Question

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Consider a five-year, 8 percent annual coupon bond selling at par of $1,000. a. What is...

Consider a five-year, 8 percent annual coupon bond selling at par of $1,000.

a. What is the duration of this bond?

b. If interest rates increase by 20 basis points, what is the approximate change in the market price using the duration approximation?

Expert Solution

a

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,000.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	80.00	1.08	74.07	74.07
2	80.00	1.17	68.59	137.17
3	80.00	1.26	63.51	190.52
4	80.00	1.36	58.80	235.21
5	1,080.00	1.47	735.03	3,675.15
			Total	4,312.13

b

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=4312.13/(1000*1)

=4.312127

Modified duration = Macaulay duration/(1+YTM)

=4.31/(1+0.08)

=3.99271

Using only modified duration

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-3.99*0.002*1000

=-7.99

%age change in bond price=Mod.duration prediction/bond price

=-7.99/1000

=-0.8%

New bond price = bond price+Modified duration prediction

=1000-7.99

=992.01

jeff jeffy answered 5 months ago

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