Greta has risk aversion of A $=3$ when applied to return on wealth over a one$-$year horizon. She is pondering two portfolios, the TSX$/$S&P Composite Index and a hedge fund, as well as a number of one$-$year strategies. $($All rates are annual and continuously compounded.$)$

The TSX$/$S&P Composite Index risk premium is estimated at $5\%$ per year, with a standard deviation of $20\%.$ The hedge fund risk premium is estimated at $10\%$ 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 TSX$/$S&P Composite Index 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 rounded to $2$ decimal places.$)$

S&P

$\%$

Hedge

$\%$

a$-2.$ What is the expected return on the portfolio? $($Do not round intermediate calculations. Enter your answers rounded to $2$ decimal places.$)$

Expected return

$\%$