Question

A 5-year 10% annual coupon bond is trading at par. when we calculate the duration of this bond ___% is the weight of the first coupon that will be paid one year from today

Answer 1

when we calculate the duration of this bond 9.09% is the weight of the first coupon that will be paid one year from today.

#1 Calculation of Duration

Time	Cash flow	PVF@10%*	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	100	0.909	90.9	0.0909	0.0909
2	100	0.826	82.6	0.0826	0.1652
3	100	0.751	75.1	0.0751	0.2253
4	100	0.683	68.3	0.0683	0.2732
5	1100	0.621	683.1	0.6831	3.4155

Duration = Time*weight

= .0909+.1652+.2253+.2732+3.4155

= 4.1701 years = 4.2 years

note:

• When face value is not given, it is general practice to take $1,000 as face value
• Since the bonds are traded at par, Yield To Maturity = Coupon rate in this case. So discount the cashflows at 10%.
• Calculation of duration is given for your reference. Question asked only for the weight of the first coupon while calculating duration. It can be directly calculated as -

1) Identify cashflow (1000*10% = 100)

2) Calculate present value by discounting at 10% (100*.909 = 90.9)

3) The value of bond is the present value of the expected cashflows from the bond. Hence total of present value all 5 year cashflows is $1,000 since the bonds are traded at par.

4)Weight = PV of year1 cashflow/current market price *100 = 90.9/1000 *100 = 9.09%

*PVF = 1 / (1+r)ⁿ