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%.

• John faces an unfavorable first-degree stochastic dominance (FSD) shift in the distribution of the risky asset

• John faces an unfavorable second-degree stochastic dominance (SSD) change in the distribution of the risky asset

• John faces a favorable first-degree stochastic dominance (FSD) shift in the distribution of the risky asset

• John faces a mean preserving spread (MPS) on the distribution of the risky asset