What are contingent convertibles (CoCos)?
– Contingent convertibles, often called CoCos, are debt securities banks issue that can automatically convert into equity (shares) or be written down when a preset stress condition occurs. They are also known in the market as AT1 (additional Tier 1) bonds or enhanced capital notes (ECNs). CoCos trade at higher yields than ordinary bank debt because they carry a material risk that principal or future coupon payments can be cut or erased if the issuer’s capital falls below a trigger level.
Key definitions
– Trigger: a predefined condition (for example, a regulatory capital ratio falling below a specified threshold) that activates conversion or write-down of the CoCo.
– Conversion: swapping the bond claim for common shares of the bank, typically at a predetermined conversion rate or price.
– Write-down: reducing—or fully wiping out—the bond’s principal value, sometimes permanently, without issuing shares.
– AT1 capital: a regulatory classification (additional Tier 1) for certain hybrid instruments that count toward a bank’s loss-absorbing capital under rules such as Basel III.
Why CoCos exist (purpose)
– They give banks a contingent source of loss absorption that kicks in automatically in stress. That helps banks meet capital requirements while reducing the likelihood of taxpayer-funded rescues. Regulators adopted these instruments in the post-2008 reforms to strengthen the banking sector’s ability to absorb sudden losses.
How CoCos work — simplified mechanics
1. Issuance: Bank issues the CoCo with face value, coupon rate, and an explicit trigger (for example, a Tier 1 capital ratio falling below X%).
2. Coupon payments: The bond normally pays periodic interest; however, the bond documents may allow the bank or regulators to suspend coupons.
3. Trigger event: If the bank’s capital metric or a supervisory decision meets the trigger condition, the CoCo either converts into shares at a pre-specified conversion rate/price or is written down (partially or fully).
4. Post-trigger: Holders either become shareholders (exposed to stock moves and dilution) or suffer a hair-cut on principal; either outcome is intended to restore capital.
How CoCos differ from ordinary convertible bonds
– Conventional convertible bonds give investors an option to convert a bond into stock when conversion is favorable (usually when the share price rises), preserving bond seniority until conversion. CoCos reverse that bargain: conversion or write-down is forced by a distress signal, often when share prices are falling and capital is strained. CoCos are designed primarily to support bank capital, not to offer upside from equity appreciation.
Common features and variations
– Trigger types: regulatory capital ratio thresholds (e.g., a Tier 1 ratio), a supervisory authority’s judgment, or sometimes a market-price-related mechanism.
– Conversion terms: fixed conversion price, fixed conversion rate, or formulaic conversion; some instruments specify a full write-down rather than conversion.
– Coupon discretion: issuers or regulators can cancel coupon payments without constituting a default.
– Subordination: AT1 instruments sit below senior debt but above equity in the capital stack.
Benefits for banks
– Immediate potential to restore capital without an external recapitalization.
– Coupons can be discretionary, reducing cash outflows in stress.
– By converting debt into equity or writing down liabilities, banks can preserve solvency metrics and continue lending.
Benefits and risks for investors
Benefits
– Higher yields relative to senior bank bonds to compensate for additional risk.
– Potential equity upside if conversion occurs when share price subsequently recovers (rare).
Risks
– Trigger timing: conversion can happen when share prices are depressed, producing immediate losses.
– Loss of principal: many CoCos permit partial or total write-downs, which can wipe out investor capital.
– Limited recovery in resolution: AT1 claims are junior to many liabilities, so recoveries in failure scenarios can be low.
– Complexity and legal risk: trigger mechanics and discretionary features vary and can be tested in crisis scenarios.
Regulatory context
– CoCos are tied closely to Basel III capital rules, which tightened banks’ capital definitions and encouraged instruments that absorb losses in stress. National supervisors in Europe embraced AT1 issuance as a way to meet these standards. Use and treatment of CoCos vary by jurisdiction; the U.S. banking market has not broadly adopted them.
Checklist — what to check before buying a CoCo
– Issuer quality: capital ratios, asset quality, and funding profile.
– Trigger specification: exact metric, level (e.g., 5.125% or 7%), and whether it is permanent or discretionary.
– Conversion mechanics: conversion price/rate and whether conversion is into common equity or a write-down.
– Coupon terms: fixed amount,
floating or step-up mechanics; whether coupons are discretionary, non-cumulative (missed coupons are lost) or cumulative (missed coupons accrue). – Call and reset features: issuer call dates, reset spreads, and make-whole provisions. – Permanent write-down vs conversion: whether trigger causes full/partial write-down of principal or converts notes into equity. – Conversion price and ratio: explicit formula and how dilution is allocated. – Trigger governance: who determines trigger activation (issuer, regulator, independent trustee) and dispute resolution. – Ranking and creditor hierarchy: position in insolvency waterfalls and interaction with senior and subordinated debt. – Documentation: read the prospectus, terms and conditions, and any regulatory notices. – Tax and accounting treatment: local tax rules on coupon deductibility and investor tax status (capital loss vs ordinary income). – Liquidity and marketability: average daily volume, dealer coverage, and bid–ask spreads. – Stress scenarios: run scenarios for CET1, share price, and funding stress to see outcomes at trigger thresholds. – Ratings and research: monitor agency opinions and caveats about trigger enforceability. – Legal and jurisdictional risk: local bail-in laws and court precedents that could affect enforceability.
How CoCos pay out — worked examples
Assumptions you can use to model outcomes:
– Face (nominal) value: 1,000 per bond. – Coupon: 8% fixed (annual payment = 80). – Trigger: CET1 ≤ 7.0%. – Conversion type A: permanent write-down of 100% on trigger. – Conversion type B: conversion into common shares at a fixed conversion price of 2.50.
1) Current yield and price example
If market price = 800 and annual coupon = 80:
– Current yield = coupon / price = 80 / 800 = 10.0%.
2) Conversion into equity — math
Conversion ratio = nominal / conversion price = 1,000 / 2.50 = 400 shares.
Value to investor at conversion = 400 × share_price_at_conversion.
Scenarios:
– If share price = 4.00, value = 1,600 → investor gains (1,600 − 1,000 = +600).
– If share price = 1.00, value = 400 → investor loses (400 − 1,000 = −600).
– If share price = 0.00, value = 0 → investor loses full principal (−1,000).
3) Permanent write-down — math
If trigger causes 100% write-down: investor immediately loses nominal = 1,000 (and any future coupons stop). If partial write-down (e.g., 50%), loss = nominal × write-down% = 1,000 × 50% = 500.
Simple loss-of-capital formulas
– Loss on conversion = nominal − (conversion_ratio × share_price_at_conversion). – Loss on write-down = nominal × write
-down%.”
Break-even conversion price (the share price at which conversion neither gains nor loses principal)
– Formula: break-even_share_price = nominal / conversion_ratio.
– Example (continuing your numbers): break-even_share_price = 1,000 / 400 = 2.50. If the share price at conversion is above 2.50 the investor recovers more than par; below 2.50 the investor suffers a net principal loss on conversion.
Expanded numeric examples (three one-line scenarios)
– Conversion profitable: share_price = 4.00 → value_after_conversion = 400 × 4.00 = 1,600 → net gain = 1,600 − 1,000 = +600.
– Conversion loss: share_price = 1.00 → value_after_conversion = 400 × 1.00 = 400 → net loss = 400 − 1,000 = −600.
– Full write-down: write-down% = 100% → loss = 1,000 × 100% = −1,000; coupons stop.
Simple expected-loss approximation (single-period)
– If p = probability(trigger) and, conditional on trigger, loss_when_trigger = L, then expected_loss =
expected_loss = p × L,
where
– p = probability of the trigger occurring (conditional on the time horizon you choose), and
– L = loss given trigger (measured in currency units or as a share of par).
Notes on L (loss given trigger)
– For a principal write-down, L is straightforward: L = write_down% × par. Example: with par = $1,000 and a 40% write-down, L = 0.40 × 1,000 = $400.
– For conversion to equity, L depends on the value after conversion. If conversion delivers N shares at share_price S, then value_after_conversion = N × S and the net P&L on principal = value_after_conversion − par. If this is negative, the loss magnitude is L = max(0, par − N×S). If conversion can also produce a net gain, you can treat L as the expected shortfall (i.e., the expected negative P&L conditional on the trigger) or use the net expected P&L conditional on trigger (which can be negative if gains on conversion outweigh losses).
Worked single-period examples
1) Simple write-down (single-period)
– Par = $1,000; write-down% = 100%; p = 2% (0.02).
– L = 1,000 × 100% = $1,000.
– expected_loss = p × L = 0.02 × 1,000 = $20 (i.e., 2.0% of par).
2) Conversion with discrete share-price outcomes
– Par = $1,000; conversion = 400 shares.
– Conditional on trigger the share price is S = $1 with prob 70% or S = $3 with prob 30%.
– Value after conversion: 400×1 = $400 (loss $600), or 400×3 = $1,200 (gain $200).
– Net expected P&L conditional on trigger = 0.7×(−600) + 0.3×200 = −300 → expected loss given trigger L = $300.
– If p = 20% (0.20) then expected_loss = 0.20 × 300 = $60 (6% of par).
Adding coupon-loss from coupon cancellation
– Many CoCos suspend coupons on trigger. The investor’s total expected loss should add the expected present value (PV) of lost coupons.
– If annual coupon = c, remaining maturity = n years, discount rate = r, PV_coupons = c × [1 − (1+r)^(−n)]/r.
– expected_coupon_loss = p × PV_coupons.
– Total expected_loss ≈ p × L + p × PV_coupons (if coupon loss only occurs when trigger occurs).
Multi-period / hazard-rate extension (discrete time)
– Let p_t be the conditional probability of trigger in period t given survival to t, and let S_{t−1} = Π_{i=1}^{t−1} (1 − p_i) be the survival probability to the start of period t.
– Let L_t be the loss if the trigger occurs in period t and let d_t be the discount factor for period t.
– Then expected present value of losses:
EL = Σ_{t=1}^{T} S_{t−1} × p_t × L_t × d_t.
– This formulation captures timing, survival, and discounting; use it when triggers are possible over multiple periods.
Practical modelling considerations and caveats
– Triggers are endogenous to issuer stress: p rises when the issuer’s capital ratios or stock price fall, often simultaneously with broader market stress. That means CoCo losses can be highly correlated with market downturns.
– Market-implied p: traders often infer p from CoCo prices, CDS spreads, and equity volatilities under a risk-neutral measure; these differ from physical (real-world) probabilities used for economic risk assessment.
– Nonlinearity: conversion mechanics (fixed share count, conversion price floor, write-down percentages) create kinks in payoff profiles; simple linear expected-loss formulas can misstate tail-risk.
– Liquidity and capital-regulatory impacts (e.g., buffers being written down) add layers of risk—secondary-market prices can be volatile
– Counterparty and systemic risk — CoCos can amplify stress beyond the issuer. When conversion/write-downs occur:
– Bank capital buffers shrink or equity is reallocated; counterparties relying on those buffers may face margin calls or credit downgrades.
– Forced sales of equity or assets to restore liquidity can depress prices, creating feedback into other CoCos or bank stocks.
– Correlation with sovereign or market stress can make CoCo losses systemic rather than idiosyncratic.
– Valuation approaches (brief overview) — Practitioners use three main families of models:
– Reduced-form (credit-style) models: treat conversion as a jump event with a hazard rate λ (risk-neutral). Price equals discounted expected cash flows conditioning on survival and conversion intensities.
– Structural models: link trigger to issuer asset values (e.g., Merton-style), making conversion probability endogenous to asset volatility and leverage.
– Market-implied calibration: back out the risk-neutral trigger probability p(t) from CoCo prices, CDS spreads, and equity option prices; then use those p(t) in discounted-expectation formulas.
– Note: all approaches require assumptions about recovery at conversion (value of equity received, or write-down fraction) and about investors’ discount rates under the risk-neutral measure.
– Practical modelling steps — a checklist to build a simple reduced-form price:
1. Define instrument terms: face F, coupon c, maturity T, conversion mechanics (conversion price Pc or conversion rate k, write-down fraction w).
2. Choose a discount curve r(t) appropriate for risk-free or risk-neutral pricing.
3. Specify conversion probability model p(t) or hazard λ(t) under the risk-neutral measure (calibrate to market data if possible).
4. Specify recovery-on-conversion R (fraction of face value or equivalent post-conversion equity value).
5. Compute scenario cash flows: for each t, cash flow if no conversion vs. cash flow if conversion occurs at t.
6. Take expectation under risk-neutral p(t) and discount: Price = E_Q[discounted cash flows].
7. Sensitivity analysis: stress p(t), R, r(t), and conversion mechanics; examine tails and correlation with market variables.
– Simple worked numeric example — single-period, reduced-form:
Assumptions:
– Face value F = 1,000
– Annual coupon c = 6% (so coupon = 60)
– Single-period to maturity T = 1 year
– Risk-free discount r = 5%
– Risk-neutral probability of conversion before payment p = 20% (0.20)
– Recovery value if conversion occurs (value investor receives) = 400 (i.e., R = 0.40 × F)
Scenarios at t = 1:
– No conversion (prob. 0.80): investor gets 1,000 + 60 = 1,060
– Conversion (prob. 0.20): investor gets 400
Expected payoff = (1 − p) × 1,060 + p × 400 = 0.80 × 1,060 + 0.20 × 400 = 928
Present value = 928 / (1 + 0.05) = 884.76
Interpretation: market price ≈ 884.76 versus par 1,000; expected loss relative to par ≈ 115.24. This simple calculation illustrates how conversion probability and recovery drive valuation; for multi-period instruments you sum discounted expected cash flows over time.
– Conversion mechanics examples and their valuation impact:
– Fixed share-count conversion (investor receives K shares): post-conversion value = K × S_post. Valuation requires a model for S_post conditional on trigger; if S_post is low, recovery is poor.
– Conversion at a pre-set conversion price Pc: number of shares = F/Pc. Lower Pc increases investor dilution risk and can reduce recovery.
– Write-down (partial or full): if a fraction w of principal is written down on trigger, investor recovery = (1 − w) × F. Write-downs are simpler to model than share conversions but still create nonlinear losses.
– Common modelling pitfalls and caveats
– Treating p as exogenous: triggers are tied to issuer distress; p typically rises when market-wide stress increases. Ignoring such endogeneity understates tail risk.
– Using physical probabilities for pricing: market prices reflect