Why does a callable bond have lower effective duration than an otherwise identical non-callable bond, and what is negative convexity?

Great question — callable bonds behave very differently from plain vanilla bonds, and understanding negative convexity is a favorite CFA exam topic.

Why Callable Bonds Have Lower Effective Duration

Recall that duration measures sensitivity of a bond's price to interest rate changes. For a callable bond, the issuer has the right to redeem the bond at the call price when rates fall. This creates an asymmetric payoff:

• When rates fall: A non-callable bond's price rises freely. But a callable bond's price is capped near the call price — the issuer will call it rather than continue paying a high coupon. The upside is truncated.
• When rates rise: Both bonds behave similarly — neither issuer would call.

Because the callable bond's price doesn't rise as much when rates fall, its average sensitivity to rate changes (effective duration) is lower.

Negative Convexity Explained

Normal (positive) convexity means a bond's price-yield curve is bowed upward: the price increases by more when rates fall than it decreases when rates rise by the same amount. This is beneficial for investors.

Negative convexity flips this: the callable bond's price increases by less when rates fall (because of the call cap) but decreases by the full amount when rates rise. Investors lose the beneficial asymmetry.

Numerical Example — Thornfield Energy 7% Bond

Compare two bonds, both 10-year 7% annual coupon:

Effective duration of non-callable: approximately 7.1 years

Effective duration of callable: approximately 4.3 years

The callable bond has 40% lower duration because the price is anchored near the call price on the downside of rates.

Effective Duration Formula:

Effective Duration = (P_down - P_up) / (2 x P_0 x delta_y)

For the callable bond: (871 - 1,022) / (2 x 985 x 0.02) = 151 / 39.4 = 3.83

For the non-callable: (871 - 1,155) / (2 x 1,000 x 0.02) = 284 / 40 = 7.10

Exam Tip: When you see a price-yield graph with the curve flattening as yields drop, that's the negative convexity region. Callable bonds trade there whenever rates are near or below the coupon rate.

Deepen your callable bond understanding with our CFA Level I Fixed Income resources.