What would be the capital allocation between the risk free asset and the optimal

Question

What would be the capital allocation between the risk free asset and the optimal risky investment portfolio for an individual with risk aversion coefficient of 3 ? If the initial investment is $100,000, how much money should the investor allocate to each of the 5 assets (risk free asset and 4 risky assets). RF RATE 2% YEARLY

Expected Avarage Return optimal investment portfolio in the risky global minimum variance portfolio. Weight Weight PG 0.010848 PG 0.2053 PG 0.336 Microsoft 0.014854 Microsoft 0.223 Microsoft 0.0065 BAC 0.011589 BAC 0.5203 BAC 0.632 Exxon 0.012043 Exxon 0.0514 Exxon 0.0255 1.000000 1.000000 Variance E[r] 0.01218804 E[r] 0.011372468 PG 0.004478 Portfolio Variance 0.003034717 Portfolio Variance 0.003082286 Microsoft 0.012820 Std Dev 0.055088262 Std Dev 0.055518341 BAC 0.005611 Sharp 0.190991196 Sharp 0.174821525 Exxon 0.002820 Covariance Cov(PG, Microsoft) -0.000649 Cov(PG, BAC) 0.000683 Cov(PG, Exxon) 0.000433 Cov(Microsoft, BAC) 0.001681 Cov(Microsoft, Exxon) 0.000804 Cov(BAC, Exxon) 0.000757

Explanation / Answer

To maximize utility,

Capital allocation between risky and risk free asset are calculated as below.

Weight of risk asset=E(RRp) +E(Rf)/3*(.055088262)2

=-.00781/.00910

=-.85824

-85.824% invested in risky asset and 185.824%in risk free asset.

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