Show me the steps to solve Problem $7-27$

Greta has risk aversion of $A=5$ 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 $7\%$ per year, with a standard deviation of

$19\%.$ The hedge fund risk premium is estimated at $11\%$ with a standard

deviation of $34\%.$ 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.

Calculate Greta's capital allocation using an annual correlation of $0\mathrm{.}3.$

$($Do not round your intermediate calculations. Round your answers

to $2$ decimal places.$)$