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Final-08

# Final-08 - ECN 712 Fall 2008 Professor Schlee Final...

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ECN 712 Fall 2008 Professor Schlee Final Examination Instructions : Attempt all questions and write your answers in the blue books provided. There are 110 points on the exam, one for each minute of the exam period. Allocate your time carefully. 1. (25 points) Consider the two-asset portfolio problem, max α R + Z u ( w + αx ) dF t ( x ) , where w > 0 is the initial wealth, α is wealth invested in a risky asset with realized rate of return, x , and, for t = 0 , 1, F t is a cumulative distribution function (cdf) with bounded support. The safe asset has a rate of return of 0. (Note that investment in the safe asset can be negative–the asset can be sold short.) The vN-M utility u on R is thrice continuously differentiable with u 0 > 0 globally. For t = 0 , 1, let α t solve this problem and assume throughout that Z xdF t ( x ) > 0 . (a) (10) Show that α t > 0 (for either t = 0 or t = 1). (b) (15) Suppose that F 0 is strictly riskier than F 1 . 1 i. Identify a condition on u which ensures that α 1 α 0 (a decrease in risk raises investment). For a vN-M utility satisfying your condition, prove that indeed α 1 α 0 ii. Consider a vN-M utility with u 00 ( z ) < 0 and u 000 (

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Final-08 - ECN 712 Fall 2008 Professor Schlee Final...

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