Michael Brenndoerfer | Data & AI, Private Equity, Technology

Michael Brenndoerfer

Credit Default Swaps (CDS) and Credit Derivatives › Recovery Rates

Michael BrenndoerferNovember 18, 20254 min read

Quantitative FinanceAll chapters

Part 4 of 15Swaps and Credit Derivatives

Chapter 22Credit Default Swaps (CDS) and Credit Derivatives › Recovery Rates

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When a credit event occurs, bondholders typically recover some fraction of the face value of their holdings. The recovery rate $R$ represents this fraction and is a critical input to CDS pricing. Understanding recovery rates requires recognizing that they are not fixed constants but rather realizations of a random variable that depends on the nature of the default, the assets available for liquidation, the seniority of the debt, and countless other factors that only become known after default occurs.

Recovery rates vary significantly across industries and seniority levels:

Senior secured debt: 50-70% recovery
Senior unsecured debt: 35-50% recovery
Subordinated debt: 20-35% recovery
Junior subordinated: 10-20% recovery

The standard assumption in CDS pricing is a recovery rate of 40% for investment-grade corporates, though this varies by sector. For sovereigns and high-yield issuers, different assumptions may apply. This 40% figure represents a historical average derived from studies of actual defaults, but individual outcomes vary widely. During systemic crises, recovery rates tend to be lower than average because distressed assets flood the market simultaneously, depressing prices.

Loss Given Default (LGD)

Loss given default is the complement of recovery rate: $\text{LGD} = 1 - R$ . If the recovery rate is 40%, the loss given default is 60%, meaning bondholders lose 60 cents for every dollar of face value upon default.

In[8]:

Code

import numpy as np

# Impact of recovery rate on expected loss
default_probability = 0.05  # 5% probability of default over some horizon

recovery_rates = np.array([0.20, 0.30, 0.40, 0.50, 0.60])
loss_given_default = 1 - recovery_rates
expected_loss = default_probability * loss_given_default

Out[9]:

Console

Expected Loss Analysis (5% default probability):
-------------------------------------------------------
  Recovery Rate        LGD   Expected Loss
-------------------------------------------------------
            20%        80%           4.00%
            30%        70%           3.50%
            40%        60%           3.00%
            50%        50%           2.50%
            60%        40%           2.00%

The table shows how sensitive expected losses are to recovery assumptions. A change from 40% to 20% recovery nearly doubles the expected loss.

Out[10]:

Visualization

Line chart showing loss given default declining linearly as recovery rate increases from 10% to 80%. — Relationship between recovery rate and loss given default (LGD). Since LGD is defined as 1 minus the recovery rate, the two variables have a perfect inverse linear relationship.

Line chart showing expected loss declining as recovery rate increases, with a vertical reference line at the 40% standard assumption. — Expected loss as a function of recovery rate for a 5% default probability. For the standard 40% recovery assumption, the expected loss is 3%, but this nearly doubles to 4.5% if the recovery rate drops to 10%.