Please write your name at the top right corner of every page in this worksheet.

You graduated from UTEP and you were immediately hired at the Wealth Management division

of J$.$P$.$ Morgan. Your first assignment is allocate your client's wealth in a mix of J$.$P$.$ Morgan's

predetermined equity and bond portfolios. You want to do this by using the single index model. The risk$-$

free rate is $3\%.$ You obtained the following summary statistics from $2018-2023$ for the expected excess

return of both assets and the market:

You survey a client and you conclude that this client's level of "risk aversion" is commensurate

with a target standard deviation ${}_T=30\%.$ Using the information above, allocate your client's wealth

into an optimal portfolio, taking into consideration your client's desired risk for the portfolio.

Hints:

Compute the alphas and the betas of the portfolio.

Compute the expected excess returns $R_i,$ standard deviations $s,$ and correlation

coefficient $$ between the stock and bond funds.

Compute the simple returns $r_i=R_i+r_{rf}$

Using the simple returns for the stock and bond funds, compute the optimal risky

portfolio.

Combine the optimal risky portfolio and the risk$-$free rate to achieve the client's target

standard deviation.