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 |
1.1 |
| H. J. Heinz |
8,755 |
36.13 |
1.05 |
| Washington Post |
1,245 |
264 |
1.05 |
| Disney |
8,750 |
134.5 |
1.25 |
| Wang Labs |
33,995 |
4.25 |
1.2 |
| Wisconsin Energy |
12,480 |
29 |
0.65 |
| General Motors |
14,750 |
48.75 |
0.95 |
| Union Pacific |
12,900 |
71.5 |
1.2 |
| Royal Dutch Shell |
7,500 |
78.75 |
0.75 |
| Illinois Power |
3,550 |
15.5 |
0.6 |
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.