Consider a 10-year zero coupon bond. A. Using the bond pricing equation, P(y), i

Question

Consider a 10-year zero coupon bond.

A. Using the bond pricing equation, P(y), illustrate the derivation (using calculus) of this bond’s modified duration. Note: the correct answer is an equation, not a number.

B. Assuming the yield-to-maturity is 5%, compute the bond’s modified duration.

C. Use your answer to part B to estimate the price of the bond and the percentage price change if interest rates instantaneously rise to 6%.

D. Use your answer to part B to estimate the price of the bond and the percentage price change if interest rates instantaneously decline to 4%.

E. How do the estimates from C. and D. compare to the true prices using the bond pricing equation P(y) if yields change to 6% and 4%? Is the estimate more accurate for part C. or D., and why?

Explanation / Answer

A. For a zero coupon bond, Macaulay duration is the maturity which is 10 years.

Modified Duration = Macaulay duration/(1+Yield)

B. Mod Duration = 10/(1+5%) = 9.52 years

C. Price of the bond = 100/(1+5%)^10 = 61.39. If the yield increases to 6%, i.e. 1 percentage point increase would lead to prices falling by Mod Duration * 1% =9.52% (Its an estimation, ignoring the convexity of the bond)

D. If the yield declines by 1%, Prices would increase by 9.52%

E. Due to convex relationship between price and yield, decline in prices is over-estimated i.e. actual decline would be slightly lower than estimated 9.52%. Similarily, increase in prices is under-estimated in D i.e. actual increase would be slightly higher than 9.52%

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.