Comparison of Duration and Convexity in Bonds

Very Hard Fixed Income Valuation Duration And Convexity

During a recent evaluation of a fixed-income portfolio, an analyst assessed two bonds: Bond X and Bond Y. Bond X is a 5-year zero-coupon bond with a face value of $1,000, trading at $800, while Bond Y is a 10-year bond with a 6% annual coupon, trading at $950. The market interest rate is currently 5%. The analyst wants to compare the interest rate risk of these two bonds using both duration and convexity.

If the analyst calculates the modified duration for both bonds, which bond would be expected to exhibit higher price sensitivity to interest rate changes, and how does this relate to the bonds' respective convexities?

Bond X will have a higher modified duration and convexity, indicating higher price sensitivity.

Bond Y will have a higher modified duration, but Bond X will have a higher convexity.

Both bonds will have similar modified durations, but Bond Y will exhibit greater convexity.

Hint

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