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Unformatted text preview: The Game II Discussion Outline The Game II Discussion 1/13 ISOM 2500 Lect 10: Game II The Game II Discussion Three Investments Let Green, Red, and White denote three hypothetical investments with the following probability distributions for their annual gross returns R . 1 Die value 1 2 3 4 5 6 Probability 1/6 1/6 1/6 1/6 1/6 1/6 Green 0.8 0.9 1.1 1.1 1.2 1.4 Red 0.06 0.2 1 3 3 3 White 0.95 1 1 1 1 1.1 1 The value of an asset at the end of a year is the product of the gross return and the value at the start of the year. If you start with S dollars and finish with F dollars, then the gross return is R = F / S . We denote gross returns by "big R" to distinguish them from "little r" returns (sometimes called net returns). These types of returns are related by R = (1 + r). 2/13 ISOM 2500 Lect 10: Game II The Game II Discussion The expected values and standard deviations of the annual gross returns for each of these random variables are Investment Expected Value, E( R ) Std Deviation SD( R ) Green 1.083 0.20 Red 1.710 1.32 White 1.008 0.04 • Which of these investments is most appealing to you? • If you hold the same investment for 20 years, do you think your choice will be better than the other choices? 3/13 ISOM 2500 Lect 10: Game II The Game II Discussion • Suppose you begin with a $ 1,000 investment in each of Green, Red, and White. • The outcome from rolling three dice determines the annual outcome of the investment of matching color. • The value of the investment changes according to the gross return given in the appropriate column of the table. • For example, suppose that on the first roll of all three dice, you obtain ( Green 2 ) ( Red 5 ) ( White 3 ) Then the values of the investments after the first year are Green: $ 1,000 x 0.9 = $ 900 Red: $ 1,000 x 3 = $ 3,000 White: $ 1,000 x 1 = $ 1,000 4/13 ISOM 2500 Lect 10: Game II The Game II...
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This note was uploaded on 12/20/2011 for the course ACCT/MGMT 2010 taught by Professor A during the Spring '11 term at HKUST.
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