Exercise 3: Why Long and Short Gilts React Differently to the Same Rate Change — Possible Solution ==================================================================== This chapter defines duration as a measure of how much a bond's own price moves for a given change in interest rates, and states directly that duration generally rises with longer maturity. Applying this to a long Gilt and a short Gilt facing the identical real rate change explains the difference. WHAT MAKES A LONG GILT MORE SENSITIVE A long-maturity Gilt locks its own fixed coupon in place for a much longer real period of time - potentially decades, per Chapter 2's own real maturity classifications. If interest rates rise, a long Gilt's now-uncompetitive coupon stays uncompetitive for a genuinely much longer stretch of time before the bond matures and returns its nominal value. Because the mismatch between what it pays and what a newly issued bond pays persists for so much longer, the market price adjustment needed to make its yield competitive again has to be larger - producing a bigger real price swing for the same rate change. WHY A SHORT GILT IS LESS AFFECTED A short-maturity Gilt, by contrast, will mature and return its nominal value relatively soon regardless of what happens to interest rates in the meantime. Its own below-market coupon only needs to be "endured" by a holder for a comparatively brief real period before the bond matures and the money becomes available to reinvest at whatever the new, higher rate happens to be. Because the mismatch is genuinely short-lived, a much smaller price adjustment is enough to make its yield competitive, producing a smaller real price swing for the identical rate change. WHY THIS IS A DIRECT APPLICATION OF DURATION This is exactly what this chapter means by duration rising with maturity: the longer a bond's own remaining life, the more total time its fixed coupon spends being mismatched against prevailing rates after a real rate change, and the larger the corresponding price movement needs to be to compensate. A short Gilt's shorter remaining life caps how long that mismatch can persist, capping the size of the real price reaction in turn. ANSWER: A long-maturity Gilt reacts more strongly than a short-maturity Gilt to the same interest rate change because of duration - the long Gilt's fixed coupon remains mismatched against new market rates for a much longer real period before maturity, requiring a larger market price adjustment to keep its yield competitive. A short Gilt matures much sooner regardless of the rate change, so its own coupon mismatch is short-lived, requiring only a small price adjustment. This is precisely why this chapter states that duration - and therefore price sensitivity to rate changes - generally rises with a bond's remaining maturity. WHY THIS WORKS AS AN ANSWER ------------------------------ This explains the underlying reason (how long the coupon mismatch persists) that connects maturity length to price sensitivity, rather than simply restating that duration is higher for longer bonds without justifying why.