conversion factor

[ajsa]

Hi David,

Could you pls clarify this question? I wonder why “as yields lower than 6% imply that the CF for long-term bonds is lower than otherwise. This will tend to favor bonds with high conversion factors, or shorter bonds”? what is the relationship between CF and maturity?
Thanks.

The Chicago Board of Trade has reduced the notional coupon of its Treasury
futures contracts from 8% to 6%. Which of the following statements are
likely to be true as a result of the change?
a. The cheapest-to-deliver status will become more unstable if yields hover
near the 6% range.
b. When yields fall below 6%, higher-duration bonds will become cheapest
to deliver, whereas lower-duration bonds will become cheapest to deliver
when yields range above 6%.
c. The 6% coupon would decrease the duration of the contract, making it
a more effective hedge for the long end of the yield curve.
d. There will be no impact at all by the change.

a. The goal of the CF is to equalize differences between various deliverable bonds.
In the extreme, if we discounted all bonds using the current term structure, the
CF would provide an exact offset to all bond prices, making all of the deliverable
bonds equivalent. This reduction from 8% to 6% notional reflects more closely
recent interest rates. It will lead to more instability in the CTD, which is exactly
the effect intended. Answer b) is not correct, as yields lower than 6% imply that
the CF for long-term bonds is lower than otherwise. This will tend to favor bonds
with high conversion factors, or shorter bonds. Also, a lower coupon increases the
duration of the contract, so c) is not correct.

 

[ajsa]

Hi David,

Here is my understanding: assuming coupon is 6%.. YTM<6% means premium bond. When maturity increases, bond price increases, so it is cheaper to deliver S/T bond... is it correct?

so does it mean CF is fixed?

Thanks.

 

[David Harper CFA FRM]

Hi asja,

The "unstable" confuses me a bit, but I think it simply means that as yields approach 6%, because the CF are calibrated on an assumption of 6% yield, the "competition" for the CTD bond becomes more crowded (i.e., the CTD and the next-CTD are nearer in price). The issue is that, as yields vary from this 6% "calibration point," higher yields (> 6%) favor high duration bonds and lower yield (< 6% ) favor low duration bonds. As Hull says, "When bond yields are in excess of 6%, the conversion factor system tends to favor the delivery of low-coupon long-maturity bonds [i.e., high duration]. When yields are less than 6%, the system tends to favor the delivery of high-coupon short-maturity bonds [i.e., low duration]. Also, when the yield curve is upward-sloping, there is a tendency for bonds with a long time to maturity to be favored, whereas when it is downward-sloping, there is a tendency for bonds with a short time to maturity to be delivered. "

...this is advanced, notoriously difficult (because you really have to first comprehend the CF mechanics; I have an XLS on member page which replicates), with low testability, so I won't have time to engage a long thread on this in the next two days. Tuckman Chapter 20 (not FRM assigned!) is the best explain I've seen anywhere...David