Page 144 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Unit 10: Interest Rate Derivatives and Euro-Dollar Derivatives

10.4 Duration Notes

The term duration has a special meaning in the context of bonds. It is a measurement of how
long, in years, it takes for an investment in a bond to be repaid by its internal cash flows. It is also
an important measure because bonds with higher durations carry more price risk and have
higher price volatility than bonds with lower durations. In other words, for the same change in
yield, the price of a bond with higher duration changes by a larger amount than that of a bond
with smaller duration.

Fredrick Macaulay, in 1938, first propounded the idea of duration, and we call his measure
Macaulay's duration.

Did u know? What is the meaning of Macaulay duration?
Macaulay duration in years is the weighted average of time periods at which the cash
flows (coupon amounts as well as principal) are received.
So, for a two-year bond with 4 coupon payments every six months, the Macaulay duration is the
weighted average of 0.5, 1, 1.5 and 2 years. The weight assigned to any time period is the present
value of the cash flow at that time period as a share of present value of all cash flows put
together; the discount factor for arriving at the present value being the yield of the bond. In very
simple terms, Macaulay Duration signifies the time it takes for a bond to pay itself out to the
investor. The other measure of Duration is Modified Duration.

Did u know? What is Modified duration?
Modified Duration is a measure of the sensitivity of a bond's value to the absolute change
in its yield.

More specifically, it is the percentage change in value of a bond for a 100 basis point change in
yield. Modified duration is, therefore, a direct measure of the interest rate sensitivity of a bond.
The higher the modified duration of a bond, greater the percentage change in price for a given
change in yield. Modified Duration of a bond is estimated as follows:

PercentageChangeinBondPrice
 100
ChangenYieldinBasisPoints
Note that 1 basis point is equal to one -hundredth of 1 percent. Thus, 25 basis points are equal to
0.25 percent and 50 basis points are equal to 0.5 percent and so on.

Example: Suppose the yield of a bond changes from 5 % to 4.5 % and as a result, the bond
price rises from 100 to 105. Thus, with 50 basis points decline in yield, the price of the bond rises
by 5 percent. The Duration of the bond would therefore be 10, using the formula given above.

Self Assessment

Fill in the blanks:
12. ………… duration in years is the weighted average of time periods at which the cash flows
(coupon amounts as well as principal) are received.

13. ……….Duration is a measure of the sensitivity of a bond's value to the absolute change in
its yield.

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