As we discussed in the chapter, futures can be used to eliminate systematic risk in a stock portfolio, leaving it essentially a risk-free portfolio. A portfolio manager can achieve the same result, however, by selling the stocks and replacing them with T-bills. Consider the following stock portfolio.
|
Stock
|
Number of Shares |
Price |
Beta |
|
Northrop Grumman
|
14,870
|
18.13
|
1.10
|
|
H. I. Heinz
|
8,755
|
36.13
|
1.05
|
|
Washington Post
|
1,245
|
264.00
|
1.05
|
|
Disney
|
8,750
|
134.50
|
1.25
|
|
Wang Labs
|
33,995
|
4.25
|
1.20
|
|
Wisconsin Energy
|
12,480
|
29.00
|
0.65
|
|
General Motors
|
14,750
|
48.75
|
0.95
|
|
Union Pacific
|
12,900
|
71.50
|
1.20
|
|
Royal Dutch Shell
|
7,500
|
78.75
|
0.75
|
|
Illinois Power
|
3,550
|
15.50
|
0.60
|
Suppose the portfolio manager wishes to convert this portfolio to a riskless portfolio for a period of one month. The price of a particular stock index futures with a $500 multiplier is 369.45. To sell each share would cost $20 per order plus $0.03 per share.
Each company's shares would constitute a separate order. The futures contract would entail a cost of $27.50 per contract, round-trip. T-bill purchases cost $25 per trade for any number of T-bills.
Determine the most cost-effective way to accomplish the manager's goal of converting the portfolio to a risk-free position for one month and then converting it back.