Über die Autorin bzw. den Autor

Dr Moorad Choudhry is Head of Treasury at KBC Financial Products in London. He is a Visiting Professor at the Department of Economics, London Metropolitan University, a Visiting Research Fellow at the ICMA Centre, University of Reading, a Senior Fellow at the Department of Mathematical Trading and Finance, Cass Business School, and a Fellow of the Securities and Investment Institute.

Von der hinteren Coverseite

Basis trading is an important part of the government bond markets. In this book we review the essential elements of this type of trading. Written by a former government bond market maker and proprietary bond trader, the book features: <ol> <li>Basic concepts of forward pricing</li> <li>The determinants of the basis</li> <li>Repo financing</li> <li>Hedging using bond futures</li> <li>Trading the basis and an introduction to trading strategy</li> <li>The concept of the <i>cheapest-to-deliver</i> bond</li> <li>The net basis and the <i>implied repo rate</i></li> </ol> <p>The book is illustrated with in-depth practical examples and written in an accessible style. It will be of vital use to anyone with an interest or involvement in the government bond futures market.</p>

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The Futures Bond Basis

John Wiley & Sons

Chapter One

A widely used trading and risk management instrument in the bond markets is the government bond futures contract. This is an exchange-traded standardised contract that fixes the price today at which a specified quantity and quality of a bond will be delivered at a date during the expiry month of the futures contract. Unlike short-term interest rate futures, which only require cash settlement, bond futures require the actual physical delivery of a bond when they are settled. They are in this respect more akin to commodity futures contracts, which are also (in theory) physically settled.

In this first chapter we review bond futures contracts and their use for trading and hedging purposes.

1.1 INTRODUCTION

A futures contract is an agreement between two counterparties that fixes the terms of an exchange that will take place between them at some future date. They are standardised agreements as opposed to 'over-the-counter' or OTC ones, as they are traded on an exchange, so they are also referred to as exchange-traded futures. In the UK financial futures are traded on LIFFE, the London International Financial Futures Exchange which opened in 1982. LIFFE is the biggest financial futures exchange in Europe in terms of volume of contracts traded. There are four classes of contract traded on LIFFE: short-term interest rate contracts, long-term interest rate contracts (bond futures), currency contracts and stock index contracts.

Bond futures contracts, which are an important part of the bond markets, are used for hedging and speculative purposes. Most futures contracts on exchanges around the world trade at 3-month maturity intervals, with maturity dates fixed at March, June, September and December each year. This includes the contracts traded on LIFFE. Therefore, at pre-set times during the year a contract for each of these months will expire, and a final settlement price is determined for it. The further out one goes the less liquid the trading is in that contract. It is normal to see liquid trading only in the front month contract (the current contract, so that if we are trading in April 2005 the front month is the June 2005 future), and possibly one or two of the next contracts, for most bond futures contracts. The liquidity of contracts diminishes the further one trades out in the maturity range.

When a party establishes a position in a futures contract, it can either run this position to maturity or close out the position between trade date and maturity. If a position is closed out the party will have either a profit or loss to book. If a position is held until maturity, the party who is long futures will take delivery of the underlying asset (bond) at the settlement price; the party who is short futures will deliver the underlying asset. This is referred to as physical settlement or sometimes, confusingly, as cash settlement. There is no counterparty risk associated with trading exchange-traded futures, because of the role of the clearing house, such as the London Clearing House (LCH). This is the body through which contracts are settled. A clearing house acts as the buyer to all contracts sold on the exchange, and the seller to all contracts that are bought. So in the London market the LCH acts as the counterparty to all transactions, so that settlement is effectively guaranteed. The LCH requires all exchange participants to deposit margin with it, a cash sum that is the cost of conducting business (plus brokers' commissions). The size of the margin depends on the size of a party's net open position in contracts (an open position is a position in a contract that is held overnight and not closed out). There are two types of margin, maintenance margin and variation margin. Maintenance margin is the minimum level required to be held at the clearing house; the level is set by the exchange. Variation margin is the additional amount that must be deposited to cover any trading losses and as the size of the net open positions increases. Note that this is not like margin in, say, a repo transaction. Margin in repo is a safeguard against a drop in value of collateral that has been supplied against a loan of cash. The margin deposited at a futures exchange clearing house acts essentially as 'good faith' funds, required to provide comfort to the exchange that the futures trader is able to satisfy the obligations of the futures contract.

1.1.1 Contract specifications

We have noted that futures contracts traded on an exchange are standardised. This means that each contract represents exactly the same commodity, and it cannot be tailored to meet individual customer requirements. In this section we describe two very liquid and commonly traded contracts, starting with the US Treasury bond (T-bond) contract traded on the Chicago Board of Trade (CBOT). The details of this contract are given in Table 1.1.

The terms of this contract relate to a US T-bond with a minimum maturity of 15 years and a notional coupon of 8%. A futures contract specifies a notional coupon to prevent delivery and liquidity problems that would arise if there was shortage of bonds with exactly the coupon required, or if one market participant purchased a large proportion of all the bonds in issue with the required coupon. For exchange-traded futures, a short future can deliver any bond that fits the maturity criteria specified in the contract terms. Of course, a long future would like to deliver a high-coupon bond with significant accrued interest, while the short future would want to deliver a low-coupon bond with low interest accrued. In fact, this issue does not arise because of the way the invoice amount (the amount paid by the long future to purchase the bond) is calculated. The invoice amount on the expiry date is given as equation (1.1):

In[v.sub.amt] 1/4 [P.sub.fut] x CF + AI (1.1)

where [Inv.sub.amt] = Invoice amount; [P.sub.fut] = Price of the futures contract; CF = Conversion factor; AI = Bond accrued interest.

Any bond that meets the maturity specifications of the futures contract is said to be in the delivery basket, the group of bonds that are eligible to be delivered into the futures contract. Every bond in the delivery basket will have its own conversion factor, which is used to equalise coupon and accrued interest differences of all the delivery bonds. The exchange will announce the conversion factor for each bond before trading in a contract begins; the conversion factor for a bond will change over time, but remains fixed for one individual contract. That is, if a bond has a conversion factor of 1.091 252, this will remain fixed for the life of the contract. If a contract specifies a bond with a notional coupon of 7%, then the conversion factor will be less than 1.0 for bonds with a coupon lower than 7% and higher than 1.0 for bonds with a coupon higher than 7%. A formal definition of conversion factor is given below.

Conversion factor

The conversion factor (or price factor) gives the price of an individual cash bond such that its yield to maturity on the delivery day of the futures contract is equal to the notional coupon of the contract. The product of the conversion factor and the futures price is the forward price available in the futures market for that cash bond (plus the cost of funding, referred to as the gross basis). Each bond that is deliverable against the futures contract is given a conversion factor.

Although conversion factors equalise the yield on bonds, bonds in the delivery basket will trade at different yields, and for this reason they are not 'equal' at the time of delivery. Certain bonds will be cheaper than others, and one bond will be the cheapest-to-deliver (CTD) bond. The cheapest-to-deliver bond is the one that gives the greatest return from a strategy of buying a bond and simultaneously selling the futures contract, and then closing out positions on the expiry of the contract. This so-called cash-and-carry trading is actively pursued by proprietary trading desks in banks. If a contract is purchased and then held to maturity the buyer will receive, via the exchange's clearing house, the cheapest-to-deliver gilt. Traders sometimes try to exploit arbitrage price differentials between the future and the cheapest-to-deliver gilt, which is basis trading. The mathematical calculation of the conversion factor for the gilt future is given in Appendix 1.A.

Conversion factors are set by the Exchange at the inception of the contract and stay unchanged for the life of the contract. They are unique to each bond and to each delivery month. Table 1.2 shows the conversion factor for the deliverable basket of gilts during 2004-2005. These are gilts that were in the deliverable basket for the Dec05 contract. If a bond has a coupon higher than the notional coupon of the contract, its conversion factor will be higher than 1, while the bonds with a coupon lower than the contract notional coupon will have a conversion factor lower than 1. This can also be seen from Table 1.2. Note how the conversion factor pulls towards 1 the nearer to expiry the deliverable bond gets. In the case of bonds with coupon below the notional coupon, this means the conversion factor steadily increases with each new futures contract, while the opposite happens with bonds whose coupon is higher than the notional coupon.

Conversion factors are NOT hedge ratios and should not be used as such. The primary use of the conversion factor is as a definition of the basis. When the conversion factor is used as a ratio to combine bonds and futures, a change in the bond's basis will generate profit for the arbitrage trader, irrespective of whether the basis moved to a change in bond price or futures price. The potential profit is also not market directional; that is, it is not relevant whether a rise or fall in bond or futures price has caused a change in the basis.

We summarise the contract specification of the long gilt futures contract traded on LIFFE in Table 1.3. There is also a medium gilt contract on LIFFE, which was introduced in 1998 (having been discontinued in the early 1990s). This trades a notional 5-year gilt, with eligible gilts being those of 4-7 years' maturity.

Figures 1.1A and 1.2 show Bloomberg screen DES for the US Treasury long bond and UK gilt contracts, respectively. The Treasury is 'listed', if one can say this, on CBOT but can of course be traded 24 hours a day on Globex, Simex and other exchanges.

Figure 1.1B shows page CTM from Bloomberg, a list of the current long bond contracts as at 1 November 2005. The 'front month' contract is the Dec05 future, trading at 112-03. The screen also shows trading volume data, we can see that the 'open interest' is 577,046 lots. Open interest is the number of contracts that have been traded and whose positions have been run overnight; that is, they were traded and are not yet closed out.

1.2 FUTURES PRICING

We now introduce the first principles behind the pricing of a futures contract. In practice, cash markets are now priced off derivatives markets, reflecting the greater liquidity of the latter. However, understanding the theory allows for a greater understanding of the nature of the contract itself.

1.2.1 Theoretical principle

Although it may not appear so on first trading, floor trading on a futures exchange is probably the closest one gets to an example of the economist's perfect and efficient market. The immediacy and liquidity of the market will ensure that at virtually all times the price of any futures contract reflects fair value. In essence, because a futures contract represents an underlying asset, albeit a synthetic one, its price cannot differ from the actual cash market price of the asset itself. This is because the market sets futures prices such that they are arbitrage-free. We can illustrate this with a hypothetical example. Let us say that the benchmark 10-year bond, with a coupon of 8%, is trading at par. This bond is the underlying asset represented by the long bond futures contract; the front month contract expires in precisely 3 months. If we also say that the 3-month London Inter-Bank Offer Rate (LIBOR) rate (here called the repo rate) is 6%, what is fair value for the front month futures contract? For the purpose of illustration let us start by assuming the futures price to be 105. We could carry out the following arbitrage-type trade:

buy the bond for 100;

simultaneously sell the future at 105;

borrow 100 for 3 months at the repo rate of 6%.

As this is a leveraged trade we have borrowed the funds with which to buy the bond, and the loan is fixed at 3 months because we will hold the position to the futures contract expiry, which is in exactly 3 months' time. At expiry, as we are short futures we will deliver the underlying bond to the futures clearing house and close out the loan. This strategy will result in cash flows for us as shown below.

Futures settlement cash flows

Price received for bond = 105:00 Bond accrued = 2:00 (8% coupon for 3 months) Total proceeds = 107:00

Loan cash flows

Repayment of principal = 100:00 Loan interest = 1:500 (6% repo rate for 3 months) Total outlay = 101:50

The trade has resulted in a profit of 5.50, and this profit is guaranteed as we have traded the two positions simultaneously and held them both to maturity. We are not affected by subsequent market movements. The trade is an example of a pure arbitrage, which is risk-free. There is no cash outflow at the start of the trade because we borrowed the funds used to buy the bond. In essence, we have locked in the forward price of the bond by trading the future today, so that the final settlement price of the futures contract is irrelevant. If the situation described above were to occur in practice it would be very short-lived, precisely because arbitrageurs would buy the bond and sell the future to make this profit. This activity would force changes in the prices of both bond and future until the profit opportunity was removed.

So, in our illustration the price of the future was too high (and possibly the price of the bond was too low as well) and not reflecting fair value because the price of the synthetic asset was out of line with the cash asset. What if the price of the future was too low? Let us imagine that the futures contract is trading at 95.00. We could then carry out the following trade:

sell the bond at 100;

simultaneously buy the future for 95;

lend the proceeds of the short sale (100) for 3 months at 6%.

This trade has the same procedure as the first one with no initial cash outflow, except that we have to cover the short position in the repo market, through which we invest the sale proceeds at the repo rate of 6%. After 3 months we are delivered a bond as part of the futures settlement, and this is used to close out our short position. How has our strategy performed?

Futures settlement cash flows

Clean price of bond = 95:00 Bond accrued = 2:00 Total cash outflow = 97:00

Loan cash flows

Principal on loan maturity = 100:00 Interest from loan = 1:500 Total cash inflow = 101:500

The profit of 4.50 is again a risk-free arbitrage profit. Of course, our hypothetical world has ignored considerations such as bid-offer spreads for the bond, future and repo rates, which would apply in the real world and impact on any trading strategy. Yet again, however, the futures price is out of line with the cash market and has provided opportunity for arbitrage profit.

Given the terms and conditions that apply in our example, there is one price for the futures contract at which no arbitrage profit opportunity is available. If we set the future price at 99.5, we would see that both trading strategies, buying the bond and selling the future or selling the bond and buying the future, yield a net cash flow of 0. There is no profit to be made from either strategy. So, at 99.5 the futures price is in line with the cash market, and it will only move as the cash market price moves; any other price will result in an arbitrage profit opportunity.

(Continues...)

Excerpted from The Futures Bond Basisby Moorad Choudhry Copyright © 2006 by Moorad Choudhry. Excerpted by permission.
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