Capital Asset Pricing Model (CAPM)

Overview

The Capital Asset Pricing Model (CAPM) links an asset’s expected return to its systematic risk relative to the market. It is used to estimate the required return for a security, price risky assets, and inform cost-of-capital decisions. CAPM assumes investors are risk-averse and that markets are competitive and efficient, producing a linear relationship between risk and expected return.

Key formula

Expected return:
ERi = Rf + βi × (ERm − Rf)

Where:
* ERi = expected return of the investment
* Rf = risk-free rate (e.g., Treasury bill yield)
* βi = beta of the investment (sensitivity to market movements)
* ERm − Rf = market risk premium

The risk-free rate compensates for the time value of money; the beta and market risk premium compensate for systematic risk.

Understanding beta

Beta measures an asset’s volatility relative to the market:
* β > 1: asset is more volatile than the market (higher systematic risk)
* β < 1: asset is less volatile than the market
Multiplying beta by the market risk premium gives the additional return demanded for taking that systematic risk. Adding the risk-free rate yields the asset’s required return.

Example

Assumptions:
* Risk-free rate (Rf) = 3%
* Expected market return (ERm) = 8%
* Stock beta (β) = 1.3

Calculation:
ER = 3% + 1.3 × (8% − 3%) = 3% + 1.3 × 5% = 9.5%

If the present value of expected dividends and capital gains discounted at 9.5% equals the current price, the stock is fairly valued relative to its systematic risk.

CAPM, the Efficient Frontier, and the Security Market Line

• Efficient frontier (from Modern Portfolio Theory) shows the set of portfolios that maximize expected return for a given risk.
• Capital Market Line (CML) connects the risk-free rate with the market portfolio and represents optimal portfolios using total risk (standard deviation).
• Security Market Line (SML) is the CAPM expression plotted with beta on the x-axis — it depicts expected return as a function of systematic risk (beta). Individual assets or portfolios should lie on the SML if priced according to CAPM.

Practical uses

CAPM is useful for:
* Producing a benchmark discount rate to value assets
* Comparing required returns across securities or portfolios
* Evaluating whether a portfolio’s performance compensates for its measured systematic risk
* Informing asset allocation and the case for indexing (since market return is the baseline)

However, CAPM should be one tool among several when valuing assets or building portfolios.

Limitations and common criticisms

CAPM relies on simplifying assumptions that often don’t hold in practice:
* Unrealistic investor behavior: assumes all investors are rational, risk-averse, and share identical expectations.
* Single-period horizon and frictionless markets: assumes no taxes, transaction costs, or borrowing constraints and that all investors use the same time horizon.
* Reliance on beta: empirical evidence shows beta alone does not fully explain cross-sectional returns; different measures of risk and return patterns (size, value, profitability) matter.
* Market portfolio ambiguity: the true “market portfolio” is theoretical; indices (e.g., S&P 500) are imperfect proxies.
* Estimation issues: historical betas and risk premiums vary by period and look-back window; future cash flows and interest rates are uncertain.

Alternatives and extensions

Several models address CAPM’s empirical shortcomings:
* Arbitrage Pricing Theory (APT): multi-factor model using macroeconomic and firm-specific factors.
* Fama–French models: add size and value factors (3-factor) and later profitability and investment factors (5-factor) to explain returns.
* International CAPM (ICAPM): extends CAPM to international investments by incorporating currency and country-specific risks.

Bottom line

CAPM provides a simple, widely used framework for linking expected return to systematic risk. While its assumptions and reliance on beta limit its precision, CAPM remains valuable as a benchmark and comparative tool. Use it alongside other models and judgment when valuing assets or constructing portfolios.