UtilityAnswersW07 - ConceptQuestions

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Concept Questions 1. Briefly explain why utility functions are increasing. Answer: Utility functions are increase to reflect that fact that investors prefer more wealth to less. 2. Briefly explain why concave utility functions represent risk averse investors. Answer: Concave utility functions represent risk-averse investors because they imply that an investor prefers a deterministic payoff of the expected value of a risky investment opportunity to the risky investment opportunity itself. More specifically, Jensen’s inequality states that for any concave function U and random variable X we have  E[U(X)] < U(E[X]).   This exactly states that the expected utility an investor has from the risky investment is less than the utility of a deterministic payoff of its expected value. Equivalently, this implies that the certainty equivalent of an investment is less than its expected value, so an investor would accept a payment less than the expected value of the investment to forego the investment opportunity.  3. Briefly explain the meaning of the axiom of independence of choice. Answer:  The axiom of independence of choice states that the choice between two alternatives should not depend on how those alternatives are presented. It means that only the alternatives themselves, not how they are phrased, or if they are part of a wider range of possibilities, should determine which alternative the investor prefers. 4. State and briefly explain one advantage and one disadvantage of mean-variance optimization when compared with expected utility maximization. Answer:  One advantage of mean-variance optimization is that it is easier. In particular, one needs to estimate only the first two moments of the probability distribution of returns on each instrument, as well as correlations between the instruments (this estimation can often be facilitated by the use of a factor model). On the other hand, expected utility maximization requires one to know the entire joint probability distribution of future returns in order to compute expected utilities. 
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One disadvantage of the mean-variance approach is that it is equivalent to maximizing a quadratic “utility” function, which is eventually decreasing (i.e. implying that at some point investors start to prefer less wealth to more). This can produce counterintuitive results, such as preferences for investments which are clearly inferior (see the answers to assignment four). 5. Briefly explain what is measured by the Arrow-Pratt coefficient of absolute risk
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This note was uploaded on 09/18/2011 for the course ACTSC 372 taught by Professor Maryhardy during the Winter '09 term at Waterloo.

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UtilityAnswersW07 - ConceptQuestions

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