Callable Bond Negative Convexity
Callable Bond Negative Convexity
A callable bond is a bond where the issuer has the right to repay you early—a feature that is worth money to them and costs money to you.
Key takeaways
- A callable bond grants the issuer the right to repay principal before maturity, usually when rates have fallen and refinancing is attractive to them.
- Negative convexity arises because your upside (capital appreciation when rates fall) is capped at the call price.
- The call option's value is highest when rates are low and the likelihood of exercise is high.
- Callable bonds compensate bondholders with higher yields, but the extra yield may not offset the convexity cost in volatile environments.
- Effective duration (not modified duration) is the correct measure of price sensitivity for callable bonds.
How callable bonds work
A typical callable bond might be issued as follows: "XYZ Corporation issues 10-year bonds, 4% coupon, redeemable at par (£100) on or after year 5."
This means:
- You, the bondholder, receive 4% annual coupons for at least 10 years.
- The corporation has the option to repay £100 per bond anytime after year 5, at their discretion.
- If they do not call the bond by year 10, you receive the full 10 years of coupons and then your principal.
The call option gives the corporation flexibility. If rates fall, they can refinance at a lower rate. If rates rise, they let the bond run to maturity and enjoy the beneficial impact on their credit cost. The bondholder bears the downside of this optionality: when rates fall and you wanted a capital gain, the call prevents it.
The mathematics of the call
From the bondholder's perspective, a callable bond can be decomposed as:
Callable Bond = Non-Callable Bond − Call Option
Suppose a non-callable 10-year bond (same coupon, credit quality, maturity) is worth £102. The call option embedded in the callable bond is worth, say, £3. Then the callable bond is worth £102 − £3 = £99.
The call option value increases as rates fall. At a yield of 4%, the call is worth £1 (unlikely to be exercised immediately). At 2%, the call is worth £4 (very likely to be exercised). At 1%, the call might be worth £6.
This is why callables underperform non-callables when rates fall. The call option embedded in the callable becomes more valuable, and that value is realized by the issuer (who exercises the call), not the bondholder.
Negative convexity in action
Let's trace what happens to a callable bond in different rate scenarios.
Initial state: 7-year callable bond, 4% coupon, callable at par, priced at par (yield 4%).
Scenario 1: Rates fall to 2%
- A non-callable bond with the same characteristics would rise in price to, say, £115 (duration gain of 12–14%, depending on convexity).
- The callable bond rises to, say, £105 (because the call will be exercised by the issuer). The maximum price is capped at par (or a small premium if the call price is above par).
- The bondholder gains only 5% instead of the 12–14% they would have realized with a non-callable bond.
- The issuer exercises the call, repays the bondholder at par, and refinances at 2% instead of 4%, saving 200 basis points annually.
The bondholder's upside is capped. This is negative convexity at work.
Scenario 2: Rates rise to 6%
- A non-callable bond would fall in price to, say, £85 (duration loss of 12–14%).
- The callable bond also falls to, say, £82. The issuer will not call the bond because refinancing at 6% is worse than 4%.
- The bondholder suffers the full duration loss.
Callable bonds lose as much as non-callables when rates rise. There is no downside protection from the call option. The option is valuable to the issuer (when rates fall), not the bondholder.
The pattern is asymmetrical:
- Falling rates: limited gains for bondholder.
- Rising rates: full losses for bondholder.
This is negative convexity: asymmetrical in the wrong direction.
The yield compensation puzzle
Because callable bonds have negative convexity, they must yield more than comparable non-callable bonds to attract investors. In 2024, a callable corporate bond might yield 4.5% while a non-callable bond yields 3.5%—a 100-basis-point spread.
The question investors face: is the extra 100 basis points worth the negative convexity? The answer depends on your rate forecast and market expectations.
If you expect rates to fall: The non-callable bond is better. The extra 100 basis points do not compensate for losing the capital gains you would have realized if rates fell. You forgo a 12% gain to earn an extra 1% per year—a bad tradeoff.
If you expect rates to rise or stay flat: The callable bond might be better. Rates are unlikely to fall, so the call is unlikely to be exercised. You pocket the extra 100 basis points annually without penalty.
If you expect very high volatility: The callable bond is likely worse. In volatile environments, rates make large moves in both directions. The callable's negative convexity amplifies losses on large moves, and the call on large downward moves caps gains. The extra yield does not compensate.
The compensation for negative convexity is not a fixed formula; it is a market price that fluctuates based on:
- The volatility implied by options markets (higher volatility = higher compensation for callables).
- The issuer's credit quality (stronger credits have less valuable call options, so less compensation needed).
- The call schedule (a call that can be exercised immediately is more valuable than a call deferred 5 years).
Effective duration for callables
When assessing the interest rate sensitivity of a callable bond, you must use effective duration, not modified duration.
Modified duration assumes the cash flows are fixed. For a callable bond, the cash flows depend on whether rates fall (call is exercised, cash flows shorten) or rise (call is not exercised, cash flows extend to maturity). Effective duration accounts for this optionality.
A 10-year callable bond might have:
- Modified duration: 6.5 years (assuming it is not called).
- Effective duration: 4.5 years (accounting for the probability the call will be exercised).
The effective duration is lower because the bond's maturity is uncertain. If rates fall, the bond is called, shortening the effective maturity. If rates rise, the bond extends. But on average (given market expectations), the effective duration is shorter than the modified duration.
Using modified duration for a callable bond overstates your interest rate risk. If you think your bond has 6.5 years of duration and rates move 1%, you expect a 6.5% price move. But with effective duration of 4.5 years, the move might be only 4.5%—and it will be asymmetrical (capped on the downside).
Callable bonds in portfolio context
In a portfolio, callable bonds introduce complexity. They are useful when:
- You want extra yield and believe rates will rise or stay flat.
- You have a specific time horizon and the callable is unlikely to be exercised before then.
- You are comfortable with negative convexity and understand the risks.
Callable bonds are problematic when:
- You have a long-term investment horizon and rates are very high (more likely to fall, triggering the call).
- You are matching liabilities and need predictable cash flows (callables introduce uncertainty).
- You already have duration risk in your portfolio; callables amplify it asymmetrically.
Professional managers often use callable bonds in tactical allocations—buying them when they expect rates to rise and selling them when they expect rates to fall.
Levels of calls and call timing
Some callable bonds have more complex call structures:
- Soft call: The issuer can call at par, but only if the bond is trading above par (a "soft" condition). If the bond price falls, the call cannot be exercised until a certain date.
- Make-whole call: The issuer can call at any time, but must pay a make-whole amount (par plus a premium based on the difference between the bond's coupon and current market yields). This is less punitive to the bondholder.
- Step-up callable: The call price increases over time (e.g., £100 for 2 years, £101 for years 2–4, £102 thereafter). The bondholder has more protection early on.
Each variation changes the effective value of the call option and thus the required yield compensation.
Callable bonds in 2022–2024
In 2022, when Federal Reserve rate hikes were aggressive, callable bonds underperformed. Investors had feared rates would fall (and trigger calls), so they had demanded high compensation. But rates rose sharply instead. Non-callable bonds fell hard (duration losses), but callable bonds did not participate in the relief rally when rate-hike expectations moderated in early 2024. The negative convexity meant callable bonds could not fully appreciate.
In 2024, callable corporates offered spreads of 50–150 basis points over non-callables. For risk-averse investors wanting extra yield, they were attractive. For investors positioning for falling rates (bullish on bonds), they were traps.
The fundamental cost of callability
At a conceptual level, callability is a cost. The issuer captures optionality at your expense. While you are compensated with extra yield, you should understand that you are systematically conceding gains when markets move in your favor (rates fall) and absorbing losses when they move against you (rates rise).
Over long periods, when rates go through multiple cycles, this asymmetry accumulates. Callable bonds will tend to underperform non-callables because the call option is exercised repeatedly to the issuer's benefit.
Process: Evaluating a callable bond
Next
Callable bonds are issued by corporations and government agencies to retain flexibility. Mortgage-backed securities are a similar case but with a twist: prepayment is driven not by the issuer's decision but by millions of individual homeowners' refinancing choices. The mechanics differ, but the negative convexity is the same—and often even more severe.