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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 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.
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 ...
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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 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.
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