Question

A newly issued bond has a maturity of 10 years and pays a 7% coupon rate (with coupon paymentscoming once annually). The bond sells at par value. Assume par value is equal to $ 100.

a) What are the convexity and the duration of the bond?

b) Find the actual price of the bond assuming that its yield to maturity immediately increases from 7% to 8% (with maturity still 10 years).

c) What price would be predicted by the duration rule? What is the percentage error of that rule?d) What price would be predicted by the duration-with-convexity rule? What is the percentage errorof that rule?

Answer 1

Bond Price	$100.00
Face Value	100
Coupon Rate	7.00%
Life in Years	10
Yield	7.00%
Frequency	1

0	($100.00)
1	7.00	6.54	6.54	11.43
2	7.00	6.11	12.23	32.04
3	7.00	5.71	17.14	59.89
4	7.00	5.34	21.36	93.29
5	7.00	4.99	24.95	130.78
6	7.00	4.66	27.99	171.11
7	7.00	4.36	30.51	213.22
8	7.00	4.07	32.59	256.21
9	7.00	3.81	34.27	299.31
10	107.00	54.39	543.93	5,226.02
		Total	751.52	6,493.30

Macaulay Duration	7.52
Modified Duration	7.02
Convexity	64.93

b

K = N

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

k=1

K =10

Bond Price =∑ [(7*100/100)/(1 + 8/100)^k]     +   100/(1 + 8/100)^10

k=1

Bond Price = 93.29

%age change in price =(New price-Old price)*100/old price

%age change in price = (93.29-100)*100/100

= -6.71%

c

Modified Duration Predicts

-7.02

-7.02%

predicted price= old price*(1+%age change) = 100*(1-7.02/100) = 92.97

Modified duration prediction = -Mod_Duration*Yield_Change*Bond_Price

%age difference = (7.02-6.71)/6.71 = 4.62%

d

Modified Duration Predicts		-7.02
Convexity Adjustment		0.32
Total Predicted Change		-6.70

Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price

predicted price= old price*(1+%age change) = 100*(1-6.7/100) = 93.3

%age difference = (6.70-6.71)/6.71 = 0.01%