# CAPM Calculator

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Instructions:
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You can use this CAPM Calculator to estimate the expected return using the Capital Asset Pricing model, providing the risk free return (\(r_f\)), beta (\beta) and market return (\(r_M\)):

## CAPM Calculator

The Capital Asset Pricing Model (CAPM) is an extremely popular model to estimate the expected return of a firm considering the market conditions, the risk free level of return and the risk of a company.

### What is the formula for the CAPM model?

The CAPM formula is very intuitive. It indicates that the expected return an investor should expect from a specific firm corresponds the risk free return, plus an amount that is proportional to the market premium. The proportionality constant is simply the beta of the company .

Mathematically, this is written as follows:

\[ r_s = r_f + \beta (r_M - r_f)\]where \(r_f\) is the risk-free return (usual the government bonds), \(\beta\) is the beta of the company (measuring its risk with respect to the market) and \(r_M - r_f\) is the market risk premium.

### Example of CAPM calculation?

Assume you have a stock that has a beta of 1.5, and that the risk-free return is 3%. Also, the return of the market is 8%. What is the expected return of the firm?

We have to use the CAPM model formula:

\[ r_s = r_f + \beta (r_M - r_f)\] \[ = 3% + 1.5 \times (8% - 3%)\] \[ = 3% + 1.5 \times 5%\] \[ = 3% + 7.5%\] \[ = 10.5%\]