# Question 1.18 from Hull's Financial Risk management CAPM

A portfolio manager maintains an active portfolio with beta of 0.2. Risk-free rate is 5% The market return for a particular year is -30% The fund produced a result of -10%. He claimed the return was good given the circumstances - discuss.

So the expected return should be:

5% +0.2x(-30%-5%)=-2%

So the alpha is negative and this is bad performance.

I think there is not too much to say. At first glance it looks good if the manager loses $10\%$ if the whole market loses $30\%$.
But plugging the beta and the risk-free rate into the CAPM formula we see that we would have expected a loss of $2\%$ only. So the $10\%$ are much worse than expected.
There would be a lot more to say if we could take into account that the -2% is the $expected$ return, but the confidence interval for an actual (observed) return can be of any width, e.g. (-22%; 20%). However, we can't compute it here because the problem doesn't supply us with the variance of beta and the error term from the fitted CAPM.