Fixed income question

i was doing practice problems for reading 66 on CFA textbooks, the question 20 says: at yield levels that are close to the bond’s coupon rate, the price of an option-free bond higher than the price of an otherwise identical callable bond, but not higher than an otherwise identical putable bond. I understand the negative convexity thing, but i don’t get what does ‘at yield levels that are close to the bond’s coupon rate’ mean? why is that identical to relatively low yield levels?

can someone help on this one? thx!!

When the coupon rates are close to yields - eg. coupon rate 6% and yield 6.001%. If the two rates are very different the statement may not hold true - (the ceteris paribus thing!). For instance if the yield is much higher the bond price of the option fee bond could actually be depressed to a value lower than the bond with a the call option. Remember the callable bond price is (other things being constant) less because of the risk of the call to the investor. I am not sure whether this helped?