9.2 Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model, developed by William Sharpe (building on Markowitz's work), describes the relationship between systematic risk and expected return. It is one of the most important concepts for the Series 65 exam.

The CAPM Formula

E(R) = Rf + beta x (Rm - Rf)

Where:

- E(R) = Expected Return

- Rf = Risk-Free Rate

- beta = Beta (systematic risk measure)

- Rm = Expected Market Return

- (Rm - Rf) = Market Risk Premium

Formula Components

- Expected Return, E(R), Required return on the security, Calculated

- Risk-Free Rate, Rf, Return on risk-free investment, 91-day T-bill rate

- Beta, beta, Measure of systematic risk, Varies by security

- Market Return, Rm, Expected return of the market, Historical about 10%

- Market Risk Premium, Rm - Rf, Extra return for market risk, Historical 5-7%

Understanding Beta

Beta is the cornerstone of CAPM. It measures a security's sensitivity to market movements - its systematic risk.

Beta Interpretation

- Beta = 0: No market risk (risk-free), Example Securities: T-bills

- Beta = 0.5: Half as volatile as market, Example Securities: Utilities, consumer staples

- Beta = 1.0: Same volatility as market, Example Securities: S&P 500 index fund

- Beta = 1.5: 50% more volatile than market, Example Securities: Technology stocks

- Beta = 2.0: Twice as volatile as market, Example Securities: High-growth/speculative stocks

- Beta less than 0: Moves opposite to market, Example Securities: Gold (sometimes), inverse ETFs

Beta Categories

- Defensive: Beta less than 1.0, Less volatile; falls less in down markets, rises less in up markets

- Neutral: Beta = 1.0, Moves with the market

- Aggressive: Beta greater than 1.0, More volatile; amplifies market movements

Calculating Portfolio Beta

Portfolio beta is the weighted average of individual security betas:

Portfolio beta = sum of (weight x beta) for each security

Example: Portfolio with:

- 60% Stock A (beta = 1.2)

- 40% Stock B (beta = 0.8)

Portfolio beta = (0.60 x 1.2) + (0.40 x 0.8) = 0.72 + 0.32 = 1.04

CAPM Calculation Examples

Example 1: Basic Calculation

Given:

- Risk-free rate (Rf) = 3%

- Expected market return (Rm) = 11%

- Stock's beta = 1.5

Calculate expected return:

E(R) = 3% + 1.5 x (11% - 3%)

E(R) = 3% + 1.5 x 8%

E(R) = 3% + 12% = 15%

Example 2: Finding Beta

Given:

- Expected return = 14%

- Risk-free rate = 2%

- Market return = 10%

Calculate beta:

14% = 2% + beta x (10% - 2%)

12% = beta x 8%

beta = 12% / 8% = 1.5

The Security Market Line (SML)

The SML is the graphical representation of CAPM.

SML Characteristics

- X-axis: Beta (systematic risk)

- Y-axis: Expected return

- Y-intercept: Risk-free rate

- Slope: Market risk premium (Rm - Rf)

Security Positioning on SML

- On the SML: Fairly priced, Investment Decision: Hold

- Above the SML: Undervalued (return greater than required), Investment Decision: Buy

- Below the SML: Overvalued (return less than required), Investment Decision: Sell

SML vs. CML: Key Differences

- Risk Measure: SML: Beta (systematic risk); CML: Standard deviation (total risk)

- What it plots: SML: Individual securities and portfolios; CML: Only efficient portfolios

- Derived from: SML: CAPM; CML: Efficient frontier + risk-free asset

- Slope: SML: Market risk premium; CML: Market Sharpe ratio

CAPM Assumptions and Limitations

Assumptions

- Investors are rational and risk-averse

- All investors have the same expectations

- Investors can borrow/lend at the risk-free rate

- No taxes or transaction costs

- Single-period investment horizon

Limitations

- Beta may not be stable over time

- Historical beta may not predict future beta

- Single-factor model (ignores other risk factors)

- Assumes returns are normally distributed

- Real-world frictions (taxes, costs) exist

In Practice

Investment professionals use CAPM to:

- Determine required returns for stocks

- Evaluate whether securities are over/undervalued

- Calculate cost of equity for corporate finance decisions

- Set return expectations based on risk

On the Exam

Series 65 frequently tests:

- CAPM calculations (expect to calculate expected return given beta, Rf, and Rm)

- Beta interpretation (defensive vs. aggressive)

- SML position and investment decisions

- Difference between SML (uses beta) and CML (uses standard deviation)

Key Takeaways

1. CAPM: E(R) = Rf + beta(Rm - Rf)

2. Beta measures systematic risk relative to the market

3. Beta less than 1 = defensive; beta greater than 1 = aggressive; beta = 1 = market

4. Portfolio beta = weighted average of security betas

5. SML plots expected return vs. beta

6. Securities above SML are undervalued; below SML are overvalued