A fixed-income analyst is comparing two option-free bonds, Bond X and Bond Y. Both bonds have a modified duration of 6.5. Bond X has a convexity of 50, while Bond Y has a convexity of 80. If interest rates are expected to decrease significantly, which bond would the analyst expect to perform better, and why?
- ABond X, because it has lower convexity, making it less sensitive to rate changes.
- BBoth bonds would perform similarly, as their modified durations are identical.
- CBond Y, because it has higher convexity, leading to greater price appreciation when rates fall.
- DBond X, because lower convexity implies less downside risk if rates unexpectedly rise.
Show answer & explanationAnswer & explanation
Correct answer: C. Bond Y, because it has higher convexity, leading to greater price appreciation when rates fall.
Convexity measures the curvature of a bond's price-yield relationship. For a given change in yield, a bond with higher convexity will experience greater price appreciation when yields fall and less price depreciation when yields rise, compared to a bond with lower convexity (assuming the same duration). Since interest rates are expected to decrease significantly, Bond Y, with its higher convexity, will benefit more from the rate drop, exhibiting greater price appreciation.
Why the other options are wrong
- A. Lower convexity means less price appreciation when rates fall, not better performance.
- B. Duration only provides a linear approximation; convexity accounts for the curvature, leading to different performance.
- D. While lower convexity does imply less downside risk if rates rise, the question specifies an expectation of falling rates, making higher convexity desirable.
Convexity and Price Sensitivity
Convexity is a second-order measure of a bond's price sensitivity to interest rate changes, accounting for the curvature of the price-yield relationship. Positive convexity means a bond's price increases more when yields fall than it decreases when yields rise by the same amount.
- Measures the rate of change of duration as yields change.
- For option-free bonds, convexity is generally positive.
- Higher convexity is desirable for investors, as it provides more upside potential and less downside risk.
- Convexity becomes more important for large interest rate changes.
Memory trick: Convexity is like a 'Smile' on the price-yield curve – more upside, less downside.