Question

A company just issued a bond with the following characteristics: Maturity = 3 years Coupon rate = 8% Face value = $1,000 YTM = 10% Interest is paid annually and the bond is noncallable.

Calculate the bond’s Macaulay duration ?Round "Present value" to 2 decimal places and "Duration" to 4 decimal place.?

Calculate the bond’s modified duration

Assuming the bond’s YTM goes from 10% to 9.5%, calculate an estimate of the price change without considering convexity

Calculate the convexity of the bond.

Answer 1

Solution :

Face value = $1000, Yield = 10% , Coupon = 8% , Time = 3 Years

Calculation is performed in the excel sheet and given below

Macaulay duration = 2.78

Modified duration = macaulay duration / ( 1 +yield / frequency) = 2.78 / ( 1 +.1/1) = 2.52

If yield goes down from 10% to 9.5% then change in price can be calculated with the help of modified duration

change in price / price = - Duration * Change in yield

Change in price = Price * ( - Duration * Change in yield )

Change in price = 950.26 * ( - 2.52 * (0.095-0.1) ) = 950.26 * 2.52 * 0.005 = 11.99

new bond price = 950.26+ 11.99 = 962.25

Convexity

For approximate convexity =

Where P+ = Price of bond by increasing yield by delta Y

P- = Price of bond by decreasing yield by delta Y

P0 = Price of the bond

Calculation is done on the excel sheet and convexity = 4.47