9.3 Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is a crucial tool in finance for understanding the relationship between risk and expected return. It builds on portfolio theory by introducing the concepts of systematic risk and beta, helping investors assess how individual securities fit into a diversified portfolio.

CAPM introduces key elements like the risk-free rate, market risk premium, and beta to calculate expected returns. By comparing a security's expected return to its actual performance, investors can identify undervalued or overvalued assets and make informed investment decisions.

Beta and Systematic Risk

Measuring Systematic Risk with Beta

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• Beta coefficient measures the sensitivity of a security's returns to changes in the returns of the overall market
• Represents the systematic or non-diversifiable risk of a security
• Calculated by dividing the covariance between the security's returns and the market's returns by the variance of the market's returns
• Securities with betas greater than 1 are more volatile than the market (aggressive), while securities with betas less than 1 are less volatile (defensive)

Market Risk and Risk Premium

• Systematic risk, also known as market risk, refers to the risk inherent in the entire market that cannot be diversified away
• Affects all securities in the market to varying degrees depending on their beta
• Market risk premium is the excess return that investors require for holding a market portfolio over a risk-free asset
• Calculated as the difference between the expected return on the market portfolio and the risk-free rate (historical average of S&P 500 returns minus Treasury bill returns)

Portfolio Diversification and Market Portfolio

• Investors can reduce unsystematic risk through portfolio diversification but cannot eliminate systematic risk
• Market portfolio represents a theoretical portfolio that includes all risky assets in the market, weighted proportionally to their market capitalization
• Serves as a benchmark for evaluating the performance of individual securities and portfolios
• In practice, broad market indices like the S&P 500 or Russell 3000 are used as proxies for the market portfolio

Risk-Free Rate and Expected Return

Risk-Free Rate and Security Market Line

• Risk-free rate is the theoretical rate of return on an investment with zero risk, typically approximated by the yield on short-term government securities (Treasury bills)
• Represents the minimum return an investor expects for any investment because they will not accept additional risk without additional compensation
• Security Market Line (SML) is a graphical representation of the Capital Asset Pricing Model (CAPM) that shows the relationship between an asset's expected return and its beta
• SML equation: Expected return = Risk-free rate + Beta * (Market risk premium)

Expected Return and Alpha

• Expected return is the return an investor anticipates receiving on an investment, considering the asset's level of risk
• In CAPM, the expected return of a security is determined by the risk-free rate, the security's beta, and the market risk premium
• Securities that plot above the SML are considered undervalued because they offer higher returns than what their risk level suggests, while securities below the SML are overvalued
• Alpha measures the excess return of a security or portfolio relative to its expected return based on its level of systematic risk (beta)
• Positive alpha indicates that a security has outperformed its benchmark index on a risk-adjusted basis, while negative alpha indicates underperformance