Capital Asset Pricing Model (CAPM)

Quick Answer

CAPM prices a security's expected return from the risk-free rate plus beta times the market risk premium, since only systematic risk is priced. Beta measures that systematic risk, alpha measures the difference between a manager's actual return and CAPM's expected return (positive, zero, or negative), and the SML (beta) and CML (standard deviation, efficient portfolios only) plot those relationships.

This section works through the formula, its five assumptions, and the risk and performance measures (beta, alpha, standard deviation, R-squared) built on top of it, ending with how the SML and CML differ.

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.

What Is the CAPM Formula?

Extends Modern Portfolio Theory by introducing the risk-free rate and the concept of a market portfolio.

Calculates the expected return of a security based on its systematic risk (beta).

Formula: E(R) equals Rf plus beta times (Rm minus Rf).

E(R): Expected return of the security.

Rf: Risk-free rate (typically 91-day T-bill yield).

Beta: Systematic risk relative to the market.

Rm: Expected return of the market (the true market portfolio of all risky assets is unobservable, so a broad index such as the S and P 500 stands in as a proxy).

(Rm minus Rf): Market risk premium (also called equity risk premium).

How Is the CAPM Expected Return Calculated?

Risk-free rate: 3 percent.

Market return: 10 percent.

Stock beta: 1.2.

Calculation:

Market risk premium equals 10 percent minus 3 percent equals 7 percent.

Expected return equals 3 percent plus (1.2 x 7 percent) equals 3 percent plus 8.4 percent equals 11.4 percent.

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 means 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).

What Are the 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.

What Does Beta Measure?

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.

Beta greater than 1.0: More volatile than the market (aggressive). Market moves plus 10 percent, stock moves more than 10 percent.

Beta equals 1.0: Moves with the market (same volatility). Market moves plus 10 percent, stock moves exactly 10 percent.

Beta between 0 and 1.0: Less volatile than the market (defensive/conservative). Market moves plus 10 percent, stock moves less than 10 percent.

Beta equals 0: No correlation with the market (for example, cash, T-bills). Market moves plus 10 percent, stock moves 0 percent.

Negative beta: Moves opposite to the market (rare; for example, gold, inverse funds). Market moves plus 10 percent, stock moves in a negative direction.

A stock with beta equals 1.5 is expected to move 1.5x the market move (market up 10 percent, stock up 15 percent).

A stock with beta equals 0.7 is expected to move 0.7x the market move (market down 10 percent, stock down 7 percent).

Portfolio beta equals 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 equals systematic risk, standard deviation equals total risk.

What Does Alpha Measure?

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.

Formula: Alpha equals Actual Return minus [Rf plus beta times (Rm minus Rf)].

Positive alpha: Manager outperformed on a risk-adjusted basis.

Zero alpha: Manager performed exactly as CAPM predicted.

Negative alpha: Manager underperformed on a risk-adjusted basis.

How Is Alpha Calculated?

Portfolio returned 14 percent, Risk-free rate: 3 percent, Market return: 10 percent, Beta: 1.2.

Step 1: Calculate CAPM expected return.

E(R) equals 3 percent plus 1.2 x (10 percent minus 3 percent) equals 3 percent plus 8.4 percent equals 11.4 percent.

Step 2: Calculate Alpha.

Alpha equals 14 percent minus 11.4 percent equals plus 2.6 percent (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 percent when CAPM predicted 10 percent has positive alpha, even if another manager earned 14 percent.

Exam Tip: Gotchas

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

What Does Standard Deviation Measure?

Measures total risk (both systematic and unsystematic) of an investment.

Represents the dispersion of returns around the average (mean) return.

Higher standard deviation equals wider range of possible outcomes equals more risk.

Used in the Capital Market Line (total risk measure).

Assumes returns follow a normal distribution (bell curve).

Normal Distribution and Standard Deviation:

Returns cluster around the mean. Wider standard deviation ranges capture progressively more outcomes.

Mean plus or minus 1 standard deviation: about 68 percent of returns.

Mean plus or minus 2 standard deviations: about 95 percent of returns.

Mean plus or minus 3 standard deviations: about 99.7 percent of returns.

Example: Mean return equals 10 percent, SD equals 5 percent.

68 percent chance returns fall between 5 percent and 15 percent.

95 percent chance returns fall between 0 percent and 20 percent.

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.

What Does R-Squared Tell You?

Measures how much of a portfolio's movement is explained by the benchmark index.

Ranges from 0 to 1.0 (or 0 percent to 100 percent).

Indicates how reliable beta is as a risk measure for the portfolio.

In plain words: an R-squared of 0.40 means about 40 percent of the portfolio's ups and downs line up with the benchmark. The other 60 percent come from something else, so beta, which only measures the benchmark-linked part, says little about the portfolio's risk.

R-Squared 1.0 (100 percent): Portfolio moves perfectly with the index; beta is fully reliable.

R-Squared 0.70 plus (70 percent plus): Generally considered high; beta is a meaningful measure.

R-Squared below 0.70: Low; beta may not be a reliable risk measure; use standard deviation instead.

An S and 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 equals 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.

R-squared is not itself a risk measure. It only tells you whether beta can be trusted. It cannot tell you how volatile the portfolio is.

How Do the SML and CML Differ?

This is a frequent exam gotcha.

Feature: Risk measure (x-axis). SML: Beta (systematic risk). CML: Standard deviation (total risk).

Feature: Applies to. SML: Any individual security or portfolio. CML: Efficient portfolios only.

Feature: Y-intercept. SML: Risk-free rate. CML: Risk-free rate.

Feature: Slope. SML: Market risk premium (Rm minus Rf). CML: Sharpe ratio of market portfolio: (Rm minus Rf) divided by standard deviation of the market.

Feature: Derived from. SML: CAPM equation. CML: Combining risk-free asset with market portfolio.

Feature: Purpose. SML: Shows required return for any given beta. CML: Shows optimal risk-return tradeoff for portfolios.

How Does the Security Market Line Work?

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 equals 0).

Slope: Market risk premium (Rm minus Rf).

The source page includes a Security Market Line graph with beta on the x-axis, expected return on the y-axis, the risk-free rate as the y-intercept, and the market risk premium as the slope. Image content is skipped per task instructions.

The SML prices systematic risk. Its X-axis is beta, its Y-axis is expected return, its Y-intercept is the risk-free rate, and its slope is the market risk premium.

How Do You Use the SML to Value a Security?

Above the SML equals actual/forecasted return exceeds required return equals undervalued equals buy.

Below the SML equals return is less than required for the beta equals overvalued equals sell.

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

How Does the Capital Market Line Work?

X-axis: Standard deviation (total risk), not beta.

Y-axis: Expected return.

Y-intercept: Risk-free rate (where standard deviation equals 0).

Slope: Sharpe ratio of the market portfolio: (Rm minus Rf) divided by standard deviation of the market.

Applies only to efficient portfolios, not individual securities.

The CML is tangent to the efficient frontier at the market portfolio.

The CML is a single straight line running from the risk-free rate (zero standard deviation) up through the market portfolio and beyond. Every point on that line is some mix of the risk-free asset and the market portfolio.

Left of the market portfolio, on the CML (lower standard deviation than the market) equals a lending portfolio: part of the money sits in the risk-free asset, part in the market portfolio, so both risk and expected return are below the market's.

Right of the market portfolio, on the CML (higher standard deviation than the market) equals a borrowing portfolio: the investor borrows at the risk-free rate to hold more than 100 percent of the market portfolio (leverage), pushing both risk and expected return above the market's.

Only efficient portfolios (the risk-free asset combined with the market portfolio, in any weighting) lie on the CML.

Lending vs. borrowing describes where a portfolio sits along the CML (its standard deviation relative to the market portfolio). That's a different question from where a portfolio sits relative to the CML: a portfolio that plots below the CML is suboptimal for its risk level, whether it happens to be a lending or a borrowing mix.

Why Does the CML Only Work for Efficient Portfolios?

The CML's x-axis is standard deviation (total risk). That axis only produces a consistent, priced-risk relationship when there's no uncompensated risk hiding inside it.

An efficient portfolio holds only the risk-free asset and the market portfolio. Combining those two eliminates unsystematic risk through diversification, so whatever standard deviation remains IS the portfolio's systematic risk. Total risk and priced risk are the same number, so standard deviation works as the risk measure.

An individual security (or any undiversified portfolio) still carries unsystematic risk inside its standard deviation. CAPM assumes the market doesn't compensate investors for that risk, so a security's standard deviation mixes priced risk with unpriced risk.

Two stocks with the same beta but different total risk should earn the same CAPM-required return, but they'd land at different points on a standard-deviation axis. Plotting them against standard deviation doesn't give a reliable return-for-risk line.

The SML avoids this problem by using beta instead of standard deviation. Beta isolates systematic risk only, which is the risk CAPM says the market actually pays for, so it works for any security or portfolio, diversified or not.

The source page includes a Capital Market Line graph with standard deviation on the x-axis, expected return on the y-axis, the risk-free rate as the y-intercept, and the line tangent to the efficient frontier at the market portfolio. Image content is skipped per task instructions.

The CML is the straight line from the risk-free rate, tangent to the efficient frontier at the market portfolio. Its X-axis is standard deviation (total risk), its Y-axis is expected return, its Y-intercept is the risk-free rate, and its slope is the market portfolio's Sharpe ratio.

Exam Tip: Gotchas

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

What Is the Sharpe Ratio?

Covered in detail in the Portfolio Performance Measures unit, but referenced here because it connects to capital market theory.

Sharpe Ratio equals (Portfolio Return minus Risk-Free Rate) divided by Standard Deviation.

Measures return per unit of TOTAL risk (uses standard deviation).

Higher Sharpe ratio equals better risk-adjusted performance.

Related to the slope of the CML (the market portfolio's Sharpe ratio defines the CML slope).

What Are the Key Risk-Measure Relationships?

Concept: CAPM / SML. Risk measure used: Beta (systematic risk). Applies to: Any security or portfolio.

Concept: CML. Risk measure used: Standard deviation (total risk). Applies to: Efficient portfolios only.

Concept: Alpha. Risk measure used: Beta (via CAPM). Applies to: Manager performance evaluation.

Concept: Sharpe Ratio. Risk measure used: Standard deviation (total risk). Applies to: Any portfolio.

Concept: R-Squared. Risk measure used: Not applicable (validates beta reliability). Applies to: Portfolio vs. benchmark.

What Should You Check on Exam Day?

Know the CAPM formula, E(R) equals Rf plus beta x (Rm minus Rf), and be ready to compute it.

Alpha requires calculating the CAPM-expected return first, then subtracting it from actual return. It is not simply actual return minus market return.

CAPM compensates only for systematic risk (beta); standard deviation is total risk. The SML uses beta and applies to any security or portfolio; the CML uses standard deviation and applies only to efficient portfolios.

Above the SML equals undervalued (buy, positive alpha); below the SML equals overvalued (sell, negative alpha).

R-squared below 0.70 means beta is unreliable; use standard deviation instead.