If your risk-aversion coefficient is A = 4.4 and you believe that the entire 1926-2015 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is U = E (r) - 0.5 * Aσ2

=> fraction of the portfolio that should be allocated to T-bills = 0.4482 = 44.82%.

=> fraction to equity = 0.5518 = 55.18%.

Explanation:

So, in this question or problem we are given the following parameters or data or information which are; that the utility function is U = E (r) - 0.5 * Aσ2 and the risk-aversion coefficient is A = 4.4.

The fraction of the portfolio that should be allocated to T-bills and its equivalent fraction to equity can be calculated by using the formula below;

The first step is to determine or Calculate the value of fraction to equity.

Hence, the fraction to equity = risk premium / (market standard deviation) ^2 - risk aversion.

= 8.10% : [ (20.48%) ^2 * 3.5 = 0.5518.

Therefore, the value for fraction of the portfolio that should be allocated to T-bills = 1 - fraction to equity = 1 - 0.5518 = 0.4482.