Question

You are hired to make investment decisions for a large pension fund. You meet with representatives from the company to figure out what kind of choices to make. To get things started you try to figure out their risk preferences. You discuss the concept of risk and return with them to figure out what their level of risk aversion is.

You ask them if they would rather invest in a portfolio that offers an expected rate of return of 7% and a standard deviation of 15% or in the short term money market which offers a risk-free 2% rate of return. They say that they prefer the risky portfolio.

What is the maximum level of risk aversion for which the risky portfolio is still preferred to the risk free investment? What can you now say about the company’s employees’ risk preferences?

Answer 1

The maximum level of risk aversion for which the risky portfolio is still preferred to the risk free investment is 4.4.

Explanation:

Level of utility U =E(r) - 1/2 * A * σ2

Risk free investment: U = 0.02-1/2*A*0 = 0.02

Risky portfolio: U = 0.07-1/2*A*0.15□2= 0.07-A*0.01125

The utility levels of the risk free portfolio and the risky portfolio are equal for A=4.4 making it the highest level of risk aversion.

If A is smaller or equal to 4.4, the Pension fund will prefer the risky portfolio but since A=4.4 the pension fund is indifferent. As such, it can be predicted that the level of risk aversion A of the pension fund will lie below 4.4.

On a different note, if the risk aversion A was higher than 4.4 they would prefer the risk-free investment to the risky portfolio.