Bond investors and advisors who want to avoid the risks of wavering corporate performance can buy government bonds and ride out the equity storms. But the bonds, which are acutely sensitive to changes in interest rates, may expose the investor to the whims of monetary policy and inflation.

Investors and advisors can protect bonds against adverse interest rate changes by what is often called “immunization.” The idea is simple: while interest rates may rise and drive down the prices of existing bonds, the coupons of the bonds can be reinvested at ever higher rates. If interest rates rise at an increasing rate, as they would under worst-case inflation assumptions, the returns from reinvested coupons could offset the decline in the market price of the bond prior to maturity. As well, the gains from reinvested coupons could compensate for much of the inflation that propels interest rates upward.

Immunizing a bond portfolio takes an understanding of the concept and operation of “duration.” Defined in 1938 by U.S. bond analyst Frederick Macaulay, the theory and its formula were dormant until the 1970s, when inflation was rising and bond managers were trying to find ways to control risk.

In operation, duration is the weighted average term to maturity of a bond’s cash flow. The duration formula multiplies the time until the receipt of each coupon by the current value of the cash flow. Add up the current discounted value of each coupon and divide the total by the sum of the weights, then solve the equation. The result is duration, which is expressed in years. If duration equals five, a bond will rise or fall by 5% for each 1% change in interest rates.
That is extremely useful information for an investor in government bonds.

Duration approaches zero for a treasury bill,
because a change in prevailing interest rates will have almost no effect on its current value. At the opposite end of the time/value continuum, the duration for a strip bond equals the term of the strip. If the strip has 30 years to run, for example, a 1% increase in interest rates will drop the market value of the strip by 30%.

Between the two limits of price volatility, an investor has to manage the risk that, should a bond be sold well before maturity, its price may be substantially above or below face value.

Duration determines the risk that a bond faces. Long bonds have more time to run and, therefore, more years of exposure to interest rate changes. The rate of change of duration, often called “convexity,” displays what one can call the “healing factor” of interest rate exposure.

Positive convexity means that when interest rates decline and bond prices rise, durations become longer. The process adds to the bondholder’s return. When interest rates rise, durations shorten, showing the rate of price declines.

The positive convexity that conventional bonds offer is actually a self-correction process that brings the bond’s return back to its mean or coupon value, says Jean François Lemay, vice president in the portfolio risk optimization division at Toronto-based Sceptre Investment Counsel Ltd. “Duration loss is compensated by higher yield on the assets you reinvest,” he says. In other words, given rising interest rates, the declining market price of a bond is cushioned by the rising return from reinvested coupons.

An investor can control duration risk and immunize bond exposure with reinvestment.
There are a few ways to do it. One is to purchase outstanding bonds with high coupons that offer more cash to reinvest than bonds with the same yield to maturity based on lower coupons. The high-coupon bonds have lower duration risk than bonds of equal term. That’s because the coupons, when reinvested at higher rates, produce income to compensate for the fall in the price of the bond.

Another way to immunize a portfolio is to “barbell” bonds, which means holding long bonds to take advantage of the potential for price increases if interest rates fall, and balancing that exposure with short bonds to provide cash for rapid reinvestment if rates rise. If rates rise, the long bonds fall in market price, but the short bonds that mature in the near future provide money to reinvest at rising rates. If rates fall, the long bonds rise in price to offset the decline in yield on the reinvestment of the short bonds.
There are reasons other than portfolio
hedging for barbelling, but the process is self-corrective for portfolio value changes in a specified holding period.