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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.
There is a time dimension to the analysis of bond values. A 10-year bond at purchase becomes a 9-year bond a year later, and the year after it becomes an 8-year bond, etc. Each year the bond moves incrementally closer to maturity, resulting in lower volatility and shorter duration and demanding a lower interest rate when the yield curve is rising.
Vasicek's model was the first one to capture mean reversion, an essential characteristic of the interest rate that sets it apart from other financial prices.Thus, as opposed to stock prices for instance, interest rates cannot rise indefinitely.
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.
Bonds will have different yields and market returns based on the duration of the note, the issuer, the rate structure and more. A 10-year Treasury bond, for example, will have an entirely ...
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.
Date through which interest is being accrued. You could word this as the "to" date, with Date1 as the "from" date. For a bond trade, it is the settlement date of the trade. Date3 (Y3.M3.D3) Is the next coupon payment date, usually it is close to Date2. This would be the maturity date if there are no more interim payments to be made.
A Technical Note on the Smith-Wilson Method, The Financial Supervisory Authority of Norway, (1 July 2010) Lagerås, Andreas & Lindholm, Mathias.