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the same time to maturity (20 years) and yield (5 but differing coupon rates (4.0 for Bond 1 and.0 for Bond 2) and the impact of an increase in yield from. These terms add.0 and serve as weights for a weighted average. Displaystyle omega _i-D i:frac partial Vpartial r_i. In derivatives pricing The Greeks the closest analogous quantity is Rho, which is the derivative of the price with respect to interest rates. Unlike Macaulay duration and modified duration, there is not a convexity function built into Excel. Modified duration is a rate of change, the percent change in price per change in yield. Strictly speaking, Macaulay duration is the name given to the weighted average time until cash flows are received, and is measured in years.

Bonds with higher durations carry more risk and higher price volatility.

A coupon payment on a bond is the annual interest payment that the bondholder receives from the bond s issue date until it matures.

Coupons are normally described in terms of the coupon rate, which is calculated by adding the sum of coupons paid per year and dividing it by the bond s face value.

Calculate Macaulay, duration, Calculate Modified Macaulay, duration, Calculate.

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Conversely, if interest rates fall, the value of bonds will increase. Mayes, a professor at the Metropolitan State University of Denver and co-author of Financial Analysis with Microsoft Excel (South-Western College Pub, 2011). A longer term to maturity means it takes longer for investors to recover their initial investment, so the market value of the bond is more sensitive to changes in interest rates. Then the exposure vector (1,n)displaystyle boldsymbol omega (omega _1,ldots,omega _n) has components iD, i:Vri. For every-day use, the equality (or near-equality) of the values for Macaulay and modified duration can be a useful aid to intuition.

Duration of a coupon bond

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