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Unformatted text preview: FINS 5513 Investments and Portfolio Selection University of New South Wales Semester 1 2012 Week 3 Russell Jame 1 Utility theory BKM 6.1 2 Utility Theory 3 Different assets will come from different PDFs and will have different: Expected returns Variances How individuals ‘value’ these different assets depends on their preferences Utility theory provides one way to measure preferences Utility Theory 4 A utility function measures an investor’s relative preference for different total levels of wealth Utility of wealth, x, is defined as U(x). Once U(x) is defined, the investment options can be ranked by the corresponding values of E[U(x)], ie expected value of utility. Utility is an ordinal (not cardinal) measure: you can rank preferences based on utility values, but the actual utility estimate is not Examples of Utility Functions 5 Risk Neutral: U(x)=x. In this case, the presentvalue of expected cash flows is the only value needed for the investment decision. Power: U(x) =bxb For some parameters b≤1, b≠0. b is a measure of risk aversion. If b=1, this is equivalent to risk neutral utility function. Graphs of the Power Utility Function with different Risk Aversions 6 2 4 6 8 10 12 Power (b=1) 2 4 6 8 10 12 Power (b=.5) 2 4 6 8 10 12 Power( b=.1) In all cases, utility is increasing in wealth. As b goes down, risk aversion increases, and the slope of the curve declines (i.e. The curve becomes more concave). Observations on Utility Functions 7 Utility is always increasing in wealth (U’(x) >0) More wealth is better. Often called the nonsatiation principle. With the exception of risk neutrality, utility is increasing at a decreasing rate (U’’(x) <0). There are diminish marginal returns to wealth. This is the intuition behind Risk Aversion . Motivating Risk Aversion 8 Risk aversion is related to the economic concept of diminishing marginal utility. When you are hungry, the marginal benefit of 1 hamburger (as opposed to 0) is much greater than the marginal benefit of having 2 hamburgers (as opposed to 1). Wealth also has diminishing marginal returns, so the marginal utility from your first dollar is more than the marginal utility of the 100th dollar. A practical utility function.. Power Utility Functions measure utility over wealth. An alternative approach is to measure utility in terms of expected returns and variances. Convenient for comparing investment options. U’(x) >0 suggests that higher expected returns increase utility. U’’(x)<0 suggests that higher variance reduces utility. 9 Utility Example You can invest in either MSFT or a risk free asset....
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This note was uploaded on 03/19/2012 for the course FINS 5513 taught by Professor Wangjianxin during the Three '10 term at University of New South Wales.
 Three '10
 WangJianxin

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