Question

Given the following information, which investment(s) would risk-averse investors prefer if the risk-free rate is 5 percent?

		Value of Investment after one year if:
Investment	Cost Today	Market Return > 0% Probability: 40%	Market Return < 0% Probability: 60%
I	$18	$36	$8
II	$14	$12	$16
III	$15	$30	$5

I only

II only

III only

I and II only

Answer 1

Solution

Since the investors are risk-averse, they would prefer a smaller but sure rate of return, even though investing in riskier assets gives them a chance of getting higher returns.

The risk-free rate is 5%. Hence, the risk-averse investors will not be interested in investing in riskier assets unless their return is higher than the risk-free rate.

To calculate the probable return on the 3 investments, we will use the probabilities of the up-move and down-move.

The probability-weighted price on Investment I after one year is ((0.4 * $36) + ($0.6 * 8)) = $19.2. Hence the return on it is (($19.2/$18)-1)*100 = 6.67%

Similarly the probability-weighted price on Investment II after one year is ((0.4* $30) + ($0.6 * 5)) = $15. Hence the return on it is (($14.4/$14)-1)*100 = 2.86%

The probability-weighted price on Investment III after one year is ((0.4 * $36) + ($0.6 * 8)) = $19.2. Hence the return on it is (($15/$15)-1)*100 = 0%

Only investment I would yield higher returns than the risk-free rate after one year, on a probability-weighted basis. Hence, only Investment I would be preferred by risk-averse investors. Option 1 is the right answer