You ran a regression of the yield of TBR Company’s 10-year bond on the 10-year U.S. Treasury benchmark’s yield using month-end data for the past year. You found the following result:
YieldTBR = 0.54 + 1.22 YieldTreasury
where YieldTBR is the yield on the TBR bond and YieldTreasury is the yield on the U.S. Treasury bond. The modified duration on the 10-year U.S. Treasury is 7.0 years, and modified duration on the TBR bond is 6.93 years.
a. Calculate the percentage change in the price of the 10-year U.S. Treasury, assuming a 50-basis-point change in the yield on the 10-year U.S. Treasury.
b. Calculate the percentage change in the price of the TBR bond, using the regression equation, assuming a 50-basis-point change in the yield on the 10-year U.S. Treasury.