Show me the steps to solve Problem $7-24$

Greta has risk aversion of $A=4$ when applied to return on wealth

over a one$-$year horizon. She is pondering two portfolios, the S&P

$500$ and a hedge fund, as well as a number of one$-$year strategies.

$($All rates are annual and continuously compounded.$)$ The S&P $500$

risk premium is estimated at $5\%$ per year, with a standard deviation of

$17\%.$ The hedge fund risk premium is estimated at $10\%$ with a

standard deviation of $32\%.$ The returns on both of these portfolios in

any particular year are uncorrelated with its own returns in other

years. They are also uncorrelated with the returns of the other

portfolio in other years. The hedge fund claims the correlation

coefficient between the annual return on the S&P $500$ and the hedge

fund return in the same year is zero, but Greta is not fully convinced

by this claim.

What should be Greta's capital allocation? $($Do not round your

intermediate calculations. Round your answers to $2$ decimal

places.$)$