, a bond's term is a linear measure of the years until repayment of principal is due; it does not change with the interest rate environment. Duration, on the other hand, is non-linear and accelerates as the time to maturity lessens.

 

KEY TAKEAWAYS

       Duration measures a bond's or fixed income portfolio's price sensitivity to interest rate changes.

       Macaulay duration estimates how many years it will take for an investor to be repaid the bonds price by its total cash flows.

       Modified duration measures the price change in a bond given a 1% change in interest rates.

       A fixed income portfolio's duration is computed as the weighted average of individual bond durations held in the portfolio.

 

How Duration Works

Duration can measure how long it takes, in years, for an investor to be repaid the bonds price by the bonds total cash flows. Duration can also measure the sensitivity of a bond's or fixed income portfolio's price to changes in interest rates.

 

In general, the higher the duration, the more a bond's price will drop as interest rates rise (and the greater the interest rate risk). For example, if rates were to rise 1%, a bond or bond fund with a five-year average duration would likely lose approximately 5% of its value.

 

Certain factors can affect a bonds duration, including:

 

Time to maturity: The longer the maturity, the higher the duration, and the greater the interest rate risk. Consider two bonds that each yield 5% and cost $1,000, but have different maturities. A bond that matures fastersay, in one yearwould repay its true cost faster than a bond that matures in 10 years. Consequently, the shorter-maturity bond would have a lower duration and less risk.

 

Coupon rate: A bonds coupon rate is a key factor in calculation duration. If we have two bonds that are identical with the exception of their coupon rates, the bond with the higher coupon rate will pay back its original costs faster than the bond with a lower yield. The higher the coupon rate, the lower the duration, and the lower the interest rate risk.

 

Types of Duration

The duration of a bond in practice can refer to two different things. The Macaulay duration is the weighted average time until all the bond's cash flows are paid. By accounting for the present value of future bond payments, the Macaulay duration helps an investor evaluate and compare bonds independent of their term or time to maturity.

 

The second type of duration is called modified duration. Unlike Macaulay's duration, modified duration is not measured in years. Modified duration measures the expected change in a bond's price to a 1% change in interest rates.

 

In order to understand modified duration, keep in mind that bond prices are said to have an inverse relationship with interest rates. Therefore, rising interest rates indicate that bond prices are likely to fall, while declining interest rates indicate that bond prices are likely to rise.

 

Macaulay Duration

Macaulay duration finds the present value of a bond's future coupon payments and maturity value. Because Macaulay duration is a partial function of the time to maturity, the greater the duration, the greater the interest-rate risk or reward for bond prices.

 

Macaulay duration can be calculated manually as follows:

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

 

Modified Duration

The modified duration of a bond helps investors understand how much a bond's price will rise or fall if the YTM rises or falls by 1%. This is an important number if an investor is worried that interest rates will be changing in the short term. The modified duration of a bond with semi-annual coupon payments can be found with the following formula:

 

​Usefulness of Duration

Investors need to be aware of two main risks that can affect a bond's investment value: credit risk (default) and interest rate risk (interest rate fluctuations). Duration is used to quantify the potential impact these factors will have on a bond's price because both factors will affect a bond's expected YTM.

 

For example, if a company begins to struggle and its credit quality declines, investors will require a greater reward or YTM to own the bonds. In order to raise the YTM of an existing bond, its price must fall. The same factors apply if interest rates are rising and competitive bonds are issued with a higher YTM.

 

The duration of a zero-coupon bond equals its time to maturity since it pays no coupon.

 

Duration Strategies

However, a long-duration strategy describes an investing approach where a bond investor focuses on bonds with a high duration value. In this situation, an investor is likely buying bonds with a long time before maturity and greater exposure to interest rate risks. A long-duration strategy works well when interest rates are falling, which usually happens during recessions.

 

A short-duration strategy is one where a fixed-income or bond investor is focused on buying bonds with a small duration. This usually means the investor is focused on bonds with a small amount of time to maturity. A strategy like this would be employed when investors think interest rates will rise or when they are very uncertain about interest rates and want to reduce their risk.

 

Why Is It Called Duration?

Duration measures a bond price's sensitivity to changes in interest ratesso why is it called duration? A bond with a longer time to maturity will have a price that is more sensitive to interest rates, and thus a larger duration than a short-term bond.

 

What Else Does Duration Tell You?

As a bond's duration rises, its interest rate risk also rises because the impact of a change in the interest rate environment is larger than it would be for a bond with a smaller duration. Fixed-income traders will use duration, along with convexity, to manage the riskiness of their portfolio and to make adjustments to it.

 

 

Bond Duration Calculator (FYI)

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

 

Computing Duration Excel (video, FYI)

 

 

DURATION function in Excel

The DURATION function, one of the Financial functions, returns the Macauley duration for an assumed par value of $100. Duration is defined as the weighted average of the present value of cash flows, and is used as a measure of a bond price's response to changes in yield.

Syntax

DURATION(settlement, maturity, coupon, yld, frequency, [basis])

Important: Dates should be entered by using the DATE function, or as results of other formulas or functions. For example, use DATE(2018,5,23) for the 23rd day of May, 2018. Problems can occur if dates are entered as text.

The DURATION function syntax has the following arguments:

Settlement: The security's settlement date. The security settlement date is the date after the issue date when the security is traded to the buyer.

Maturity: The security's maturity date. The maturity date is the date when the security expires.

Coupon: The security's annual coupon rate.

Yld Required. The security's annual yield.

Frequency: The number of coupon payments per year. For annual payments, frequency = 1; for semiannual, frequency = 2; for quarterly, frequency = 4.

Basis Optional. The type of day count basis to use.

https://support.microsoft.com/en-us/office/duration-function-b254ea57-eadc-4602-a86a-c8e369334038

 

0:02 / 1:54

Excel DURATION function - how to use DURATION function (video)

 

 

 

Convexity in Bonds: Definition, Meaning, and Examples (FYI only)

By JAMES CHEN Updated January 02, 2023 Reviewed by CIERRA MURRY Fact checked by PETE RATHBURN

https://www.investopedia.com/terms/c/convexity.asp#:~:text=Convexity%20is%20a%20measure%20of%20the%20curvature%20in%20the%20relationship,said%20to%20have%20negative%20convexity.

 

 

bond-convexity-calculator

 

convexity bond formula

 

 

 

 

 

 

Change in price = [Modified Duration *Change in yield] +[1/2 * Convexity*(change in yield)2]

 

https://www.wallstreetmojo.com/convexity-of-a-bond-formula-duration/\

 

What Is Convexity?

Convexity is a measure of the curvature, or the degree of the curve, in the relationship between bond prices and bond yields.

 

Convexity is thus a measure of the curvature in the relationship between bond prices and interest rates. It reflects the rate at which the duration of a bond changes as interest rates change. Duration is a measure of a bond's sensitivity to changes in interest rates. It represents the expected percentage change in the price of a bond for a 1% change in interest rates.

 

KEY TAKEAWAYS

       Convexity is a risk-management tool, used to measure and manage a portfolio's exposure to market risk.

       Convexity is a measure of the curvature in the relationship between bond prices and bond yields.

       Convexity demonstrates how the duration of a bond changes as the interest rate changes.

       If a bond's duration increases as yields increase, the bond is said to have negative convexity.

       If a bond's duration rises and yields fall, the bond is said to have positive convexity.

 

Before explaining convexity, it's important to know how bond prices and market interest rates relate to one another. As interest rates fall, bond prices rise. Conversely, rising market interest rates lead to falling bond prices. This opposite reaction is because as rates rise, the bond may fall behind in the payout they offer a potential investor in comparison to other securities.

Bond Duration

Bond duration measures the change in a bond's price when interest rates fluctuate. If the duration of a bond is high, it means the bond's price will move to a greater degree in the opposite direction of interest rates.

Duration, on the other hand, measures the bond's sensitivity to the change in interest rates. For example, if rates were to rise 1%, a bond or bond fund with a 5-year average duration would likely lose approximately 5% of its value.

 

Convexity and Risk

Convexity builds on the concept of duration by measuring the sensitivity of the duration of a bond as yields change. Convexity is a better measure of interest rate risk, concerning bond duration. Where duration assumes that interest rates and bond prices have a linear relationship, convexity allows for other factors and produces a slope.

 

Duration can be a good measure of how bond prices may be affected due to small and sudden fluctuations in interest rates. However, the relationship between bond prices and yields is typically more sloped, or convex. Therefore, convexity is a better measure for assessing the impact on bond prices when there are large fluctuations in interest rates.

 

As convexity increases, the systemic risk to which the portfolio is exposed increases. The term systemic risk became common during the financial crisis of 2008 as the failure of one financial institution threatened others. However, this risk can apply to all businesses, industries, and the economy as a whole.

 

The risk to a fixed-income portfolio means that as interest rates rise, the existing fixed-rate instruments are not as attractive. As convexity decreases, the exposure to market interest rates decreases and the bond portfolio can be considered hedged. Typically, the higher the coupon rate or yield, the lower the convexityor market riskof a bond. This lessening of risk is because market rates would have to increase greatly to surpass the coupon on the bond, meaning there is less interest rate risk to the investor. However, other risks, like default risk, etc., might still exist.

 

Example of Convexity

Imagine a bond issuer, XYZ Corporation, with two bonds currently on the market: Bond A and Bond B. Both bonds have a face value of $100,000 and a coupon rate of 5%. Bond A, however, matures in 5 years, while Bond B matures in 10 years.

 

Using the concept of duration, we can calculate that Bond A has a duration of 4 years while Bond B has a duration of 5.5 years. This means that for every 1% change in interest rates, Bond A's price will change by 4% while Bond B's price will change by 5.5%.

 

Now, let's say that interest rates suddenly increase by 2%. This means that the price of Bond A should decrease by 8% while the price of Bond B will decrease by 11%. However, using the concept of convexity, we can predict that the price change for Bond B will actually be less than expected based on its duration alone. This is because Bond B has a longer maturity, which means it has a higher convexity. The higher convexity of Bond B acts as a buffer against changes in interest rates, resulting in a relatively smaller price change than expected based on its duration alone.

 

Negative and Positive Convexity

If a bond's duration increases as yields increase, the bond is said to have negative convexity. In other words, the bond price will decline by a greater rate with a rise in yields than if yields had fallen. Therefore, if a bond has negative convexity, its duration would increasethe price would fall. As interest rates rise, and the opposite is true.

 

If a bond's duration rises and yields fall, the bond is said to have positive convexity. In other words, as yields fall, bond prices rise by a greater rateor durationthan if yields rose. Positive convexity leads to greater increases in bond prices. If a bond has positive convexity, it would typically experience larger price increases as yields fall, compared to price decreases when yields increase.

 

Under normal market conditions, the higher the coupon rate or yield, the lower a bond's degree of convexity. In other words, there's less risk to the investor when the bond has a high coupon or yield since market rates would have to increase significantly to surpass the bond's yield. So, a portfolio of bonds with high yields would have low convexity and subsequently, less risk of their existing yields becoming less attractive as interest rates rise.

 

Consequently, zero-coupon bonds have the highest degree of convexity because they do not offer any coupon payments. For investors looking to measure the convexity of a bond portfolio, it's best to speak to a financial advisor due to the complex nature and the number of variables involved in the calculation.