Question

For a given change in interest rates, market prices of bonds move in an inversely proportional manner with interest rate by a higher degree if

		Duration value is lower
		Duration value is higher
		If the amount of Equity is higher
		If the amount of Equity is lower

What is of the following about Duration is correct?  

		Duration is the weighted average time needed to receive the  present value of the cash flows
		duration is the same as the time of maturity
		With higher coupon rate, the value of duration increases
		All of the answers are correct

Answer 1

Ans of the First Question:. Duration Value is higher

Reason = Duration is a measure of approximate sensitivity on bond price for given change in market interest rate. It measures how much the price of the bond would change inversely if there is 1% change in the Market Interest Rate.

So, if the duration of the bond is higher, it shows that there will be higher degree of change in the price of the bond if there is change in market interest interest rate.

Ans of the second Question:.  Duration is the weighted average time needed to receive the  present value of the cash flows.

Reason : We will see the following example to find out the reason why other answers are incorrect.

Basic Information to find out the duration of bonds

Particulars	Bond-A	Bond-B
Life of the bond in Years	4	4
Face Value in $	1000	1000
Coupon Rate of the bond	7%	8%
Yield of the bond (Discount Rate)	6%	6%

Calculation of Duration of Bond-A

Time	Cash Flows	Discount Factor @6%	P.V. of Cash Flows	Weight (P.V. of CF/Total P.V. of CFS)	Weight * Time
1	70	0.9434	66.0380	0.0638	0.0638
2	70	0.8900	62.3000	0.0602	0.1204
3	70	0.8396	58.7720	0.0568	0.1704
4	1070	0.7921	847.5470	0.8192	3.2766
Total	1280		1034.6570	1	3.6313

So, the Duration of Bond-A is 3.631 years.

Calculation of Duration of Bond-B

Time	Cash Flows	Discount Factor @6%	P.V. of Cash Flows	Weight (P.V. of CF/Total P.V. of CFS)	Weight * Time
1	80	0.9434	75.4720	0.0706	0.0706
2	80	0.8900	71.2000	0.0666	0.1332
3	80	0.8396	67.1680	0.0628	0.1884
4	1080	0.7921	855.4680	0.8000	3.2001
Total	1320		1069.3080	1	3.5923

So, the Duration of Bond-B is 3.5923 Years

THUS, BASED OF ABOVE ANALYSIS, WE CAN CONCLUDE THAT,

1. Duration is not the same as maturity, in both bonds, maturity is 4 years and duration is different i.e. 3.6313 years for Bond-A and 3.5923 years of Bond-B

2. With Higher coupon rate, duration of the bond decreases, as can be seen above, the difference between the 2 bonds is that the coupon rate of Bond-B is higher than the coupon rate of Bond-A and so that the duration of Bond-B i.e. 3.5923 years is lower than the duration of Bond-A i.e. 3.6313 years.