Chapter 5 · Van Horne, 13th Ed.

Risk and Return

Quick MBA study notes — read in 10 minutes

1The Big Idea

Every investment involves a trade-off: the higher the risk, the higher the return investors demand. This chapter builds the toolkit to measure both — return, risk, and how they behave when securities are combined into portfolios.

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Key Concept Return = price change + income, divided by beginning price. Risk = the variability of that return around what you expected.

Analogy: a fixed deposit and a startup investment might both average a 12% return over time — but the startup's return could swing wildly year to year. That swing is risk.

2Measuring Risk: Standard Deviation & CV

Expected return is a probability-weighted average of possible outcomes. Standard deviation (σ) measures how far actual returns might stray from that expectation.

CV = σ / Expected Return

Example

Proposal A: σ = $548, expected value $4,000 → CV = 0.14. Proposal B: σ = $1,095, same expected value → CV = 0.27. B is riskier per dollar expected.

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Key Concept Standard deviation alone can mislead when comparing investments of different sizes. The coefficient of variation (CV) — "risk per unit of return" — fixes that scale problem.

3Investors Are Risk-Averse

Given a choice between a certain amount and a gamble with the same expected value, most investors prefer the certain amount.

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Key Concept A 50/50 shot at $10,000 or $0 has an expected value of $5,000 — yet most people accept far less (say $3,000) just to remove the uncertainty. That gap is the essence of risk aversion.

4Portfolio Risk: Covariance Is King

A portfolio's expected return is just a weighted average of its securities' returns. But portfolio risk is not — it depends heavily on how the securities move together (covariance), not just their individual volatility.

σⱼ,ₖ = rⱼ,ₖ · σⱼ · σₖ

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Key Concept For a large portfolio, total risk depends mostly on the weighted covariances between securities — not their individual standard deviations. Low or negative covariance is where real risk reduction comes from.

Analogy: holding an umbrella company and an ice-cream company together is safer than holding two ice-cream companies — their fortunes move in opposite directions on a rainy day.

5Diversification: Two Types of Risk

Risk type	Also called	Can diversification remove it?
Systematic	Market / unavoidable risk	No — affects all securities
Unsystematic	Company-specific / diversifiable risk	Yes — spread across enough securities

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Key Concept Once a portfolio is well-diversified, only systematic risk remains — and only systematic risk is what the market actually rewards investors for taking on.

6Beta & the Characteristic Line

Plot a stock's excess returns (over the risk-free rate) against the market's excess returns. The slope of that line is beta — an index of systematic risk.

Beta value	Meaning
β = 1.0	Moves in lockstep with the market
β > 1.0	"Aggressive" — amplifies market moves
β < 1.0	"Defensive" — dampens market moves

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Key Concept The tighter the data points cluster around the characteristic line, the lower the unsystematic risk of that stock — and the more its movements are explained by the market alone.

7CAPM & the Security Market Line (SML)

Rⱼ = R_f + (R̄_m − R_f) × β_j

Example

Risk-free rate 8%, market return 13%, β = 1.3 → Required return = 8% + (13%−8%)(1.3) = 14.5%

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Key Concept The Security Market Line shows this relationship graphically: expected return on the vertical axis, beta on the horizontal. Higher systematic risk → higher required return, in a straight line.

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Challenges to CAPM Anomalies like the small-firm effect and P/E effect suggest beta alone doesn't fully explain returns — firm size and market-to-book ratio also matter (Fama-French). CAPM remains a useful starting framework nonetheless.

8Efficient Markets

A market is "efficient" when security prices fully and quickly reflect all available information — meaning it's hard to consistently beat the market using that information.

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Key Concept Even in efficient markets, occasional anomalies (like the 1987 crash) remind us that pricing isn't perfect all the time — but it's a reasonable working assumption most of the time.

9Formula Cheat-Sheet

Concept	Formula
Coefficient of variation	CV = σ / Expected Return
Covariance	σⱼ,ₖ = rⱼ,ₖ·σⱼ·σₖ
CAPM required return	Rⱼ = R_f + (R̄_m−R_f)β

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Only systematic risk earns a reward in the market — diversification eliminates the rest, so beta, not total volatility, is what should drive a security's required return.