Breaking Down The CAPM Formula

CAPM might be a theoretically sound method for the investor to determine expected return in relation to the market. However, in practice, it might not be as easy.

There are many things we learnt in school that seem almost irrelevant today. So many theories, mathematical equations, and so on. This is because while indeed some of these things are practicable, a large chunk of them are all too theoretical and only useful in ideal situations.

A good example of this is the CAPM Formula. While the CAPM looks like an ideal way to ensure that an investor gets the best returns for his investment, experts have raised their doubts about CAPM's validity.

Reasons for this are embedded within elements of the CAPM formula. Some elements seem to be just too theoretical and ideal to work. First, the formula:

ra = rrf + Ba (rm – rrf)

Meaning:

– ‘ra’ refers to the required rate of return in an asset

– ‘rrf’ refers to the rate of return on a risk-free security (like treasury bills)

– ‘Ba’ is the beta of the asset (measure of investment risk)

– ‘rm’ is the market’s expected return/ market risk premium

Expected or Required Rate of Return

This is simply the rate of return that the investment is expected to yield on an asset or security over a period of time. It takes into cognizance all of the other variables of the equation including risk, returns on a risk-free security, and it is the result of the CAPM computation itself.

It can also be regarded as a long-term assumption that shows how an investment strategy will play out over its entire life.

Return on risk-free security

The return on a risk-free security is simply the interest rate that an investor is expected to earn on an investment that carries zero risk. For example, the rate used in real life can be said to be the interest paid on 3-month government Treasury bill.

In computing CAPM, the risk-free rate that is used has to correspond to the country where the investment is being made. The risk-free rate in the CAPM formula accounts for the time value of money and affects the entire formula in a few ways.

For one, a rise in the return on a risk-free security will force the market risk premium which is the actual expected return on your risky investment, to increase. This is only logical because there is no sense in a risk-free investment giving comparative returns to a risky one.

An increase will thus spur riskier assets to perform better than before so that investors can be compensated for the higher risk they are taking.

Beta

This is where most of the challenges arising from the relevance and validity of the CAPM formula is tested – and doubted. The beta is simply a measure of the risk element. That is, it shows how volatile the investment is in relation to its returns.

If you were solving a CAPM formula in class, you would probably see something like, “use a beta of 1.5.” in the real world, you have to measure the fluctuation of a security’s price changes in relation to the entire market.

To do this, you can run a straight-line statistical regression on data points showing price changes of a broad market index versus price changes in your risky asset. This is known as the stock’s sensitivity to market risk.

Another challenge is in determining the period the beta should be calculated for. Researchers have said that it doesn’t matter the length of period used in computing the beta (whether 5 months or 5 years). The rationale of the analyst is what matters.

The final result of your beta is thus analyzed: Where a stock is riskier than the market, it is said to have a beta that is greater than one. On the other hand, where a stock has a beta of less than one, the entire risk of the portfolio is reduced.

A beta of -1 means security has a perfect negative correlation with the market. When beta is compared with the equity risk premium, it shows the amount of compensation that equity investors need to get for taking on additional risk.

While some experts believe that there is a linear relationship between beta and individual stock returns, others believe it does not really determine the performance of stocks especially over long periods.

Market’s Expected Return/ Market Risk Premium

The last piece of the CAPM puzzle is the expected return which is the market risk premium. A simple way to look at this is that the expected return of the market minus the risk-free rate, would reveal the premium element of the investment that is borne out of taking additional risk.

The higher the volatility of an investment, the higher the market risk premium will be. As far as the CAPM formula goes, when the risk-free rate is added to the product of the stock’s beta and the market risk premium, the investor would be able to determine the rate of return to value the security with.

Even with the challenges that come with employing the CAPM formula, it can still serve as a good guide to determining the rate of return that should be expected from an investment in relation to the market.

Written by Lawretta Egba.