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:

$$E(R_i)=2\mathrm{\%}+1.2(8\mathrm{\%}-2\mathrm{\%})=2\mathrm{\%}+1.2(6\mathrm{\%})=2\mathrm{\%}+7.2\mathrm{\%}=9.2\mathrm{\%}$$

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.