©David Dubofsky and 6-1 Thomas W. Miller, Jr. Chapter 6 Introduction to Futures Because futures are so very similar to forwards, be sure that you have read Section 3.1. A futures contract is an agreement to buy (if you are long) or sell (if you are short) something in the future, at an agreed upon price (the futures price). Futures exist on financial assets (debt instruments, currencies, stock indexes), and real assets (gold, crude oil, wheat, cattle, cotton, etc.)

©David Dubofsky and 6-2 Thomas W. Miller, Jr. A Comparison of Futures Contracts and Forward Contracts Both types of contracts specify a trade between two counter-parties: –There is a commitment to take delivery of an asset (this is the buyer, or the long) –There is a commitment to deliver an asset (this is the seller, or the short) Many times, futures contracts and forward contracts are substitutes. However, at specific times, the relative costs, liquidity, and convenience of using one market versus the other will differ.

©David Dubofsky and 6-3 Thomas W. Miller, Jr. Futures and Forwards: A Comparison Table FuturesForwards

©David Dubofsky and 6-4 Thomas W. Miller, Jr. Other Unique Features of Futures Contracts Some futures contracts have daily price limits. Some futures contracts (Euro$, T-bills, stock index futures, currencies) have one specific delivery date; others (T-bonds, crude oil) give the short the option of choosing which day (usually in the delivery month) to make delivery. Some futures contracts (e.g., T-bonds) let the seller choose the quality of good to deliver, within a specified quality range. Some futures contracts (Euro$, stock index futures, feeder cattle) are cash settled. Note that a futures contract is like a portfolio of forward contracts (time series).

©David Dubofsky and 6-5 Thomas W. Miller, Jr. Futures Contracts Payoff Profiles profit F(1,T) The long profits if the next day’s futures price, F(1,T), exceeds the original futures price, F(0,T). The short profits if the next day’s futures price, F(1,T), is below the original futures price, F(0,T). Long futures Short futures F(0,T)

©David Dubofsky and 6-6 Thomas W. Miller, Jr. Reading Futures Prices (8/28/02)

©David Dubofsky and 6-7 Thomas W. Miller, Jr. Margin Requirements, I. Futures exchanges require good faith money from counter- parties to futures contracts, to act as a guarantee that each will abide by the terms of the contract. This money is called margin. Each futures exchange is responsible for setting the minimum initial margin requirements for their futures contracts. –The initial margin is the money a trader must deposit into a trading account (margin account) when establishing a futures position. –Many futures exchanges establish initial margin requirements by using computer algorithms, the most popular of which is called SPAN (Standard Portfolio ANalysis of risk).

©David Dubofsky and 6-8 Thomas W. Miller, Jr. Margin, August 1, 2001

©David Dubofsky and 6-9 Thomas W. Miller, Jr. Margin Requirements, II. SPAN uses historical price data to set initial margin to what is believed to be a worst case one-day price movement. An exchange can change the required margin anytime. Initial Margin will increase if price volatility increases, or if the price of the underlying commodity rises substantially. The margin required for trading futures differs from the concept of margin when buying common stock or bonds. –Margin for Common Stock: The fraction of the asset's cost that must be financed by the purchaser's own funds. The remainder is borrowed from the purchaser’s stock broker. –Margin for Futures: A good faith deposit, or collateral, designed to insure that the futures trader can pay any losses that may be incurred. Futures margin is not a partial payment for a purchase.

©David Dubofsky and 6-10 Thomas W. Miller, Jr. Margin Requirements, III. If the equity in the account falls to, or below, the maintenance margin level, additional funds must be deposited to restore the account balance to the initial margin level. E.g., suppose the initial margin required to trade one gold futures contract is $1000, and the maintenance margin level is $750. Then, an adverse change of $2.60/oz. will result in a margin call. Because one gold futures contract covers 100 oz. of gold, a decline of $2.60/oz. in the futures price will deplete the equity of a long position by $260. The trader with losses must then deposit sufficient funds to bring the equity in the account back to the initial margin of $1000. The margin that is deposited in order to meet margin calls is called variation margin. If the trader does not promptly meet the margin call, his FCM will liquidate the position.

©David Dubofsky and 6-11 Thomas W. Miller, Jr. Margin Requirements, IV. Note that once a trader receives a margin call, he must meet that call, even if the price has subsequently moved in his favor. For example, suppose the futures price of gold declines to a level that triggers a margin call on day t. On day t+1, the trader who is long a gold futures contract will receive a margin call, regardless of the futures price of gold on day t+1. Even if the gold futures price has substantially rebounded, the trader must still deposit variation margin into his account.

©David Dubofsky and 6-12 Thomas W. Miller, Jr. Margin Requirements, V. FCM's will often set initial and maintenance margin requirements at higher levels than the minimum requirements specified by the exchanges. Margin requirements also differ for different traders, depending on whether the position is part of a spread, a hedge or a speculative trade. Margin requirements on spreads and hedges are less than those on speculative positions. Hedgers must sign a hedge account agreement, declaring that the trades in the account will in fact be hedges as defined by the Commodity Exchange Act of 1936, and as specified by the CFTC.

©David Dubofsky and 6-13 Thomas W. Miller, Jr. Margin Requirements, VI. In a spread, a trader will be long one contract, and also be short another related contract. The two contracts may be on the same good, but for different delivery months (called a calendar spread, or an intermonth spread), or be on two similar goods for delivery in the same month (called an intercommodity spread, or an intermarket spread).

©David Dubofsky and 6-14 Thomas W. Miller, Jr. Marking to Market, Example. The entire daily resettlement process is illustrated with the following example. On November 6, 2001, you sell one gold futures contract for delivery in December You sell the contract at 10 AM, when the futures price is $285/oz. The initial margin requirement is $1000, and that sum of money is transferred from your cash account to your margin account. The settlement price at the close on November 6 is $286.40/oz. Your account is marked to market, and your equity at the close is $860. The futures price rose by $1.40/oz, and one contract covers 100 oz of gold; therefore, you have lost $140 on the short position.

©David Dubofsky and 6-15 Thomas W. Miller, Jr. Marking to Market, Table. On all subsequent days, the account is marked to market. If the futures price falls, your equity rises. If the futures price rises, your equity declines. Maintenance margin calls will have to be met if your account equity falls to a level equal to or below $750.

©David Dubofsky and 6-16 Thomas W. Miller, Jr. Basis Understanding the basis is a key to hedging. Basis = futures price - spot price (financial futures) Basis = spot price - futures price (agricultural futures) Basis = “net cost of carry” (see chapter 5) – F = S(1 + r) = S + rS = S + carry costs – F - S = carry costs – For stock index futures, F = S(1 + r) - FV(divs). – If we define the dividend yield over the life of the contract as d: F = S + rS - dS = S(1 + r - d) F - S = S(r - d) = net cost of carry

©David Dubofsky and 6-17 Thomas W. Miller, Jr. Convergence On the delivery date, S T = F T That is, at delivery (expiration) the basis equals zero. Question: What if S T did not equal F T ? BTW, this is not the last time we will ask one of these ‘arbitrage’ questions.

©David Dubofsky and 6-18 Thomas W. Miller, Jr. Types of Futures Contract Orders Every order must include: –Whether the trader wants to buy or sell –The name of the commodity –The delivery month and year of the contract –The number of contracts –The exchange on which they trade –Day order or “good-til-canceled” order –Market or limit order; if a limit order, then specify a limit price –There are other order types; see section 6.10.

©David Dubofsky and 6-19 Thomas W. Miller, Jr. Should Futures Prices Equal Forward Prices? Assume perfect markets. If interest rates are non-stochastic (i.e., known), then futures prices = forward prices. This is because futures can be transformed into forwards and the impact of the daily resettlement in futures contracts can be eliminated. If corr(  F  r) > 0, then futures prices > forward prices If corr(  F  r) < 0, then futures prices < forward prices

©David Dubofsky and 6-20 Thomas W. Miller, Jr. For More Information The major futures exchanges have websites. For links to some of them, see: The exchanges offer many free brochures, booklets and information. Call them (or go to their websites) to get catalogs. For example: – CBOT: (1-800-THE-CBOT) – CME: