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 .

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