FIN509 • Week 6 — Chapter 13: Risk & Return

Week 6 — Chapter 13: Risk & Return

Compute expected return, variance/standard deviation, covariance/correlation, portfolio risk, CAPM expected return, and holding period return. Includes mini-calculators and course exercises.

Intro

We model returns with probabilities (states) or time series. Key objects:

E[R] = Σ p_iR_i
Var(R) = Σ p_i(R_i−E[R])²; σ = √Var
Cov(R₁,R₂) = Σ p_i(R_1i−E[R1])(R_2i−E[R2])
ρ = Cov / (σ₁σ₂)
Portfolio: E[R_p] = w₁E[R₁]+w₂E[R₂]; Var(R_p) = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov
CAPM: E[R_i] = R_f + β_i(E[R_m]−R_f)

Single Stock — Expected Return & Standard Deviation

Enter states as CSV. Example probs: 0.1,0.2,0.4,0.2,0.1; returns (%): -30,-2,10,18,40

Probabilities p_i Returns R_i (in %)

E[R]:

Var:

σ:

Two-Stock Portfolio — E[R], σ, Covariance & Correlation

Enter the same state probabilities; returns (%) for Stock 1 and 2; choose weights w₁, w₂ (w₂ auto = 1−w₁).

Probabilities p_i Stock 1 returns (%) Stock 2 returns (%)

w₁ (0–1) w₂ (auto)

0.50

E[R₁], σ₁:

E[R₂], σ₂:

Cov(1,2):

ρ(1,2):

E[R_p]:

σ_p:

CAPM — Expected Return

Risk-free rate R_f (%) Market return E[R_m] (%) Beta β

E[R] (CAPM):

Formula: E[R]=R_f + β (E[R_m] − R_f)

Holding Period Return (HPR)

Purchase price P₀ Sell price P₁ Dividends D

HPR:

Formula: HPR = (P₁ − P₀ + D) / P₀

Exercises — Preload Buttons

Stock A (states)

E[R] ≈ 8.2%, σ ≈ 16.98%.

Stocks A & B

Cov ≈ −0.54% (−0.0054), ρ ≈ −0.93 with the given inputs.

For data pulls in Sheets: =GOOGLEFINANCE("NVDA","close",DATE(2020,7,31),DATE(2025,7,31)) then month-end filter. Market proxy: "INDEXSP:.INX".

Homework (Due with Final) — Quick Helpers

Q1 — Discrete States (Answer: 9%)

Probs: 0.25, 0.50, 0.25; Returns (%): 30, 12, −18

Q2 — CAPM (Answer: 12%)

R_f=7, MRP=5, β=1 ⇒ set E[R_m]=12.

Q3 — Portfolio β (Answer: 0.988)

Use value weights × betas; sum.

Q4 — Target Return via β (Answer: 1.76)

Solve for β_new given mix and target E[R].

Q5 — Stock A (states)

E[R]=8.2%, Var≈0.02884, σ≈16.98%.

Q6 — Market Risk Premium (Answer: 11%)

MRP = E[R_m] − R_f.

Q7, Q9–Q12

Weighted averages of returns or betas as specified.

Quick Quiz

Click to check answers.

Resources

Expected Return & Risk (zenwealth): E[R], Var, SD
Course calculator — Return / Risk
CAPM explainer (Investopedia) and SML
Normal distribution visual (UIowa applet)

Note: Classroom calculators are for instruction; verify key numbers in Excel or approved tools when grading.