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Purdue University
Krannert School of Management
MGMT 411: INVESTMENTS
Assignment #3
Solution
1. Suppose that your job is to hire two portfolio managers and let each one of them run his
investment strategy independently. Unfortunately, you know little about these managers, and
have no better guess than to assume that the monthly returns that each one’s portfolio will
generate are distributed with a mean of 1% and a standard deviation of 9% (i.e., the assets under
management have identical distributions). After hearing descriptions of their strategies, you
believe that it is reasonable to assume that the returns on their portfolios will be uncorrelated.
Your colleague says that since all managers are basically equivalent there is no point to hiring
more than one. Prove that a portfolio that is 50% invested in one manager ("manager 1") and
50% invested in another manager ("manager 2") would be strictly preferred by a riskaverse
investor over an investment in either one individually.
The mean return of the portfolio P is the valueweighted average of the means of the
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 Spring '09
 Clarke
 Management

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