The Capital Asset Pricing Model (CAPM) is a fundamental financial theory used to determine the expected return of an investment based on its systematic risk. It provides a relationship between risk and return, helping investors and companies decide whether an asset is fairly valued. Here’s a breakdown of the CAPM model:
Contents
Formula:
E(Ri)=Rf+βi(E(Rm)−Rf)E(R_i) = R_f + \beta_i \left( E(R_m) – R_f \right)
Where:
- E(Ri)E(R_i): Expected return of the asset
- RfR_f: Risk-free rate of return (e.g., return on government bonds)
- βi\beta_i: Beta of the asset (systematic risk relative to the market)
- E(Rm)E(R_m): Expected return of the market portfolio
- E(Rm)−RfE(R_m) – R_f: Market risk premium
Explanation of Components:
- Risk-Free Rate (RfR_f):
- Represents the return on a risk-free investment.
- Typically based on government treasury bonds.
- Market Risk Premium (E(Rm)−RfE(R_m) – R_f):
- The additional return investors demand for taking on market risk.
- Reflects the difference between the expected return of the market and the risk-free rate.
- Beta (βi\beta_i):
- Measures an asset’s sensitivity to market movements.
- β=1\beta = 1: Asset moves in line with the market.
- β>1\beta > 1: Asset is more volatile than the market.
- β<1\beta < 1: Asset is less volatile than the market.
Key Assumptions:
- Investors are rational and risk-averse.
- Markets are efficient, meaning all information is reflected in stock prices.
- Investors can borrow or lend at the risk-free rate.
- Portfolio returns are normally distributed.
Applications of CAPM:
- Investment Decisions:
- Helps investors determine if an asset is undervalued or overvalued.
- Cost of Equity Calculation:
- Used in corporate finance to estimate the cost of equity in the Weighted Average Cost of Capital (WACC).
- Portfolio Optimization:
- Aids in balancing risk and return in portfolio management.
Criticism of CAPM:
- Simplistic Assumptions:
- Assumes all investors have access to the same information.
- Assumes a single-period investment horizon.
- Empirical Issues:
- The model doesn’t always hold in real-world data.
- Actual returns often deviate from those predicted by CAPM.
- Ignores Other Factors:
- Other models like the Fama-French Three-Factor Model include size and value factors, which CAPM excludes.
Example Calculation:
Assume:
- Rf=3%R_f = 3\% (risk-free rate)
- E(Rm)=8%E(R_m) = 8\% (market return)
- β=1.5\beta = 1.5 (asset beta)
E(Ri)=3%+1.5×(8%−3%)E(R_i) = 3\% + 1.5 \times (8\% – 3\%) E(Ri)=3%+1.5×5%=3%+7.5%=10.5%E(R_i) = 3\% + 1.5 \times 5\% = 3\% + 7.5\% = 10.5\%
The expected return on the asset is 10.5%.
