Bond portfolio immunization strategy

The problem

Say you must pay a known amount on a future date, such as a child’s tuition in 5 years. You invest in bonds today. Two risks pull in opposite directions when interest rates change:

• Price risk: if rates rise, your bonds lose value.
• Reinvestment risk: if rates rise, the coupons you reinvest earn more.

When rates fall, the effects reverse: bond prices rise, but coupons are reinvested at lower rates.

The solution: match the durations

Immunization sets the portfolio’s duration equal to the time until the liability is due. Then the two effects roughly cancel out, and the portfolio’s value on the due date is protected from small rate changes.

Example

Tuition is due in 5 years. You can buy two bonds:

• Bond A, duration 2 years
• Bond B, duration 8 years

A portfolio’s duration is the weighted average of its bonds’ durations. Find the weight w in Bond A:

w × 2 + (1 − w) × 8 = 5 → w = (8 − 5) ÷ (8 − 2) = 50%

Invest 50% in each bond. The portfolio’s duration is 5 years, matching the tuition date. The simplest alternative is a single 5-year zero-coupon bond, whose duration is exactly 5 years.

It needs maintenance

Immunization isn’t set-and-forget:

• As time passes, the portfolio’s duration and the liability’s remaining time don’t fall at the same pace.
• When rates change, durations change too.

So the portfolio must be rebalanced from time to time to keep the durations matched.

Limits

It protects against small, parallel shifts in the yield curve. Large moves, or short and long rates moving differently, can still leave a gap. Convexity helps explain why.

This lesson is for education only and isn’t investment advice.

Next: convexity.