Duration help...

Hey everyone, Please explain the following statement: “Declining yields should lead to decreases in duration.” I don’t understand this statement, isn’t duration higher at low interest rates?

From where you read this statement??

This statement comes from the answer to Question #105 of Schweser Practice Volume 2, Exam 1 (Morning Session).

don’t have access to Schweser, but are we talking about callable bond, not straight bond?

elcfa, Could you explain the difference between the two. I believe the above statement to be true for a callable bond given its negative convexity. For a straight bond, however, the above statement should be false, correct?

5carrots I believe so. If you draw the relationship of price as function of market interest rate(YTM), you will see that - for straight bond, the curve shoots straight up at lower yield, i.e., the curve gets steeper (positive convexity). - for callable bond, the price flattens and stops at call price. Since duration is delta price/delta yield, you see that duration increases with straight bond and duration decreases with callable bond. Alternatively, you can also deduct it with the year length definition of duration: weighted average length of all payments. When interest rate goes down, the bondholders not willing to pay coupon at higher rates than market --> more likely to call it back --> bond’s life gets shortened --> duration lower. Hope it clarifies.