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Problem $7-03$

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:

Portfolio Actual Avg. Return Standard Deviation Beta

Manager Y $11\mathrm{.}10\%13\mathrm{.}70\%1\mathrm{.}50$

Manager Z $6\mathrm{.}50\%8\mathrm{.}70\%0\mathrm{.}90$

Additionally, your estimate for the risk premium for the market portfolio is $4\mathrm{.}00$ percent and the risk$-$free rate is currently $4\mathrm{.}50$ percent.

For both Manager Y and Manager Z$,$ calculate the expected return using the CAPM. Round your answers to two decimal places.

Manager Y:

$\%$

Manager Z:

$\%$

Calculate each fund manager$$s average $$alpha$($i$.$e$.,$ actual return minus expected return$)$ over the five$-$year holding period. Round your answers to two decimal places.

Manager Y:

$\%$

Manager Z:

$\%$

Choose the correct SML graph.

The correct graph is

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$.$

A$.$

The graph titled Security market Line shows the relationship between the expected rate of return on an asset and its systematic risk, as measured by beta. The horizontal axis labeled Beta ranges from negative $1$ to $2.$ The vertical axis labeled E$($R$)$ ranges from $0$ to $0\mathrm{.}15.$ The graph shows a line which passes through the following points: $(-1,0\mathrm{.}025)$ and $(1\mathrm{.}6,0\mathrm{.}129).$ There are $4$ data points labeled Y$,$ Z$,$ Alpha Y$,$ and Alpha Z$,$ each represented by a small circle and located at $(1\mathrm{.}5,0\mathrm{.}105),(0\mathrm{.}9,0\mathrm{.}081),(1\mathrm{.}5,0),(0\mathrm{.}9,0),$ respectively.

B$.$

The graph titled Security market Line shows the relationship between the expected rate of return on an asset and its systematic risk, as measured by beta. The horizontal axis labeled Beta ranges from negative $1$ to $2.$ The vertical axis labeled E$($R$)$ ranges from $0$ to $0\mathrm{.}15.$ The graph shows a line which passes through the following points: $(-1,0\mathrm{.}005)$ and $(1\mathrm{.}6,0\mathrm{.}109).$ There are $4$ data points labeled Y$,$ Z$,$ Alpha Y$,$ and Alpha Z$,$ each represented by a small circle and located at $(1\mathrm{.}5,0\mathrm{.}105),(0\mathrm{.}9,0\mathrm{.}081),(1\mathrm{.}5,0\mathrm{.}111),(0\mathrm{.}9,0\mathrm{.}065),$ respectively.

C$.$

The graph titled Security market Line shows the relationship between the expected rate of return on an asset and its systematic risk, as measured by beta. The horizontal axis labeled Beta ranges from negative $1$ to $2.$ The vertical axis labeled E$($R$)$ ranges from $0$ to $0\mathrm{.}15.$ The graph shows a line which passes through the following points: $(-1,-0\mathrm{.}015)$ and $(1\mathrm{.}6,0\mathrm{.}089).$ There are $4$ data points labeled Y$,$ Z$,$ Alpha Y$,$ and Alpha Z$,$ each represented by a small circle and located at $(1\mathrm{.}5,0\mathrm{.}105),(0\mathrm{.}9,0\mathrm{.}081),(1\mathrm{.}5,0\mathrm{.}111),(0\mathrm{.}9,0\mathrm{.}065),$ respectively.

D$.$

The graph titled Security market Line shows the relationship between the expected rate of return on an asset and its systematic risk, as measured by beta. The horizontal axis labeled Beta ranges from negative $1$ to $2.$ The vertical axis labeled E$($R$)$ ranges from $0$ to $0\mathrm{.}15.$ The graph shows a line which passes through the following points: $(-1,0\mathrm{.}005)$ and $(1\mathrm{.}6,0\mathrm{.}109).$ There are $4$ data points labeled Y$,$ Z$,$ Alpha Y$,$ and Alpha Z$,$ each represented by a small circle and located at $(1\mathrm{.}5,0\mathrm{.}105),(0\mathrm{.}9,0\mathrm{.}081),(0\mathrm{.}9,0),(1\mathrm{.}5,0),$ respectively.

Explain whether you can conclude from the information in Part b if:

either manager outperformed the other on a risk$-$adjusted basis.

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outperformed the

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on a risk$-$adjusted basis.

either manager outperformed market expectations in general.

Manager Y

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market expectations in general.

Manager Z

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market expectations in general.