3. Suppose there are only two period, this and next year. There are two states of the economy in the next year: good state and bad state, each happening with probability 0.5. Amy has a stable job and her income is constant at 500 unit of money across both states. Amy currently has an initial wealth of 2000 available for investing either in stock or in bond. Each unit of the stock, selling at a price of 1.3 now, pays off 2 (unit of money) in the good state and 1 (unit of money) in the bad state. The bond, on the other hand, guarantees an interest rate of 5 percent next year (regardless of states). Assume next year is the last relevant period, so consumption coincides with wealth in either state. (a) Suppose Amy does not face short-sale constraint. Describe, in terms of state-wealth, the budget set facing Amy. (b) Suppose Amy has a von-Neumann Morgenstern utility function of uA (c) = -2c-7. What is her optimal state-wealth combination? (c) What portfolio, i.e., stock and bond holdings, would Amy choose?
3. Suppose there are only two period, this and next year. There are two states of the economy in the next year: good state and bad state, each happening with probability 0.5. Amy has a stable job and her income is constant at 500 unit of money across both states. Amy currently has an initial wealth of 2000 available for investing either in stock or in bond. Each unit of the stock, selling at a price of 1.3 now, pays off 2 (unit of money) in the good state and 1 (unit of money) in the bad state. The bond, on the other hand, guarantees an interest rate of 5 percent next year (regardless of states). Assume next year is the last relevant period, so consumption coincides with wealth in either state. (a) Suppose Amy does not face short-sale constraint. Describe, in terms of state-wealth, the budget set facing Amy. (b) Suppose Amy has a von-Neumann Morgenstern utility function of uA (c) = -2c-7. What is her optimal state-wealth combination? (c) What portfolio, i.e., stock and bond holdings, would Amy choose?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:3. Suppose there are only two period, this and next year. There are two states of the economy in
the next year: good state and bad state, each happening with probability 0.5. Amy has a stable
job and her income is constant at 500 unit of money across both states.
Amy currently has an initial wealth of 2000 available for investing either in stock or in bond.
Each unit of the stock, selling at a price of 1.3 now, pays off 2 (unit of money) in the good state
and 1 (unit of money) in the bad state. The bond, on the other hand, guarantees an interest
rate of 5 percent next year (regardless of states). Assume next year is the last relevant period, so
consumption coincides with wealth in either state.
(a) Suppose Amy does not face short-sale constraint. Describe, in terms of state-wealth, the
budget set facing Amy.
(b) Suppose Amy has a von-Neumann Morgenstern utility function of uA (c) = -2c-¹. What is
her optimal state-wealth combination?
(c) What portfolio, i.e., stock and bond holdings, would Amy choose?
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