$12.$ You expect equities to have a real $($after inflation$)$ return of $5\%$ with a standard deviation of $20\%,$ and you expect fixed income securities to have a real return of $2\%$ with a standard deviation of $5\%.$ Assume the correlation of equities and fixed income is $25\%.$

a$.$ What is the expected return and risk $($standard deviation$)$ of a portfolio that is $60\%$ equity and $40\%$ fixed income?

b$.$ Suppose that you can tolerate a maximum risk of $10\%.$ What portfolio will provide that level of risk? What is its expected return?

Hints: The expected return of the portfolio is just the weighted average of the expected returns of the various assets.

The variance of the portfolio is just:

$\backslash$sigma $2=$ w$12\backslash$sigma $12+$w$22\backslash$sigma $22+2$ w$1$w$2\backslash$sigma $1\backslash$sigma $2\backslash$rho

where

wi $=$ weight on asset i

$\backslash$sigma i $=$ standard deviation of the expected return of asset i

$\backslash$rho $=$ correction between assets $1$ and $2$

If you have more than two risky assets, the variance of the portfolio is:

$\backslash$sigma $2=$ w$\backslash$Sigma wT

where w $=$ the vector of weights on the individual assets in the portfolio, $\backslash$Sigma is the covariance matrix, and wT is the transpose of the weights on the individual assets. In order to do this in Excel, you should use the MMULT function for matrix multiplication.

Another hint: Use Solver in Excel. Solver can be found on the Data tab in the Excel ribbon. However, it is not normally loaded in the default installation. You may have to go to File then Options then Add$-$Ins to load Solver, which comes with Excel.