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 $1-$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.

a$-1.$ Assuming the correlation between the annual returns on the two portfolios is indeed zero,

what would be the optimal asset allocation? $($Do not round intermediate calculations. Enter

your answers as decimals rounded to $4$ places.$)$

a$-2.$ What is the expected risk premium on the portfolio? $($Do not round intermediate

calculations. Enter your answer as decimals rounded to $4$ places.$)$