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CFRM 415 - Introduction to Financial Markets
Assignment 5
Due: May 17, 2019 - 11:59 pm
Late submissions will receive an automatic grade of zero.
Question 1: i) Suppose an investor has initial wealth W0 and has the opportunity for an investment such
that the end-of-period wealth is W = W0 + H. If the investor uses exponential utiliy, show that WC W0
does not depend on W0.
ii) Suppose an investor has initial wealth W0 and has the opportunity for an investment such that the
end-of-period wealth is W = HW0. If the investor uses power utility show that WC
W0
does not depend on
W0.
Question 2: Let W, a random variable, represent the amount of future wealth held by an investor, and
let u1 and u2 be two different utility functions. The certainty equivalent of W under u1 is denoted W
and the certainty equivalent of W under u2 is denoted W. Using the definition of certainty equivalent
and the definition of equivalent utility functions, show that if u1 ～ u2 then W
You may assume
u1 and u2 are strictly increasing.
1