Duration of a Bond

 

Duration of a bond refers to its weighted average life. Bond duration is a measurement of how long in years it takes for the price of a bond to be repaid by its internal cash flows. The duration is always lesser than its maturity period for coupon paying bonds as the coupons received can be reinvested and money can be generated. The more frequent the coupon payments the lesser will be the effective life of a bond. For a zero coupon bond there are no intermittent coupon payment and hence the duration and maturity period are same.

Let’s us discuss duration with a simple example.

Consider Rs1000 bond, paying annual coupons at 10% p.a. and the life of the bond is 5 years.
So a coupon of Rs100 (1000*10/100) is paid out annually. The principal and last coupon payment would be paid out at the end of the 5th year. Consider a discount rate of 12%.

Year

Cash Flow

Present Value Factor

Present Value of Cash Flow

PV of Cash Flow/Total PV of cash Flow

Year X Weight

1

100

1/(1+0.12) = 0.893

89.3

0.09628

0.09628

2

100

1/(1+0.12)2 = 0.797

79.7

0.08593

0.17186

3

100

1/(1+0.12)3 = 0.712

71.2

0.076765

0.230296

4

100

1/(1+0.12)4 = 0.636

63.6

0.068571

0.274286

5

1100

1/(1+0.12)5 = 0.567

623.7

0.672453

3.362264

Total

927.5

1.0000

4.134987

The duration of the bond is 4.134987 years (where as the maturity is 5 years) i.e. the investment on this bond will be repaid in 4.134987 years. Bonds with higher durations are more risky and have higher price volatility than bonds with lower durations.

Duration is a price sensitivity measurement and it tells us that how many years we should stay invested to get back the amount.

 

 

The above graph explains the relationship between coupon rate and duration. Its self explanatory that for zero coupon bonds the duration is maturity period (30 years in the graph) and as the coupon rate increases duration falls and stabilizes at a point.

We have considered 12% as discount rate for the life of the bond, but this rate varies depending on the market conditions. We should calculate duration for every change in discount rate. The duration calculated by above method is called Macaulay duration.

 

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June 14, 2008 | Filed Under Bonds 

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