Research & Publications
Back-to-Basics

The following article is reprinted from the April, 1997 issue of On the Edge,
the CMS bimonthly newsletter.

Back-to-Basics: Using Interest Rate Futures in BondEdge

Teri Geske
Senior Vice President, Product Development


Since a growing number of CMS clients are initiating or expanding the use of interest rate futures in their portfolios, this month's Back-to-Basics article is an introduction to the way interest rate futures contracts are incorporated in reports and simulations throughout BondEdge for Windows.

Despite the negative publicity generated by some derivatives-related fiascoes, more and more institutional investors recognize that futures, swaps and other derivatives can be prudent and effective risk management tools. The concept of futures contracts originated in the agriculture business, as farmers wanted a way to lock in the price at which their crops would be sold when harvested some months in the future, and food products companies wanted to secure their cost of raw materials. The idea was easily extended to other markets (interest rates, currencies, precious metals, etc.), and interest rate futures are now among the most commonly used derivatives in the world.

A futures contract represents the obligation to buy or sell a particular underlying instrument (or commodity or currency) on a particular date in the future at a price determined today. No money is exchanged when a futures contract is created; however, the buyer of the contract (the "long" position) has increased his exposure to changes in the market price of the underlying, just as if an outright purchase had been made. Similarly, the seller of the contract (the "short" position) has reduced his or her exposure to changes in the value of the underlying.

To see how this works, imagine that I enter into a contract today to buy a ton of bricks from the Acme Brick company three months from now for $1000. If the market price of bricks rises to $1100/ton at the end of the three month period, I make a $100 profit because I pay only $1000 for something that is worth $1100. I am therefore just as affected by the change in the price of bricks as if I had actually purchased them today. In fact, at the end of three months I may not actually take delivery of the bricks. When the expiration date of the contract arrives, in order to come up with the money needed to make the purchase I can simply tell Acme to sell the bricks at the prevailing market price of $1100, keep the $1000 I owe them and send me the $100 difference as my profit.

Similarly, interest rates futures contracts allow us increase or decrease a portfolio's sensitivity to changes in interest rates without actually buying or selling bonds. Since "sensitivity to changes in interest rates" is another way of saying "duration", we see that futures contracts should be viewed as one way to adjust a portfolio's effective duration; the choice of the type and number of contracts used depends upon your time horizon and duration target. The BondEdge database includes all listed futures contracts on the 30 year, 10 year and 5 year Treasuries, using a four-digit cusip (e.g., USM8 for the June 1998, 30-year Treasury bond contract). Futures are added to a portfolio by specifying the number of contracts in the "Par" field (use a negative sign to indicate a short position).

There are a number of issues to consider with respect to incorporating interest rate futures in BondEdge, such as:

  • how to compute the duration of the futures contract itself;
  • how to calculate the impact of a long or short position in futures on a portfolio's duration;
  • how to define the way futures are treated in Instantaneous and Aged simulations.

Let's examine each of these points in order. First, as with all other securities in BondEdge, the effective duration of a futures contract is computed by taking the average change in its price, given +/-100bp shifts in the Treasury spot curve. The duration of a futures contract is related to the duration of the underlying bond which will be delivered on the expiration date, but the two are not identical. As interest rates fluctuate, the actual Treasury security which is "cheapest-to-deliver" can change, and this is reflected in the duration of a futures contract in BondEdge. In Security Calculator, you can bring up a screen which shows each of the deliverable treasuries for the selected contract, in descending order of "cheapness" with respect to delivery.

How do we calculate the impact of a long or short position in futures on a portfolio's duration in BondEdge? Even though there is no change in the portfolio's market value when a futures contract is added (or shorted), we must compute the percentage of the portfolio's market value the contract represents. Since an interest rate futures contract represents an obligation to purchase or deliver a certain number of bonds (e.g., 100,000 face value for each Treasury Bond futures contract) on the expiration date, adding a futures contract to a portfolio may be thought of as purchasing the underlying bonds with borrowed funds. When the expiration date arrives, the implicit assumption is that the Treasuries delivered would be sold to pay off the borrowing; if interest rates have fallen, the market price of the bonds is above the futures price agreed upon today and the portfolio realizes a profit. The opposite occurs if interest rates rise before the expiration date.

With this in mind, BondEdge Appraisal reports and Compare Distribution reports implicitly compute a futures contract's contribution to portfolio duration using a long position in the underlying cheapest-to-deliver security and a short position in cash. (Similarly, shorting a futures contract is computed as a short position in the underlying bonds and an increase in cash; on the expiration date, the cash is used to purchase the underlying at the prevailing market price to close out the contract). This approach ensures that there is no change in the market value of the portfolio, as no money changes hands when a futures contract is bought or sold:

Consider the following portfolio:


Par ($000)
Holdings
Price		 Conv.*
Factor		 Market
Factor		 % of
Port.		 Effec.
Dur.		 Contrib.
To Dur.
10,000 XYZ Corporation Bond 98.205 N/A 9,821 100.00 7.25 7.25
=1 Contract 10 year Tsy Futures expiring in 6 months:
100 U.S. Treasury 8.00% of 05/15/01 ** 107.53 1.00 1,075 10.95 5.30 0.58
(100) Cash (duration = time to expiration) (107.53) 1.00 1,075 (10.95) 0.50 (0.05)
TOTAL   9,821 100.0%   7.78
* The conversion factor reflects the fact that different Treasury securities are eligible to be delivered on the expiration date; it is used to adjust the amount delivered based on established rules which are beyond the scope of this article.
** The cheapest-to-deliver Treasury (computed daily for all futures contracts in the CMS database).

In this example, the portfolio consists of a corporate bond with a duration of 7.25 and a six month futures contract on the 10 year Treasury with a duration of 5.30. The contribution to the portfolio's duration from the futures contract is based on the exposure to the underlying cheapest-to-deliver Treasury Note and an offsetting position in cash. Even though the duration of the futures contract is less than the duration of the corporate bond, adding the futures contract increases the portfolio's duration. In other words, the sensitivity to changes in interest rates has increased, due to the "leveraging effect" of a futures contract, i.e. of purchasing the underlying bonds with borrowed funds.

The standard Appraisal report in BondEdge shows futures contracts in a separate section, including the contribution to the portfolio's yield, duration and convexity from the positions. In Compare Distribution reports, the exposure resulting from a futures contracts is expressed in the Effective Duration distribution breakdown as a long or short position in the underlying Treasury offset by a long or short position in Cash. This approach illustrates the portfolio's sensitivity to different points on the yield curve.

In Portfolio simulations, the choice of "Aged" or "Instantaneous" significantly affects the way futures contracts are treated. In an "Instantaneous" simulation, BondEdge assumes the portfolio at the Horizon Date still contains futures contracts with the same characteristics as the current position. Using our example above, under a 12-month Instantaneous simulation the horizon date portfolio would still contain a futures contract with six months to expiration. This is consistent with the idea that in Instantaneous simulations, the portfolio is rebalanced so that securities do not shorten with the passage of time. In an "Aged" simulation, since securities do shorten the futures contract can expire; if the horizon is beyond the expiration date of the contract, BondEdge assumes the portfolio no longer contains the futures position. In both types of simulations, the impact of changes in interest rates is incorporated in the market value of the portfolio, categorized as a price return effect.

Since futures contracts are marked-to-market, BondEdge simulations include an "income" return for futures using the following logic: as the expiration date of the contract approaches, the price of the futures contract must converge to the price of the underlying instrument (otherwise, a risk-free arbitrage opportunity arises). In a simulation, the change in the value of the futures position due solely to this passage of time is categorized as an income effect.

There are many situations where interest rate futures are a logical, expedient choice for duration management. As with all investment and risk management alternatives, the decision to use futures contracts should be evaluated in a portfolio context, as BondEdge allows you to do.