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 $7\%$ 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 $0\mathrm{.}3.$

Note: Do not round your intermediate calculations. Round your answers

to $2$ decimal places.