Question

4. (35 points) A bond with a yield to maturity of 3% and a coupon rate of 3% has 3 years re- maining until maturity. Calculate the duration and the modified duration for this bond assuming annual interest payments and a par value of $1,000. Why is the duration of this bond higher than the 3-year 10% coupon bond yielding 10% we looked at in class that had a duration of 2.7 years? If the required market yield on this bond increases to 4%, what approximate per- cent change in the bond price would you have based on the modified duration?

Show Work Please

Answer 1

Face Value = 1000

Cash Flows , Year 1 - 30, Year 2 - 30, Year 3 - 1030

PV of Cashflows, Year 1 - 30/1.03, Year 2 - 30/(1.03^2), Year 3 - 1030/(1.03^3)

Year 1 - 29.162 ,Year 2 - 28.277, Year 3 - 942.5959 Total 3 year CF = 1000.035

Macaulay Duration = (PV/Total)*Time

(29.162/1000.035) + (28.277/1000.035)*2 + (942.5959/1000.035)*3 = .02916 + .05654 + 2.827 = 2.913

Modified Duration = 2.913/1.03 = 2.8285

The duration of this bond is higher because of the time to maturity of the bond. In the abve case it is mentioned that the time to maturity left is 3 years which means that the actual time must be more than 3 years whereas in the second case of 3 year bond the maturity time is 3 years.

Change in Bond price = Modified duration * Change in yield

= -2.8285 * .01

= -.2825