CFA Level II ExamFixed IncomeMedium
A fixed-income analyst is comparing a zero-coupon bond and a coupon bond, both with the same maturity and credit quality. Assuming an instantaneous and parallel shift upwards in the yield curve, which bond will exhibit greater price volatility?
- ABoth bonds will exhibit similar price volatility if their modified durations are equal.
- BThe zero-coupon bond, due to its longer duration.
- CThe coupon bond, due to its reinvestment risk.
- DThe zero-coupon bond, due to its lower liquidity.
Show answer & explanationAnswer & explanation
Correct answer: B. The zero-coupon bond, due to its longer duration.
Zero-coupon bonds have all their cash flows (principal) at maturity, meaning their duration is equal to their maturity. Coupon bonds, by contrast, have interim coupon payments, which effectively shorten their duration relative to their maturity. Higher duration implies greater price volatility for a given change in interest rates.
Why the other options are wrong
- A. Incorrect. While duration is a measure of price volatility, for bonds of the same maturity, a zero-coupon bond will always have a longer duration than a coupon bond (assuming positive yield).
- C. Incorrect. Reinvestment risk affects the total return, not directly the price volatility in response to an instantaneous yield curve shift. Coupon bonds generally have shorter durations than zero-coupon bonds of the same maturity, meaning less price volatility.
- D. Incorrect. While liquidity can affect pricing, it is not the primary factor explaining the difference in price volatility between zero-coupon and coupon bonds due to interest rate changes; duration is the key factor.
Duration and Price Volatility
Duration is a measure of a bond's price sensitivity to changes in interest rates. Bonds with longer durations exhibit greater price volatility.
- Zero-coupon bond duration equals its time to maturity.
- Coupon bond duration is less than its time to maturity.
- Higher duration implies higher interest rate risk (price volatility).
Memory trick: Longer duration 'rides' the rate changes 'harder'.