Greta has risk aversion of $A=3$ and a $1-$year Investment horizon. She is pondering two portfollos, the S&P $500$ and a hedge fund, as

well as a number of $1-$year strategles. $($All rates are annual and continuously compounded.$)$ The S&P $500$ risk premium is estimated at

$9\%$ per year, with a standard deviation of $23\%.$ The hedge fund risk premlum Is estimated at $11\%$ with a standard devlation of $38\%.$ 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.

What should be Greta's capital allocation?

Note: Do not round your Intermedlate calculations. Round your answers to $2$ decimal places.