INTEREST RATE FUTURES

The price of interest-bearing securities, like bills, bonds and debentures, is inversely related to the prevailing market rate of interest. Thus a rise in market interest rate leads to a fall in the price of bills, bonds and the like, while a fall in interest rates leads to a rise in the price of bills, bonds etc. These price changes occur so that the yield on an already – issued security is the same as that on a new one issued at the current rate.

• In 1991, the prevailing market interest rate on long dated gilt – edged securities is 10%. The Government issues a new security with a coupon rate of 10%. By 1994, the market interest rate for long-dated gilts is 14%. New issues of gilts bear a coupon rate of 14%. An investor in the gilt edged market can now choose either to buy the new gilt-edged stock (producing a return of 14%) or to buy the old stock. Naturally, he will not buy the old (10%) stock at its issue price when he can get 14% on the latest issue. If however the price falls to a level such that the yield is 14%, he will be willing to buy it. If this level is x then

example

• 10 = 14 x 100x = 10 x 100 = Rs. 71.42 per Rs. 100 of nominal or par value 14For every Rs. 100 of nominal value, the holder gets interest of Rs. 10 (since this is a 10% coupon security). But since he only pays Rs. 71.42, his yield is 10/71.42 = 14%Thus the price of a Rs. 100 gilt will fall to Rs. 71.42Now assume that in 1998, the rate of interest falls to 9%. Persons holding the old (10%) stock, acquired at part, can get a higher return than on fresh issues. Sellers of the gilt know that the market rate is 9% and will thus be unwilling to sell the gilt at any yield in excess of 9%. The new price of the gilt will be y such that 10 = 9 y 100

• The buyer of Rs. 100 nominal gets Rs. 10 as annual interest but has paid Rs. 111.11. His effective yield is thus 10/111.11 = 9%Thus rises in interest rates lead to falls in prices of interest-bearing securities and vice versa. (The simple relationship illustrated here applies only to perpetual securities; for redeemable securities, the formula is more complicated but the principle is the same) Interest rate futures are used for hedging by banks, financial institutions, pension funds and others whose assets or liabilities can be affected by changes in interest rates. In the interest rate futures markets, short hedgers are those seeking protect against rising interest rates while long hedgers are those seeking protection against falling interest rates.

• The method of quotation is structured so that a short hedger sells futures and benefits from a fall in price (rise in interest rate) in his futures transaction while a long hedger buys futures and benefits from a rise in price (fall in interest rates) in his futures transaction. This mirrors the situation in any other futures market. The main interest rate futures are described below.

SHORT – TERM DEPOSIT FUTURES

• These are contracts on the value of a short-term bank deposit or (Certificate of Deposit). Examples are the CBOT’s ‘30-day US Dollar’ contract, the LIFFE ‘Short Sterling’ (90-day) contract, the LIFFE Euromark, Euroswiss Franc and Eurolire (90-day) contracts and the TIFFE / LIFFEE Euroyen (90-day) contract. (Readers should not that, in contrast to its normal use in futures trading, the word ‘short’ in the short sterling contract refers to the short-term nature of the instrument, not to a ‘short position’.)

• A characteristic feature of short-term interest rate futures is their manner of quotation. They are quoted by deducting the yield per annum from 100.

• The yield would be the one applicable to the contract term – for instance the rate applicable to the short sterling contract will be the three month sterling LIBOR while for the 30-day dollar contract the one month dollar LIBOR would apply.

• The short sterling futures contract for June is quoted at 91.00 while that for September is quoted at 90.50. This means the yield on a three – month deposit made in June is expected by the market to be

100 – 91.00 = 9.00%

The yield on a three – month deposit made in September is expected to be

100 – 90.50 = 9.50%

Example 2

TREASURY BILL FUTURES

• Expect for the fact that the underlying asset is a Treasury Bill, the manner of quotation and the modalities of trading are the same as for any other short – term interest rate contract.

BOND INDEX FUTURES There are futures contracts on bond indices, i.e. indices of bond prices. Since bond prices are inversely related to interest rates the index also is inversely related to them. The Municipal Bond Index future based on US municipal bonds, and traded in CBOT is an example of a bond index future enabling hedging of municipal bond holdings.

Example 3 Long gilt futures

• In March, a British financial institution finds it has a temporary surplus cash of £ 100,000, which it will require for other uses by September. It wishes to invest the amount in gilt-edged stock because of the attractive interest yield but is apprehensive about a possible rise in market interest rates which may reduce the bond price. It therefore buys £ 100,000 (nominal) of 9% Treasury Stock, whose current spot market rate is £ 92% (i.e. £ 92 per £ 100 of stock). It also hedges the transaction on the futures market :

Date

Action

Spot Market Futures Market

March 1 Buy £ 100,000 nominal @ 92%

Pay £ 92,000

Sell £ 100,000 nominal of September futures @93% pay £ 9,300 as margin (deposit)

August 31 Sell £ 100,000 nominal @ ruling rate of 89%

Receive £ 89,000

Buy £ 100,000 nominal of September futures @89%

Receive £ (93,000 – 89,000)

= £ 4,000 as profit + £ 9,300 margin refund

• As shown above, interest rates did indeed increase by August, resulting in a fall in gilt prices from 92 to 89. The financial institution has received interest for the half year of £ 4,500, but if it had not hedged itself, it would have lost £ 3,000 through fall in bond values. However because it had hedged itself, its spot market loss of £ 3,000 is compensated for by a gain of £ 4,000 on the futures trade. (The slight gain reflects the change in futures – spot spread.)

Example 4 Short – term interest rate (long hedge

• Q Inc., an American company, is notified on April 1 that it will be receiving $5 million from a debtor on June 1. These funds will not be needed till July 1, so they can be lent during June (a month having 30 days, exactly corresponding to the term of the 30-day US dollar futures contract). The company is apprehensive of a fall in interest rates between April and the actual receipt of the funds in June. It therefore hedges on the CBOT 30 – day interest rate futures contract. Interest rates turn out to be as follows :

April 1 6.25 %

June 1 5.00%

June 30 4.50%

Date

Action

Spot Market Futures Market

April 1 Acquire deferred asset ($ 5m due on 1st June)

Buy one contract (i.e. $ 5m) June 30-day futures @93.75

Pay margin of 93.75 x 5,000,000

100

X 10% = $ 468,750

June 1 Deposit $ 5m @ 5%

(Prevailing LIBOR)

Sell one contract June 30 – day futures @95.00

Receive refund of $ 468,750 plus

Profit of (95.00 – 93.75) x 1

100 12

x $ 5,000,000 = $ 5,208.33

June 30 Receive back $ 5m :

Receive interest thereon of 5 x 1 x 5,000,000

100 12

= $ 20,833.33

• Total return from hedge : Interest on deposit $ 20,833.88Profit on futures $ 5,208.33

----------------Total $ 26,041.66

Rate of return for 30 days = 26,041.66 = 0.520833% --------------

5,000,000Annualized rate of return = 0.520833 x 12 = 6.2499984%i.e 6.25%By hedging the company has managed to obtain the desired interest rate of 6.25%, though market rates have fallen. A simpler way of looking at it is that the futures contract appreciated by 1.25 percentage points (125 basis points) compensating for a fall in interest rate of 1.25 percentage points.

Example 5 Short – term interest rate (short hedge)

• In July, a British company secures an order which will require borrowing of £ 500,000 for working capital for three months from September. The company’s borrowing rate is 1% above LIBOR. It is apprehensive that interest rates will rise before then and hedges the risk in the short sterling futures market. Interest rates (3 month LIBOR) turn out to be as follows :

• July 1 8.50%

September 1 8.25%

September 30 8.00%

Date

Action

Spot Market Futures Market

July 1 Acquire deferred liability £ 500,000 from 1st September)

Sell one contract (£ 500,000) of short sterling @ 91.50

Pay margin of 91.50 x 500,000

100

X 10% = £ 45,750

September 1

Borrow £ 500,000 @ LIBOR + 1% i.e. 9.25%

Buy back one contract of short sterling @ 91.75

Receive margin refund of £ 45,750

Less loss of (91.75-91.50) x 3

100 12

X 500,000 = £ 312.5

December 31

Repay £ 500,000 along with interest thereon of

9.25 x 3 x 500,000

100 12

= £ 11,562.5

•Total cost of borrowing £

Interest paid 11,562.2

Loss on futures 312.5

------------

11,875.0Effective rate of interest for 3 months = 11,875 x 100 = 2.375%

500,000

Annualized rate of interest = 2.375 x 12 = 9.5%

3

The company ends up paying 9.5% (i.e 8.5% + 1% margin over LIBOR) – the rate which it wanted to ensure. (Its expectation that rates of interest would rise was belied and it would have been better off by not hedging, in this particular instance – but that is with hindsight!)

• Movement of 1 basis point (i.e. 1/100th of 1%) in the discount yield will cause the contract value to change by

$(1,000,000)(90/3600)x0.0001=$25As shown above, the minimum size of price movements in T-bill contracts or the “tick” corresponds to movement of (1/2) basis point of $12.50. After buying the futures contracts at a price of 91.455, suppose I close my position by selling a contract at a later date when the futures price is92.050. This corresponds to a gain of (92.050 – 91.455)/0.005]or 119 “ticks”. I will have made a profit of $ (12.50)(119) = $ 1487.50 ignoring marking to market. T BILL FUTURES PRICES---------------------------------------------------------------------------------------------------------Treasury Bills (IMM) -$1 million: points of 100%CME US Treasury Bills:Pries as of 12 / 15 / 100 11:30 AMMTH SESSION PT EST - PRIOR DAY -

OPEN HIGH LOW LAST CHGE VOL VOL POINTDECOO 94.13 94.145 94.13 94.145 +5 5.61 1165MAR01 - 94.41 94.38 94.41 +.52 15 1568

EURODOLLAR AND STERLING DEPOSIT FUTURES

• These are short-term interest rate futures contract traded on the IMM of CME and LIFFE. LIFFE also trade a Eurodollar deposit contract. The underlying asset is a three-month Eurodollar of $1 million for the Eurodollar contract and a.50,000 pound sterling three month deposit for the sterling contract. The delivery cycle is March, June, September, December.

• As in the case of T-bill contracts, for the Eurodollar contracts on the IMM and sterling time deposit contract on the LIFFE, the prices are stated on an index basis. That is, price of the contract is stated as (100-implied interest rate in%). Obviously, the implied interest rate is (100-the futures price). However, here the interest rate is on an add-on basis and not a discount yield. Thus buying a sterling time deposit contract at 93.73 means, if held to maturity, the buyer will acquire a 3 month sterling time deposit in a bank at an effective interest rate of 6.27% p.a (=100 – 93.73). If the interest rate increases, the price will decrease and the long position will lose. We will discuss this in greater detail below.

• The meaning of the various numbers in the quotations of interest rate futures is same as in the case of currency futures. The minimum price movement – one tick – is 0.01% and corresponds to a change in contract value of $25 for the Eurodollar deposit contract. Table presents an extract from eurodollar futures prices on CME and the Pound sterling time deposit contract on LIFFE.

Eurodollar and Sterling Interest Rate Futures Quotations 16/8/2000

Open Settlement

Change High Low Open Interest

Sept. 93.28 93.28 -- 93.28 93.28 589636

Dec. 93.11 93.11 -- 93.12 93.11 550400

Mar.01 93.17 93.16 -0.01 93.19 93.16 488562

STERLING (LIFFE) - £50,000 ; 100 – rate

Sept. 93.73 93.69 -0.04 93.75 93.68 187755

Dec. 93.63 93.56 -0.06 93.65 93.55 198748

Mar.01 93.60 93.53 -0.07 93.63 93.53 151418

• The Eurodollar contract traded on the IMM is settled exclusively by cash settlement while LIFFE offers option is taking physical delivery. The cash settlement procedure is very simple as brought out by the following example :

• Cash Settlement in the Eurodollar Contract On day 1 a trader buys a Eurodollar contract at 90.45. The initial margin requirements is $2000 with a maintenance margin of $1500. On day 2, settlement price is 90.32. The trader’s loss is $325 (=13 ticks x $25 per tick). His margin account drops to $1675. On day 3, the settlement price is 90.38. The trader’s margin account is credited with $150. The balance is now $1825.

• On day 4, the last trading day, the settlement price drops sharply to 90.05. The trader loses $800. The balance in his account is $1025. This is paid to him and his position is closed.

• The LIFFE Eurodollar contract has a provision for physical delivery i.e the long can, if he or she chooses to actually acquire a Eurodollar deposit in a Eurobank by paying an amount calculated from the actual yield on the deposit. For details of the delivery process see the appendix to this chapter. Fitzgerald (1983) explains why a long may prefer cash settlement.

LONG – TERM INTEREST RATE FUTURES

• Futures contracts on long-term debt instruments are traded on a number of exchanges. The US treasury bond or T-bond contract traded on the CBT is one of the most heavily traded financial futures contract. We will briefly describe this contract.

• A US treasury bond is coupon bond with original maturities in the range of 15-30 years. Most of them have a call provision with the first call date five years before maturity. Interest payments are semiannual. The face or par value of the bond is $1,00,000.

• In the cash as well as futures market, bond prices are stated in the form of percent of par value with the digits coming after the hyphen denoting 32nds of 1 percent. Thus a price quoted as 90-19 means the buyer must pay an amount equal to 90(19/32)% of the face value i.e

• $(0.9059375) (100,000) = $90593.75 • There is the added complication of accrued interest. The

purchaser of the bond has to pay, in addition to the price quoted, the interest accrued since the last coupon date.

• Table gives an extract from CBT T-bond futures quotations. Let us see how to interpret these. The notional asset underlying the CBT T-bond contract is a 6% coupon bond with 20 years to maturity from the date of delivery. It is notional because no such T-bond may actually trade in the cash market. That is irrelevant for futures pricing. The settlement price of 104-25 for the March 2001 contract means that the market will pay 104(25/32)% of the par value for such a bond if it did exist.

• The next column headed “Chg” shows that the settlement price increased by (8/32)% from the previous day. The size of one “tick” is (1/32)% which represents a change in the value of the contract of :

• $[100.000 x (1/32) OF 1%] = $(100,000 X 0.0003125)

= $31.25