Sovereign CDS and Bond-CDS Basis
The sovereign bond-CDS basis is the difference between a bond’s credit-implied spread and the CDS premium on the same reference sovereign, but it is not a pure default-arbitrage signal. Funding, deliverability, recovery assumptions, bond liquidity, repo specialness, currency, and legal terms can all create a persistent basis.
Put both legs on comparable footing
For a risky bond, derive a z-spread or model-implied credit spread over the appropriate risk-free discount curve. For CDS, bootstrap a hazard-rate curve from quoted premiums using the same currency and maturity convention. A simple basis is:
basis(T) = bond_credit_spread(T) - CDS_par_spread(T)
Positive basis means the bond appears wider than CDS. It may invite long bond / long protection, but only after financing and contract terms are aligned.
| Component | Can widen positive basis | Can narrow basis |
|---|---|---|
| bond liquidity | illiquid cash bond discount | liquid bond demand |
| repo/funding | expensive financing | special repo benefit |
| CDS deliverability | cheap-to-deliver option | restrictive deliverables |
| recovery convention | low bond-implied recovery | high CDS calibration recovery |
| currency/redenomination | local-law uncertainty | hard-currency protection |
The correct benchmark curve is crucial. A euro sovereign bond versus USD CDS is not a same-risk comparison without modelling cross-currency basis and contract currency. A domestic-law bond may embed redenomination or capital-control risk that standard CDS does not match.
CDS pricing and hazard curves
Ignoring accrual-on-default, the stylized par-spread relation is:
CDS_spread × Σ α_i D(0,t_i) S(t_i)
≈ (1 - R) × Σ D(0,t_i) [S(t_(i-1)) - S(t_i)]
Here S(t) is survival probability and R is recovery. A production bootstrap includes protection-payment timing, premium accrual on default, standard coupons and upfront, and ISDA conventions.
import numpy as np
def flat_hazard_spread(hazard, recovery):
return hazard * (1.0 - recovery)
def basis(bond_spread, cds_spread):
return bond_spread - cds_spread
def carry_after_funding(bond_yield, repo_rate, cds_premium):
return bond_yield - repo_rate - cds_premium
The last function is not trade P&L: it omits bond price pull-to-par, CDS accrual, haircut funding, default settlement, and hedge notionals. It is useful only to show why a wide positive basis can have negative carry.
Trade construction and failure modes
A textbook positive-basis trade buys the bond and buys CDS protection. Match maturity, currency, notional, and default-event exposure as closely as possible. Hedge duration separately with a government future or swap if the bond is not floating-rate. A negative-basis trade reverses the position, but shorting or borrowing a sovereign bond can be operationally impossible.
| Failure mode | Mechanism | Control |
|---|---|---|
| funding shock | repo cost exceeds spread pickup | haircut and term-repo stress |
| CTD option | CDS settles into cheaper bond | deliverable-basket analysis |
| basis persistence | liquidity segmentation | horizon and stop limits |
| legal event | bond and CDS trigger differ | counsel/documentation review |
| curve mismatch | mismatched tenors | bootstrap and hedge checks |
Sovereign credit risk interacts with domestic banks, local currency, and capital flows. A bond may cheapen because dealers cannot finance inventory even when CDS remains stable; that is a valuable liquidity signal, but not evidence of a convergence date. The hazard-rate mechanics are developed in CDS pricing and hazard rates.
Monitoring and attribution
Attribute daily P&L into bond spread, CDS spread, risk-free rates, FX, repo, and carry. Recalculate hedge ratio after bond duration changes and use actual executable bid/ask. Stress jump-to-default with a recovery grid, CDS auction outcomes, repo withdrawal, and currency conversion restrictions. The assumption that two “sovereign credit” legs always offset is precisely what a crisis tests.
Key takeaways
- Bond-CDS basis is a multi-factor spread difference, not a clean default arbitrage.
- Align curve, currency, maturity, conventions, recovery, and legal terms before trading.
- Financing, repo specialness, liquidity, and the CDS deliverable option can dominate carry.
- Hedge rate risk separately and attribute P&L across cash, CDS, funding, and FX components.
- Stress sovereign-specific legal, settlement, and capital-control scenarios before sizing.