You are given the following set of data:
|
Historical Rates of Return
|
|
Year
|
NYSE
|
Stock X
|
|
1
|
-26.5%
|
-14.0%
|
|
2
|
37.2
|
23.0
|
|
3
|
23.8
|
17.5
|
|
4
|
-7.2
|
2.0
|
|
5
|
6.6
|
8.1
|
|
6
|
20.5
|
19.4
|
|
7
|
30.6
|
18.2
|
a. Use a spreadsheet (or a calculator with a linear regression function) to determine Stock X"s beta coefficient.
b. Determine the arithmetic average rates of return for Stock X and the NYSE over the period given. Calculate the standard deviations of returns for both Stock X and the NYSE.
c. Assume that the situation during Years 1 to 7 is expected to prevail in the future (i.e., ^r x ¼ ¯rx; ^rM ¼ ¯rM, and both sX and bX in the future will equal their past values). Also assume that Stock X is in equilibrium-that is, it plots on the Security Market Line. What is the risk-free rate?
d. Plot the Security Market Line.
e. Suppose you hold a large, well-diversified portfolio and are considering adding to that portfolio either Stock X or another stock, Stock Y, which has the same beta as Stock X but a higher standard deviation of returns. Stocks X and Y have the same expected returns: ^r x ¼ ^ry ¼ 10:6%. Which stock should you choose?