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 6% per year, with a standard deviation of 18%. The hedge fund risk premium is estimated at 10% with a standard deviation of 33%. 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 Gretas capital allocation using an annual correlation of 0.3. (Do not round your intermediate calculations. Round your answers to 2 decimal places.)

S&P =

Hedge =

Risk-free asset =

Now, I know how to calculate the capital allocation, but I am unsure how to factor in the annual correlation of 0.3. Can someone help with that. For the rest of the calculations that I came up with, please refer to my breakdown below.

Risk premium S&P				6.00%
Risk Premium on Hedge Fund				10.00%
Standard Deviation of S&P 500				18.00%
Standard Deviation of Hedge Fund				33.00%
Covariance between S&P 500 and Hedge Fund				0.00%
Proportion of S&P 500 in Optimal Risky Portfolio				66.85%
Proportion of Hedge Fund in Optimal Risky Portfolio				33.15%
Expected Return of Optimal Portfolio				7.33%
Standard Deviation of Optimal Portfolio				16.26%
Risk Aversion				3
Proportion invested in risky assets				92.34%
Proportion invested in Risk-free Asset				7.66%
% to be invested in S&P 500				61.73%
% to be invested in Hedge Fund				30.61%
% to be invested in Risk-free Asset				7.66%