Income Builder - Bond Math Basics

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The primary formula that you must learn to understand bond math 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.

From the corollary formula, you can see that the more the interest rate (i) increases, the bigger the denominator and therefore the lower the present value.  Thus, as interest rates rise, the price of a bond falls.

Likewise, the longer the maturity of the bond -  here represented by n or the number of periods -  the bigger the denominator and therefore the lower the value.  Thus, bonds with longer maturities suffer greater price declines than shorter maturity bonds, when interest rates rise.

The table below, reproduced from a recent issue of the AAII Journal, shows the price sensitivity of bonds with various maturities 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.  The message is clear:  if you want to minimize interest rate risk, invest in bonds with short- to intermediate maturities.  On the other hand, if you believe that interest rates will fall, then buy long term bonds.

Table 1
Bond Price Sensitivity Assuming a 2% Rate Rise

Source:  AAII Journal, December 2007

With recent declines in interest rates, long-term government bonds have been the best performers.  However, rates have fallen to extremely low levels, so it is unlikely that they will fall much more.  At the same time, the risk of an increase in rates has now, I believe, risen appreciably.

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Originally published February 28, 2008

Stephen P. Percoco
Income Builder
P.O. Box 1409
Mashpee, MA  02649
(732) 763-0763
incomebuilder@larkresearch.com

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