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Probability of default (PD)

The estimated chance a borrower defaults over a stated horizon, derived from ratings history, structural models, or implied from credit spreads.

There are two families. Real-world PD comes from historical default frequencies by rating. Risk-neutral PD is backed out of market spreads and is always higher, because the spread also pays for liquidity and for bearing the risk itself.

The quick market approximation is that the annual risk-neutral default probability is roughly the spread divided by one minus the recovery rate. It is crude, but it converts a spread into something you can sanity check against default experience.

Example: a 5-year CDS trades at 300 basis points with assumed 40% recovery. Implied annual PD is about 0.0300 / 0.60 = 5.0%, so cumulative five-year survival is roughly 0.95 to the fifth power, or 77%.

Related: loss-given-default, recovery-rate, credit-default-swap, credit-spread-bonds, default

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

Bid-ask spread in an order bookSell orders stacked above buy orders with a gap between the best of each.SELLERS (asks)50.0690050.051,40050.0460050.011,10050.002,30049.99800spread = 0.03BUYERS (bids)
The bid-ask spread. Buy orders sit below, sell orders above, and the gap between the best bid (50.01) and best ask (50.04) is the spread you pay to cross. Bar length shows the size resting at each price.
An equity curve and its drawdownAn account balance rising over a year, falling from a peak to a trough, then climbing back to the old peak.ACCOUNT EQUITY$20k$12k$8k024681012TIME (MONTHS)PEAK $16,000TROUGH $12,000DRAWDOWN−25%RECOVERY
Equity curve and drawdown. An account balance plotted month by month. The fall from the $16,000 peak to the $12,000 trough is a 25% drawdown, and the shaded area lasts until the balance climbs back to the old peak.

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