Question

a) Compute the modified duration of a 9% coupon, 4-year corporate bond with a yield to maturity of 10%.
b) Using the modified duration, If the market yield drops by 25 basis points, there will be a __________% (increase/decrease) in the bond's price.

Answer 1

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =4

Bond Price =∑ [(9*1000/100)/(1 + 10/100)^k]     +   1000/(1 + 10/100)^4

k=1

Bond Price = 968.3

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =4

Bond Price =∑ [(9*1000/100)/(1 + 10/100)^k]     +   1000/(1 + 10/100)^4

k=1

Bond Price = 968.3

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($968.30)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	90.00	1.10	81.82	81.82
2	90.00	1.21	74.38	148.76
3	90.00	1.33	67.62	202.85
4	1,090.00	1.46	744.48	2,977.94
			Total	3,411.37

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

=3411.37/(968.3*1)

=3.523053

Modified duration = Macaulay duration/(1+YTM)

=3.52/(1+0.1)

=3.202775

Using only modified duration

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

=-3.2*-0.0025*968.3

=7.75

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

=7.75/968.3

=0.8%

b