Question

a. A 6% coupon bond paying interest annually has a modified duration of 7 years, sells for $820, and is priced at a yield to maturity of 9%. If the YTM decreases to 8%, what is the predicted change in price ($) using the duration concept? (2 marks) b. A bond with annual coupon payments has a coupon rate of 6%, yield to maturity of 7 % , and Macaulay duration of 12 years. What is the bond's modified duration? (2 marks) c. Which bond has the longest duration? Explain. (3 marks) i. 10-year maturity, 4% coupon. ii. 10-ycar maturity, 9% coupon. ii. 15-year maturity, 4% coupon. iv. 15-ycar maturity, 9% coupon.

Answer 1

a. Modified Duration of a Bond tells us how much the price of a bond will rise or fall if YTM increases or decreases by 1%.

In the given question, Modified Duration = 7 years

Thus, if YTM of 9% decreases to 8%, then the price of bond will increase by $ 7. The price of Bond will be ($820+$7) = $ 827.

b. Given in the question,

Coupon Rate = 6% Annual Payments

Yield To Maturity = YTM = 7%

Macaulay Duration = 12 years

Macaulay Duration Modified Duration = = (1 + YTM)

were, n = Number of compounding per year

Modified Duration = 12 (1 + 0.07)

                                          = 11.21495.

c. Duration of a Bond is the average time required to receive the investment in a bond back. A coupon paying bond will have a duration less than its maturity.

Duration is affected by a number of factors.

Coupon Rate : If two bonds have all the same features but different coupon rate, then the bond with higher coupon rate will be able to repay faster and thus have a lower duration. Thus, higher the coupon rate, lower the duration.

Time To Maturity : If there are two identical bonds with different time to maturity, the bond with the longer maturity, will have higher duration as it will take longer to repay the original investment. Longer the time period for maturity, the duration will be higher.

Options given :

i. 10 year maturity, 4% Coupon

ii. 10 year maturity, 9% Coupon

iii. 15 year maturity, 4% Coupon

iv. 15 year maturity, 9% Coupon

In the above given options, the bond with longer time to maturity(15 years) and lower Coupon Rate(4%) will have the longest duration. Thus, option (iii) 15 year maturity and 4% Coupon Rate Bond will have the longest duration.