Question

Suppose the stock prices of Dreamy Cruise Line, Inc. (DCL) and Penny Saver (PS), a department store, are negatively correlated. If the economy is good, the value of DCL stocks will gain by 15%, and the value of PS stocks will drop by 5%. If the economy is bad, exactly the opposite will happen: DCL will drop by 5% and PS will gain by 15% in value. You have $100, which you can invest in these two stocks. You believe that the economy will be "good" and "bad" with equal probability. Suppose also that your utility function is ?(?) = ln ?, where w denotes net wealth.

a.) Use calculus to find the optimal way for you to diversify, i.e., how much to invest in each stock.

b.) Is your result in a.) surprising? Can you give some intuition for it?

Answer 1

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