Question

Suppose that an investor uses the following mean-variance utility function:

U(E(Rp), portfolio_variance)=E(Rp)-0,5*A*portfolio_variance
Dr Activitus Riskusson with a risk aversion coefficient of 7 currently owns a portfolio with an expected return of 8,5 per cent, and a volatility of 25,8 per cent. Suddenly, the volatility changes to 23 per cent. What is the lowest possible new expected return such that Dr Riskusson's utility remains at least on the previous level? Instructions: The answer is given in per cent using one decimal place. This means that a return of, say, 10.1 per cent, is expressed as 10.1. Do not add anything else, not even the "%" sign. Should there be intermediate steps in your calculations, please remember to keep a large number of decimal places in all intermediate calculations, as the final answer needs to be exact. Although the final answer is given in per cent, in this question all intermediate calculations should be done in decimal format in order to get it right.

Answer 1

. By setting up and solving an equation, we can find the new expected return that satisfies the utility function. The lowest possible new expected return is 79.2%.

Step-by-step explanation:

To find the lowest possible new expected return such that Dr. Riskusson's utility remains at least on the previous level, we need to use the mean-variance utility function and the given information.

The mean-variance utility function is given as U(E(Rp), portfolio_variance) = E(Rp) - 0.5 * A * portfolio_variance.

Dr. Riskusson's portfolio has an expected return of 8.5% and a volatility of 25.8%.

Let's assume the new expected return is x% and the new volatility is 23%.

Using the mean-variance utility function, we can set up the following equation:

x - 0.5 * 7 * 23 = 8.5 - 0.5 * 7 * 25.8

Simplifying the equation, we get:

x - 7 * 0.5 * 23 = 8.5 - 7 * 0.5 * 25.8

x - 80.5 = 8.5 - 90.3

x - 80.5 = -81.8

x = -1.3 + 80.5

x = 79.2%

Therefore, the lowest possible new expected return such that Dr. Riskusson's utility remains at least on the previous level is 79.2%.