Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) determines expected returns based on systematic risk. The Series 65 exam tests CAPM, beta, alpha, standard deviation, R-squared, and the distinction between the Security Market Line and Capital Market Line.

CAPM Formula

• Extends Modern Portfolio Theory by introducing the risk-free rate and the concept of a market portfolio
• Developed by William Sharpe (1964), John Lintner, and Jan Mossin
• Calculates the expected return of a security based on its systematic risk (beta)

• $E(R)$: Expected return of the security
• $R_f$: Risk-free rate (typically 91-day T-bill yield)
• $\beta$: Systematic risk relative to the market
• $R_m$: Expected return of the market
• $(R_m - R_f)$: Market risk premium (also called equity risk premium)

Formula Example

• Risk-free rate: 3%
• Market return: 10%
• Stock beta: 1.2

Calculation:

• Market risk premium = 10% - 3% = 7%
• Expected return = 3% + (1.2 x 7%) = 3% + 8.4% = 11.4%

Think of it this way: Start with the risk-free rate (what you'd earn with zero risk). Then add extra return based on how risky the investment is (beta x market risk premium). Higher beta = more extra return required.

Exam Tip: Gotchas

• CAPM only compensates investors for systematic (market) risk, not total risk. Unsystematic risk is assumed to be diversified away. If a question asks what return an investor should expect, use beta (systematic risk), NOT standard deviation (total risk).

CAPM Assumptions

CAPM assumes:

• Investors are rational and risk-averse
• Markets are efficient (all investors have the same information)
• No transaction costs or taxes
• Investors can borrow and lend at the risk-free rate
• All investors have the same time horizon

Beta

Beta measures a security's sensitivity to market movements - systematic (nondiversifiable) risk only.

• The market portfolio has a beta of 1.0 by definition
• Beta measures volatility relative to the market, not absolute volatility

• A stock with beta = 1.5 is expected to move 1.5x the market move (market up 10% -> stock up 15%)
• A stock with beta = 0.7 is expected to move 0.7x the market move (market down 10% -> stock down 7%)
• Portfolio beta = weighted average of individual asset betas

Exam Tip: Gotchas

• Beta measures systematic risk ONLY. A stock can have a low beta but high total risk (high standard deviation) if it has significant unsystematic risk. Beta does NOT capture company-specific risk. The exam tests whether you know that beta = systematic risk, standard deviation = total risk.

Alpha

Alpha measures the excess return of a portfolio relative to its CAPM-expected return. It indicates whether a portfolio manager added or destroyed value after adjusting for risk.

Alpha Example

• Portfolio returned 14%, Risk-free rate: 3%, Market return: 10%, Beta: 1.2

Step 1: Calculate CAPM expected return

• E(R) = 3% + 1.2 x (10% - 3%) = 3% + 8.4% = 11.4%

Step 2: Calculate Alpha

• Alpha = 14% - 11.4% = +2.6% (manager outperformed)

Think of it this way: Alpha answers the question "Did the manager beat what we expected given the risk they took?" A manager who earns 12% when CAPM predicted 10% has positive alpha, even if another manager earned 14%.

Exam Tip: Gotchas

• Alpha is NOT simply the difference between portfolio return and market return. If a portfolio returned 14% and the market returned 10%, the alpha is NOT 4%. You must first calculate the CAPM-expected return using the portfolio's beta, THEN subtract. The exam specifically tests this mistake.

Standard Deviation

• Measures total risk (both systematic and unsystematic) of an investment
• Represents the dispersion of returns around the average (mean) return
• Higher standard deviation = wider range of possible outcomes = more risk
• Used in the Capital Market Line (total risk measure)
• Assumes returns follow a normal distribution (bell curve)

Normal Distribution and Standard Deviation:

• Example: Mean return = 10%, SD = 5%
  • 68% chance returns fall between 5% and 15%
  • 95% chance returns fall between 0% and 20%

Exam Tip: Gotchas

• Standard deviation measures TOTAL risk; beta measures only SYSTEMATIC risk. If a question asks about a well-diversified portfolio's risk, beta is the appropriate measure (unsystematic risk has been diversified away). If a question asks about a single stock's total risk, standard deviation is the appropriate measure.

R-Squared (Coefficient of Determination)

• Measures how much of a portfolio's movement is explained by the benchmark index
• Ranges from 0 to 1.0 (or 0% to 100%)
• Indicates how reliable beta is as a risk measure for the portfolio

• An S&P 500 index fund has R-squared near 1.0 (tracks the index almost perfectly)
• A sector fund or single stock will typically have a lower R-squared
• R-squared is the square of the correlation coefficient (r): R-squared = r-squared

Exam Tip: Gotchas

• If R-squared is low, beta is unreliable. The exam tests whether you know to use standard deviation (total risk) instead of beta when R-squared is low, because the benchmark does not explain the portfolio's movements. A high R-squared validates the use of beta as a meaningful risk measure.

Security Market Line (SML) vs. Capital Market Line (CML)

This is one of the highest-frequency gotchas on the exam.

Security Market Line (SML)

The SML is the graphical representation of CAPM, plotting expected return against beta.

• X-axis: Beta (systematic risk)
• Y-axis: Expected return
• Y-intercept: Risk-free rate (where beta = 0)
• Slope: Market risk premium (Rm - Rf)

SML Valuation Rule

• Above the SML = actual/forecasted return exceeds required return = undervalued = buy
• Below the SML = return is less than required for the beta = overvalued = sell
• On the SML = fairly valued
• Securities above the SML have positive alpha; securities below have negative alpha

Think of it this way: If a stock is above the SML, it's giving you more return than it should for its level of risk. That's a bargain. If it's below, you're not being compensated enough for the risk.

Exam Tip: Gotchas

• Above the SML = undervalued (good buy). Below the SML = overvalued (avoid or sell). "Above = overvalued" is a common wrong answer.

Capital Market Line (CML)

• Uses standard deviation (total risk), not beta
• Applies only to efficient portfolios, not individual securities
• The CML is tangent to the efficient frontier at the market portfolio
• Points left of the market portfolio = lending (holding some risk-free asset)
• Points right of the market portfolio = borrowing (leveraging)
• Only efficient portfolios (risk-free asset combined with the market portfolio in various weights) lie on the CML
• Portfolios below the CML are suboptimal

Exam Tip: Gotchas

• CML uses standard deviation; SML uses beta. CML evaluates efficient portfolios; SML evaluates all assets including individual securities.

Sharpe Ratio (Review)

• Covered in detail in the Portfolio Performance Measures unit, but referenced here because it connects to capital market theory
• Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Standard Deviation
• Measures return per unit of TOTAL risk (uses standard deviation)
• Higher Sharpe ratio = better risk-adjusted performance
• Related to the slope of the CML (the market portfolio's Sharpe ratio defines the CML slope)

Key Relationships Summary