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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.

Is there anything more that can be said about this apart from this naive calculation?

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  • $\begingroup$ It seems there are some typos in the question or solution, you find it here under: [1.14] $\endgroup$ – emcor Sep 15 '14 at 13:09
  • $\begingroup$ This is under further question. It is 1.18, sorry for the typo $\endgroup$ – Lost1 Sep 15 '14 at 13:36
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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.

Note however that there are various reason's why CAPM just does not hold. But in the text book world, where CAPM holds perferctly. The manager simply did worse than expected.

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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.

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