Problem $7-26$

Greta has risk aversion of $A=3$ 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 $8\%$ per year, with a standard deviation of $18\%.$ The hedge fund risk premium is estimated at $10\%$ with a

standard deviation of $33\%.$ 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.

a$-1.$ Assuming the correlation between the annual returns on the two portfolios is $0\mathrm{.}3,$ what would be the optimal asset allocation? $($Do

not round intermediate calculations. Enter your answers as decimals rounded to $4$ places.$)$

Answer is complete but not entirely correct.

a$-2.$ What is the expected risk premium on the portfolio? $($Do not round intermediate calculations. Enter your answers as a decimal

rounded to $4$ places.$)$

Answer is complete but not entirely correct.