CFA Level II ExamFixed IncomeMedium
A portfolio manager is constructing a portfolio of fixed-income securities and is keen on understanding the impact of interest rate changes on bond prices. The manager is particularly interested in a bond's convexity. Which of the following statements about convexity is most accurate?
- ACallable bonds exhibit positive convexity when interest rates are low, leading to larger price increases.
- BConvexity is a linear measure of a bond's price sensitivity to interest rate changes.
- CFor option-free bonds, convexity is always positive, meaning price sensitivity decreases as yields rise.
- DConvexity is less important for bonds with embedded options than for option-free bonds.
Show answer & explanationAnswer & explanation
Correct answer: C. For option-free bonds, convexity is always positive, meaning price sensitivity decreases as yields rise.
For option-free bonds, convexity is always positive. This means that as yields fall, the bond's price increases at an increasing rate, and as yields rise, the bond's price decreases at a decreasing rate. This positive convexity is generally beneficial to investors.
Why the other options are wrong
- A. Callable bonds exhibit negative convexity when interest rates are low because the call option becomes more valuable, limiting upside price potential as rates fall.
- B. Convexity is a non-linear, second-order measure of price sensitivity, correcting for the linear approximation of duration.
- D. Convexity is even more crucial for bonds with embedded options, as their price-yield relationship can be highly non-linear and even negatively convex.
Convexity of Bonds
Convexity measures the curvature of a bond's price-yield relationship, providing a more accurate estimate of price changes than duration alone, especially for large yield changes.
- It is a second-order measure.
- Option-free bonds typically have positive convexity.
- Callable bonds can exhibit negative convexity.
Memory trick: Convexity curves the duration, making it more precise.