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This will give modified duration a numerical value close to the Macaulay duration (and equal when rates are continuously compounded). Formally, modified duration is a semi- elasticity , the percent change in price for a unit change in yield, rather than an elasticity , which is a percentage change in output for a percentage change in input.
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 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.
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.
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 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 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.
The effective spread is the average margin over the benchmark rate that is expected to be earned over the life of the security. For a floating rate note selling at par value, the effective margin is merely the contractual spread over the benchmark rate specified in the note's prospectus.