Interplanetary starship captain Jose Ching has been pondering the investment of his recent pilot's bonus of 1,000 stenglers. His choice is restricted to two securities: Galactic Steel, selling for 20 stenglers per share, and Nova Nutrients, at 10 stenglers per share. The future state of his solar system is uncertain. If there is a war with a nearby group of asteroids, Captain Ching expects Galactic Steel to be worth 36 stenglers per share. However, if peace prevails, Galactic Steel will be worth only 4 stenglers per share. Nova Nutrients should sell at a future price of 6 stenglers per share in either eventuality.
(a) Construct the payoff table that summarizes the starship captain's assessment of future security prices, given the two possible future states of the solar system. What are the prices of the pure securities implicit in the payoff table?
(b) If the captain buys only Nova Nutrients shares, how many can he buy? If he buys only Galactic Steel, how many shares can he buy? What would be his final wealth in both cases in peace? At war?
(c) Suppose Captain Ching can issue (sell short) securities as well as buy them, but he must be able to meet all claims in the future. What is the maximum number of Nova Nutrients shares he could sell short to buy Galactic Steel? How many shares of Galactic Steel could he sell short to buy Nova Nutrients? What would be his final wealth in both cases and in each possible future state?
(d) Suppose a third security, Astro Ammo, is available and should be worth 28 stenglers per share if peace continues and 36 stenglers per share if war breaks out. What would be the current price of Astro Ammo?
(e) Summarize the results of (a) through (d) on a graph with axes W1 and W2.
(f) Suppose the captain's utility function can be written as U = W1.8W2.2.If his investment is restricted to Galactic Steel and/or Nova Nutrients, what is his optimal portfolio (i.e., how many shares of each security should he buy or sell)?