Question

There are two stock investments, I or II, available in the market. Stock I generates net-payoffs of $80 with probability 0.3, $100 with probability 0.4; and $120 with probability 0.3. Stock II generates net-payoffs of $80 with probability 0.1, $100 with probability 0.8; and $120 with probability 0.1.

Scott’s utility function is U(I) = (100I)^0.5 , where I is income.

(i) Which stock should Scott select, I or II? Why?

(ii) What general point about risk-averse preferences have your illustrated?

Answer 1

(i)Both stocks have the same expected payoff which is 100 but the distribution of those payoffs differs which means that Scott should go for stock 1 if he wants to take on the higher risk of getting 80 dollars or he should go for stock 2 if he is okay with the possiblity of 120 dollars being the pay out only 10 percent of the times.Use Scott's utility function to determine which stock he should choose(Hint- He is risk averse)

(ii)Risk averse preferences means that investors prefer a minimum guaranteed return with a lower probablity of loss or lower returns and will not choose to go for risky ventures like stock 1 where the potential for 120 dollars as a return is 20 percent greater but so is the potential for 80 dollars as a return.