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# How Bonds React to Interest-Rate Changes

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If you buy a standard plain-vanilla fixed-rate bond, you can expect to receive its coupon interest payment on a regular basis, until that bond matures or the company declares bankruptcy. Assuming that the company stays out of bankruptcy court, you'll get the last coupon payment -- and regain the bond's face value -- on its maturity date.

That's the great part about bonds: As long as the company behind a bond remains solvent, you can predict what you're going to get by owning it. And because those cash flows are so predictable, you can get a pretty good feel for how those bonds will react to changes in interest rates.

How price and yield are related
The relationship between a bond's price and changes in interest rates is known as its modified duration. In essence, the modified duration will tell you how far a bond will fall (in percent terms) if interest rates rise by a percentage point. For example, if the modified duration of a bond is 10.5, then if rates rise from 4% to 5% overnight, the price of that bond can be expected to drop 10.5%.

While the math behind the formula is somewhat complicated, there are websites that can do the calculations for you, as can spreadsheets like Microsoft Excel. At its core, though, there are only a handful of factors that play into that value. The most critical ones are:

• The bond's yield to maturity, which determines what your annual rate of return would be if you held that bond until it paid back its principal at the end of its life.
• The bond's coupon yield, which is the interest rate you would get if you bought the bond at exactly its face value.
• The bond's time to maturity, which measures how much life is left in the bond.

The higher the yield to maturity and the coupon yield, the lower the modified duration; and the shorter the time until maturity, the lower the modified duration.

Put it all together, and you get modified durations like these:

Company

S&P Debt
Rating

Bond
Maturity Date

Coupon Yield

Yield to Maturity

Modified Duration

Microsoft (Nasdaq: MSFT  )

AAA

6/1/2039

5.20%

4.63%

15.43

General Electric (NYSE: GE  ) Capital

AA+

11/21/2011

4.38%

0.83%

1.37

Wal-Mart (NYSE: WMT  )

AA

4/1/2040

5.63%

4.99%

14.88

Merck (NYSE: MRK  )

AA-

11/15/2011

5.13%

0.21%

1.35

AFLAC (NYSE: AFL  )

A-

12/17/2039

6.90%

6.59%

12.81

Spectra Energy

BBB

9/15/2013

5.90%

2.35%

2.92

Alcoa (NYSE: AA  )

BBB-

6/1/2011

6.50%

2.21%

0.91

Sources: Scottrade; author calculations. As of June 21.

Keep your durations short when rates rise
As you can tell by the table, the interplay between length of time to maturity and modified duration can dwarf every other factor. That's why the top-rated Microsoft bond with 29 years to maturity could lose a whopping 15.4% in value if interest rates rise a single percentage point, but the barely investment-grade Alcoa would lose less than 1%.

Of course, the other factors matter, too. The lower yields on the Wal-Mart bond explain why a 1-percentage-point rise in rates would hit the Wal-Mart bond by about 2% more than the AFLAC bond that matures just a few months sooner, nearly 30 years from now. Yet the tiny differences between the Merck bond and the General Electric bond show how a higher coupon yield can offset a lower yield to maturity to result in similar modified durations.

Regardless of the particular driver behind the numbers, the message is the same. If you're a bond investor who is expecting interest rates to rise, keep your durations short to minimize the swings in your portfolio. It's certainly true that if you hold to maturity, and the bond issuer makes all its expected payments, your return will be the yield to maturity. But if there's a chance you'll need to sell before maturity, then with some of those high-duration bonds, it'd take several years of coupon payments to make up for the principal hit from even a modest rise in interest rates.

At the time of publication, Fool contributor Chuck Saletta owned shares of Microsoft, General Electric, and Merck. In addition, at the time of publication Chuck's wife owned shares of Spectra Energy. Microsoft and Wal-Mart are Motley Fool Inside Value recommendations. AFLAC is a Motley Fool Stock Advisor pick. Spectra Energy is a Motley Fool Income Investor selection. Motley Fool Options has recommended a diagonal call position on Microsoft. Try any of our Foolish newsletter services free for 30 days. The Motley Fool has a disclosure policy.

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Chuck Saletta
TMFBigFrog

Chuck Saletta has been a regular Fool contributor since 2004. His investing style has been inspired by Benjamin Graham's Value Investing strategy. Chuck also can be found on the "Inside Value" discussion boards as a Home Fool.

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