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 $5\%$ 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 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 $0\mathrm{.}3?($Do not round your intermediate

calculations. Round your answers to $2$ decimal places.$)$