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Modified duration can be extended to instruments with non-fixed cash flows, while Macaulay duration applies only to fixed cash flow instruments. Modified duration is defined as the logarithmic derivative of price with respect to yield, and such a definition will apply to instruments that depend on yields, whether or not the cash flows are fixed.
The price sensitivity of a stock versus duration, often called modified duration, is the percentage change in price in response to a 1% change in the long-term return that the stock is priced to deliver. The modified duration is duration divided by (1 + growth rate).
Therefore, increases in r must decrease the duration (or, in the case of zero-coupon bonds, leave the unmodified duration constant). [13] [14] Note that the modified duration D differs from the regular duration by the factor one over 1 + r (shown above), which also decreases as r is increased.
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The modified duration of a bond assumes that cash flows do not change in response to movements in the term structure, which is not the case for an MBS. For instance, when rates fall, the rate of prepayments will probably rise and the duration of the MBS will also fall, which is entirely the opposite behavior to a vanilla bond.
Formally, the duration gap is the difference between the duration - i.e. the average maturity - of assets and liabilities held by a financial entity. [3] A related approach is to see the "duration gap" as the difference in the price sensitivity of interest-yielding assets and the price sensitivity of liabilities (of the organization) to a change in market interest rates (yields).
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This is equal to the Macaulay duration times the discount rate, or the modified duration times the interest rate. If the elasticity is below -1, or above 1 if the absolute value is used, the product of the two measures, value times yield or the interest income for the period will go down when the yield goes up.