A friend wants your advice. His aunt recently left him $100,000 that he must invest in one or both of two different corporations. The current price per share of each is $100. Each stock has exactly the same expected return per share, $5, and the return on each has the same standard deviation, $3. Now, assume that the returns on the stocks are NOT independent. When one goes up the other, more often than not, goes down. The correlation between the return on a share of the first stock and the return on a share of the second stock is -0.20.
Since each stock has the same expected return and standard deviation, your friend has tentatively decided to buy 1000 shares of the first corporation. An alternative would be for your friend to diversify by buying 300 shares of the first corporation and 700 shares of the second corporation.
a. If your friend buys 1000 shares of the first corporation, what will be the mean of the annual return of this portfolio?
b. If your friend buys 1000 shares of the first corporation, what will be the standard deviation of the annual return of this portfolio?
c. If your friend buys 300 shares of the first corporation and 700 shares of the second corporation, what will be the mean of the annual return of this portfolio?
d. If your friend buys 300 shares of the first corporation and 700 shares of the second corporation, what will be the standard deviation of the annual return of this portfolio?