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In contrast to Macaulay duration, modified duration (sometimes abbreviated MD) is a price sensitivity measure, defined as the percentage derivative of price with respect to yield (the logarithmic derivative of bond price with respect to yield). [15] Modified duration applies when a bond or other asset is considered as a function of yield.
The modified Dietz method [1] [2] [3] is a measure of the ex post (i.e. historical) performance of an investment portfolio in the presence of external flows. (External flows are movements of value such as transfers of cash, securities or other instruments in or out of the portfolio, with no equal simultaneous movement of value in the opposite direction, and which are not income from the ...
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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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.
The more curved the price function of the bond is, the more inaccurate duration is as a measure of the interest rate sensitivity. [ 2 ] Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest rate, i.e. how the duration of a bond changes as the interest rate changes. [ 3 ]
The time-weighted return (TWR) [1] [2] is a method of calculating investment return, where returns over sub-periods are compounded together, with each sub-period weighted according to its duration. The time-weighted method differs from other methods of calculating investment return, in the particular way it compensates for external flows.
Studies show that keeping your head at the appropriate height—about 2 inches (or 5 centimeters) off the bed—helps air flow into the lungs and stabilizes your respiratory function. However ...