FIN301 • Chapter 6 • Risk & Return (Spring 2026)

Chapter 6 Links

PPT (Chapter 6) Quiz on Diversification Quiz on CAPM ICE Data & Results

Course calculators (jufinance.com)

Expected Return / Risk Holding Period Return CAPM 2-Stock Portfolio

We’ll use these to verify hand calculations.

Topic 1: Single Stock — Risk/Return Tradeoff

Given a probability distribution of returns, compute expected return and risk (variance / standard deviation).

Formulas (expected return, variance, standard deviation)

Expected return: $E[R]=\sum_{i=1}^{N} p_i R_i$
Variance: $Var(R)=\sum_{i=1}^{N} p_i (R_i - E[R])^2$
Standard deviation: $ \sigma = \sqrt{Var(R)}$

External reference calculators: Expected Return, Measures of Risk.

Exercise (Stock A: states and returns)

State of the Economy	Probability	Stock A Return
Recession	10%	-30%
Below Average	20%	-2%
Average	40%	10%
Above Average	20%	18%
Boom	10%	40%

Solution

Expected return: 8.2%

Standard deviation (FYI): 16.98%

You can verify using www.jufinance.com/return.

Drawbacks of holding one stock

High concentration risk (“all eggs in one basket”).
Company-specific bad news can severely hurt your portfolio.
High volatility and uncompensated risk (risk that can be diversified away).

Mini-calculator (expected return + stdev from your own table)

Paste 5 rows as: probability, return (prob in %, return in %). Example: 10, -30

Results

Expected return: —

Variance: —

Standard deviation: —

Variance shown in decimal units (e.g., 0.028 = 2.8%).

Topic 2: Two-Stock Portfolio — Diversification

Diversification can reduce risk without necessarily reducing expected return. The key is correlation.

Key insights (correlation matters)

Diversification lowers risk as long as stocks are not perfectly correlated.
Correlation:
- +1: move together → little risk reduction
- ~0: move independently → meaningful risk reduction
- -1: move opposite → can eliminate risk in a 2-asset case
Example intuition: airline stock + social media stock (low correlation) smooths swings.

2-stock portfolio formulas

Expected return: $E[R_p]=w_1E[R_1]+w_2E[R_2]$
Variance: $ \sigma_p^2=w_1^2\sigma_1^2+w_2^2\sigma_2^2+2w_1w_2\sigma_{12}$
Covariance: $ \sigma_{12}=\rho_{12}\sigma_1\sigma_2$

Use www.jufinance.com/portfolio to verify.

Exercise (Stocks A and B)

State	Probability	Stock A	Stock B
Recession	10%	-30%	-10%
Below Average	20%	-2%	2%
Average	40%	10%	1%
Above Average	20%	18%	2%
Boom	10%	40%	-5%

Solutions (provided)

Stock A: E[R]=8.2%, SD (FYI) 16.98%
Stock B: E[R]=1.7%, SD (FYI) 3.41%
Covariance (FYI): -0.54%
Correlation (FYI): -0.93

Interpretation

A strong negative correlation means the stocks offset one another, which can substantially reduce portfolio volatility.

Topic 3: Three-Stock Portfolio — More Diversification

Adding a third stock creates three correlation pairs and reduces company-specific (unsystematic) risk further.

Key insights

More stocks = lower risk (especially with low correlations).
Three stocks create three correlation pairs, spreading unsystematic risk.
Rule of thumb: ~20 well-chosen stocks capture most diversification benefits.
Good mix example: Tech + Consumer Staples + Utilities (different sectors).

In-class project workflow (3 stocks + S&P500)

Pick three leading firms in three different industries.
Download monthly adjusted close prices for the past five years from finance.yahoo.com.
Compute monthly returns, average return, standard deviation, and correlations.
Download S&P500 monthly series and compute beta using Excel:
- =SLOPE(stock_return_range, sp500_return_range)
Use CAPM expected returns and draw the SML.

App: Monthly Returns (5 years)

Template: “Stock Prices Raw Data, Risk, Beta, CAPM (Stock 1, Stock 2, Stock 3, S&P500)” — update based on the stocks chosen in class.

Conclusion

In practice, 20–25 stocks across industries usually eliminate most diversifiable risk.

Topic 4: Capital Asset Pricing Model (CAPM)

CAPM links expected return to systematic risk (beta). Unsystematic risk is diversified away.

CAPM formula + definitions

CAPM: Ri = Rf + βi × (Rm − Rf)

Ri = expected return of investment
Rf = risk-free rate
βi = beta (systematic risk)
Rm = expected market return
(Rm − Rf) = market risk premium

Verify with www.jufinance.com/capm.

CAPM mini-calculator (Ri)

Risk-free rate (Rf, %)

Market risk premium (Rm − Rf, %)

Beta (β)

Result

Expected return (Ri): —

Example in homework #9: Rf=3.9%, MRP=6.2%, β=1.21 → Ri ≈ 11.4%.

Chapter 6 Homework (due with the second midterm exam)

Show your steps. Use Excel functions where appropriate: SUMPRODUCT, STDEV, CORREL, SLOPE.

Homework questions (with provided answers)

Stock A expected return? Answer: 8.2%
Holding period return for Robotics stock (buy $3, sell $3.45)? Answer: 15%
Portfolio expected return (Boom/Normal/Recession)? Answer: 9.05%
Electric Circuit holding period return (Jan–Mar 2019)? Answer: 2.12%
Market risk premium if Rm=15% and Rf=4%? Answer: 11%
Portfolio beta (A/B/C with dollar weights)? Answer: 1.99
Expected return of portfolio (three dollar investments)? Answer: 13%
Portfolio beta (A/B/C with values 8k/10k/2k)? Answer: 1.15
CAPM expected return (Rf=3.9, MRP=6.2, β=1.21)? Answer: 11.4%
Portfolio beta + expected return (weights + betas; Rf=3%, Rm=10%)? Answers: βp=1.15; E[Rp]=11.05%
Holding period return (Jazman vs Solomon, period 1→3)? Answers: 50%, -25%
Expected return (two states 30%/70%)? Answer: 12%
Expected returns (T-bill; Apple; Wal-Mart)? Answers: 4%, 5%, 2.5%
Rank risk (least → most risky)? Answer: 1, 3, 2
Portfolio beta (A/B/C with dollar weights)? Answer: 1.1

Expected Return Calculator HPR Calculator CAPM Calculator 2-Stock Portfolio Calculator