Question

Which is riskier? Why?

2. (20pts) You have the option to choose between investments A and B represented in the following decision tree 0.5 $10000 0.2$5000 0.3 $2000 0.6 0.1 0.3 $13000 $5000 $500 a. (6pts) Assuming a risk-neutral attitude, what is the best decision? b. (5pts) Assume a risk-averse attitude with a utility function U(x) -In(x). What is the best decision?

Answer 1

a.

Expected monetary value for decision A = 0.5 * 10000 + 0.2 * 5000 + 0.3 * 2000 = $6600

Expected monetary value for decision B = 0.6 * 13000 + 0.1 * 5000 + 0.3 * 500 = $8450

For risk neutral, the best decision would be of maximum EMV which is decision B.

b.

Expected utility value for decision A = 0.5 * log(10000) + 0.2 * log(5000) + 0.3 * log(2000) = 8.58888

Expected utility value for decision B = 0.6 * log(13000) + 0.1 * log(5000) + 0.3 * log(500) = 8.399725

For risk averse, the best decision would be of maximum expected utility which is decision A

Decision B has lower expected utility than decision A. Thus, the riskier decision is Decision B.