Two specific questions about CAPM's assumptions and implications

Question

I have two questions about the CAPM model: the first is theoretical while the second is related to observed market data.

First question: let's say we have company A and company B and we want to estimate their expected returns within the CAPM model.

In this model the percentage of systematic risk is given by the $R^2$ of the regression of an investment's returns and market portfolio returns. Let's say that company A has 30% systematic risk while company B has 80% systematic risk. Then CAPM tells us that the Beta of an investment (market returns coefficient in the CAPM regression) is to be used as a scaling factor of the market portfolio expected extra-return in order to obtain the investment expected extra-return.

Let's now suppose that the two companies have the same Beta.

What are the implications of this problem in the CAPM model? Is the model suggesting that Company A has a much greater total risk than Company B?

Second question: if we use real data to estimate Betas and we obtain the following results:

• Beta = 1.41
• $R^2$=0.27
• CAPM estimated expected return = 11%

but the historical average return for the same period is 60% (with a volatility of 70%).

What would most likely be the CAPM assumption that did not hold?

Answer 1

1. If the two companies have indeed the same beta, then company A will have more total risk. Or in other words company A has more idiosyncratic risk (i.e. the risk that is not explained by the model);

2. If the historical average return is 60% (is this yearly?) and the CAPM implies an expected return of 11% for that company, that means that the company has a massive alpha (of 49%). There is likely either an error or an inconsistency in your calculations since that alpha seems massively large (unless the time-series is short).