Question

. Calculate the requested measures in parts (a) through (f) for bonds A and B (assume that each bond pays interest semiannually):

	Bond A	Bond B
Coupon	8%	9%
Yield to maturity	8%	8%
Maturity (years)	2	5
Par	$1000.00	$1000.00
Price	$1000.00	$1040.55

(a) What is the price value of a basis point for bonds A and B?

(b) Compute the Macaulay durations for the two bonds.

(c) Compute the modified duration for the two bonds.

(d) Compute the convexity measure for both bonds A and B.

Answer 1

a) Price value of basis point (PVBP) is change in the price of bond with change in yield of 1 basis point. We can calculate PVBP with the help of modified duration.

100 bp= 1%,

1bp= .01% or .0001

Therefore,

PVBP = Modified duration *Par Value of bond* 1bp

For Bond A:

PVBP= 3.775*1000*.0001= 0.3775

For Bond B:

PVBP= 8.3083*1000*.0001 = 0.8308

This shows proportional change in price when yield changes by .01%

b)

Macaulay's duration: (Sum of PV of Cash flows*time period) / PV of cash flows

Macaulay's duration for Bond A:

For Bond A
Period	Cash flows	Disc fact	Time period * PV of cash flows	PV of cash flows
1	1000*4%=40	1/1.04=.9615	1*40*.9615=38.4615	40*.9615=38.4615
2	1000*4%=40	1/1.04^2=.9246	2*40*.9246=73.9645	40*.9246=36.98225
3	1000*4%=40	1/1.04^3=.889	3*40*.889=106.6796	40*.889=35.55985
4	(1000*4%)+(1000)=1040	1/1.04^4=.8548	4*1040*.8548=3555.985	1040*.8548=888.9964
PV of cash flows			3775.091
Current bond price				1000
Macaulays duration			=3775.091/1000
			=3.775

For Bond B
Period	Cash flows	Disc fact	Time period *PV of cash flows	PV of cash flows
1	1000*4.5%=45	1/1.04=.9615	1*45*.9615=43.2692	45*.9615=43.2692
2	1000*4.5%=45	1/1.04^2=.9246	2*45*.9246=83.2101	45*.9246=41.605
3	1000*4.5%=45	1/1.04^3=.889	3*45*0.889=120.0145	45*0.889=40.0048
4	1000*4.5%=45	1/1.04^4=.8548	4*45*.8548=153.8648	45*.8548=38.4662
5	1000*4.5%=45	1/1.04^5=.8219	5*45*.8219=184.9336	45*.8219=36.9867
6	1000*4.5%=45	1/1.04^6=.7903	6*45*.7903=213.3849	45*.7903=35.5642
7	1000*4.5%=45	1/1.04^7=.7599	7*45*.7599=239.3741	45*.7599=34.1963
8	1000*4.5%=45	1/1.04^8=.7307	8*45*.7307=263.0485	45*.7307=32.8811
9	1000*4.5%=45	1/1.04^9=.7026	9*45*.7026=284.5476	45*.7026=31.6164
10	(1000*4.5%)+1000=1045	1/1.04=.6756	10*1045*.6756=7059.6456	1045*.6756=705.9646
wtd cash flows			8644.4195
Current bond price				1040.45
Macaulays duration			8644.4195/1040.45
			=8.3083

c) Modified duration:

[Macaulay's duration/ (1+(YTM/n)]

	Bond A	Bond B
Macaulay's Duration	3.775	8.3083
YTM	8%	8%
No of coupon periods per year (n)	2	2
Modified Duration	3.775/(1+(8%/2)) = 3.6298	8.3083/(1+(8%/2) = 7.9887