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Winter 2008 - Newhouse's Class - Problem Set 1

# Winter 2008 - Newhouse's Class - Problem Set 1 - Econ 171...

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Econ 171 Winter 2008 Problem Set 1 1. You can invest in either a mutual fund or a money market fund. In the next year, the mutual fund will increase 20%, increase 10%, not change or decrease 10%. The money market fund will definitely increase by 5%. a. What actions are available to you? Invest in mutual fund (MF), Invest in money market fund. b. What states of nature could occur? Mutual fund increases 20% next year, Mutual fund increases 10% next year, Mutual fund does not change next year, Mutual fund decreases 10% next year. c. What are the possible outcomes? 20% increase, 10% increase, No change, 10% decrease, 5% increase. There is a 10% chance that the mutual fund will increase by 20%. There is a 60% chance the mutual fund will increase by 10%. There is a 20% chance that there will be no change in the mutual fund and there is a 10% chance that the mutual fund will decrease by 10%. In which fund would you invest given each of the below criteria. d. Maximax. Mutual fund. The maximum outcome in the mutual fund (+20%) is higher than the maximum outcome in the money market (+5%). e. Maximin. Money market. The minimum outcome in the money market (+5%) is higher than the minimum outcome in the mutual fund (-10%).

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f. Minimax regret. The regret matrix is given below. MF 20% increase MF 10 % increase MF does not change MF 10% decrease Invest in mutual fund 0 0 5%-0=5% 5%-(- 10)%=15% Invest in money market fund 20%- 5%=15% 10%- 5%=5% 0 0 Either. The maximum regret is 15% in both. g. First order stochastic dominance. The CDFs are graphed below. The black line is the CDF for the mutual fund. The blue line is the CDF for the money market. Neither graph is always equal or below the other. Neither option FOSD the other. h. The expected value criterion. The mutual fund. The expected value for the mutual fund is 20%(0.1) + 10%(0.6) + 0(0.2) + (-10%)(0.1) = 7%. The expected value for money market fund is 5%. -10% 0 5% 10% 20%
2. Repeat question 1 parts (a) – (c) if you have \$100 to allocate between the two funds. For instance, you now have the option of investing \$25 in the mutual fund and \$75 in the money market fund. You could do any other split where you invest a non-negative amount in each fund so that your total investment is \$100. a. If x is the amount invested in the mutual fund the available actions are ( x , 100 – x ) where 0 < x < 100.

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