Problem $3$

You are an analyst for a large public pension fund and you have been assigned the task of evaluating two

different external portfolio managers $(Y$ and $Z).$ You consider the following historical average return,

standard deviation and CAPM beta estimates for these two managers over the past five years:

Additionally, your estimate for the risk premium for the market portfolio is $5\mathrm{.}00$ percent and the risk$-$

free rate is currently $4\mathrm{.}50$ percent.

a$.$ For both Manager $Y$ and $Z,$ calculate the expected return using the CAPM.

b$.$ Calculate each fund manager's average "alpha" $($actual minus expected return$)$ over the period.

Show graphically where the alpha statistics would plot on the security market line $($SML$).$

c$.$ Explain whether you can conclude from the information in part $($b$)$ if $(1)$ either manager

outperformed the other on a risk$-$adjusted basis, and $(2)$ either manager outperformed the

market.