Recovery rate: Definition & Examples

The recovery rate is the value recovered on a defaulted obligation as a fraction of a specified claim or exposure. It measures how much value remains after default. For a given exposure, lower recovery means a larger loss if default occurs, even when the probability of default is unchanged: it is the severity side of credit risk. A recovery assumption is incomplete until its denominator, valuation date and treatment of costs are clear.

For a positive claim $C$ and recovered value $V_{\text{rec}}$ measured on the same basis,

R=\frac{V_{\text{rec}}}{C},\qquad \text{LGD}=1-R,\qquad L=C-V_{\text{rec}}.

Here loss given default, or LGD, is the loss fraction and

L

is the loss amount. The complement identity requires consistent definitions: a gross recovery percentage cannot be subtracted from one and treated as a net economic LGD if collection costs have been omitted.

Forty recovered from a claim of one hundred

Suppose a fictional USD claim is 100 at default and the net cash-equivalent value recovered, valued at that same date, is 40. Then recovery is $40/100=40\%$ , LGD is $60\%$ , and the loss is USD 60. The 40% describes this stipulated scenario; it is not a general recovery forecast.

The recovered value need not arrive as immediate cash. In an alternative synthetic workout, the creditor receives USD 52.50 and pays USD 10.50 in collection costs exactly one year after default. At a stipulated 5% annual discount rate,

V_{\text{rec}}=\frac{52.50-10.50}{1.05}=40.

The nominal net receipt is USD 42, while its default-date value is USD 40. Using the later gross receipt would count neither the costs nor the delay. The discount rate here is an illustrative assumption: an economic, accounting or regulatory application must use the basis appropriate to that application. In the Basel IRB framework, CRE36.76 requires economic-loss estimation to include material discount effects and collection costs.

Synthetic USD claim of 100 splits into recovered value 40 and loss 60; an alternative year-end workout nets 42 and discounts at 5% to the same default-date value of 40.

Original synthetic USD ledger. All recovery and loss ratios use a claim of 100 at time 0. The delayed illustration stipulates a 5% annual discount rate and year-end receipts and costs; it is not a market estimate or regulatory calibration.

Three numbers that can be called recovery

Measure	What the number represents	What to check
Postdefault market-price recovery	A traded or quoted value of the defaulted debt, often expressed relative to face value	Price date, quote basis and the obligation being priced
Credit-event auction price	A final price produced by the applicable auction process	Eligible obligations, auction terms and the contracts using that price
Workout recovery	Value obtained through collections, restructuring or asset realisation	Claim or exposure denominator, receipt dates, costs and discounting

Hull's bond convention uses market value shortly after default as a percentage of face value. That is one recovery measure. A postdefault price reflects the market's valuation of remaining rights, rather than a promise that the holder will eventually collect that same percentage in cash.

Similarly, ICE explains that a credit-event auction final price is used for cash settlement of eligible credit-derivative contracts. It does not establish the eventual workout proceeds on every debt of the issuer. The credit default swap contract determines how a settlement price affects its payment.

Even the denominator can change the answer. If a stipulated claim includes USD 100 principal and USD 5 accrued interest, a recovered value of USD 40 is approximately $40/105=38.10\%$ of that claim, while it remains 40% of principal. Whether accrued interest belongs in a legal claim depends on the obligation and applicable rules; it should not be assumed from a price quoted per unit of face value.

Using recovery in a model

Before inserting $R$ into a credit model, identify what the model pays at default. Recovery of face value, recovery of a corresponding default-free bond, and recovery of the debt's predefault market value are different payoff assumptions. The same numerical parameter need not generate the same price under each convention.

For a worked pricing treatment, Recovery assumptions in bond pricing develops the model-specific Recovery of Treasury convention with risk-neutral survival probabilities. The full lesson requires membership; its preview is public. A pricing assumption should still be distinguished from an estimate of realised workout recovery.

Sources

John C. Hull, Options, Futures, and Other Derivatives, ninth Global Edition, Pearson, 2018, §24.3, p. 568: postdefault market-price convention and the separately stated US claim footnote.
Alexander J. McNeil, Rüdiger Frey and Paul Embrechts, Quantitative Risk Management: Concepts, Techniques and Tools, revised edition, Princeton University Press, 2015, §10.4.3, pp. 399–400: recovery-model conventions.
Basel Committee, CRE36.76: economic loss for LGD estimation.
ICE, Credit Event Auctions: final prices and eligible credit-derivative settlement.

Forty recovered from a claim of one hundred

Three numbers that can be called recovery

Using recovery in a model

Sources

Related terms

Credit default swap

Credit risk

Default

Loss given default