5.4 The Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) provides a formula for estimating the expected return on an investment based on its risk. It connects a single measure of risk (beta) to the return investors should demand, making it one of the most widely used tools in portfolio management and corporate finance.

Capital Asset Pricing Model Assumptions

Investor Behavior and Market Conditions

CAPM is built on a set of simplifying assumptions. These assumptions don't perfectly reflect reality, but they allow the model to produce a clean, usable relationship between risk and return.

• Investors are risk-averse and want to maximize expected utility (they prefer less risk for a given level of return).
• All investors can borrow and lend at the risk-free rate.
• Investors have homogeneous expectations, meaning everyone agrees on the expected returns, variances, and correlations of all assets.
• There are no transaction costs or taxes.
• All assets are infinitely divisible and perfectly liquid.
• The market is in equilibrium, so all assets are fairly priced.

These assumptions are clearly unrealistic, but they're the foundation that makes the math work. In practice, CAPM still provides a useful benchmark even though real markets violate several of these conditions.

Key Components of CAPM

Three inputs drive the model:

• Risk-free rate ($R_f$): Typically the yield on a government bond, such as the 10-year U.S. Treasury. This represents the return you'd earn with zero risk.
• Expected market return ($E(R_m)$): The return on a theoretical portfolio containing all risky assets, weighted by market capitalization. In practice, a broad index like the S&P 500 serves as a proxy.
• Beta ($\beta_i$): A coefficient measuring how sensitive an asset's returns are to movements in the overall market. This captures the asset's systematic risk.

Expected Return Calculation with CAPM

CAPM Formula and Inputs

The CAPM formula calculates expected return as:

$E(R_i) = R_f + \beta_i \times (E(R_m) - R_f)$

Where:

• $E(R_i)$ = expected return of asset $i$
• $R_f$ = risk-free rate
• $\beta_i$ = beta of asset $i$
• $E(R_m) - R_f$ = market risk premium (the extra return the market earns above the risk-free rate)

The logic: you start with the risk-free rate (your baseline for doing nothing risky), then add a premium that scales with how much systematic risk the asset carries.

Step-by-step calculation:

1. Find the risk-free rate. Use the yield on a government bond with a maturity matching your investment horizon (e.g., the 10-year U.S. Treasury yield, say 4.0%).

2. Determine the asset's beta. Estimate it from historical return data or look it up on a financial data provider like Bloomberg or Yahoo Finance (e.g., $\beta = 1.3$).

3. Estimate the expected market return. Use historical average returns or forward-looking estimates (e.g., 10.0%).

4. Calculate the market risk premium. $E(R_m) - R_f = 10.0\% - 4.0\% = 6.0\%$

5. Plug into the formula. $E(R_i) = 4.0\% + 1.3 \times 6.0\% = 4.0\% + 7.8\% = 11.8\%$

So an asset with a beta of 1.3 should offer an expected return of 11.8% to compensate investors for its level of systematic risk.

Implications of CAPM for Expected Returns

• Expected return is linearly related to beta. Higher beta means higher required return.
• Assets with $\beta > 1$ are expected to return more than the market. Assets with $\beta < 1$ are expected to return less.
• A stock with $\beta = 0$ would theoretically earn just the risk-free rate.
• The model implies you cannot earn excess returns above what CAPM predicts without taking on additional systematic risk. In other words, there's no free lunch: more return requires more exposure to market-wide risk.

Beta Coefficient and Systematic Risk

Interpreting Beta as a Risk Measure

Beta measures how much an asset's returns move relative to the overall market. It quantifies the systematic (non-diversifiable) risk of an asset.

• $\beta = 1$: The asset moves in lockstep with the market.
• $\beta > 1$: The asset amplifies market movements. A stock with $\beta = 1.5$ is expected to rise 1.5% when the market rises 1%, and fall 1.5% when the market drops 1%.
• $\beta < 1$: The asset is less volatile than the market. A stock with $\beta = 0.6$ would move only 0.6% for every 1% market move.
• $\beta < 0$: Rare, but the asset moves opposite to the market.

Higher-beta assets are riskier because they magnify market swings. Lower-beta assets provide more stability but offer lower expected returns.

Systematic vs. Unsystematic Risk

CAPM only prices systematic risk, which is risk that affects the entire market and cannot be diversified away. Sources include changes in interest rates, inflation, recessions, and geopolitical events.

Unsystematic risk (also called company-specific or idiosyncratic risk) comes from factors unique to a single firm: a CEO departure, a product recall, a lawsuit. Because investors can eliminate unsystematic risk by holding a diversified portfolio, the market does not reward them for bearing it. That's why beta ignores it entirely.

This is a core insight of CAPM: only systematic risk earns a risk premium.

Cost of Equity Estimation with CAPM

Applying CAPM to Estimate Cost of Equity

The cost of equity is the rate of return investors require to hold a company's stock. It represents the opportunity cost of investing in that stock instead of another investment with similar risk.

CAPM gives a straightforward way to estimate it. You use the same formula, substituting the company's beta:

$R_e = R_f + \beta_{company} \times (E(R_m) - R_f)$

To get the company's beta, you have two main options:

1. Regression approach: Regress the company's historical stock returns against a market index (like the S&P 500) over 3-5 years. The slope of the regression line is the estimated beta.
2. Published betas: Use betas from financial data providers such as Morningstar or Value Line. These are often adjusted betas that blend the raw estimate toward 1.0, reflecting the tendency of betas to revert to the mean over time.

The risk-free rate and expected market return should be forward-looking and consistent with the investment horizon.

Applications of Cost of Equity in Corporate Finance

Once you have a cost of equity estimate, it feeds into several important applications:

• Valuation models: The cost of equity serves as the discount rate in the dividend discount model (DDM) and discounted cash flow (DCF) model to estimate a stock's intrinsic value.
• Weighted average cost of capital (WACC): The cost of equity is blended with the after-tax cost of debt, weighted by the company's capital structure, to produce WACC. This is the hurdle rate for evaluating investment projects and capital budgeting decisions.
• Value creation benchmark: Companies create shareholder value when they invest in projects that generate returns above their cost of equity. If a project's expected return falls below the cost of equity, it destroys value for shareholders.