Greta has risk aversion of $A=5$ and a $1-$year investment 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 $20\%.$ The hedge fund risk premium is estimated at $12\%$ with a standard deviation of $35\%.$ 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.

Required:

a$-1.$ Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset

allocation?

a$-2.$ What is the expected risk premium on the portfolio?

Complete this question by entering your answers in the tabs below.

Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset

allocation?

Note: Do not round intermediate calculations. Enter your answers as decimals rounded to $4$ places.

S&P

Hedge