## Analyzing Bond Investments

A bond investment is defined by the bond's credit rating, coupon rate, yield to maturity and time to maturity. Calculating a bond's duration combines the yield and maturity into a single number which can be used to evaluate the risk of the bond and compare it to other ones. One definition of bond duration is a measurement of how long it takes the cash flow from the bond in interest and principal payments to return the current price of the bond to an investor. The result of the bond duration calculation is a number which indicates the bond's price sensitivity to changes in interest rates.

This article will not discuss the math of calculating duration. The calculation is boring and the duration of any bond can be quickly calculated using a bond calculator or spreadsheet template. In addition, the duration numbers an investor needs are most likely published with other information about the bond. More important is to understand how the different facets of the bond itself affect the duration number.

## The Math and Effects

The duration of a bond is the present value of all the cash flows coming from the bond, interest and final principal payment, calculated using the current market rate. The calculation provides a mathemetical figure which represents the time to recover the price of a bond, based on current interest rates. Duration is not a measure of yield or maturity. Some of the effects of changing bond factors on duration are:

- Higher coupon bonds have a shorter duration. Low coupon bonds will have a longer duration.
- Rising interest rates cause the duration to lengthen, falling rates will shorten them.
- Longer term bonds will have a longer duration than short term bonds.
- For bonds paying annual coupon interest, the duration will always be shorter than the time until maturity. Zero coupon bonds have a duration equal to the time to maturity.

The calculation for duration was created in the 1930's by Frederick R. Macauley. Mr. Macauley later developed a modified duration formula which more closely alligns the calculated duration with expected bond price changes.

## Evaluating Bonds With Duration

For investors, bond duration is used as a measure of potential bond price volatility in relation to changing interest rates. The calculated duration of a bond is an approximation of the percentage the bond price will change for a one percent change in market interest rates. If a bond has a duration of five years and interest rates go up one percent, the market price of the bond will decline by approximately five percent. If interest rates fall, the market price will increase.

Investors who want less volatility in bond prices should look for bonds with shorter durations. A short duration can be accomplished by buying bonds with high coupon rates and shorter times to maturity. Low volatility is important if interest rates are expected to increase. If rates are forecast to decline, an investor wants bonds with more rate sensitivity to acheive greater price increases as the rates decline. The path to greater volatility is with longer duration bonds. Longer duration comes from low coupon rates and longer times to maturity.

The duration of a bond is of little extra value when looking at a single bond. The coupon rate, yield to maturity and time to maturity gives an investor enough information to make a decision whether to buy the bond. Duration is more useful in evaluating a portfolio of bonds. The duration of a full portfolio condenses all of the coupon rates and maturities into a single number which predicts the value change of the overall portfolio as interest rates change.

## Evaluation Examples

Bond duration is a very useful tool to compare different bond mutual funds or bond ETFs. At a glance, comparing the duration of two funds gives an investor an idea how much the value of a fund's share price will change as interest rates change. Most bond funds provide the duration of a fund's portfolio in the data about a fund on its web page. Here is a trio of government or Treasury bond funds, all considered to be intermediate term funds:

- SPDR Barclays Intermediate Term Treasury ETF: The numbers as of mid-June 2011 for this Treasury ETF were: a portfolio average maturity of 4.24 years, with a modified adjusted duration of 3.94 years and dividend yield of 1.9 percent.

- Vanguard Intermediate Term Treasury Fund: At the time of publication, this bond fund had a portfolio average maturity of 5.7 years and a portfolio duration of 5.0 years. The distribution yield was 2.16 percent.

- Thornburg Limited Term U.S. Government Fund: Thornburg uses a laddered approach to its bond fund portfolios and the limited term government fund holds bonds with maturities of one to eight years. The funds average maturity was 3.4 years and had an effective duration of 2.7 years. The dividend yield on the class A shares of this fund was 3.03 percent.

In this comparison, the Thornberg government bond fund provided an attractive combination of more share price stability due to the lower portfolio bond duration and a higher current dividend yield.

Using these calculations and understanding the full extent of duration in the bond market, one can choose the correct investing options that best fit his or her needs.

## References

Regent School Press, https://www.regentschoolpress.com/BondDuration.pdf

My SMP, https://www.mysmp.com/bonds/bond-duration.html

SPDRs, https://www.spdrs.com/index.seam

Thornberg Investment Management, https://www.thornburginvestments.com/funds/fund_index.asp

Vanguard Mutual Funds, https://personal.vanguard.com/us/funds/vanguard

Image: Assorted US Coins by Elembis at Wikimedia Commons