Question

Assume that over some period, a CAPM was estimated. The results are Assume that over the same period, two mutual funds had the following results: 3. shown below Fund A Actual return-10% Beta 0.8 FundB Actual return-15% Beta-|.2 What can be said about the fund performance? R, = 0.06 + 0.19B

Answer 1

CAPM can be used to calculate a stock or a fund's expected returns given the amount of risk that it carries. The idea is that if a certain fund or stock carries a risk higher than the risk inherent in the overall market, it should provide returns that are higher than the market as well, in order to compensate for that risk. The measure of risk that is used in CAPM is beta. A beta of 1 implies that the fund in question has a risk comparable to the market as a whole and so, it is expected to yield a return equal to that of the whole market.

The CAPM equation in the given question is:

$\bar{R_{i}}=0.06 + 0.19\beta_{i}$

If we substitute beta values of the given funds, we can calculate a threshold return that each fund should have had in order to compensate for their risk. Using this threshold and the actual returns that each fund had, we can comment on each fund's performance. So, for fund A

$\bar{R_{A}}=0.06 + 0.19(0.8)=0.212$ or 21.2%

Similarly, for fund B

$\bar{R_{B}}=0.06 + 0.19(1.2)=0.288$ or 28.8%

Now, it can be seen that both funds have expected returns much higher than their actual returns. Fund A had an actual return of 10%, when it should have yielded 21.2% based on the estimated CAPM. Similarly B had an actual return of 15%, when it should have yielded 28.8%.

So, based on this, it can be said that both funds A and B under performed in the given period.