Questions: Interest Rate Risk and Duration Strategy

Question 1

A bond has a modified duration of 6 years. Interest rates rise by 100 basis points (1 percentage point). What is the approximate percentage change in the bond's price?

• A. +6% — bond prices rise when rates rise
• B. −6% — the bond loses approximately 6% of its price
• C. −1% — only the coupon payments are affected, not the price
• D. −0.6% — duration must be divided by 10 when working with basis points

Answer: (B)

The duration approximation is ΔP/P ≈ −D* × Δy. With D* = 6 and Δy = +0.01 (100 bps expressed as a decimal), ΔP/P ≈ −6 × 0.01 = −0.06 = −6%. Bond prices and yields move inversely, so rising rates produce price losses. Option A reverses the relationship. Option D confuses the units — 100 basis points = 1 percentage point = 0.01 in decimal, not 0.001.

Question 2

Which of the following bonds has the greatest interest rate sensitivity?

• A. A 5-year bond with a 10% annual coupon
• B. A 5-year zero-coupon bond
• C. A 10-year bond with a 10% annual coupon
• D. A 30-year bond with a 15% annual coupon

Answer: (B)

A zero-coupon bond pays nothing until maturity, so its Macaulay duration equals its maturity exactly — 5 years here. A coupon bond of the same maturity receives intermediate cash flows that pull the weighted-average time forward, giving it duration less than 5 years. The 10-year and 30-year coupon bonds have longer maturities but large coupon payments drag their durations considerably below maturity. The 5-year zero-coupon bond has the highest duration relative to its maturity structure among these choices.

Question 3

A pension fund can protect its funding ratio from interest rate movements by setting the duration of its bond portfolio equal to the duration of its future liabilities.

• T. True
• F. False

Answer: True

This is duration matching (immunization). If portfolio duration equals liability duration, a change in rates moves the present value of assets and liabilities by approximately the same percentage, preserving the funding ratio. A 1% rate rise that reduces bond values by 7% also reduces the present value of future liabilities by approximately 7% — leaving the fund just as well-funded. Pension funds and insurance companies use exactly this strategy to guarantee they can meet future obligations regardless of rate movements.

Question 4

A bond's duration usually equals its time to maturity.

• T. True
• F. False

Answer: False

Duration equals maturity only for zero-coupon bonds, which pay nothing until maturity. For any coupon bond, intermediate cash flows received before maturity pull the weighted average time below the maturity date. Macaulay duration is always less than or equal to maturity, with equality only at the zero-coupon extreme. A 10-year bond with a 6% annual coupon might have a Macaulay duration of roughly 7–8 years — confusing duration with maturity would significantly overestimate its interest rate risk.

Question 5

Why does a zero-coupon bond have greater interest rate sensitivity than a coupon bond of the same maturity, and what does this imply for portfolio construction?

Model answer: A zero-coupon bond's entire value is a single payment at maturity — no early cash flows cushion against rate changes. Its Macaulay duration equals its maturity, the longest possible for a bond of that term. A coupon bond of the same maturity receives coupon payments along the way; those early payments shorten the cash-flow-weighted average time, reducing duration and price sensitivity. For portfolio construction, zero-coupon bonds are the most powerful tool for extending portfolio duration — a small allocation dramatically raises rate sensitivity. Conversely, high-coupon bonds shorten duration without reducing nominal maturity.

The insight connects the mechanical definition (Macaulay duration as a weighted average of cash flow timing) to practical portfolio management. Duration is a design variable: choosing between zero-coupon and coupon bonds lets a manager tune interest rate exposure precisely, which is exactly what immunization and liability-matching strategies require.