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Default Probability (PD)

Annualized probability of issuer default, implied from credit spread and assumed recovery rate.

The market-implied default probability is derived from credit spreads: PD = 1 − exp(−Spread / (1 − Recovery Rate)), the constant-hazard form. This is a risk-neutral (market-implied) probability, not a historical default rate: it embeds the credit risk premium, so it runs several times higher than agency default frequencies for the same issuer — a 271 bp BBB name implies ~4.4% here against a long-run Moody's 1-year BBB rate nearer 0.2%. Example: 150 bp spread, 40% recovery → hazard = 0.0150 / 0.60 = 0.025, so PD = 1 − e^−0.025 = 2.47% annually. (The older linear shortcut PD ≈ Spread / (1 − RR) gives 2.5% here, but it is unbounded and breaches 100% at distressed spreads.) Key assumptions: constant hazard rate, spread = pure credit compensation (no liquidity premium). In practice, CDS-implied PDs are more accurate. Recovery rate varies by seniority: senior secured ~65%, senior unsecured ~40%, subordinated ~25%. Think of it as the break-even default rate that justifies the spread over Treasuries.

Formula
PD=1eSpread1RRPD = 1 - e^{-\frac{\text{Spread}}{1 - RR}}