Question

Mary's risk aversion is 1.4. What percent of her savings should she invest in a portfolio with E(r)=13% and standard deviation of 20%, if the risk free rate to invest in is 4.7% and the rate at which money can be borrowed is 6.5%?

Answer 1

For this question, basis the data that has been provided, I am assuming that Mary has only two options to choose from in order to allocate her savings; the risky portfolio and the risk-free security.

1. In case of the risk-free security which yields 4.70%, since Mary's cost of borrowing itself is 6.50% she would avoid investing in the security because irrespective of her risk aversion, the investment wouldn't even be able to meet her borrowing cost. Thus the allocation of savings towards the risk free security should be 0%.

2. In case of the risky portfolio, we need to calculate the Utility of the portfolio, which adjusts the return on the portfolio for the risk associated with the same after factoring in the investor's risk aversion. Thus it gives us the utility of the investment for the investor after adjusting for the risk in line with the investor's risk aversion.

Utility = Expected return on the portfolio - 0.5 * Risk Aversion coefficient * (Standard Deviation)^2

= 13% - 0.5 * 1.4 * (20%)^2

= 13% - 0.5 * 1.4 * 0.04

= 12.972%

After factoring in the borrowing costs for Mary, the effective annual return will be 12.972% - 6.50% = 6.472%.

Since the net return after borrowing costs is positive, Mary should allocate 100% of her savings to this portfolio (since it is a portfolio and not a single security, the risks associated with individual securities are assumed to have been diversified across the portfolio).