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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.
To address this, an effective convexity must be calculated numerically. [18] Effective convexity is a discrete approximation of the second derivative of the bond's value as a function of the interest rate: [ 18 ]
The duration of an equity is a noisy analogue of the Macaulay duration of a bond, due to the variability and unpredictability of dividend payments. The duration of a stock or the stock market is implied rather than deterministic. Duration of the U.S. stock market as a whole, and most individual stocks within it, is many years to a few decades.
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Frederick Robertson Macaulay (August 12, 1882 – March 1970) was a Canadian economist of the Institutionalist School. He is known for introducing the concept of bond duration . [ 1 ] Macaulay's contributions also include a mammoth empirical study of the time series behavior of interest rates published in 1938 and a study of short selling on ...
Adjust bond allocations based on duration. In a lower-rate environment, long-term bonds benefit the most because they lock in higher yields over time. Consider rethinking the role longer-term ...
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.
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).