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
Expected Return = Risk-Free Rate + Beta × (Market Return − Risk-Free Rate)
Or mathematically:
E(R) = Rf + β × (Rm − Rf)
Formula Components
| Component | Symbol | Description | Typical Value |
|---|---|---|---|
| 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 | β | Measure of systematic risk | Varies by security |
| Market Return | Rm | Expected return of the market | Historical ~10% |
| Market Risk Premium | Rm − Rf | Extra return for market risk | Historical 5-7% |
Understanding Beta (β)
Beta is the cornerstone of CAPM. It measures a security's sensitivity to market movements—its systematic risk.
Beta Interpretation
| Beta Value | Interpretation | Example Securities |
|---|---|---|
| β = 0 | No market risk (risk-free) | T-bills |
| β = 0.5 | Half as volatile as market | Utilities, consumer staples |
| β = 1.0 | Same volatility as market | S&P 500 index fund |
| β = 1.5 | 50% more volatile than market | Technology stocks |
| β = 2.0 | Twice as volatile as market | High-growth/speculative stocks |
| β < 0 | Moves opposite to market | Gold (sometimes), inverse ETFs |
Beta Categories
| Category | Beta Range | Characteristics |
|---|---|---|
| Defensive | β < 1.0 | Less volatile; falls less in down markets, rises less in up markets |
| Neutral | β = 1.0 | Moves with the market |
| Aggressive | β > 1.0 | More volatile; amplifies market movements |
Calculating Portfolio Beta
Portfolio beta is the weighted average of individual security betas:
Portfolio Beta = Σ (Weight × Security Beta)
Example: Portfolio with:
- 60% Stock A (β = 1.2)
- 40% Stock B (β = 0.8)
Portfolio Beta = (0.60 × 1.2) + (0.40 × 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 (β) = 1.5
Calculate expected return:
E(R) = 3% + 1.5 × (11% − 3%) E(R) = 3% + 1.5 × 8% E(R) = 3% + 12% E(R) = 15%
Example 2: Finding Beta
Given:
- Expected return = 14%
- Risk-free rate = 2%
- Market return = 10%
Calculate beta:
14% = 2% + β × (10% − 2%) 12% = β × 8% β = 1.5
The Security Market Line (SML)
The SML is the graphical representation of CAPM.
SML Characteristics
| Feature | Description |
|---|---|
| X-axis | Beta (systematic risk) |
| Y-axis | Expected return |
| Y-intercept | Risk-free rate |
| Slope | Market risk premium (Rm − Rf) |
Security Positioning on SML
| Position | Meaning | Investment Decision |
|---|---|---|
| On the SML | Fairly priced | Hold |
| Above the SML | Undervalued (return > required) | Buy |
| Below the SML | Overvalued (return < required) | Sell |
SML vs. CML: Key Differences
| Feature | Security Market Line (SML) | Capital Market Line (CML) |
|---|---|---|
| Risk Measure | Beta (systematic risk) | Standard deviation (total risk) |
| What it plots | Individual securities and portfolios | Only efficient portfolios |
| Derived from | CAPM | Efficient frontier + risk-free asset |
| Slope | Market risk premium | 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
- CAPM: E(R) = Rf + β(Rm − Rf)
- Beta measures systematic risk relative to the market
- β < 1 = defensive; β > 1 = aggressive; β = 1 = market
- Portfolio beta = weighted average of security betas
- SML plots expected return vs. beta
- Securities above SML are undervalued; below SML are overvalued
Using CAPM, if the risk-free rate is 3%, the expected market return is 11%, and a stock's beta is 1.5, the expected return is:
A stock plotting ABOVE the Security Market Line (SML) is considered:
The primary difference between the Security Market Line (SML) and Capital Market Line (CML) is that the SML:
9.3 Efficient Market Hypothesis
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