BOND BASICS - II
Modified Duration The exact measurement of the price sensitivity of a fixed-income security to a very small change in yield, expressed as a % change in price to a 1% change in yield. Since the price/yield relationship is not linear, the calculation is only exact for very small changes around the initial yield.
Dollar Duration, dPdY, or Risk Essentially a tool for calculating the hedge ratio between different securities, this measurement of duration is defined to be the product of the modified duration of the bond and its full price (dollar price plus accrued interest).
Price value of an 01, Yield value of a 32nd The concept of duration is frequently used by market participants to "immunize" portfolios (see Immunization). Since many institutional investors have liabilities that must be met on schedule with the proceeds of a bond portfolio, immunization attempts to ensure that regardless of what happens to interest rate levels between the present and the due date of one's liabilities, enough cash will be available to meet them.
Duration and convexity are risk estimation tools which allow the manager to structure the portfolio so as to offset the two counterbalancing risks in the fixed-income world: market risk, whereby prices and yields move inversely in proportion to "longness"; and reinvestment risk, whereby as prices rally securities sold and new cash flows are reinvested at lower yield levels, and conversely.
Duration (Macaulay's) If a bond is viewed as a series of cash flows, this concept of duration measures price sensitivity (in years) as the present value-weighted average of the cash flows of the bond, according to the formula: DurMac = ( Formula to be represented at a later date) where N = total number of compounding periods to maturity P$ = dollar price of the bond As such, it is a good measure for ranking different bonds as to their price sensitivity, and for constructing portfolios which will fully defease a future series of cash flows (see Immunization).
Duration (Modified) The exact measurement of the price sensitivity of a fixed-income security to a very small change in yield, expressed as a % change in price to a 1% change in yield. Since the price/yield relationship is not linear, the calculation is only exact for very small changes around the initial yield.
The main difference between modified duration and dollar duration, dPdY or risk lies in that modified duration is expressed as a percentage, whereas the modified duration is expressed in terms of actual dollar
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