Default Probability and Recovery Rate

Default probability, often abbreviated PD, is the likelihood that a borrower will fail to make payments on its debt over a given period. It is the core input in pricing bonds and loans, setting bank capital, managing credit portfolios and valuing credit derivatives. There are three broad ways to estimate it: from historical default data by rating, from market prices such as bond spreads and CDS, and from structural models that link default to a company's balance sheet and stock price.

Expected loss#

Default probability is only part of credit risk. The full expected loss combines three pieces:

expected loss = probability of default × loss given default × exposure at default

• PD: chance of default.
• Loss given default (LGD): the share lost if default happens, equal to 1 minus the recovery rate.
• Exposure at default (EAD): how much is owed when default happens.

Banks use these three parameters to set loan pricing and regulatory capital under the Basel framework.

Historical default rates#

Rating agencies publish long histories of defaults by rating. They show that default probabilities rise steeply as ratings fall and that defaults cluster in recessions. See Credit Ratings.

Approximate long run figures from agency studies; actual rates vary by period. In recessions, speculative grade default rates have exceeded 10%.

Market implied default probability#

Bond spreads and CDS spreads imply a default probability under "risk neutral" pricing:

annual PD ≈ spread / (1 - recovery rate)

Structural models: Merton#

In 1974, Robert Merton modelled a company's equity as a call option on its assets, with the debt's face value as the strike. If asset value falls below debt at maturity, the company defaults. Using the stock price and its volatility, the model estimates asset value, asset volatility and the "distance to default".

distance to default ≈ (asset value - default point) / (asset value × asset volatility)

Moody's KMV (now Moody's Analytics EDF) built a commercial model on this idea, mapping distance to default to empirical default frequencies. See Black-Scholes Model.

Accounting based models#

The Altman Z score (1968) combines financial ratios, such as working capital, retained earnings, operating profit, market value of equity and sales relative to assets, into a score that predicts bankruptcy. Low scores signal distress. It remains widely used as a screening tool. See Reading Financial Statements.

Recovery rates#

Recovery depends on seniority, collateral and the economic environment.

Approximate historical averages; recoveries are lower in recessions, when many defaults occur at once. See Bankruptcy and Restructuring.

Default correlation#

Defaults are not independent. In recessions, many companies default together. Underestimating default correlation was a key failure in pricing mortgage linked CDOs before 2008. See The 2008 Financial Crisis and CLOs.

Frequently asked questions#

What is default probability?#

The likelihood that a borrower will fail to meet its debt payments over a given period.

How do you calculate implied default probability from a spread?#

Divide the credit spread by one minus the expected recovery rate to get an approximate annual default probability.

What is the Merton model?#

A model that treats a company's equity as a call option on its assets and estimates the chance that asset value falls below debt, causing default.

Next, learn how investors trade troubled companies' debt in Distressed Debt and Bankruptcy Trading.