Most bond futures contracts are based on a hypothetical benchmark bond. The Chicago Board of Trade’s U.S. Treasury bond futures contract is based on a 6 percent bond with at least 15 years from the futures expiration to maturity or the first call date. Even though the benchmark bond has a 6 percent coupon, any bond meeting the maturity requirement can be delivered. At any time, a single bond exists that the holder of the short position would find optimal to deliver if current conditions continued. That bond is called the cheapest to deliver and can be thought of as the bond on which the futures contract is based. In other words, the cheapest to deliver bond is the underlying. The responsiveness of the futures contract to an interest rate change is equivalent to the responsiveness of that bond on the futures expiration day to an interest rate change.
We can think of this concept as the responsiveness of the underlying bond in a forward context. This responsiveness can be measured as that bond’s modified duration on the futures expiration and, as such, we can use the price sensitivity formula to capture the sensitivity of the futures contract to a yield change. Accordingly, we shall, somewhat loosely, refer to this as the implied duration of the futures contract, keeping in mind that what we mean is the duration of the underlying bond calculated as of the futures expiration. Moreover, we also mean that the underlying bond has been identified as the cheapest bond to deliver and that if another bond takes its place, the duration of that bond must be used. We use the term implied to emphasize that a futures contract does not itself have a duration but that its duration is implied by the underlying bond. In addition to the duration, we also require an implied yield on the futures, which reflects the yield on the underlying bond implied by pricing it as though it were delivered at the futures contract expiration.
Hence, we can express the sensitivity of the futures price to a yield change as
where MDURf is the implied modified duration of the futures, f is the futures price, and Ayf is the basis point change in the implied yield on the futures.
Now that we have a measure of the responsiveness of a bond portfolio and the responsiveness of a bond futures contract to interest rate changes, we should be able to find a way to balance the two to offset the risk.
When individuals engage in a voluntary exchange, both parties are made better off. In the above example, Janet has the option of accepting or declining Brad’s offer of a trade. If she accepts his offer, she does so voluntarily. Janet would agree to this exchange only if she expects to be better off as a result. Because she likes tomatoes better than onions, Janet’s enjoyment of her salad will be greater with this trade than without it. On the other side, Brad has voluntarily made this offer of an exchange to Janet because Brad believes he will also be better off as a result of the exchange.
People tend to think of making, building, and creating things as productive activities.
Agriculture and manufacturing are like this. They create something genuinely new, something that was not there before. On the other hand, trade-the mere exchange of one thing for another4oes not create new material items. You might be tempted to think that if goods are merely being traded, one party will be better off and the other worse off. A closer look at the motivation for trade helps us see through this popular fallacy. Exchange takes place because both parties expect it will make them better off. If they didn’t, they wouldn’t agree to do it. For example, if Janet liked onions better than tomatoes, she wouldn’t have traded with Brad. The fact that she agreed to the trade means she thinks she has something to gain by doing so. Brad thinks the same thing when it comes to his tomatoes. In other words, because their exchange is voluntary, both Janet and Brad are made better off.
Why do individuals trade with each other, and what is the significance of this exchange? We have learned that value is subjective. It is wrong to assume that a particular good or service has a fixed objective value just because it exist^.^ The value of goods and services generally depends on who uses them, and on circumstances, such as when and where they are used, as well as on the physical characteristics. Some people love onions, whereas others dislike them exceedingly. Thus, when we speak of the “value of an onion,” this makes sense only within the context of its value to a specific person. Similarly, to most people an umbrella is more valuable on a rainy day than on a sunny one.
Consider the case of Janet, who loves tomatoes but hates onions, and Brad, who loves onions but hates tomatoes. They go out to dinner together and the waiter brings their salads. Brad turns to Janet and says, “I’ll trade you the tomatoes on my salad for the onions on yours.” Janet gladly agrees to the exchange. This simple example will help us illustrate two important aspects of voluntary exchange.
Bond futures | admin | 
March 29, 2010 10:05 am | 
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