Duration Measure

This article provides a brief definition and explanation on the duration measure for bonds. Duration measure is an artificial benchmark that allows bonds of differing maturities and rates to be compared against one another. It is a handy tool for comparing these bonds that would otherwise be impossible to compare in an apples to apples fashion. Investors can use this as a tool to more effectively analyze different bonds they are considering to come up with more astute decisions on which ones match up with their investment goals and figure to perform best.

Bond Maturity Explained

Most investors are aware that the maturity of a bond is the amount of time that remains until it matures. As the maturity of a bond lengthens, the volatility in price it may experience is bound to go up. Since so much time passes and interest rates go up and down with the natural cycles of the market, it is inevitable that bonds which take longer to mature will be more volatile than those with shorter maturity cycles. Some accredited investors avoid these types of bonds, not realizing that neither maturity nor volatility are really that great of indicators of the value or the worth of a bond. This is where duration measure comes in.

Bond maturity fails as an accurate assessor of the measure of a bond because it fails to account for differences in bond coupons. For example, a bond with a ten year maturity and a five percent coupon will be much more volatile than a ten year bond with an eight percent coupon. A zero coupon five year bond is probably going to be more sensitive to interest rate changes than a seven year bond with a six percent coupon. So it is clear that maturity by itself is not an adequate benchmark by which to measure bonds, because of the complicating influence of bond coupons.

Duration Measure Explained

Since maturity has proven to be an inadequate predictor of volatility and performance in bonds, investment experts had to come up with a better way to make meaningful comparisons between different bonds. What they came up with is called duration or duration measure. Duration is a weighted average of the number of times in which interest payments are received (adding in the final principal payment as well). The weights used have to do with the amount discounted by the yield to maturity of the bonds in question. In other words, the weights are the present values of the payments discounted by the bond's yield to maturity.

In a duration formula, the percentage change in the price of the bond in question is the duration multiplied by the change in interest rates. So according to this formula, if a bond with a ten year duration and interest rates in that time span fall from eight to six percent (a reduction of two percentage points), the bond's price will rise by about twenty percent. There is some somewhat complex math involved, but anyone with a little mathematical acumen and some patience can work through the formulas to punch out some solid numbers and come to conclusions about bonds with respect to maturity and coupons.

It's interesting to note that any bond with a nonzero coupon will have a duration measure that ends up being shorter than its maturity. When we consider the fact that in this formula, the price change of a bond in percentage points approximately equals its duration times the interest rate change in that intervening period, it's easy to see the higher volatility in a zero than a coupon bond.

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