A financial analyst is comparing two option-free bonds: Bond A has a modified duration of 6.0 and a convexity of 50. Bond B has a modified duration of 6.0 and a convexity of 80. Both bonds have the same yield to maturity. If interest rates are expected to fall significantly, which bond would the analyst prefer, and why?
- ABond B, because higher convexity provides better protection against rising rates.
- BBond B, because higher convexity provides greater price appreciation when rates fall.
- CBond A, because its lower convexity implies less interest rate risk.
- DBond A, because lower convexity is preferred when rates fall.
Show answer & explanationAnswer & explanation
Correct answer: B. Bond B, because higher convexity provides greater price appreciation when rates fall.
When interest rates fall, bond prices increase. Positive convexity means that the bond's price increases at an accelerating rate as yields fall. Therefore, a bond with higher convexity (Bond B) will experience a greater price increase than a bond with lower convexity (Bond A) for the same magnitude of yield decrease, assuming equal duration. This makes Bond B more attractive in a falling rate environment.
Why the other options are wrong
- A. Higher convexity does provide better protection against rising rates (smaller price decrease), but the question specifically asks about a 'significant fall' in rates, where higher convexity leads to greater gains.
- C. While lower convexity does imply less 'curvature' risk, it does not mean less 'interest rate risk' in general, especially when duration is the same. Furthermore, it's not preferred when rates are expected to fall.
- D. Lower convexity is not preferred when rates fall; higher convexity leads to greater gains.
Convexity and Price Sensitivity
Convexity measures the curvature of a bond's price-yield relationship. For bonds with positive convexity, the price appreciation from a yield decrease is greater than the price depreciation from an equivalent yield increase, making higher convexity generally desirable.
- Higher convexity is more beneficial when interest rates fall, leading to larger price gains.
- Higher convexity is also beneficial when interest rates rise, leading to smaller price losses.
- Investors generally prefer bonds with higher convexity, all else being equal.
Memory trick: High convexity's curve, for gains and protection, it serves.