# How to Calculate Spread Duration

by Patrick Gleeson, Ph. D., Registered Investment Adv ; Updated July 27, 2017The two most popular investments for retail investors are stocks and bonds. Bonds are generally recognized as the more conservative investment, offering lower risks and returns. When you're buying a bond, you're giving up potential return in exchange for greater safety. Therefore, you want to know how safe the bond actually is. There are several ways of quantifying the risk a specific bond represents, one of them being bond spread duration.

## Interest Rates and Bond Values

A bond provides a return on your investment expressed as a percentage of the face amount on the bond. A 5 percent 10-year $1,000 U.S. Treasury bond, for instance, pays $50 a year every year for 10 years. However, if you decide to sell the bond before 10 years are up, you may discover that the bond is worth more or less than the $1,000 you paid when you bought it. This happens because you're competing with all other sellers, including the U.S. Treasury. If interest rates have gone up, your bond loses value and is worth less than a new $1,000 bond offering a higher interest rate. If interest rates have declined, your $1,000 bond becomes worth a little more than a new bond with a lower interest rate.

## The Interest Rate Risk of a Bond

Bond values always move opposite bond rates, but some bonds are more sensitive to rate changes than others. When you buy a bond, you may want to know how much your bond will change in value as interest rates change. One of the calculations used to determine this is bond spread duration, which estimates the price sensitivity of an asset relative to a 100 basis-point movement in the interest rates of U.S. Treasury Bonds. It determines this by measuring the difference -- called the spread -- between your bond's rate and the treasury bond rate. One-hundred basis points equals 1 percent.

## Meaning of "Duration"

The word "duration" has a different meaning in the context of a bond spread than in other contexts. Bond duration refers to the length of time before a bond matures. But in the context of a bond's interest rate risk, duration is a complex term that incorporates the bond's maturity, yield, coupon rate and call features -- the terms and conditions related to bond payoffs prior to maturity. If, for example, a corporate bond can be paid off at the company's sole discretion earlier than its maturity date, the bond has additional risk, because the company can wait until interest rates are low, then borrow more money to pay off your bond. Now you're stuck with cash in a low-interest-rate bond environment. A bond spread duration calculation incorporates all these risk factors in a single number.

## Bond Spread Duration Examples and Calculation

The bond spread duration of a 10-year Treasury bond equals 0. Corporate bonds with low spread durations of 1, for instance, represent comparatively low interest rate risk. Bonds with higher spread durations, of 3, for example, represent greater interest rate risk. You can find bond spread duration formulas in advanced economics texts and on the web.

Spread duration = ((1C/(1 +y)(supernumery 1) + 2C/(1+y) (supernumery2) ... n/C/(1+y)(supernumeryx) + nM/(1+y)(supernumeryx)) divided by P

where P = bond price, C = semiannual coupon interest (in dollars), y = one-half the yield to maturity and n = number of semiannual periods and M equals value at maturity. To determine the spread duration for a given bond, insert the values in the equation, repeating the 1C/(1+y) part of the formula for as many times as there are semi-annual time periods remaining to maturity.

However, you don't need to do the calculation from scratch. Ready-made bond duration spreadsheets and calculators are widely available, and most of them walk you through the process one step at a time.

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