The standard deviation of the market$-$index portfolio is $20\%.$ Stock A has a beta of $2\mathrm{.}80$ and a residual standard deviation of $30\%.$

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 sure rate of $5\mathrm{.}5\%.$ The probability distributions of the risky funds a

Expected Return Standard Deviation

Stock fund $($S$)16\%40\%$

Bond fund $($B$)10\%31\%$

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

Problem $6-8($Algo$)$

Required:

What is the expected return and standard deviation for the minimum$-$variance portfolio of the two risky funds?

Note: Do not round intermediate calculations. Round your answers to $2$ decimal places.

Scenario Probability Stock Fund

Rate of Return Bond Fund

Rate of Return

Severe recession $0\mathrm{.}1035\%14\%$

Mild recession $0\mathrm{.}2015\%20\%$

Normal growth $0\mathrm{.}4020\%13\%$

Boom $0\mathrm{.}3025\%10\%$

Required:

Calculate the values of mean return and variance for the stock fund.

Note: Do not round intermediate calculations. Round "Mean return" value to $1$ decimal place and "Variance" to $2$ decimal places.

Calculate the value of the covariance between the stock and bond funds.