The CAPM is a model that helps in determining the price of securities keeping in view the risk an investor takes, and the return that he will get from that particular investment.

## Formula of CAPM

The formula for calculating the Capital Asset Pricing Model is as follows:

ra = rf + βa(rm – rf), where…

- rf = risk free rate
- βa = Beta of the security
- rm = Expected market return

This formula takes into consideration some of the major factors while pricing as well as individual security. Basically it aims at determining the amount of risks taken by the investor in addition to the time value of the security being bought.

The risk free rate in the CAPM formula represents the money value of the time invested in a certain security. In other words, it encourages investors to invest their money in one long-term investment compensating them for this move, rather than having them invest in several short-term bonds overtime.

In addition to that, a risk assessment is also needed while investing in a certain security, which takes us to the second part of the formula –Beta. It assesses the amount of risk that an investor takes by investing in a certain security. In short, the Beta takes into account the volatility of the security overtime.

The Beta is then multiplied by the risk premium of the security. This is where the expected market return comes in. In order to see the risk premium on the security, simply subtract the risk free return of your security from the expected market return and you get the premium on your risk.

Placing the terminology into the CAPM formula, we get,

Expected return = Risk free rate – Risk (Risk Premium)

It is clear from the above termed formula that in order to get the expected returns on your investment, one of the major components to be considered is the amount of risk being taken.

## Example

Suppose that,

– rf = 5%

– β = 4

– rm = 12%

Putting the values,

5% + 4 (12% – 5%)

OR

0.05 + 4 (0.12 – 0.05)

Expected Return = 0.33 → 0.33*100 = 33%

This means that this particular stock will return at 33%.

## Should the investor go for this investment?

The answer entirely depends upon the expectations of the investor from the investment. If the expected return is worth the risk being taken, he should go for it.

For instance, in this case, if the expected return of the investor was 24%, and the formula shows a possible return of 33%, then investing in this security is a wise decision to take.

## Further Reading

- The capital asset pricing model (CAPM): the history of a failed revolutionary idea in finance? – onlinelibrary.wiley.com [PDF]
- The CAPM in thin experimental financial markets – www.sciencedirect.com [PDF]
- Heterogeneity in financial market participation: appraising its implications for the C-CAPM – academic.oup.com [PDF]
- CAPM risk adjustment for exact aggregation over financial assets – kuscholarworks.ku.edu [PDF]
- Multifactor models do not explain deviations from the CAPM – www.sciencedirect.com [PDF]
- The capital asset pricing model (CAPM), short-sale restrictions and related issues – www.jstor.org [PDF]
- Multi-beta CAPM or equilibrium-APT?: a reply – www.jstor.org [PDF]
- Risk and return: CAPM and CCAPM – www.sciencedirect.com [PDF]