ps3solutions

ps3solutions - 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 #3 1. A worker whose utility function U ( W ) = W has received a job offer which pays $80,000 with a bonus. The bonus is equally likely to be $0, $10,000, $20,000, $30,000, $40,000, $50,000, or $60,000. Assume that initial wealth is $0. A. What is the expected value of this pay package? Solution: To compute the expected value of this pay package, we must solve the following equation: 1 () n ss s E W p W = (1/7)(80,000) + (1/7)(90,000) + (1/7)(100,000) + (1/7)(110,000) + (1/7)(120,000) + (1/7)(130,000) + (1/7)(140,000) = $110,000. B. What is the certainty equivalent of this pay package? Solution: There are two ways to compute the certainty equivalent. One method is to first compute the expected utility of this job offer, set the utility of the certainty equivalent equal to expected utility, and then solve for the certainty equivalent. The other method requires computing the risk premium using the Arrow-Pratt absolute risk aversion coefficient. First Method: 1 ( ( )) ( ) n s E U W p U W = (1/7)(80,000) .5 + (1/7)(90,000) .5 + (1/7)(100,000) .5 + (1/7)(110,000) .5 + (1/7)(120,000) .5 + (1/7)(130,000) .5 + (1/7)(140,000) = 330.27. Therefore, the certainty equivalent is 2 ( ( )) CEQ W E U W = 330.27 2 = $109,075.82. Second Method: First, compute variance:    2 2 1 n W s s s p W E W = (2/7)(30,000) 2 + (2/7)(20,000) 2 + (2/7)(10,000) 2 = 400,000,000. Next, compute the Arrow-Pratt absolute risk aversion coefficient: R A ( W ) = - U WW / U W = .25 W - 1.5 /.5 W - .5 = .5/ W . Next, compute the risk premium:  2 ( ) .5 ( ) A W R W = 400,000,000(.5)(.5)/110,000 = $909.09.
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PROBLEM SET #3 SOLUTIONS 2 Finally, compute the certainty equivalent:  ( ) ( ) CEQ W E W W = $110,000 - $909.09 = $109,090.91.
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ps3solutions - BAYLOR UNIVERSITY HANKAMER SCHOOL OF...

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