Question No. 3 Suppose that you have $50,000 in wealth to invest for one year. You are considering buying stocks. There are many companies whose stock you could potentially buy. Suppose that each company you are considering is very risky: in one year, the company's stock will either be worth nothing, or worth $125,000, with each outcome equally likely (that is, each outcome has a probability of one half). Assume for simplicity that there are no dividends and no inflation. Assume that each companys fate is independent of each other companys fate. Finally, assume for now that there is no brokerage or other transactions costs to buying stocks.

(a) Suppose you invest your entire $50,000 in one company's stock. What is probability distribution of your wealth after one year? (In other words, what are the possible outcomes, and what are their probabilities)? What is the expected (or mean) value of your wealth after one year?

(b) Now suppose that split your savings between 2 companys stocks, buying $25,000 worth of each. What is the probability distribution of your wealth after one year? (What are the possible outcomes for wealth after one year, and what are the probabilities of each outcome?) What is the expected value of your wealth after one year? [HINT: recall that the companies' outcomes are independent--whether one company succeeds or fails does not depend on whether the other company fails. Thus the probability that both company A and company B both succeed (for instance) is similar to the probability that two coin flips will both come up heads].

(c) Explain why in this example it might be a better idea to be diversified--that is, to own two companies' stocks rather than just one company's stock. Does having two companies' stock increase the expected value of your portfolio? If not, then why is diversification a good thing in this example?