Question

The current risk-free rate is 4%. You look at two investments and see the following:

AAPL - Er = 10% with S.D 20%; XOM - Er 20% with S.D. 27%. If your current risk aversion is 2, you would find that:

1. Neither AAPL nor XOM is acceptable

2. Both stocks are acceptable

3. Only AAPL is acceptable

4. Only XOM is acceptable

Please show your method of calculation.

Answer 1

We can ascertain which stock is acceptable by using the Utility formula.

Utility = E(r) - 0.5 * A * standard deviation^2

where E(r) = Expected return

A= Aversion score

Utility for AAPL = 0.10 - 0.5 * 2*(0.20^2)

= 0.10 - 0.04

= 6%

Utility for XOM = 0.20 - 0.5*2* (0.27^2)

= 0.20 - 0.0729

= 12.71%

The ans is both the stocks are acceptable as both have positive utility although XOM has higher utility