Question
An investor puts $15,000 into each of four stocks, labeled A, B, C, and D. The table shown below contains the means and standard deviations of the annual returns of these four stocks.
Stock Mean Annual Return Standard Deviation of Annual Return
A 0.15 0.05
B 0.18 0.07
C 0.14 0.03
D 0.17 0.06
a. Assuming that the returns of these four stocks are independent of each other, find the mean and standard deviation of the total amount that this investor earns in one year from these four investments.
b. Now assume that the returns of the four stocks are no longer independent of one another. Specifically, the correlations between all pairs of stock returns are given in the table below.
Correlations Stock A Stock B Stock C Stock D
Stock A 1.00 0.5 0.80 -0.55
Stock B 0.50 1.00 0.60 -0.30
Stock C 0.80 0.60 1.00 -0.75
Stock D -0.55 -0.30 -0.75 1.00
Find the mean and standard deviation of the total amount that this investor earns in one year from these four investments
c. Compare the results of Question “a” and “b”. Explain the differences in your answer.
d. Continue to assume that the returns of the four stocks are no longer independent of one another, and the correlations between all pairs of stock returns are as given in Question “b”. Now, suppose that this investor decides to place $20,000 each in stocks B and D, and $10,000 each in stock A and C. Find the mean and standard deviation of the total amount that this investor earns in one year from these four investments.
e. How do the mean and standard deviation of the total amount that this investor earns in one year change as the $60,000 in cash available is reallocated for investment? Provide an intuitive explanation for the changes you observe here.
1 answer