Consider the Arrows portfolio model. John has certain wealth (W), face a given interest rate of the riskless asset (r), and the probability distribution of the return of the risky asset x = (r1, r2; a, 1-a). r1 = 1%, and r2 = 5%, so that Pr(x = 1%) = a, Pr(x = 5%) = 1 a. Assume Ex > r, and that the optimal investment in the risky asset is less than his wealth. The utility function of John is u(x) = ln w, where w is wealth. If r1 increases from 1% to 2%

a). John faces an unfavorable first-degree stochastic dominance (FSD) shift in the distribution of the risky asset b). John faces an unfavorable second-degree stochastic dominance (SSD) change in the distribution of the risky asset c). John faces a favorable first-degree stochastic dominance (FSD) shift in the distribution of the risky asset d). dohn faces a mean preserving spread (MPS) on the distribution of the risky asset

Consider the Arrows portfolio model. Two individuals, John and Peter, have the same wealth, face the same interest rate of the riskless asset (r), and the same probability distribution of the return of the risky asset (x). Assume Ex > r, and that the optimal investment in the risky asset is less than their individual wealth. The utility function of John is u(x) = 4 ln x, and the utility function of Peter is v(x) = ln x, where x is wealth, ln denotes natural log.

a). We need more information to compare the optimal investment in the risky asset of Peter and John b). The optimal investment in the risky asset of John is less than the optimal investment in the risky asset of Peter c). The optimal investment in the risky asset of John is larger than the optimal investment in the risky asset of Peter d). The optimal investment in the risky asset of John is equal to the optimal investment in the risky asset of Peter

Consider the Arrows portfolio model. John has certain wealth (W), face a given interest rate of the riskless asset (r), and the probability distribution of the return of the risky asset (x). Assume Ex > r, and that the optimal investment in the risky asset is less than his wealth. The utility function of John is u(x) = 5 x1/2, where x is wealth. If wealth increases

a). We will expect that John will increase his optimal investment in the risky asset b). We will expect that John will not change his optimal investment in the risky asset c). We will expect that John will reduce his optimal investment in the risky asset d). With this information it is not possible to know what change will experience his optimal investment in the risky asset