Question

QUESTION 1 What is the duration of a five year, $1,000 Treasury bond with a 10 percent coupon (paid semiannually) if its yield to maturity is 12 percent? SUGGESTION: use the duration calculation spreadsheet provided for this problem. QUESTION 2 What is the modified duration of the bond in question one? QUESTION 3 Using the modified duration value from question two, what is the predicted price change for the bond if its yield falls to 11 percent?

This was all the information that I was given.

Answer 1

1

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =5x2

Bond Price =∑ [(10*1000/200)/(1 + 12/200)^k]     +   1000/(1 + 12/200)^5x2

k=1

Bond Price = 926.4

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($926.40)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	50.00	1.06	47.17	47.17
2	50.00	1.12	44.50	89.00
3	50.00	1.19	41.98	125.94
4	50.00	1.26	39.60	158.42
5	50.00	1.34	37.36	186.81
6	50.00	1.42	35.25	211.49
7	50.00	1.50	33.25	232.77
8	50.00	1.59	31.37	250.96
9	50.00	1.69	29.59	266.35
10	1,050.00	1.79	586.31	5,863.15
			Total	7,432.07

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

=7432.07/(926.4*2)

=4.011263

2

Modified duration = Macaulay duration/(1+YTM)

=4.01/(1+0.12)

=3.78421

3

Using only modified duration

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

=-3.78*-0.01*926.4

=35.06

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

=35.06/926.4

=3.78%

New bond price = bond price+Modified duration prediction

=926.4+35.06

=961.46