The wonderful world of interest rate derivatives

Whether you're a borrower, lessee, building society saver or professional investor, virtually all of us are directly affected in some way by fluctuations in interest rates. Generally, however, this is something which attracts much less attention than, say, events on the stock markets. Over the last few weeks, the situation has changed somewhat owing to the US mortgage crisis. As an instrument, interest rates have long been among the most important and most liquid for futures traders.

Eurodollar: the world champ among futures

The discounted listing

Logic from the hedger‘s perspective

This type of market quotation, which at first glance may seem rather exotic, has a plausible reason behind it, which can be explained thus: let‘s assume that our Russian oil company is aware that repairs to a technical facility have to be carried out in three months‘ time. The repairs will cost one million dollars. The company‘s CFO wants to secure funds immediately, which will allow suppliers to be paid straight away. A good method would be to invest exactly the amount in dollars for three months (at the 3-month LIBOR rate) which would equate to one million after interest has been paid. If you know that the LIBOR, just like any other reference interest rate, is annualized (5.27% for one year), you can work it out easily: the interest year is traditionally 360 days and the 3-month LIBOR is fixed at 90 days. To calculate the effective interest payment, we have to „reduce“ the annualized interest rate to 90 days by multiplying it by the time fraction 90/360. This gives us the following formula for calculating the sum of money which would give us one million dollars after three months based on the 3-month LIBOR:

1,000,000 - 1,000,000 * 5.27% * 90/ 360 =
1,000,000 - 1,000,000 * 0.013175 =
1,000,000 - 13,175 = 986,825
What would happen if the current interest rate were to fall? The cash requirement would increase by exactly 25 dollars for each basis point of the interest rate (0.01%). The proof:

1,000,000 - 1,000,000 * 5.26% * 90/ 360 =
1,000,000 - 1,000,000 * 0.01315 =
1,000,000 - 13,150 = 986,850
If, by contrast, the current interest rate were to increase, then the cash requirement would fall in the same ratio. The price of the Eurodollar futures contract also follows this logic. If the anticipated interest rate on the settlement day is 5.27%, the price of the future would be 94.73. If interest rates rise, the price of the futures contract falls and vice versa.
The quotation is therefore from the perspective of the investor, whose intention it is to hedge a sum of money invested at a variable rate of interest against falling interest rates. If he buys a Eurodollar futures contract (“goes long”), the hedger profits if the interest rate then falls. By the same token, the seller (the holder of the short position) benefits from rising interest rates. We have already demonstrated how much that is in our calculations above: 25 dollars per basis point (0.01). The value of the futures contract is calculated using the same method, we have to adapt the formula only slightly to return to our original model:

Instead of
1,000,000 - 1,000,000 * 5.27% * 90/ 360
we use
1,000,000 - 1,000,000 * [(100-94.73)/100] * 90/ 360
and come back to
1,000,000 - 1,000,000 * 0.0527 * 0.25 =
1,000,000 - 13,175 = 986,825

Generally, the formula for calculating the value (V) of the Eurodollar and similarly constructed futures contracts in interest rates is:

V = CS - CS * [(100-p)/100] * d/360
Where CS equals contract size (USD 1 million), p equals the futures price and d equals the number of days on which interest is paid (90).
Other short-term futures contracts in interest rates are also governed by this principle. This includes, for example, the Euroyen (Japanese yen-denominated 3-month deposits held in banks outside Japan) or the 1-month LIBOR on the CME as well as the Euribor future on the Eurex.
Money market futures are - once you have understood the basics - very easy to manage and uncomplicated settlement through cash payment makes them an attractive instrument for trading short-term interest. The current margin for a contract is around 750 dollars - which makes for acceptable leverage in relation to the controlled value. Given that short-term interest tends to demonstrate distinct trends, money market futures are also an attractive instrument for speculative traders focusing on long-term trends. The Eurodollar perfectly reflected both the US interest rate cut cycle between 2000 and 2003 as well as the streak of interest rate hikes that began in 2004.

Long-term interest: bond futures

The world of long-term futures contracts in interest rates, whose underlying instruments are bonds, is altogether more complex. World-wide, the most significant contract in this sector is the Bund future on Europe‘s futures and options exchange, Eurex. The underlying instrument is a fictitious Euro-Bund future with the following characteristics:
Par value: 100,000 euro
Residual term: 8.5 to 10.5 years
Nominal interest: 6% p.a.

The price of the Bund future indicates the price of this bond (and not the interest payment) as a percentage. If the price is 110, this implies a bond price of 110,000 euro.
Bond futures therefore react to the same influences as bonds themselves. Actual and anticipated changes in the interest rate level are a strong factor, since rising interest rates generally lead to a drop in the prices of bonds in circulation (and vice versa). Which is why we also speculate on falling interest rates in the euro zone with a long position in the Bund future. But bond futures do not react anywhere near as directly to interest rate policy as money market futures, since there are a whole range of other factors influencing bond prices.
This was very evident most recently in August 2007, when a capital flight from the stock markets to the safe haven of government bonds could be observed. Skyrocketing demand drove bond prices up drastically, even before speculation about possible interest cuts began.

Considerable leverage

Despite the tendency of bond futures to fluctuate much more than money market derivatives, the Bund future does not, at first glance, seem that adventurous, given its long-term fluctuation between 102 and 125 points. But leverage is considerable here, too: a change by one single basis point (0.01) in the price of a futures contract results in a change in the contract value of 10 euro. It is not unusual to see fluctuations of 50 basis points in a day. Let‘s assume an average contribution margin of EUR 1,600 per contract - a total loss could occur very quickly, as indeed could a profit of 100%, based on the margin.

Warning: delivery!

Dealing with bond futures can become extremely tricky if a contract actually has to be settled. With Bund futures, physical delivery of the underlying instrument is supposed to take place at the end of the maturity period. So anyone with a (short) selling position up to the end must have sufficient bonds ready - which in practice is very rarely the case, given that over 97% of all contracts are settled prematurely.
Nevertheless, what if settlement is on the cards? German government bonds with a nominal interest of 6% and a residual term of 8.5 to 10.5 years do not grow on trees. In September 2007, there wasn‘t a single security which met these criteria. The solution to this dilemma involves the index of deliverable bonds, which Eurex provides for each individual futures contract. It lists all accepted bonds for a specific delivery date, their ISIN codes and a multi-digit conversion factor. For the September contract, for which the last trading day was 6.9.2007, this would have been the security with the ISIN DE 0001135309. The term of this government bond runs until 4.7.2016, has a nominal interest of 4% and a conversion factor of 0.865938.
On September 6, 2007, the closing price of this bond on the spot market, in denominations of EUR 100, was 98,7547. The price of the Bund September contract on the last trading day closed at 113.99. It would be a highly profitable transaction indeed if the seller were actually to receive the contract value of the future (EUR 113,990) as the price for 1,000 denominations (100,000 euro par value) of a lower interest-bearing bond traded at a much lower level. Which is precisely why there is a conversion factor for calculating the actual amount which the holder of the long position has to pay the deliverer of the bond. We use the following formula:

(KW * f) + AZ
where
KW = contract value of the future
f = conversion factor
AZ = interest for periods of less than a year on all delivered bonds on the delivery day since the last coupon payment

Let’s stick with the aforementioned bond, which would give us the following values:

KW =113,990
f = 0.865938
AW = 700 (interest between the last coupon payment and the valuation date September 6 for 1,000 bond denominations)

Giving us:
((113,990 * 0.865938) + 700 =
98,708.27 + 700 = 99,408.27

The holder of the short position (seller) can purchase these bonds at a spot price of EUR 98,754.70 plus the proportionate coupon payment (EUR 700). His purchase price would therefore be 99,454.27 at a loss of EUR 45.57. Anyone wishing to settle a Bund contract through physical delivery will try to identify the cheapest bond from a list of deliverable instruments. In some cases, this “cheapest to deliver” bond can actually bring the seller an arbitrage profit.

A formidable market

Most other bond futures work like the Bund contract. Alongside, there are the 2, 5 and 10-year US Treasury Notes on the CBOT or the Euro-Schatz and Euro-Bobl futures on the Eurex. Bond and money market futures together represent the second largest sector of the international futures exchanges after stock indices. In 2006, around 3.2 billion futures contracts in interest rates were traded - more than in any other commodity or currency markets put together.
One of the reasons for the high rate of increase in trading in interest rate derivatives lies in the fact that they are so flexible. As well as simple long and short trades in individual instruments, the fixed-interest futures offer a whole number of additional options for speculation which allow highly complex strategies to be put into practice. For example, through a combination of different maturity periods, from short-end (one and three-month interest rates) to long-end (10 or even 30-year) bonds: this allows specialists to speculate on very varied interest curve expectations. Numerous arbitrage variations are also feasible - for example through combinations of different currencies or settlement days. This fixed-income arbitrage is an independent branch of hedge funds.
But the core focus of every futures market is, of course, hedging: hedging largely against unfavorable trends in interest rates with the help of derivatives of every kind is the domain of the big players, namely the banks.

The history of interest rate futures

Historically, interest rate futures are still a relatively new instrument. The first market was opened pretty much 110 years to the day after the launch of the first standardized futures contract, on October 20, 1975, on the Chicago Board of Trade (CBOT). It was issued in mortgage certificates of the Government National Mortgage Association (GNMA), also referred to as „Ginnie Mae“. It was also the first mortgage-backed securities derivative - an instrument which, owing to the US sub-prime crisis, everyone is talking about right now. However, it was a future without any future: trading in the GNMA contract ceased in 1985 owing to a lack of volume. Instead, the first short-term federal treasury bill futures soon flourished: in 1976, a contract for 3-month treasury bills was launched on the CME, soon becoming its most liquid contract. The Eurodollar futures contract followed in 1981, and finally, in 1982, the series of long-term treasury notes and bonds on the CBOT. In the same year, the London LIFFE (now Euronext NYSE) issued its first futures contract in interest rates. The Bund future was born on September 29, 1988, when it was still denominated in D-Mark.

For anyone for whom the pure form of these already classic futures contracts in interest rates isn‘t enough of a challenge, then perhaps swap futures are worth considering. These contracts, launched on the CBOT in 2001, are based on the swap rate for swapping a coupon bond with a 6% fixed rate of interest for a variable floating rate note determined by the 3-month LIBOR (all contracts in denominations of 100,000 dollars with varying residual terms of between 5 and 30 years). This derivative-based derivative allows for even more precise strategies for hedging against undesirable interest rate fluctuations.
In the USA, the entire spot market for swaps is already four times bigger than that for notes and bonds. On the futures exchanges the ratio is the other way round, but the swap contracts are already sufficiently liquid for most speculative strategies.

(FUTURES, issue October 2007)