Capital Asset Pricing Model (CAPM) Calculator

What is the Capital Asset Pricing Model (CAPM)?

The Capital Asset Pricing Model (CAPM) is a financial model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. It describes the relationship between systematic risk and expected return for assets, particularly stocks.

The CAPM Formula

The formula for the Capital Asset Pricing Model is:

\[E(R_i) = R_f + \beta_i(E(R_m) - R_f)\]

Where:

• \(E(R_i)\) = Expected return of investment
• \(R_f\) = Risk-free rate
• \(\beta_i\) = Beta of the investment
• \(E(R_m)\) = Expected return of the market
• \(E(R_m) - R_f\) = Market risk premium

Step-by-Step CAPM Calculation

1. Determine the risk-free rate (\(R_f\)), typically using the yield of a 10-year government bond.
2. Calculate or obtain the beta (\(\beta_i\)) of the investment, which measures the investment's volatility compared to the market.
3. Estimate the expected return of the market (\(E(R_m)\)), often using historical data or future projections.
4. Calculate the market risk premium by subtracting the risk-free rate from the expected market return: \(E(R_m) - R_f\)
5. Multiply the market risk premium by the investment's beta.
6. Add the risk-free rate to the result from step 5 to get the expected return of the investment.

Example Calculation

Let's calculate the expected return for an investment with the following parameters:

• Risk-free rate (\(R_f\)) = 2%
• Beta (\(\beta_i\)) = 1.2
• Expected market return (\(E(R_m)\)) = 8%

Plugging these values into the CAPM formula:

\[E(R_i) = 2\% + 1.2(8\% - 2\%) = 2\% + 1.2(6\%) = 2\% + 7.2\% = 9.2\%\]

Therefore, the expected return of the investment is 9.2%.

Visual Representation

This graph illustrates the CAPM. The blue line represents the Security Market Line (SML). The green point (Rf) is the risk-free rate, the red point (Rm) is the market return, and the yellow point (E(Ri)) is the expected return of the asset based on its beta.