Suppose a 10-year zero coupon bond with a face value of 100...

Suppose a 10-year zero coupon bond with a face value of $\$ 100$ trades at $\$ 69.20205$ a. What is the yield to maturity and modified duration of the zero-coupon bond? b. Calculate the approximate bond price change for a 50 basis point increase in the yield, based on the modified duration you calculated in parta). Also calculate the exact new bond price based on the new yield to maturity. c. Calculate the convexity of the 10 -year zero-coupon bond. d. Now use the formula (equation 7.15 ) that takes into account both duration and convexity to approximate the new bond price. Compare your result to that in part b).

Suppose a 10-year zero coupon bond with a face value of $\$ 100$ trades at $\$ 69.20205$
a. What is the yield to maturity and modified duration of the zero-coupon bond?
b. Calculate the approximate bond price change for a 50 basis point increase in the yield, based on the modified duration you calculated in parta). Also calculate the exact new bond price based on the new yield to maturity.
c. Calculate the convexity of the 10 -year zero-coupon bond.
d. Now use the formula (equation 7.15 ) that takes into account both duration and convexity to approximate the new bond price. Compare your result to that in part b).

Key Concepts

Zero-Coupon Bond

A zero-coupon bond is a debt instrument that does not make periodic interest payments; it is issued at a discount to its face value and matures at par. This structure makes its valuation dependent solely on the time until maturity and the yield to maturity, which simplifies the analysis of time value of money concepts.

Yield to Maturity

Yield to maturity (YTM) is the internal rate of return of a bond, equating the present value of its future cash flows to its current market price. It provides a comprehensive measure of return by taking into account the timing, amount of cash flows, and the bond's current price relative to its face value.

Modified Duration

Modified duration measures the sensitivity of a bond's price to changes in interest rates. It represents the percentage change in bond price for a one percentage point change in yield, making it an essential tool for assessing interest rate risk, especially in linear approximations of price changes.

Convexity

Convexity quantifies the curvature in the relationship between bond prices and yields, providing a correction to the linear duration approximation. It becomes particularly important when dealing with larger changes in yield, as it enhances the accuracy of estimated price movements by incorporating second-order effects.

Bond Price Change Approximation

The bond price change approximation uses the concepts of duration and convexity to estimate how a bond's price will change in response to changes in yield. The duration component provides a linear estimate, while the convexity adjustment accounts for the non-linear price response, resulting in a more accurate prediction of the bond's new price after a yield change.

Transcript

Please give Ace some feedback