Perpetual Bonds and Consols
Perpetual Bonds and Consols
A perpetual bond has no maturity date. You receive coupons forever (or until called). The simplicity of the cash flow—an infinite stream of equal payments—creates unusual pricing dynamics and infinite duration risk.
Key takeaways
- Perpetual bonds pay coupons indefinitely; there is no maturity date or principal repayment.
- Price is determined by the coupon divided by the yield: Price = Coupon / Yield.
- Perpetual bonds have infinite duration—they're extraordinarily sensitive to interest-rate changes.
- Most perpetuals are callable, giving the issuer an option to exit when rates fall.
- Perpetuals are issued mainly by banks (as capital) and some governments (historically); they're rare and illiquid in modern markets.
How perpetual bonds work
A perpetual bond pays a fixed coupon forever. The U.K. Consolidated Loan of 1752 (known as a "consol") paid 3% per year and never matured—some are still outstanding, though most were redeemed. Modern perpetuals are less common but exist.
Unlike a traditional bond (where you receive coupons and then repayment of principal at maturity), a perpetual bond provides only coupons. There is no principal repayment unless the issuer decides to call (redeem) the bond.
The simplicity of perpetuals allows for a simple pricing formula:
Price = Annual Coupon / Yield
If a perpetual pays a $50 annual coupon and the market yield is 5%, the price is:
Price = $50 / 0.05 = $1,000
If yields rise to 6%, the price falls to:
Price = $50 / 0.06 = $833
If yields fall to 4%, the price rises to:
Price = $50 / 0.04 = $1,250
This is the defining relationship: a small change in yield causes a large change in price because the coupon (the numerator) never changes.
Why perpetuals are issued
Perpetuals are issued for several reasons:
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Capital relief for banks: Banking regulators (Basel III and similar frameworks) treat certain perpetuals as equity-like capital, giving issuers flexibility. Banks have issued hundreds of billions in perpetuals to shore up capital ratios after the 2008 financial crisis.
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Lower cost than equity: Perpetuals are cheaper than issuing stock (no dilution of ownership) but still count as capital. From a cost perspective, if you can issue perpetuals at 5% (instead of raising equity at a higher cost), the savings are substantial.
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Historical habit: Governments issued perpetuals for centuries because they simplified borrowing (no need to repay principal, just service the coupon). The U.K. consol tradition persists.
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Subordinated debt: Some perpetuals are issued as subordinated debt (behind other creditors in bankruptcy). They're similar in structure to preferred stock.
The problem: infinite duration
A perpetual has infinite duration. Mathematically, the weighted-average time to cash flow is infinite (because one of the cash flows is infinite, at the end of time). Practically, this means perpetuals are extraordinarily sensitive to interest-rate changes.
Using the perpetual pricing formula, the price sensitivity to a 1 percentage point yield change is:
Price change (%) = −Duration × Yield change = −∞ × 1% = undefined (but very large)
A more practical calculation: if a perpetual yields 5% and yields rise to 6% (a 20% change in yield), the price falls from $1,000 to $833, a 16.7% loss. If yields fall to 4% (a 20% yield change the other way), the price rises to $1,250, a 25% gain.
This asymmetric sensitivity is called convexity, and it's extreme for perpetuals.
Callable perpetuals and the call option problem
Most modern perpetuals are callable. An issuer can redeem the bond at par (or a specified price) after a certain date. This is crucial: if a perpetual is callable and yields fall, the issuer will call it, depriving you of the benefit of capital appreciation.
Consider a perpetual issued at 5% (price $1,000, coupon $50). If yields fall to 3%, the bond's theoretical price would be $1,667. But if the perpetual is callable at par, the issuer calls the bond, forcing you to accept $1,000. You lose the $667 upside.
This is call risk magnified: on a perpetual with infinite duration, call risk is particularly acute. You have unlimited downside (prices can fall indefinitely as yields rise) but capped upside (the call price, usually par).
Callable perpetuals are priced similarly to callable traditional bonds: investors demand a yield premium to compensate for the embedded call option. A callable perpetual might yield 5.5%, while a non-callable perpetual (if one existed) might yield 4.8%.
Perpetuals issued by banks
Banks are the primary issuers of modern perpetuals. After the 2008 financial crisis, banks issued perpetuals to rebuild capital. Examples include:
- Deutsche Bank's 5.5% perpetual issued in 2013, callable after 5 years.
- HSBC's 4.5% perpetual issued in 2015, callable after 5 years.
- Credit Suisse's various perpetuals, some still outstanding or recently redeemed.
These perpetuals trade in the institutional bond market and are not typically available to retail investors through standard brokerages. They're held by mutual funds (particularly bond and income funds) and by institutional investors comfortable with subordinated debt and call risk.
The yields on bank perpetuals are typically 2 to 4 percentage points higher than bank senior debt, compensating for subordination (lower priority in bankruptcy) and call risk.
Preferred stock as perpetual-like instruments
Preferred stock issued by corporations and banks functions similarly to perpetuals in many ways. Preferred stock pays a fixed dividend indefinitely, with no maturity date (usually). The dividend is not a tax-deductible expense for the corporation (unlike bond coupon interest), but in the hands of corporate investors, preferred dividends often receive favorable tax treatment.
From a pricing perspective, preferred stock uses the same perpetual pricing formula:
Price = Annual Dividend / Yield
A preferred share paying $5 per year with a 5% yield trades at $100. This creates the same duration and call-risk dynamics as perpetuals.
Preferred stock is often callable as well. The issuer can force redemption at a set price (usually $25 per share for common preferreds) if rates fall.
Duration and rate sensitivity of perpetuals
The duration of a perpetual is:
Duration = (1 + Yield) / Yield
For a perpetual yielding 5%, the duration is:
Duration = 1.05 / 0.05 = 21 years
This is very high—much higher than a traditional 10-year bond (which might have duration of 7 to 8 years). A 1 percentage point rate increase causes a price decline of about 21%.
As yields fall (and approach zero), duration approaches infinity. This is why perpetuals are so sensitive to very low interest-rate environments.
Liquidity and spread considerations
Perpetuals trade over-the-counter, like most bonds. Liquidity varies widely depending on the issuer and the specific bond. A perpetual issued by a large global bank (JPMorgan, HSBC) might have decent liquidity. A perpetual issued by a smaller bank or in an emerging market might be quite illiquid.
Bid-ask spreads on perpetuals are typically wider than spreads on comparable traditional bonds, sometimes 25 to 50 basis points or more. This illiquidity can be costly if you need to exit quickly.
Example: price sensitivity of a perpetual
Suppose you buy a 5% perpetual (coupon $50, price $1,000) with a 5-year call protection. Rates immediately fall to 4%. The perpetual's price rises to:
Price = $50 / 0.04 = $1,250
You have a $250 unrealized gain (25%). But if the perpetual is callable at par after 5 years, you're at risk of having the gain capped. You might sell at $1,200, locking in a profit while avoiding maximum call risk.
Alternatively, if you believe rates will fall further (to 3%), you might hold, hoping the perpetual's price rises to $1,667 before being called. But if the issuer calls at year 5 and rates are still at 4%, you receive par and must reinvest at 4% yields—worse than if you'd sold proactively.
Historical and modern perpetual bonds
Related concepts
Next
We've now covered the major bond varieties: standard bonds, callable and puttable, zero-coupon, and perpetuals. It's time to step back and see how they fit together in a coherent taxonomy. The final article in this chapter synthesizes everything.