Impact of Interest Rate Changes on Bond Prices

Very Hard Fixed Income Valuation Duration And Convexity

A bond investor is analyzing two bonds, Bond X and Bond Y, both with a face value of $1,000, a coupon rate of 5%, and 10 years to maturity. Bond X has a modified duration of 7 years, while Bond Y has a modified duration of 5 years. The yield to maturity for Bond X is currently 4%, and for Bond Y, it is 6%. Given that the interest rates are expected to rise by 1%, the investor wants to assess the price impact of this rate change on both bonds demonstrating an understanding of duration and convexity. What is the best assessment of the bond prices' responses to the interest rate increase?

Bond X will decrease in price by approximately 7% and Bond Y will decrease by approximately 5%.

Bond Y will decrease in price by approximately 6% and Bond X will decrease by approximately 4%.

Bond X will decrease in price less than Bond Y due to its higher modified duration.

Hint

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