CAPM – Calculating the Return of an Asset or Portfolio

After evaluating and calculating the risk a portfolio contains, we need to conclude by evaluating and calculating its return.

It’s easier to understand with an example. If I’m watching a football game, and I bet $100 on the strong team playing against a much weaker team, I have a low risk of losing my money, but there is a risk. There’s a great chance most people would want to bet on the stronger team, therefore the return for those betting on the stronger team will be low, if the stronger team wins.

This happens because there is a high probability of a return, in other words, there’s less risk. Now let’s look at it from the opposite corner. There will always be someone willing to bet $100 on the weaker team, even with the understanding that there’s a high risk of loosing the money. However, since there are fewer people betting on the weaker team, if this team wins, which can happen, these people will have a high return on their investment.

The Portfolio Theory assists on calculating the risk, but does not calculate the return. Therefore, the theory was complimented by William Forsyth Sharpe and others with a model of pricing financial assets, better known as CAPM – Capital Asset Pricing Model. The Portfolio Theory together with the CAPM rewarded Markowitz and Sharpe with the Nobel Price in Economics in 1990.

The Capital Asset Pricing Model will assist us in calculating the return of each asset in the financial markets, so that, just like the betting example above, we will know what’s the expected return as well as the expected risk. This will take us to the efficient frontier, which was calculated with specific given returns, numbers that we will now explain how they were calculated.

The mathematical model in it itself is simple and based on the coefficient Beta, which correlates the return of an asset to the average of the markets.

Below is the formula:

Capital Asset Pricing Model

Where

E = Expected return of an asset or portfolio

Rf = Return of the risk-free asset

Beta = Coefficient that relates the return of an asset to the relation of the market’s average

Rm = Expected return of the market

A risk-free asset in the United States can be something like a Treasury Bond, where there is a fixed interest payment. Beta could be of a specific asset or portfolio, and Rm would be the expected return for the market. The subtraction (Rm – Rf) is usually a factor that does not vary much, which signifies the excess return of the market beyond the return that’s free of risk. For example, if in the last few years we observed that (Rm – Rf) = 10%, we apply this value to the next calculation. The Rf will be automatically given.

Let’s track back. Once we have calculated the expected return of an asset by using the CAPM, we must remember that this return is associated to a the risk of variable-income market. In a betting house it is known that the return of a bet on team A will be of 10%, and betting on team B the return will be of 100%, and since nothing comes for free, the lower return comes with a lower risk. The Stock Market works the same way, understanding that the risk will always exist.

Another part that isn’t calculated is the systemic risk, meaning, the overall risk of the system where assets are negotiated. This risk will always be present, because it is the risk of the market itself, therefore it isn’t calculated even though it exists.

Since the real life in the financial markets is much more complex than the examples shown here, the precision of the CAPM isn’t directly related to the facts and it is dependent of many factors, which brought many people to strongly criticize this model with a unending list of reasons. However, there isn’t another method to forecast returns that is more widely accepted than this one, so therefore, we will continue to use the Capital Asset Pricing Model, because it is better to have an estimate, than to not have anything. 

 
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