A government bond currently carries a yield to maturity of 8 percent and market price of...

A government bond currently carries a yield to maturity of 8 percent and market price of $1,080. If the bond promises to pay $100 in interest annually for five years, what is its current duration?

Expert Solution

Market price =				1080
Annual interest =				100
Time =				5 Years
YTM =			8% or	0.08


Duration is measurement of sensitivity of bond's price in regard to change in interest rate. Higher the duration, higher the sensitivity of bond and vice versa.
Duration formula = Present Value of Weighted cash flows / Current Market price

Period	Cash flow	Weighted Cash flows	P.V. F. @ 8%	Present Value of Weighted cash flows
		(Period * Cash flows)		(Weighted cash flows * P.V.F.)

1	100	100	0.925925926	92.59259259
2	100	200	0.85733882	171.4677641
3	100	300	0.793832241	238.1496723
4	100	400	0.735029853	294.0119411
5	1100	5500	0.680583197	3743.207584
				___________________
				4539.429554
				___________________
	Duration =	4539.429554	/1080
	Duration =	4.203175513


So, Current duration of bond is 4.20 years

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jeff jeffy answered 1 year ago

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