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P A R T V I
Options, Futures, and Other Derivatives
Creating Synthetic Stock Positions: An Asset Allocation Tool
One reason stock-index futures are so popular is that they can substitute for holdings in
the underlying stocks themselves. Index futures let investors participate in broad market
movements without actually buying or selling large amounts of stock.
Because of this, we say futures represent “synthetic” holdings of the market portfo-
lio. Instead of holding the market directly, the investor takes a long futures position in
the index. The transaction costs involved in establishing and liquidating futures posi-
tions are much lower than taking actual spot positions. “Market timers,” who speculate
on broad market moves rather than on individual securities, are large players in stock-
index futures for this reason.
One means to market time, for example, is to shift between Treasury bills and broad-
based stock market holdings. Timers attempt to shift from bills into the market before
market upturns, and to shift back into bills to avoid market downturns, thereby profiting
from broad market movements. Market timing of this sort, however, can result in huge
trading costs. An attractive alternative is to invest in Treasury bills and hold varying
amounts of market-index futures contracts, which are far cheaper to trade.
The strategy works like this. When timers are bullish, they will establish many long
futures positions that they can liquidate quickly and cheaply when expectations turn
bearish. Rather than shifting back and forth between T-bills and stocks, they buy and hold
T-bills and adjust only the futures position.
You can construct a T-bill plus index futures position that duplicates the payoff to
holding the stock index itself. Here is how:
1. Purchase as many market-index futures contracts as you need to establish your
desired stock position. A desired holding of $1,000 multiplied by the S&P 500
index, for example, would require the purchase of four contracts because each
contract calls for delivery of $250 multiplied by the index.
2. Invest enough money in T-bills to cover the payment of the futures price at the
contract’s maturity date. The necessary investment is simply the present value of
the futures price.
Suppose that an institutional investor wants to invest $140 million in the market for
1 month and, to minimize trading costs, chooses to buy the S&P 500 futures contracts
as a substitute for actual stock holdings. If the index is now at 1,400, the 1-month
delivery futures price is 1,414, and the T-bill rate is 1% per month, it would buy 400
contracts. (Each contract controls $250
3
1,400 5 $350,000 worth of stock, and
$140 million/$350,000 5 400.) The institution thus has a long position on $100,000
times the S&P 500 index (400 contracts times the contract multiplier of $250). To cover
payment of the futures price, it must buy bills with 100,000 times the present value of
the futures price. This equals 100,000 3 (1,414/1.01) 5 $140 million market value of
bills. Notice that the $140 million outlay in bills is precisely equal to the amount that
would have been needed to buy the stock directly. (The face value of the bills will be
100,000 3 1,414 5 $141.4 million.)
Example 23.3
Synthetic Positions Using Stock-Index Futures
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C H A P T E R
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Futures, Swaps, and Risk Management
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The bills-plus-futures contracts strategy in Example 23.3 may be viewed as a 100%
stock strategy. At the other extreme, investing in zero futures results in a 100% bills
position. Moreover, a short futures position will result in a portfolio equivalent to that
obtained by short-selling the stock market index, because in both cases the investor gains
from decreases in the stock price. Bills-plus-futures mixtures clearly allow for a flexible
and low-transaction-cost approach to market timing. The futures positions may be estab-
lished or reversed quickly and cheaply. Also, because the short futures position allows the
investor to earn interest on T-bills, it is superior to a conventional short sale of the stock,
where the investor may earn little or no interest on the proceeds of the short sale.
The nearby box illustrates that it is now commonplace for money managers to use
futures contracts to create synthetic equity positions in stock markets. The article notes
that futures positions can be particularly helpful in establishing synthetic positions in
foreign equities, where trading costs tend to be greater and markets tend to be less liquid.
This is an artificial, or synthetic, stock position. What is the value of this portfolio at
the maturity date? Call S
T
the value of the stock index on the maturity date T and, as
usual, let F
0
be the original futures price:
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