Thank you in advance, PL. Hi PL, Those are just Hull's statements of course.
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Tuckman actually explains it, see my extraction below from Tuckman Chapter The short position purchases the bond at the quoted bond price which reflects the actual yield curve; i. But the conversion factor abstracting the details "standardizes" the basket of choices by assuming a flat 6. So, in real shorthand terms, the short is buying the actual yield curve and receiving credit for a flat 6.
That assumes a flat "notional" yield of 6. As yield increases above below 6.
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But, because conversion factors are fixed, the delivery price of the 5s of August 15, , stays the same relative to that of all other bonds. In other words, as yields increase above the notional coupon rate, the cost of delivering the 5s of August 15, , falls more than that of any other bond. Graphically, the ratio of the price to conversion factor of the 5s of August 15, , falls below that of all other bonds.
As yield falls below the notional coupon rate, the prices of all bonds increase but the price of the bond with the lowest duration, namely the 4. At the same time, since the conversion factors are fixed the delivery price of the 4. It is for this reason that the CTD is either the 4.
In reality, of course, the term structure can take on a wide variety of shapes that will affect the determination of the CTD. In general, anything that cheapens a bond relative to other bonds makes that bond more likely to be CTD. If, for example, the curve steepens, then long-duration bonds e. On the other hand, if the curve flattens, then short-duration bonds e. As a result the 6. For lower yields the 4. Thanks a lot for your prompt and detailed response.
Mark W Active Member Oct 26, David, This is a great explanation - really appreciate your never ending efforts to explain these things in an easy manner.
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The new Tuckman book is great by the way. I have given it praise elsewhere, but Tuckman certainly complements hull when it comes to fixed income. Indeed, I would be surprised if GRAP does not source material from his newest edition for next years exam. I have Fabozzi - worth updating to Tuckman? IMO Tuckman is clearer than Fabozzi on most topics, including the - according to number of forum posts on the topics - the dreaded "duration family" and convexity questions.
Fabozzi has been around for a long time, but I get the feeling that he has read his book too many times, and the value of his incremental updates have converged asymptotically towards zero. Contrast that with Tuckman's new edition, which has not been updated until now for 10 years. Ships from and sold by Amazon.
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