# Interest Rate Futures

Interest rate futures are futures contracts based on interest rates, which can be used to either hedge or speculate on future interest rates. Some interest rate futures require the delivery of specific types of bonds, usually government bonds, with a minimum term until maturity on the delivery date. Other interest rate futures are cash settled: the short position pays, and the long position receives, the interest earned on a notional amount, which is the face value of the contract at the delivery date.

Like bonds, the prices of interest rate futures contracts varies inversely with market interest rates, so higher interest rates will lower the prices of interest rate futures, and vice versa. Most interest rate futures are based on government securities and bank deposits, so there is virtually no default risk. Thus, their prices are only influenced by interest rates. Interest is calculated using the banker's year of 360 days.

Generally, the price of the futures contract is primarily determined by the spot price of the underlying asset, modified by the cost of carry, which in the case of interest rate futures, is the opportunity cost of holding the security instead of cash until the delivery date minus the interest earned from holding the security.

Interest rate futures, along with interest-rate options, interest rate swaps, and forward rate agreements provide a means for managing interest-rate risk on loans, both price risk and reinvestment risk: the prices of debt securities decline but reinvestment risk decreases when interest rates rise, and vice versa. For banks, especially, loans are usually long-term, while deposits are short-term, so interest rate futures are an important tool for asset-liability management.

There is a wide variety of interest-rate contracts, which can be characterized as either short-term or long-term. A **short-term interest futures** has an underlying security that matures in less than 1 year; otherwise, it is a **long-term futures contract**. The most popular contract is the Treasury bond futures, where the underlying assets are United States Treasury bonds with at least 15 years to maturity on the delivery date.

## Treasury Bond Futures

Treasury bond futures are traded on the Chicago Board of Trade (CBOT), which requires the delivery of Treasury bonds with more than 15 years remaining to maturity and that is not callable within those 15 years. The short position has a choice of any Treasury bond futures that satisfies the exchange's requirements for the delivered asset.

Treasury bond future prices are quoted just as Treasury bond prices. Each contract has a face value of $100,000, so a $1 change in the quoted futures price is equal to a $1000 change in the value of the futures contract. Delivery is allowable at any time during the delivery month.

### Cheapest to Deliver Bond

Because bonds are issued and retired continually, futures contracts do not stipulate a particular bond issue for delivery. To allow the greatest flexibility, the short party can generally choose from a wide variety of bonds that differ in coupon and maturity, as long as the terms of the contract are satisfied. Since the party with the short position receives the settlement price times a conversion factor plus the accrued interest and the cost of buying a bond is the quoted bond price plus accrued interest, the cheapest to deliver bond will be the least of the following equation:

Cheapest to Deliver Bond = Quoted Bond Price – (Settlement Price × Conversion Factor)

When bond yields exceed 6%, the conversion factor favors low coupon, long maturity bonds; with yields less than 6%, high coupon, short maturity bonds are more desirable. With an upward sloping yield curve, bonds with a long time to maturity are favored; with a downward sloping, then bonds with a short time to maturity would be more desirable.

The short position has an option known as a **wildcard play**. Trading in Treasury bond futures ceases at 2 PM Central Standard Time, but the Treasury bonds themselves continue trading until 4 PM. The short position has until 8 PM to issue a notice of intention to deliver to the clearinghouse, in which case, the invoice price is calculated based on the 2 PM settlement price. If bond prices decline after 2 PM on the 1st delivery day month, then the short position can issue a notice of intention to deliver shortly before 4 PM, allowing the short position to buy cheaper bonds. If bond prices do not decline, then the short position can keep his position open and wait until this next day to retry the strategy. Because it gives an advantage to the short position, the wildcard play lowers the futures price to less than what it would be without the option.

### Conversion Factor

The CBOT contracts are based on a Treasury bond paying a 6% coupon. Therefore, the price of the contracts must be adjusted by a **conversion factor** that reflects the interest rate of long-term Treasury bonds at the time of the agreement. The price received by the short position and the price paid by the long position depends on the conversion factor.

The cash received by the short position and paid by the long position for each $100 of face value delivered is equal to:

Treasury Bond Futures Price = Settlement Price × Conversion Factor + Accrued Interest

So if the settlement price is 95 and the conversion factor is 1.0245 and the accrued interest is $3, then the cash paid by the long party for the bonds is: 95 × 1.0245 + 4 = $101.33 per $100 of face value, or $101,330 per contract.

The CBOT conversion factor is equal to the quoted price per dollar of principal on the 1^{st} day of the delivery month calculated at 6% annually and compounded semiannually — what a 20-year Treasury bond would sell for at the beginning of the delivery month if it were yielding 6%. The bond maturity and the times to the coupon payment dates are rounded down to the nearest 3 months for the purposes of the calculation. Since most Treasuries pay less than 6%, the conversion factor is usually less than 1. The conversion factor for a given bond and delivery month is constant, and is not affected by changes in bond prices or in the price of the futures contract.

### Determining the Futures Price

Pricing a Treasury bond contract is difficult because of the uncertainty with the timing of delivery and the choice of the bond that will be delivered. However, if both of those factors are known, then the futures price is based on the following equation:

Futures Price = (Spot Price – Present Value of the Coupon Payments) × e^{Risk-Free Interest Rate × Holding Period in Days/360}

## Treasury Note Futures

Also popular in the United States are the 2-year, 5-year, and 10-year Treasury note futures.

The 10-year Treasury note futures contract has a $100,000 par value of a hypothetical 10-year 6% Treasury note. Any US government bond with a maturity between 6½ and 10 years from the 1^{st} day of the delivery month can be delivered.

5-year Treasury note futures also have a $100,000 par value. Delivery options: original maturity and remaining maturity that does not exceed 5 years and 3 months; and a remaining maturity of not less than 4 years and 2 months.

2-year Treasury note futures have a $200,000 par value. Any note with a remaining maturity of not greater than 2 years nor less than 1 year and 9 months can be delivered. The original maturity cannot be greater than 5 years and 3 months for the 2 years futures contracts.

## Short-Term Interest Rate Futures

Most short-term contracts, like most financial futures, have as delivery months in the March quarterly cycle — March, June, September, and December — plus the nearest 4 consecutive months that are not in the March quarterly cycle. For instance, before the last settlement day in December, there will be contracts for December, January, February, March, April, and May, with January, February, April, and May being the 4 months that are not part of the March quarterly cycle. Most contracts are quoted in terms of the prices of the contracts rather than their interest rates at a notional value of 100, which is the price index. The price of the futures contract is equal to 100 minus the interest rate:

Price = 100 – Annualized Interest Rate as a Percentage

Most short-term interest rate futures are based on a 3-month, or 90 days, period; nonetheless, the interest rate is annualized, so for a 90-day period, the actual interest earned on a futures contract would be 25% of the annualized interest rate.

There are many types of short-term interest rates futures, including T-bills, sterling, fed funds, Euribor (3-month LIBOR contract for the Euro), Euroswiss, Eurodollar, and Euroyen — only a few are discussed here.

The seller of the futures contract is given a choice of which bonds to deliver, so that at least some of them will be available during the delivery month. The conversion factor is calculated thus:

Conversion Factor = Bond Value/100 = Present Value of the Bond's Cash Flows/100

### Treasury Bill Futures

T-bill futures were the 1^{st} short-term interest rate contracts, traded on the International Monetary Market; other contracts for short-term debt are modeled after the T-bill futures contract, which have a face value of $1 million and are based on 3-monthTreasury bills.

The price of T-bill futures contracts is calculated differently from Treasury bonds: the annualized futures rate is subtracted from 100, which is the interest rate for the Treasury bills. So a futures price of 98 means that the Treasury bills are trading in the futures market at a 2% interest rate.

Futures Price Paid at Delivery = $1 million × [1 – Rate × (Days to Maturity/360)]

1 basis point change equals $25 change in the invoice price for a 90-day T-bill contract.

Treasury bill futures are simpler than either T-bond or T-note futures contracts: there is only 1 deliverable issue, which is T-bills with 3 months to maturity; that they have 3 months of original maturity is not required. There are no conversion factors or wildcard plays. The span of the delivery date must be within a 3-day period.

### Eurodollar Futures

Eurodollar certificates of deposit (CDs) are US denominated CDs with a face value of $1 million, issued in London by US, Canadian, European, and Japanese banks that pay a fixed rate of interest based on the dollar LIBOR. Unlike futures contracts based on Treasuries, Eurodollar futures contracts are cash-settled. Contracts are based on the 3-month Eurodollar CD, traded on IMM of the Chicago Mercantile Exchange and the London International Financial Futures Exchange (LIFFE), now NYSE Liffe. The underlying is the spot USD LIBOR interest rate that is fixed on the 2^{nd} business day before the 3^{rd} Wednesday of the contract's expiration month. Eurodollar futures are the most actively traded short-term interest-rate futures. Quarterly contracts are available for up to 10 years in the future.

Contract prices are based on an index price with a basis equal to 100 minus the annualized futures LIBOR, so a price of 98 means that the 3-month dollar LIBOR is 2% annualized. The minimum price fluctuation or tick is 0.005% (= 0.00005) or ½ basis point, using the 30/360 day-count convention:

Tick value = $1 million × 0.00005 × 90/360 = $12.50

Often, a series of Eurodollar futures will be bought or sold as a strip to more effectively hedge interest-rate risk. A **Eurodollars futures strip** is a series of futures maturing on sequentially deferred months with an initial cash investment for the initial 3 months, called the **front tale** or **stub** of the strip transaction.

Eurodollar futures can also be used to profit from changes in the yield curve: if the curve is expected to steepen, then buy the curve by purchasing near-term and selling long-term Eurodollar futures; if the yield curve is expected to flatten or invert, then sell the curve by selling the near-term and buying the long-term futures.

### Fed Funds Futures

The 30-day federal funds futures contract is based on the average overnight federal funds rate for the delivery month. Each contract has a notional value of $5 million, spanning anywhere from the current month to 24 months in the future. These contracts are cash-settled on the last business day of the month. Like T-bills, prices are quoted at 100 minus the overnight federal funds rate for the delivery month. These contracts are also mark-to-market using the effective daily federal funds rate as reported by the Federal Reserve Bank of New York.

## Profiting or Hedging with Interest Rate Futures

Interest rate futures can be used to either profit or to hedge. Profits can be made from directional trading, by going short if interest rates are expected to increase, or going long, if interest rates are expected to decrease. Profits can also be made from arbitrage if the price of the underlying asset deviates from the futures price. Calendar spread trading can be profitable if the interest rates for given terms deviates from historical spreads. So if the difference between a 30-year treasury bond and a 2-year treasury note is larger than usual, then a profit can be earned by going short on the overpriced contract and going long on the underpriced contract.

Interest rate futures are also used extensively for hedging, primarily by altering the duration of fixed income portfolios, which is a primary means of managing price and reinvestment risk. Adding short interest rate futures to a fixed income portfolio will shorten duration, reducing price decreases because of higher interest rates; long positions will lengthen the duration of the portfolio, so that there will be a greater gain in price from falling interest rates.

**Synthetic fixed-rate and floating-rate loans** can also be created using interest rate futures. For instance, a corporation could obtain a fixed-rate loan from a bank for certain term, but it may be cheaper to create a synthetic fixed-rate loan, by accepting a floating rate loan from the bank, which will have a lower rate of interest, and going short in interest rate futures. If interest rates rise, the bank will increase the floating-rate, but the short futures position will increase in value that, if calculated correctly, will offset the increased interest rate charged by the bank. Analogously, a synthetic floating-rate loan can be created with a fixed-rate loan and by taking a long position in interest rate futures. If interest rates rise, then the long position with decline in value, but that will be offset by the increased interest income on the loan; if interest rates decline, then the long position will increase in value, offsetting the decline in interest rates on the floating-rate loan, thus keeping the interest rate flat.