# Understanding Interest Rate Risk And Duration Of A Bond

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Includes: AGG, BND, TIP, TZD, TZI
by: Robert Wagner

I recently wrote an article titled "Why Long-term Government Bonds are the 'Dumbest Investment.'" In this article, I will attempt to quantify why long-term government bonds are the "dumbest investment." To do that, I've created a spreadsheet that measures the percent change in a bond's present value verses its par value with incremental changes in interest rates. It also calculates the bond's "duration" which is the percent change in the value of the bond with each percent increase in interest rates.

The first bond we will examine is the current 3-yr treasury bond yielding 0.39%. The first column are the annual numbers, the second column is the bond's \$10,000 par value, the third column is the annual interest payment, the fourth column is the total cash flow, the fifth column is the current interest rate for that maturity, and each column after that adds 1% to the previous, so there are 1% incremental increases. The row "PV" is the summation of the present value of the total cash flows. The first PV should always be equal to \$10,000. Each column over from that is the present value of the bond after a 1% increase in interest rates. The % Change from Par measures the total decrease in the value of the bond for the interest rate associated with that column. The duration measures the incremental change in the present value of the bond for each 1% increase in interest rates.

Reviewing the table, we get a feel for how increasing interest rates affects the price of a bond.

3-Year Treasury

1) As rates increase from 0.39 to 10.39%, the bond loses 24.70% of its value.

2) As rates increase from 0.39 to 10.39%, the bond's present value drops from \$10,000 to \$7,530.

3) The duration of the portfolio is about 2.85. Each 1% increase decreases the bond's value by about 2.85%.

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5-Year Treasury

1) As rates increase from 0.80 to 10.80%, the bond loses 37.15% of its value.

2) As rates increase from 0.80 to 10.80%, the bond's present value drops from \$10,000 to \$6,285.

3) The duration of the portfolio is about 4.5. Each 1% increase decreases the bond's value by about 4.5%.

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10-Year Treasury

1) As rates increase from 1.93 to 11.93%, the bond loses 56.66% of its value.

2) As rates increase from 1.93 to 11.93%, the bond's present value drops from \$10,000 to \$4,334.

3) The duration of the portfolio is about 8.0. Each 1% increase decreases the bond's value by about 8.0%.

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20-Year Treasury

1) As rates increase from 2.75 to 12.75%, the bond loses 71.32% of its value.

2) As rates increase from 2.75 to 12.75%, the bond's present value drops from \$10,000 to \$2,868.

3) The duration of the portfolio is about 12.0. Each 1% increase decreases the bond's value by about 12.0%.

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30-Year Treasury

1) As rates increase from 3.13 to 13.13%, the bond loses 74.28% of its value.

2) As rates increase from 3.13 to 13.13%, the bond's present value drops from \$10,000 to \$2,572.

3) The duration of the portfolio is about 15.0. Each 1% increase decreases the bond's value by about 15.0%.

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In conclusion, with interest rates trading at or near record lows, it is important for investors to understand the interest rate risk of their bond, balanced and target retirement date portfolios. The above tables are a useful tool to help quantify the impact interest rate changes will have on the value of portfolios with various maturities, coupons and durations.

Symbols that may be relevant are:

AGG, BND, BSCD, BSCE, BSCF, BSCG, BSCH, BSCI, BSCJ, BSCK, BSJD, BSJE, BSJF, BSJG, BSJH, BSJI, HYG, JNK, LQD, SHY, TIP AOA, AOK, AOM, AOR, GTAA, TDD, TDH, TDN, TDV, TDX, TGR, TZD, TZE, TZG, TZI, TZL, TZO, TZV, TZW, TZY

Disclaimer: Opinions expressed herein by the author are not an investment recommendation and are not meant to be relied upon in investment decisions. The author is not acting in an investment advisor capacity. This is not an investment research report. The author's opinions expressed herein address only select aspects of potential investment in securities of the companies mentioned and cannot be a substitute for comprehensive investment analysis. Any analysis presented herein is illustrative in nature, limited in scope, based on an incomplete set of information, and has limitations to its accuracy. The author recommends that potential and existing investors conduct thorough investment research of their own, including detailed review of the companies' SEC filings, and consult a qualified investment advisor. The information upon which this material is based was obtained from sources believed to be reliable, but has not been independently verified. Therefore, the author cannot guarantee its accuracy. Any opinions or estimates constitute the author's best judgment as of the date of publication, and are subject to change without notice.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.