The Capital Asset Pricing Model (CAPM) is a cornerstone of modern finance theory. It provides a framework for understanding the relationship between the systematic risk of an asset and its expected return. This model is crucial for investors to determine the appropriate required rate of return for an investment, considering its risk relative to the overall market.

The CAPM is expressed by the following formula:

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

Where:

• $E(R_i)$ = Expected return of asset $i$
• $R_f$ = Risk-free rate of return
• eta_i = Beta of asset $i$ (a measure of its systematic risk)
• $E(R_m)$ = Expected return of the market
• $(E(R_m) - R_f)$ = Market risk premium

The risk-free rate represents the theoretical return of an investment with zero risk. In practice, it's often proxied by the yield on government securities (like U.S. Treasury bills) with maturities matching the investment horizon. This rate compensates investors for the time value of money.

Beta measures an asset's volatility relative to the overall market. A beta of 1 indicates the asset's price tends to move with the market. A beta greater than 1 suggests the asset is more volatile than the market, while a beta less than 1 indicates it's less volatile. A negative beta implies the asset moves inversely to the market.

The market risk premium is the excess return that investors expect to receive for investing in the market portfolio over the risk-free rate. It reflects the compensation demanded by investors for bearing the systematic risk of the market.

CAPM relies on several simplifying assumptions, which are often not met in the real world. These include:

• Investors are rational, risk-averse, and maximize their utility.
• Investors have homogeneous expectations about asset returns, volatilities, and correlations.
• Markets are perfectly competitive, with no transaction costs or taxes.
• Investors can borrow and lend any amount at the risk-free rate.
• Investors hold portfolios that are diversified across all available assets.

CAPM is used in various financial applications:

• Cost of Equity: Calculating the required rate of return for equity investors, which is a key component of a company's weighted average cost of capital (WACC).
• Investment Appraisal: Evaluating the attractiveness of potential investments by comparing their expected returns to their CAPM-derived required returns.
• Performance Evaluation: Assessing the performance of investment managers by comparing the actual returns of their portfolios to what CAPM would predict given their risk levels.