On the topic of one-sided durations, the Schweser book says that the price change of a callable when rates fall is smaller than the price change for an equal incerase in rates. Can anyone explain why that is the case? My logic is that when rates fall, the bond is more likely to get called by the issuer, but why is the price change smaller than when rates rise??
The upside on the bond’s price is capped by the call price. When rates fall, the call option starts to come into the money, and the price/yield curve starts to display negative convexity: the price increases, but at a decreasing rate. Therefore, the lower one-sided duration is less than the upper one-sided duration.
Thanks. So if I understood you correctly and by using the same logic, the downside of a puttable bond is capped by the put price, so its lower one-side duration is larger than the upper one-sided duration. Assuming lower duration means duration when rates drop and upper duration is when rates rise?
Correct.