A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long$-$term government Required information

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A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long$-$term government

and corporate bond fund, and the third is a T$-$bill money market fund that yields a risk$-$free rate of $5\mathrm{.}5\%.$ The probability

distributions of the risky funds are:

The correlation between the fund returns is $0\mathrm{.}12.$

$[$YOU SHOULD USE EXCEL TO CHECK YOUR CALCULATIONS$]$

Required:

Compute the proportions of stock fund and bond fund of the optimal risky portfolio, and calculate the expected return and standard

deviation of the optimal risky portfolio. Assume that short sales of mutual funds are allowed. $($Do not round intermediate calculations.

Enter your answer as a percentage rounded to two decimal places.$)$and corporate bond fund, and the third is a T$-$bill money market fund that yields a rate of $8\%.$ The probability distribution of the risky funds is as follows:

Expected Return Standard Deviation

Stock fund $($S$)20\%30\%$

Bond fund $($B$)1215$

The correlation between the fund returns is $0\mathrm{.}10.$

Tabulate the investment opportunity set of the two risky funds $($use a similar table as below$)$:

Proportion

in Stock Fund Proportion

in Bond Fund Expected

Return Standard

Deviation

$0\mathrm{.}00\%100\mathrm{.}00\%$

$17\mathrm{.}3982\mathrm{.}61$

$20\mathrm{.}0080\mathrm{.}00$

$40\mathrm{.}0060\mathrm{.}00$

$45\mathrm{.}1654\mathrm{.}84$

$60\mathrm{.}0040\mathrm{.}00$

$80\mathrm{.}0020\mathrm{.}00$

$100\mathrm{.}000\mathrm{.}00$

If the risk free rate is $8\%,$ what is the optimal risky portfolio $($the tangency portfolio, i$.$e$.$ what are its weights, return and variance$)?$

Portfolio invested in the stock

Portfolio invested in the bond

Expected return

Standard deviation

What is the minimum variance portfolio?