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Capital Asset Pricing Model (CAPM)

Investment Framework Pricing Model Portfolio Analysis

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk (the risk that cannot be eliminated through diversification) and the expected return of an investment. It is one of the foundational models in modern finance.

CAPM provides a formula for calculating the return an investor should expect from an asset given its level of market risk. The model says that the only risk investors are compensated for is systematic risk, measured by a statistic called beta. Risk that can be diversified away, such as the risk specific to a single company, earns no additional expected return.

Definition

CAPM expresses expected return as the risk-free rate plus a premium for bearing market risk. That premium depends on how sensitive the asset is to overall market movements.

Formula

Expected Return = Risk-Free Rate + Beta × (Market Return − Risk-Free Rate)

Risk-Free Rate: The return on a theoretically riskless investment, typically approximated by the yield on short-term government Treasury bills.
Beta: A measure of an asset's sensitivity to market movements. A beta of 1.0 means the asset moves in line with the market. A beta above 1.0 means it is more volatile than the market, and below 1.0 means it is less volatile.
Market Risk Premium: The difference between the expected market return and the risk-free rate (Market Return − Risk-Free Rate). This represents the extra return investors demand for holding a diversified portfolio of risky assets instead of risk-free bonds.

Core Assumptions

CAPM is built on a set of simplifying assumptions. These assumptions make the math tractable, but they also limit the model's real-world accuracy. Understanding them is essential for knowing when the model applies and when it does not.

Investors are rational and risk-averse. All investors prefer higher returns and lower risk, and they make decisions by weighing expected return against variance (a measure of how spread out returns are).
Markets are efficient. All relevant information is already reflected in asset prices, and no investor can consistently earn excess returns through private information.
Single-period model. All investors plan over the same single time horizon. The model does not account for multi-period investing or changing conditions over time.
Homogeneous expectations. Every investor agrees on the expected returns, variances, and correlations of all assets. There is no disagreement about how risky or rewarding an investment is.
No transaction costs or taxes. Buying and selling assets is free, and tax consequences do not influence investment decisions.
Unlimited borrowing and lending at the risk-free rate. Any investor can borrow or lend any amount at the same risk-free interest rate.

How CAPM Is Used

Despite its simplifying assumptions, CAPM remains widely used in practice across several areas of finance.

Estimating cost of equity. Corporate finance teams use CAPM to estimate the return that shareholders require for holding a company's stock. This cost of equity feeds into discount rates for valuing projects and companies.
Evaluating portfolio performance. The difference between a portfolio's actual return and the return predicted by CAPM is called alpha. Positive alpha means the portfolio outperformed what CAPM expected given its level of risk. Negative alpha means it underperformed.
Security valuation. CAPM seeks to identify whether a security's expected return is consistent with its market risk. If the expected return implied by the current price is higher than the CAPM-predicted return for that level of risk, researchers may view the security as potentially undervalued, and vice versa.

Practical Example

Suppose the risk-free rate is 4%, the expected market return is 10%, and a stock has a beta of 1.3. The CAPM expected return for that stock is:

4% + 1.3 × (10% − 4%) = 4% + 1.3 × 6% = 4% + 7.8% = 11.8%

This means that, according to CAPM, investors should expect an 11.8% annual return from this stock to compensate them for its level of market risk. If the stock is expected to return more than 11.8%, it sits above the Security Market Line and may be undervalued. If less, it sits below the line and may be overvalued.

Known Limitations

Limitations to Keep in Mind

Single-factor model. CAPM uses only market beta to explain expected returns. Research has shown that other factors, including company size, valuation, and momentum, also drive returns. The Fama-French three-factor model extended CAPM to include size and value factors.
Assumes beta is stable. In practice, a stock's beta changes over time as the company's business evolves, its capital structure shifts, or market conditions change. Using a historical beta to predict future returns introduces measurement error.
Empirical challenges. Fama and French (1992) demonstrated that beta alone does not explain the cross-section of stock returns. Low-beta stocks have historically earned higher returns than CAPM predicts, and high-beta stocks have earned lower returns than predicted.
Assumes normal distributions. The model assumes returns follow a bell curve, with extreme outcomes being rare and symmetric. In reality, financial returns exhibit fat tails (extreme events happen more often than the bell curve predicts) and skewness (large losses can be more frequent than large gains).
Ignores transaction costs and taxes. Real-world investors face brokerage fees, bid-ask spreads, and tax consequences that affect net returns. These frictions can change which investments are optimal.

The Security Market Line

The Security Market Line (SML) is the graphical representation of CAPM. It plots expected return on the vertical axis against beta on the horizontal axis. The line starts at the risk-free rate (where beta equals zero) and slopes upward through the market portfolio (where beta equals one).

According to the model, every asset whose return is consistent with its risk should fall on the SML. Historically, assets plotting above the line have been viewed by researchers as potentially offering returns in excess of their measured market risk. Assets plotting below the line offer lower expected returns than predicted, suggesting they may be overpriced relative to the model's expectations. The vertical distance from the SML is the asset's alpha.

Academic Origin

CAPM was independently developed by three researchers: William F. Sharpe (1964), John Lintner (1965), and Jan Mossin (1966). All three built on Harry Markowitz's earlier work on mean-variance portfolio theory, which showed how investors can construct optimal portfolios by balancing expected return against risk.

Sharpe received the 1990 Nobel Memorial Prize in Economics (shared with Markowitz and Merton Miller) in part for his development of CAPM. The model's influence extends far beyond academia. It shaped how practitioners think about the relationship between risk and return and laid the groundwork for later multi-factor models, including the Sharpe ratio as a practical tool for measuring risk-adjusted performance.