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Q1. A UL student wants to invest $100,000 for 1 year. After analyzing and eliminating numerous possibilities, she has narrowed her choice to one of three alternatives: D1: Invest in a well-diversified portfolio of bonds; D2: Invest in a well-diversified portfolio of bonds and stocks; D3: Invest in a well-diversified portfolio of stocks. She believes that the payoffs associated with the alternatives depend on a number of factors, foremost among which are the new global trade frameworks. She concludes that there are three possible states of nature: S1: Significant decrease in global trade volumes; S2: Global trade volumes stay about the same; S3: Significant increase in global trade volumes. After further forecasting analysis, she determines the amount of profit she will make for each possible combination of a decision and a state of nature. The profits from each alternative investment are summarized in the following payoff table: PAYOFF TABLE ($) S1 S2 S3 D1 102,000 100,000 103,000 D2 90,000 108,000 110,000 D3 80,000 105,000 120,000 Still based on forecasting techniques, she also determines the probabilities of the states of nature: P (S1) = .35 P (S2) = .40 P (S3) = .25 a) Determine the optimal investment strategy. b) Determine the expected value of perfect information. However, after taking ECON2900Y, our student wants to improve her decision-making capabilities. She learns about Calgary Campus Consultants (CCC), who, for a fee of $ 1,000, will analyze the economic conditions and forecast the behaviour of global trade statistics over the next 12 months. CCC has been forecasting global trade frameworks for many years and so provides her with various conditional probabilities: I1: CCC predicts significant decrease in global trade volumes; I2: CCC predicts global trade volumes stay about the same; I3: CCC predicts significant increase in global trade volumes. We assume that the following assessments are available for these conditional probabilities: CCC MARKET RESEARCH S1 S2 S3 I1 P(I1|S1) = .6 P(I1|S2) = .1 P(I1|S3) = .1 I2 P(I2|S1) = .3 P(I2|S2) = .8 P(I2|S3) = .2 I3 P(I3|S1) = .1 P(I3|S2) = .1 P(I3|S3) = .7 c) Construct a decision tree for the complete investment decision problem. d) Determine the expected value of sample information. e) Determine the optimal investment strategy.

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