A new design of bond future

Julian D. A. Wiseman

Abstract: The current design of bond future resembles an agricultural contract. A better design would prevent squeezes, and thus allow a bond future to better represent its underlyings.

Contents: Introduction, The new design, An example delivery, Conclusion.

Publication history: only here. Usual disclaimer and copyright terms apply.

Introduction

In 1976 the Chicago Board of Trade listed a future on long-dated US Treasuries, and in 1981 LIFFE listed a future on British government debt. There are now futures based on the debt of many governments, and the largest futures contract in the world is based on 10-year German debt. But the design of these all these bond futures is somewhat strange:

The interest-rate markets exist to allow borrowers to raise funds and investors to purchase assets. They allow the various types of interest-rate and credit risks to be repackaged into a form that someone is willing to hold. For the most part, the instruments that are traded are well designed for their purpose. Some of these instruments are complicated, but their complications are necessary, perhaps to make them into a better hedge for something else, or to reduce credit risk, or for some other need.

Bond futures are a partial exception to this. Their complications exist for a purpose, but at least to this author, do not seem optimally designed for that purpose. Indeed, the specification of the bond contract seems to resemble that of an agricultural contract, perhaps because they were first listed on an exchange that then traded agricultural contracts. Still, that’s history. Bond futures exist, and are very important, and so they must be described as they are, rather than as the author believes that they should be. But readers are warned that bond futures are complicated instruments.

(The quotations above and below are taken from chapter 13 of Pricing Money: A Beginner’s Guide to Money, Bonds, Futures and Swaps.)

This paper describes a better design of futures contract.

Currently, bond futures trade in price terms. The short chooses which of several deliverable bonds to deliver, and receives for it a price of the EDSP (the Exchange Delivery Settlement Price, the final price of the future) times the conversion factor for that bond, plus the accrued. (This is described in more detail on pages 155-163 of Pricing Money.) The effect is that, often, one bond is far cheaper to deliver than any other. If the contract is above par this is the shortest bond; if below par, the longest. In either case the lone cheapest-to-deliver (CTD) is vulnerable to being squeezed.

The problem stems from the fact that bond markets trade in terms of yield, not in terms of prices and their ratios. So instead consider the following design of contract.

The new design

We work with a 10-year future, with a nominal semi-annual coupon of 6% and a contract size of 100,000. At expiry, the EDSP of the contract is converted to a yield. So if the expiry price were 110.00, the (semi-annual) expiry yield would be 4.73317005395568%. For each deliverable this yield is converted to a dirty price. The short then chooses which deliverable to deliver and does so, in return receiving the price equivalent to the expiry yield.

Of course, the short would choose to deliver the CTD, and the CTD would always be the highest yielding, whether the contract were above or below par. Hence the maximum possible CTD squeeze would be the yield difference between it and the deliverable with the next highest yield. The future would be much less susceptible to security-specific mischief.

However, this would not fix all the abuses of the current design. Currently, market players have an incentive to manipulate the last price of a contract:

If the conversion factor of the delivered bond is greater than 1, then both the long and short positions increase in size over delivery. If it is less than 1, both positions become a little smaller. Usually, which bond is CTD is known long before the delivery day. Hence both longs and shorts know the conversion factor of the bond that will be delivered. If this conversion factor is above 1, then the longs would benefit from an artificially low … EDSP … , and likewise, the shorts would like the EDSP to be artificially high. Because of these incentives, sometimes the price action can be somewhat anomalous as a contract expires.

The new design eliminates this incentive by adjusting the amount of each bond that is to be delivered. Since the problem arises from the change of risk of delivery, the problem is eliminated by specifying that the amount to be delivered is the amount that has the same DV01 (the same risk) as the contract.

An example delivery

So, let’s imagine that there are three deliverables into a 10-year 6%-semi future: an 8.5% 10.75-year; a 6% 10-year; and a 4% 9-year. The following table shows for each deliverable, over a range of EDSPs from 159.99 to as low as 10.00, what nominal amount would be deliverable, and what price would be paid for it if it were delivered.

Note that:

• Because the 8.5% 10.75-year has a greater DV01 than a 6% 10-year, its deliverable amount is always less than the nominal size of the contract.

• And because the 4% 9-year has a smaller DV01 than a 6% 10-year, its deliverable amount is always more.

• But the deliverable amount of the 6% 10-year bond is always exactly 100,000 and its delivery price is always the same as the contract’s EDSP. Therefore the future, in some sense, indeed behaves as a future on a 6% 10-year bond.

• For all the deliverables, the deliverable amount never spikes towards infinity: delivery would be possible under all market conditions.

Conclusion

So a contract in this new design would still track the ‘cheapest’ of a set of deliverables, but would do so in a manner that prevented security-specific squeezes, and that did not change a trader’s risk over delivery.

Julian D. A. Wiseman, January 2002