Question

Questions 1-4 show excel formulas

The coupon rate and market price for the 10-year US Treasury bond are 2.50% and 96.3828 respectively. Note, the price is expressed as a percentage of par (like other bonds). If par is $1000, then this bond is selling for $963.828.

1. Assume that this bond will mature in precisely 10 years, pay coupons semi-annually, and has a par value of $1000. Determine the yield to maturity for this bond.

2. Compute the duration of this bond and use it to estimate the new value of the bond if rates were to suddenly decline by 0.80%.

3. Calculate the bond's value directly (using the present value approach) assuming that rates declined 0.80% from the yield to maturity you estimated in the first question.

4. Compare your answers to Questions 2 and 3. Explain the source of any difference. Which is more correct

Answer 1

K = Nx2

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

k=1

K =10x2

963.828 =∑ [(2.5*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM% = 2.92

2

Period	Cash Flow	PV Cash Flow	Duration Calc
0	($963.83)
1	25.00	24.29	24.29
2	25.00	23.60	47.20
3	25.00	22.93	68.80
4	25.00	22.28	89.13
5	25.00	21.65	108.25
6	25.00	21.03	126.21
7	25.00	20.44	143.07
8	25.00	19.86	158.87
9	25.00	19.29	173.65
10	1,025.00	768.65	7,686.46
		Total	8,625.91

Macaulay Duration	17.90
Modified Duration	17.39

Modified Duration Predicts

67.52

7.01%

1031.344

Modified duration prediction = -Mod_Duration*Yield_Change*Bond_Price = 67.52

new price = 963.83+67.52 = 1031.44

3

K = Nx2

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

k=1

K =10x2

Bond Price =∑ [(2.5*1000/200)/(1 + 2.12/200)^k]     +   1000/(1 + 2.12/200)^10x2

k=1

Bond Price = 1034.08

4

Price estimate using modified duration is lesser than other method. Other method is more correct, price difference is due to convexity of yield curve which is not captured with modified duration method