Suppose that two firms are competing for a government contract and have equal chance of winning. Because only one firm can win, the other must lose, so the two events are perfectly negatively correlated. You can buy a share of stock in either firm for N$20. The stock of the firm that wins the contract will be worth N$40, whereas the stock of the loser will be worth N$10. If you buy two shares of the same company your share are going to be worth either N$80 or N$20 after the contract awarded.
(a) What is their expected value?
(b) What is variance?
(c) Now suppose that the values of two stocks are uncorrelated. Each of the two firm has 50% chance of getting government contract, and whether one firm gets a contract does not affect the other firm wins one. Because of this independence, the chance each firm’s share is worth N$40 is ¼ , the chance that each one is worth N$40 and the other worth N$10 is ½ , and the chance that each is worth N$10 is ¼ . If you buy one share of each firm, what is the expected value? What is the variance and comment?