Practice Quiz 2 Solutions — Duration & Interest Rate Risk
Setup: Two bonds, each with face value $1,000 and YTM of 5%. Bond X is a 3-year zero-coupon. Bond Y is a 3-year 10% annual coupon.
(a) Which bond has a higher Macaulay duration?
Bond X has a higher Macaulay duration. A zero-coupon bond’s Macaulay duration equals its maturity (3 years), because the entire cash flow is received at maturity. Bond Y pays coupons at years 1 and 2, pulling the weighted-average timing of cash flows forward — so its duration is less than 3 years.
(b) Bond X has modified duration of ~2.86 years. If yields rise 50bp, estimate the percentage price change.
\[\%\Delta P \approx -D_{\text{mod}} \times \Delta y = -2.86 \times 0.50\% = -1.43\%\]The bond’s price falls by approximately 1.43%.
(c) Is the client right that Bond Y has the same risk as Bond X because they share the same maturity?
The client is wrong. Bond Y has a lower duration than Bond X because its coupon payments return cash earlier, reducing its sensitivity to interest rate changes. Same maturity does not mean same risk — duration, not maturity, is the correct measure of interest rate risk. Bond Y will experience a smaller price swing for a given change in yields.