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# lect10 - The Game II Discussion Outline The Game II...

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The Game II Discussion Outline The Game II Discussion 1 / 13 ISOM 2500 Lect 10: Game II

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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

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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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lect10 - The Game II Discussion Outline The Game II...

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