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The primary math formula for bonds is basic compound interest:
fv = pv * (1+ i) n
and its corollary:
fv
pv = (1 + i) n
where pv = present value, fv = future value, I = interest rate and n = number of periods.
The corollary formula demonstrates that higher interest rates (i) increase the the denominator and decrease present value. Thus, as interest rates rise, the price of a bond falls.
Likewise, longer bond maturities – here represented by n or the number of periods – also increase the denominator and reduce present value. So bonds with longer maturities suffer greater price declines than shorter maturity bonds, when interest rates rise.
The table below shows the price sensitivity of bonds to an increase in bond yields of 2% (or 200 basis points). For example, a 2% increase in interest rates will cause a price decline of 8.5% in a bond with a 4% coupon and 5 year maturity. That same 2% rate rise will cause a similar coupon bond with a 30-year maturity to fall 27.7% in price. Investing in bonds with short- to intermediate maturities reduces interest rate risk.
Table 1
Bond Price Sensitivity Assuming a 2% Rate Rise
| Years to Maturity | 2% Coupon Bond | 4% Coupon Bond | 6% Coupon Bond |
| 1 | -1.9% | -1.9% | -1.8% |
| 5 | -9.0% | -8.5% | -8.1% |
| 10 | -16.4% | -14.9% | -13.5% |
| 20 | -27.4% | -23.1% | -19.7% |
| 30 | -34.8% | -27.7% | -22.6% |
Source: AAII Journal, December 2007 and Lark Research calculations
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Updated May 8, 2014
Stephen P. Percoco
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