Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) is a foundational concept in finance that describes the relationship between systematic risk and expected return for assets, particularly stocks. It is widely used to estimate the cost of equity and helps in understanding how to assess risk and formulate the expected return on investments.

Definition

CAPM posits that the expected return on an investment is equal to the risk-free rate of return plus a risk premium. The risk premium is determined by the beta of the investment (which measures the sensitivity of the investment’s returns to the returns of the market as a whole) multiplied by the expected market return minus the risk-free rate. The formula highlights that the return on an asset or a portfolio equals the risk-free return plus a premium for the risk taken over the risk-free rate.

Calculation

The CAPM formula is:

E(R_i​) = R_f ​+ β_i​(E(R_m​) − R_f​)

Where:

• E(R_i​) is the expected return on the capital asset,
• R_f​ is the risk-free rate,
• β_i​ is the beta of the investment,
• E(R_m​) is the expected return of the market,
• E(R_m​) − R_f​ is known as the market risk premium.

Example

Let’s assume the following:

• The risk-free rate (R_f) is 2%,
• The expected return of the market (E(R_m​)) is 10%,
• The beta ($\beta$) of a stock is 1.5.

Using the CAPM formula to calculate the expected return E(R_i​) of the stock:

E(R_i​) = 2% + 1.5(10% − 2%)

E(R_i​) $=2\%+1.5\times 8\%$

E(R_i​) = 2% + 12%

E(R_i​) $=14\%$

So, according to CAPM, the expected return on the stock is 14%. This means that, given its level of risk (as measured by $\beta$), investors should expect a 14% return on investment in order to be compensated for the risk taken over the risk-free rate.

Usage in Financial Analysis

CAPM is used extensively in financial analysis for:

• Estimating the cost of equity.
• Portfolio management for assessing the performance of assets relative to their risk.
• Corporate finance for capital budgeting and strategic planning.
• Determining the expected returns of securities given their risk profile and comparing these with observed returns to identify under- or overvalued investments.

CAPM provides a theoretical framework that explains how risk and return are related for securities and is crucial for the valuation of risky assets. However, it relies on several assumptions, including market efficiency and the idea that investors hold diversified portfolios, which may not hold true in all market conditions.