In structor s Ma nual Chapter 12 Page 148

9. Determine the correlation between price movements of stock A and B using the forecasts of their rate of return and the assessments of the possible states of the world in the following table. The standard deviations for stock A and stock B are 0.065 and 0.1392, respectively. Before doing the calculation, form an expectation of whether that correlation will be closer to 1 or -1 by merely inspecting the numbers.

SOLUTION:

Expectation: correlation will be closer to +1.

E[「A] = .05*(-.02) + .15*(-.O1) + .60*(.15) + .20*(.15) = .1175, or, 11.75%

E[r B] = .05*(-.20) + .15*(-.10) + .60*(.15) + .20*(.30) = .1250, or, 12.50%

Covaria nce = .05*(-.02-.1175)*(-.20-.125) + .15*(-.01-.1175)*(-.10-.125) +

.60*(.15-.1175)*(.15-.125) + .20*(.15-.1175)*(.30-.125)=

.008163

Correlation = .008163/(.065)*(.1392) = .902

10. Analyze the “ expert ' s” answers to the following questions:

a. Question:

I have approx. 1/3 of my investments in stocks, and the rest in a money market. What do you suggest as a somewhat

“ safer ” place to invest another 1/3? I like to keep 1/3 accessible for emergencies. Expert ' s answer:

Well, you could try 1 or 2 year Treasury bonds. You ' d get a littlelUiwmtoreoyiiiesk.

b. Question:

Where would you invest if you were to start today?

Expert ' s answer:

That depends on your age and short-term goals. If you are very young -say under 40 -and don ' t need the money you ' re investing for a home or college tuitionsuch, you would put it in a stock fund. Even if the market tanks, you have time to recoup. And, so far, nothing has beaten stocks over a period of 10 years or more. But if you are going to need money fairly soon, for a home or for your retirement, you need to play it safer.

SOLUTION:

a. You are not getting a little bit more yield with no risk. The real value of the bond payoff is subject to inflation risk. In addition, if you ever

need to sell the Treasury bonds before expiration, you are subject to the fluctuation of selling price caused by interest risk.

b. The expert is right in pointing out that your investment decision depends on your age and short-term goals. In addition, the investment

decision also depends on other characteristics of the investor, such as the special character of the labor in come (whether it is highly correlated with the stock market or no t), and risk tolera nce. Also, the fact that over any period of 10 years or more the stock beats everyth ing else cannot be used to predict the future.