Question

1. Given the following investment opportunities, with , and O2 representing two states of nature in and assuming that the states probabilities II, and Il2 are equal to 0.6 and 0.4 respectively: Investment No. Initial investment -1000 -1000 - 1000 011 1250 1300 1300 02 1750 1500 1800 2 a. Does any of this investments state-by-state dominate the others? b. Does any of this investments mean-variance dominate the others? c. Is there any contradiction between these two dominance measures? Which one is stronger?

Answer 1

Kindly refer to the attached excel for all the calculations:

a. After multiplying the state probabilities with the expected payoffs, we notice that Investment 3 dominates other investments state-by-state.

b. Upon using the variance formula for each of these investments, we notice that Investment 2 has the maximum variance with Investments 1 and 3 having the same, higher variance.

c. There is no direct contradiction between the two. Investment 3 has the maximum payoffs but also exhibits the maximum variance in its states.

Investment number 1,250 1,300 1,300 02 1,750 1,500 1,800 Probabilities 0.6 0.4 750 780 Expected payoffs 700 600 720 780 62,500 Variance 10,000 62,500