APPENDIX 4A: CONTINUOUS COMPOUNDING
5.3 FUTURES CONTRACTS
The major problem with forward contracts is that forwards are pure credit instru- ments. Whichever way the spot rate of exchange moves, one party has an incentive to default. Consider a forward contract on pounds sterling at a rate of $1.5000/£.
If the pound appreciates to $1.6000/£ on the expiration date, then whoever has agreed to sell pounds at the forward rate of $1.5000/£ has an incentive to default.
If the pound depreciates to $1.4000/£, then the party obliged to buy pounds at the forward rate of $1.5000/£ has an incentive to default.
The Futures Contract Solution
Futures contracts provide a remedy for the default risk inherent in forward contracts through the following conventions (see Figure 5.3):
Forwards Exchange-traded futures
1. Location Bank Exchange floor or electronic trading system
2. Maturity Negotiated; CME contracts expire on the Monday before the third Wednesday typically from of the month; last trading day is the previous Friday; seller 1 week to 10 years chooses when to make delivery during the delivery month 3. Amount Negotiated In increments of a contract amount, such as €125,000 for euros
on the CME; “open interest” = number of contracts 4. Fees Bid-ask spread Commissions charged per “round turn”
(usually about $30 per contract on the CME)
5. Counterparty Bank Exchange clearinghouse
6. Collateral Negotiated; depends Purchaser must deposit an initial margin (bank letter of credit, on customer’s cash, T-bills, etc.); contract is then “marked-to-market” daily; an credit risk initial margin and a maintenance margin ensure daily payment 7. Settlement Nearly all Less than 5% settled by physical delivery; most positions are
closed early by buying the opposite futures position;
open interest is then netted out
8. Trading Banking hours The CME’s Globex trading platform allows 24-hour trading;
hours (possibly 24 hours) open outcry trade is during exchange hours only
FIGURE 5.3 Forwards versus CME Futures Contracts.
■ An exchange clearinghouse takes one side of every transaction.
■ Futures contracts are marked-to-market on a daily basis.
■ An initial margin and a maintenance margin are required.
Futures have less default risk than forwards.
With an exchange clearinghouse on one side of every transaction, futures market participants are ensured daily settlement of their contract by the clearinghouse. The exchange insures itself against loss through a margin requirement and by settling changes in the value of each contract on a daily basis, ormarking-to-market. The clearinghouse matches buy and sell orders and then takes one side of each contract, so that it has a zero net position in each contract. Consequently, at any given time the clearinghouse faces at most one day’s risk in each contract.
A margin account protects the broker, although margin accounts on futures perform this function in a different way than margin accounts on stock do. A margin account on an equity account allows an equity investor to borrow from the broker in order to buy additional shares of stock. A maintenance margin serves as a down payment on the price of the stock, with the difference between the price of the stock and the maintenance margin borrowed from the broker. The borrower must pay back the broker when the stock position is liquidated. On a futures contract, the margin is not a down payment on a loan; rather, it is a performance bond ensuring that the customer will make required payments as the contract is marked-to-market.
Suppose a 125,000 futures contract is purchased at a price of $1.1754/ on the CME. The purchaser must deposit an initial margin, although no dollars or euros are exchanged upon purchase of the contract. If the futures price rises by $0.0010/ to
$1.1764/ at the close of trading on the following day, then the clearinghouse adds ($0.0010/ )( 125,000) =$125 to the purchaser’s margin account. If the contract
price subsequently falls back to $1.1754/ , $125 is transferred from the customer’s margin account to the clearinghouse. This daily marking-to-market ensures that the clearinghouse’s exposure to currency price risk is limited to the gain or loss from a single day’s change in price.
Maintenance margins and price limits for futures are determined by the indi- vidual futures exchanges and vary by contract and by exchange. The CME has no price limits during the first 15 minutes of trade. A schedule of expanding price limits follows the 15-minute opening period. Limits also are waived during the last 15 min- utes of trade for expiring contracts. Margin requirements and daily price limits are revised periodically by the exchanges according to volatility in the underlying asset.
Suppose the maintenance margin is $2,000 for a 125,000 futures contract on the CME. The minimum dollar price tick of one basis point (0.01 percent) on the CME euro futures contract is worth ($0.0001/ )( 125,000/contract) =$12.50 per contract. If the maximum price move before a limit is reached is 100 basis points (plus or minus 1 percent), then the value of the contract can move up or down by
$1,250. Since the $2,000 maintenance margin is greater than the daily price limit of
$1,250, the clearinghouse can recoup 1-day price variations (up to the price limit) in the futures contract. Maintenance margins are set large enough to cover all but the most extreme price movements. If an investor cannot meet a margin call, the exchange clearinghouse cancels the contract and offsets its position in the futures market on the following day.
Don’t be fooled by price limits. Just because futures prices are artificially limited to a trading band around the current price does not mean that true prices can’t exceed these bounds. If the true price moves more than the price limit in a single day, default risk exists on the difference. Fortunately, since the exchange clearinghouse is on the other side of every transaction, the holder of a futures contract can rest assured payment will be received. The futures exchange clearinghouse further reduces its risk by requiring that futures be traded through a brokerage house (called a ‘‘futures commission merchant’’ in the United States) rather than an end customer. If an end customer cannot meet its margin call, it is the broker rather than the clearinghouse that bears the consequences.
A Futures Contract as a Portfolio of One-Day Forward Contracts
Because futures are marked-to-market each day, a futures contract can be viewed as a bundle of consecutive 1-day forward contracts. Each day, the previous day’s forward contract is replaced by a new 1-day forward contract with a delivery price equal to the closing (or settlement) price from the previous day’s contract. At the end of each day, the previous forward contract is settled and a new 1-day forward contract is created. The purchaser of a futures contract buys the entire package. A 3-month futures contract, for instance, contains 90 renewable 1-day forward contracts. The futures exchange clearinghouse renews the contract daily until expiration so long as the maintenance margin is satisfied. On the investor’s side of the futures contract, an offsetting transaction can be made at any time to cancel the position.
A futures contract is a portfolio of renewable 1-day forwards.
Forward and futures contracts are equivalent once they are adjusted for differ- ences in contract terms and liquidity. Indeed, the difference between a futures and a forward contract is operational rather than valuational, in that it depends on the contracts themselves (the deliverable asset, settlement procedures, maturity dates, and amounts) and not directly on prices.1As with forward contracts, the price Futtd/f of a futures contract is determined by relative interest rates and the current spot rate of exchange according to interest rate parity.
Futtd/f=Ftd/f=s0d/f[(1+id)/(1+if)]t (5.1) As with forwards, futures contracts allow you to hedge against nominal, but not real, changes in currency values. If inflation in the foreign currency is more than expected, then the forward rate won’t buy as much purchasing power as you expected. Currency forward and futures contracts can eliminate currency risk, but not inflation or interest rate risk within any single currency.