# Default Probability and Recovery Rate

> Default probability is the chance a borrower fails to pay. Learn historical default rates, probabilities implied by spreads, the Merton model and recovery rates.

Source: https://learn.tradelabsai.com/bonds-credit/default-probability/  
Track: Bonds, Rates and Credit · Level: Advanced · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Default Probability and Recovery Rate", https://learn.tradelabsai.com/bonds-credit/default-probability/

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](https://learn.tradelabsai.com/bonds-credit/credit-ratings/).

| Rating | Approximate average 1 year default rate |
|---|---|
| AAA to A | Close to 0% |
| BBB | About 0.1% to 0.2% |
| BB | About 0.5% to 1% |
| B | About 3% to 4% |
| CCC and below | About 25% or more |

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)
```

**Example: Implied PD from a CDS spread**
A company's 5 year CDS spread is 400 basis points (4%). Assuming 40% recovery, the implied annual default probability is about 4% / 0.60 ≈ 6.7%. The probability of surviving five years is roughly (1 minus 0.067)^5 ≈ 71%, implying about a 29% chance of default over five years. Market implied probabilities are usually higher than historical rates, because spreads include risk and liquidity premiums. See [Credit Default Swaps (CDS)](https://learn.tradelabsai.com/bonds-credit/credit-default-swaps/) and [Credit Spreads](https://learn.tradelabsai.com/bonds-credit/credit-spreads/).

## 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](https://learn.tradelabsai.com/options/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](https://learn.tradelabsai.com/fundamentals/reading-financial-statements/).

## Recovery rates

Recovery depends on seniority, collateral and the economic environment.

| Debt type | Approximate average recovery |
|---|---|
| First lien loans | About 60% to 80% |
| Senior secured bonds | About 50% to 60% |
| Senior unsecured bonds | About 35% to 45% |
| Subordinated bonds | About 25% to 30% |

Approximate historical averages; recoveries are lower in recessions, when many defaults occur at once. See [Bankruptcy and Restructuring](https://learn.tradelabsai.com/fundamentals/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](https://learn.tradelabsai.com/history/the-2008-financial-crisis/) and [CLOs](https://learn.tradelabsai.com/bonds-credit/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](https://learn.tradelabsai.com/bonds-credit/distressed-debt/).

## Continue learning

- Next lesson: [Distressed Debt and Bankruptcy Trading](https://learn.tradelabsai.com/bonds-credit/distressed-debt/)
- Previous lesson: [Credit Default Swaps (CDS)](https://learn.tradelabsai.com/bonds-credit/credit-default-swaps/)
- Related: [Credit Default Swaps (CDS)](https://learn.tradelabsai.com/bonds-credit/credit-default-swaps/): A credit default swap is insurance like protection against a borrower defaulting. Learn how CDS work, spreads and upfront pricing, credit events, uses and risks.
- Related: [Credit Ratings](https://learn.tradelabsai.com/bonds-credit/credit-ratings/): Credit ratings from S&P, Moody's and Fitch grade the risk of default on bonds. Learn the scales, investment grade vs high yield, default rates by rating and limits.
- Related: [Credit Spreads](https://learn.tradelabsai.com/bonds-credit/credit-spreads/): A credit spread is the extra yield a risky bond pays over a safe benchmark. Learn how spreads are measured, what drives them and what they signal about risk.
- Related: [Distressed Debt and Bankruptcy Trading](https://learn.tradelabsai.com/bonds-credit/distressed-debt/): Distressed debt is the bonds and loans of companies near default, bought at deep discounts. Learn how investors value it, the bankruptcy process and strategies.
- Related: [Probability for Traders](https://learn.tradelabsai.com/math/probability-for-traders/): Probability is the language of uncertainty in trading. Learn the core rules, independent vs dependent events, odds, and how probability shapes sizing and edge.