Question

A 4-year 12% coupon bond has a yield of 10%.

a) What are its Macaulay Duration, Modified duration, and convexity

b) What is the actual price change, Modified Duration predicted price change and Modified Duration + convexity predicted change in price for an increase of 50 basis point in the yield.

Assume a flat term structure before and after the increase and annual coupons.

Answer 1

ANSWER

y = 10%, N = 4, Assume FV = $100

FV = $100, y = 10%, N = 4, PMT = $12; compute PV =?

PV = (12/0.10)*(1 – 1/1.10^4) + 100/1.10^4 = 106.339731

Macaulay Duration: D = 3.420934

Modified Duration: MD = D/(1 + y) = 3.420934/1.10 = 3.109940

Convexity: CV = 13.363235

Δy = 50 basis point = 0.50% = 0.005

Actual price change:

FV = $100, y = 10.50%, N = 4, PMT = $12; compute PV = 104.703788

ΔP/P = (104.703788 / 106.339731) – 1 = -0.015384 = -1.54%

Modified Duration predicted price change:

ΔP/P = - MD*Δy = -3.109940*0.005 = -0.015550 = -1.56%

Modified Duration + convexity predicted price change:

ΔP/P = - MD*Δy + 0.5*CV*(Δy)^2

ΔP/P = -3.109940*0.005 + 0.5*13.363235*(0.005)^2 = -0.015383

ΔP/P = -1.54%

N	CF	DCF = CF/(1+y)^N	w = DCP/P	w*N	w*N*(N+1)/(1 + y)^2
1	12	10.909091	0.102587	0.102587	0.169566
2	12	9.917355	0.093261	0.186522	0.462452
3	12	9.015778	0.084783	0.254348	0.840821
4	112	76.497507	0.719369	2.877476	11.890397
SUM =		106.339731	1.000000	3.420934	13.363235
		P = 106.339731		D = 3.420934	CV = 13.363235

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