Let us consider the two investments described in Table 7.3. The first table gives the percentage return of the two investments in five states of the world. Clearly, there is no state-by-state dominance between the returns of the two alternatives. The second table shows the two CDFs for relevant values of return. Note that the CDF does not bear any relationship with the states of the world. The CDF of \(r_{X}\) never exceeds the CDF of \(r_{Y}\) and is strictly less at one point (return 3%). Hence, \(r_{X}\) first-order stochastically dominates \(r_{Y}\).

Data From Table 7.3

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Table 7.3 An example of first-order stochastic dominance. State WI W2 W3 W4 W5 Probability 0.2 0.2 0.2 0.2 0.2 Return rx (%) 3 4 5 6 7 Return ry (%) 7 6 5 3 3 Return (%) 2 3 4 5 6 7 8 P{rx B} 0.0 0.2 0.4 0.6 0.8 1.0 1.0 P{ry } 0.0 0.4 0.4 0.6 0.8 1.0 1.0