Question

7. You have a 3-year maturity, 5% coupon bond traded at par. If the interest rate were to increase by 125 basis points, your predicted new price for the bond based on duration only is _________ (round to the nearest dollar).

   1. $955

   2. $966

   3. $1,000

   4. $1,042

   5. None of the above

Answer 1

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	50.00	1.05	47.62	47.62
2	50.00	1.10	45.35	90.70
3	1,050.00	1.16	907.03	2,721.09
			Total	2,859.41

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

=2859.41/(1000*1)

=2.85941

Modified duration = Macaulay duration/(1+YTM)

=2.86/(1+0.05)

=2.723248

Using only modified duration

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

=-2.72*0.0125*1000

=-34.04

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

=-34.04/1000

=-3.4%

New bond price = bond price+Modified duration prediction

=1000-34.04

=966