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 FX f ( X 2s ) F ( X 2s ) 2 1 n s s 1 1 n s s - 2 1 n s s $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   12 1 ( ) ( ) 0 n ss s F X F X  , this means that there is no second order stochastic dominance.
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PROBLEM SET #4 SOLUTIONS 2 B. Is either prospect preferred to the other according to the mean-variance rule?
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ps4solutions - BAYLOR UNIVERSITY HANKAMER SCHOOL OF...

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