5.4 The Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is a key tool in finance for estimating expected returns on investments. It considers the relationship between risk and return, using factors like the risk-free rate, market return, and an asset's sensitivity to market movements.

CAPM helps investors and companies make informed decisions about investments and project valuations. By understanding an asset's expected return based on its risk level, financial professionals can better assess whether an investment is worth pursuing or if it's fairly priced.

Capital Asset Pricing Model Assumptions

Investor Behavior and Market Conditions

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• The CAPM assumes that investors are risk-averse and seek to maximize their expected utility
• Investors can borrow and lend at the risk-free rate and have homogeneous expectations about asset returns
• The model assumes that there are no transaction costs or taxes, all assets are infinitely divisible and perfectly liquid, and that the market is in equilibrium

Key Components of CAPM

• The risk-free rate is typically the yield on a government bond
• The expected return on the market portfolio represents the return of a theoretical portfolio that includes all risky assets in the market, weighted by their market capitalization
  • In practice, a broad market index like the S&P 500 is often used as a proxy for the market portfolio
• The beta coefficient of the asset measures its level of systematic risk

Expected Return Calculation with CAPM

CAPM Formula and Inputs

• The CAPM formula states that the expected return of an asset is equal to the risk-free rate plus the product of the asset's beta and the market risk premium (the difference between the expected return on the market and the risk-free rate)
  • The formula is expressed as: $E(R_i) = R_f + \beta_i * (E(R_m) - R_f)$, where $E(R_i)$ is the expected return of asset $i$, $R_f$ is the risk-free rate, $\beta_i$ is the beta of asset $i$, and $E(R_m)$ is the expected return of the market
• To calculate the expected return using the CAPM, one needs to determine the risk-free rate, the beta of the asset, and the expected return of the market
  • The risk-free rate can be obtained from the yield on a government bond with a maturity matching the investment horizon (10-year US Treasury bond)
  • The beta of the asset can be estimated using historical data or published sources (Bloomberg, Yahoo Finance)
  • The expected return of the market can be based on historical average returns or forward-looking estimates

Implications of CAPM for Expected Returns

• The CAPM implies that the expected return of an asset is linearly related to its beta, with higher-beta assets requiring higher expected returns to compensate for the increased systematic risk
• Assets with betas greater than 1 are expected to offer returns above the market return, while assets with betas less than 1 are expected to offer returns below the market return
• The model suggests that investors cannot earn excess returns above the CAPM-implied expected return without taking on additional systematic risk

Beta Coefficient and Systematic Risk

Interpreting Beta as a Risk Measure

• Beta is a measure of the sensitivity of an asset's returns to changes in the overall market and quantifies the systematic or non-diversifiable risk of an asset
  • A beta of 1 indicates that the asset's returns move in line with the market
  • A beta greater than 1 suggests that the asset is more volatile than the market, while a beta less than 1 implies that the asset is less volatile than the market
    • For example, if an asset has a beta of 1.2, it is expected to experience a 1.2% change in return for every 1% change in the market return
• Assets with higher betas are considered riskier because they tend to amplify the movements of the market, while assets with lower betas are less risky as they are less sensitive to market fluctuations

Systematic vs. Unsystematic Risk

• Beta only captures the systematic risk of an asset, which is the risk that cannot be eliminated through diversification
• Systematic risk arises from factors that affect the entire market, such as changes in interest rates, inflation, or economic growth
• Unsystematic or company-specific risk, such as management changes or product recalls, is not accounted for by beta and can be reduced through diversification

Cost of Equity Estimation with CAPM

Applying CAPM to Estimate Cost of Equity

• The cost of equity capital is the required rate of return that investors demand for investing in a company's equity, representing the opportunity cost of investing in the company's stock instead of alternative investments with similar risk
• The CAPM can be used to estimate the cost of equity capital by plugging in the company's beta, the risk-free rate, and the expected return on the market into the CAPM formula
  • To estimate a company's beta, one can regress the company's stock returns against the returns of a market index over a historical period (usually 3-5 years)
    • The slope of the regression line is the company's beta
  • Alternatively, published betas from financial data providers (Morningstar, Value Line) can be used, which are often adjusted for the tendency of betas to revert to the mean over time
• The risk-free rate and expected market return should be based on forward-looking estimates that align with the investment horizon and current market conditions

Applications of Cost of Equity in Corporate Finance

• The resulting cost of equity estimate can be used as an input in company valuation models, such as the dividend discount model or the discounted cash flow model, to determine the intrinsic value of the company's stock
• The cost of equity is also a key component of a company's weighted average cost of capital (WACC), which is used to evaluate investment projects and make capital budgeting decisions
  • WACC represents the overall required return on the company's assets and is calculated as the weighted average of the cost of equity and the after-tax cost of debt
• Companies strive to invest in projects that generate returns above their cost of equity to create shareholder value