Chartered Financial Analyst (CFA) Practice Exam Level 2

What is the nature of convexity in option-free bonds?

1. Negative convexity throughout

2. Positive convexity throughout

3. Variable convexity based on market conditions

4. Zero convexity in a stable market

The correct answer is: Positive convexity throughout

The nature of convexity in option-free bonds is characterized by positive convexity throughout their lifespan. Positive convexity indicates that as interest rates decrease, the price of the bond will increase at an accelerating rate, and conversely, as interest rates increase, the price will decrease at a decelerating rate. This relationship reflects the curvature of the price-yield function of the bond, where the price will change in a more pronounced manner for movements in interest rates compared to linear estimates. This positive convexity is advantageous for bondholders because it provides a measure of price sensitivity to interest rate changes, enhancing the bond’s total return potential in declining yield environments. Typical bonds exhibit this behavior because they do not have embedded options, allowing them to maintain a consistent convexity profile without the complications introduced by features like call or put options, which can alter price dynamics. Understanding this property is crucial, as it differentiates option-free bonds from those with embedded options, which may demonstrate negative convexity at certain points, particularly when interest rates are low and the option to redeem at par becomes more valuable. Thus, recognizing the inherently positive convexity of option-free bonds helps investors assess risk and returns more effectively in their fixed-income portfolio management.