Why do callable bonds exhibit negative convexity and what does that mean for investors?

Negative convexity means the bond's price-yield curve bends downward at low yields, causing the bond to gain less than expected when rates fall. This happens because the call option held by the issuer caps the bond's upside.

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The Mechanics:

A callable bond = Non-callable bond - Call option value (to issuer)

As yields fall:

• A non-callable bond's price keeps rising, accelerating due to positive convexity
• A callable bond's price approaches the call price (e.g., par + one coupon) and gets 'compressed' — the issuer will call the bond and refinance at lower rates
• The call option becomes more valuable to the issuer, offsetting the bondholder's price gain

Example — Stockton Utilities 6.5% Callable at 102 (fictional):

At 3% yield, the non-callable bond is worth $1,121, but the callable bond is stuck near$1,020 because the issuer would call at $1,020.

Investor Implications:

1. Price compression: You lose upside in a rally
2. Reinvestment risk: When called, you must reinvest at the new lower rates
3. Higher yield required: Callable bonds must offer a higher yield (option-adjusted spread) to compensate for negative convexity
4. Duration shortens: As yields fall, effective duration decreases because the expected life shortens toward the call date

Exam Tip: The CFA exam tests the price-yield behavior of callable bonds. Remember: negative convexity means the price-yield curve is concave (bends toward the x-axis) at low yields. The callable bond underperforms the non-callable bond in rallies.

Explore callable bond analysis in our CFA Level I practice questions.