Futures, the Easy Derivative

### By John SuccoJUN 13, 2003 12:21 PM

Editors note: This is the fifth in a six-part series. Click here to read part one, here for part two, here for part three and here for part four.

You can look at a futures contract as a formalized bet over a certain period of time on the price direction of its underlying cash instrument. A futures contract is merely a promise to deliver either the underlying cash instrument (or its value in cash) sometime in the future. It follows that if an investor expects the price of the cash security to rise during the duration of the contract, the investor will buy the futures contract; if the expectation is that the price will drop, the investor will be a seller.

Futures are used by speculators making these bets, but also by hedgers. For example, a producer of gold may want to lock in the current price of gold to ensure a profit based on production cost by selling gold futures in the amount of the gold expected to be produced over the life of the contract. If the price drops by the time the gold is to be sold, the loss in price will be offset by the gain in the futures contract.

There are futures contracts on just about every cash instrument (equity indexes, stocks, bonds, commodities, currencies, etc.). The one thing they all have in common is an expiration date and that they employ leverage: Buyers and sellers must only post a small amount of the contract’s value in margin. Each futures contract also has a denomination: each contract is worth some amount of the underlying cash instrument. The pricing of a futures contract is very straightforward as illustrated by the following example:

Let’s say a mutual fund manager receives \$3.6 million of new cash into her fund and decides to invest it in the S&P 500 (she wants immediate exposure to the market and will sell the contracts over time while buying certain stocks in the equivalent dollar amount). The manger can buy all 500 of the S&P 500 stocks for cash (very awkward) or very simply buy the equivalent amount of S&P 500 futures contracts. Assuming the S&P 500 cash index is at 900 and each futures contract is worth \$250, the manager will buy \$3,600,000/900/250 = 16 contracts. She decides to buy the March contracts that expire on the morning of March 21 (by then she will have sold the contracts and bought the stocks she thinks will outperform the market). If today is Jan. 17, then the contract has 62 days to expiration. During this period of time there are \$2.86 in dividends that will be paid per index share. The margin requirement for S&P 500 futures is \$18,000 per contract; the manager only needs to post \$18,000 x 16 = \$288,000.

Given all this information let’s calculate the price of the futures contract (fair value): The manager in buying the futures contract will not receive the dividends she would have if she had bought the stocks; she will be willing to pay \$2.86 less than the cash index of 900 (the amount of dividends per 900 cash index share). Because she only has to post margin, she can invest the net cash (\$3,600,000 - \$288,000 = \$3,312,000) at the risk free rate of 1.37%: she will essentially be willing to pay \$900 x .0137 x 62/365 = \$2.10 more than the cash index for the futures contract. So netting these cash flows out, the fair value of the futures contract with the cash index at 900 is 900 – 2.86 + 2.10 = 899.24. Because the dividends are high for the period and interest rates are low, the futures contracts will trade at a .76 discount to the cash index. This calculation will change each day as the dividend amounts change and interest rates fluctuate.

The most important aspect of futures is leverage. The more leverage in a system, the higher the potential for volatility.