Even though bonds usually offer one of the most reliable sources of investment income, they still impose risk. The two main sources are default risk – when bond issuers fail to pay interest or principal on time – and interest rate risk. Whereas the issuer’s creditworthiness bears on default risk, changes in prevailing interest rates bear on interest rate risk. If bonds are new to you, please take about two minutes to read the “Bond Background” at the bottom of the page.

When prevailing interest rates increase, fixed interest-paying bond values decline. The inverse is true, but nobody worries much about rising bond values. Increasing interest rates in the economy do not affect fixed-interest bond coupon amounts; the bonds keep on paying the coupon regardless of changes in prevailing interest rates. Interest rate risk threatens the value of fixed interest-paying bonds more than other kinds of bonds, and its impact is greater on bonds with longer maturities and smaller coupon payments. Also, interest rate risk presents a greater threat to the value of bond mutual funds and other packaged bond products than it does to individual bond issues.

Somebody once said, “if it’s worth managing, it’s worth measuring.” Interest rate risk is worth managing, and duration provides the best measure of a bond’s exposure to it.

**How Interest Rate Changes Affect Bond Values**

The chart titled “10-Year Treasury Interest Rate and Estimated Bond Value” offers an extreme example of how rapidly interest rates can change and how they can impact bond value. For the year starting at the end of August 2012, prevailing interest rates as measured by the 10-year Treasury note, increased from 1.57% to 2.98%[1], an 89% increase.[2]Even stock values don’t change this much in such a short time.

- By the end of this one-year period, a 10-year Treasury note purchased at the beginning of the period would have lost almost 12%, declining from $1,000 to about $881.
- A triple-A-rated long-term corporate bond with a coupon rate greater than the Treasury’s would have lost almost 15% during the same period, declining from $1,000 to about $851.

**Modified Duration**

These illustrations of interest rate risk – the effects of interest rate increases on bond values – are based on duration, the best measure of bond sensitivity to changes in prevailing interest rates. There’s more than one duration form; the form used to measure sensitivity is called “modified” duration. Modified duration answers two questions:

- Approximately how many years will it take for the bond to pay all future discounted cash flows (interest and principal)?[3]
- How much does a bond’s value change if prevailing interest rates change 1% for every year of duration?[4]

In the 10-year Treasury note example, the modified duration equals 9.22 years. This answers the first question. That’s a little less than its 10-year maturity. Duration always equals a value greater than zero and less than the maturity if the bond pays fixed interest.

To find the bond’s sensitivity to interest rate changes, divide duration years by 100 and express as a percentage. In the 10-year Treasury note example, sensitivity equals 9.22%. That result means a 1% change in the applicable interest rate will cause the bond value to decline 9.22% for each year of duration. In the example, the estimated value loss equaled more than 9.22% because:

- the interest rate increase exceeded 1%, and
- the one year in duration terms was shorter than one year in calendar terms.

**Modified Duration Sources and Uses**

- Investors can calculate modified duration using a spreadsheet[5], an online calculator[6], or pencil and paper. The math is not complicated; collecting the inputs takes the most time, though they are readily available.
- When comparing bonds, duration enables apples-to-apples comparisons across bonds. Duration should be a key input in deciding which bonds to buy or sell.
- Investors can sum the value-weighted durations of all portfolio bonds to find the portfolio duration.
- Duration can serve as a more precise measure than maturity for bond owners who construct bond ladders – one of the Modern Traditional investments.

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**Bond Background**

- Bonds are loans investors make to corporations and governments, called issuers. Bond issuers usually[7]pay interest – coupons – every six months and repay principal – the amount borrowed – upon maturity. Maturity is the date the loan agreement ends. Consumer loans are different mainly because consumers usually pay both interest and principal every month.

- Issuers usually get $1,000 for each bond – par – and pay a fixed coupon rate at six-month intervals with half of the coupon rate paid twice per year. When investors buy bonds in the secondary market after the original issue, they might pay more or less than $1,000 depending on interest rates and other factors. Issuers continue paying the fixed coupon rate until maturity.

- Bonds paying fixed coupon rates lose market value when prevailing interest rates rise. Here’s why: You own a bond maturing in five years with a 4% coupon. For whatever reason, U.S. interest rates increase so investors buying bonds like yours expect 5%. Who wants to buy your bond if it only pays 4%? Nobody. To compensate prospective buyers, the 4% bond’s price must drop. This is interest rate risk, and it is where “yield” comes in play.

- “Yield” is the total rate of return an investor earns if a bond is held to maturity. It is “total” return because it includes both bond price and coupon, the only two sources of bond income.

**[1]** 10-Year Constant Maturity Rate. *Federal Reserve Bank of St. Louis*. Retrieved from https://fred.stlouisfed.org/series/DGS10/.

**[2]** Although this period was unusual for the size of the increase, sudden spurts in interest rates are not uncommon.

**[3]** To get a precise answer, use the other duration form, Macaulay duration. The difference in Macaulay and modified duration results is usually close to zero.

**[4]** Chen, J. (2019 June 8). Duration. *Investopedia.* Retrieved from https://www.investopedia.com/terms/d/duration.asp.

**[5]** Microsoft Excel provides a duration function.

**[6]** Here is one of many online calculators: https://www.investopedia.com/calculator/bonddurcdate.aspx

**[7]** The “usual” bond has many exceptions.

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