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Bond duration closed-form formula. ... Download QR code; Wikidata item; Print/export Download as PDF; Printable version; Appearance.
For a standard bond, the Macaulay duration will be between 0 and the maturity of the bond. It is equal to the maturity if and only if the bond is a zero-coupon bond. Modified duration, on the other hand, is a mathematical derivative (rate of change) of price and measures the percentage rate of change of price with respect to yield.
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 the New York Stock Exchange (Macaulay and Durand, 1951). The term "Macaulay duration" is named after him.
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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).
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]
In finance, a bond is a type of security under which the issuer owes the holder a debt, and is obliged – depending on the terms – to provide cash flow to the creditor (e.g. repay the principal (i.e. amount borrowed) of the bond at the maturity date and interest (called the coupon) over a specified amount of time. [1])
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.