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ps4solutions

# ps4solutions - BAYLOR UNIVERSITY HANKAMER SCHOOL OF...

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B AYLOR U NIVERSITY H ANKAMER S CHOOL OF B USINESS D EPARTMENT OF F INANCE , I NSURANCE & R EAL E STATE Dr. Garven Name ___SOLUTIONS_________ Problem Set #4 1. Consider two risky prospects, X l and X 2 , with payoffs given by: 1 0 with probability .25 10 with probability .50 20 with probability .25 X and 2 0 with probability 1/3 10 with probability 1/3 20 with probability 1/3 X Assume that your initial wealth ( W 0 ) is \$0, and your utility U ( W ) = W . A. Is either prospect preferred to the other according to first or second order stochastic dominance? SOLUTION: The FOSD rule says that investment i First Order Stochastic Dominates investment j if F ( X js ) F ( X is ) for all s. Computing cumulative probabilities across the various states for X 1 and X 2 , we find the following: Payoffs F ( X 1s ) F ( X 2s ) \$0 25.00% 33.33% \$10 75.00% 66.67% \$20 100.00% 100.00% Since F ( X 1s ) is not greater than or equal to F ( X 2 s ) for all s , it follows that there is no first order stochastic dominance. Next, we consider whether there is second order stochastic dominance (SOSD). The SOSD rule states that F ( X is ) Second Order Stochastic Dominates F ( X js ) if 1 ( ) ( ) 0. n js is s F X F X X s f ( X 1s ) F ( X 1s ) 1 1 ( ) n s s F X f ( X 2s ) F ( X 2s ) 2 1 ( ) n s s F X 1 1 ( ) n s s F X - 2 1 ( ) n s s F X \$0 25.00% 25.00% 25.00% 33.33% 33.33% 33.33% -8.33% \$10 50.00% 75.00% 100.00% 33.33% 66.67% 100.00% 0.00% \$20 25.00% 100.00% 200.00% 33.33% 100.00% 200.00% 0.00% Since 1 2 1 ( ) ( ) 0 n s s s F X F X , this means that there is no second order stochastic dominance.

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P ROBLEM S ET #4 SOLUTIONS 2 B. Is either prospect preferred to the other according to the mean-variance rule?
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