为什么 “as yields lower than 6% imply that the CF forlong-term bonds is lower than otherwise. This will tend to favor bondswith high conversion factors, or shorter bonds”?

what is therelationship between CF and maturity?  

what is the relationship betweenCF and coupon?
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.