Recovery Rates and Loss Given Default

Why Recovery Matters After Default

A default does not usually mean that a creditor loses the entire amount owed. Payments may still come from collateral, a liquidation of the borrower’s assets, a guarantor, or a later settlement. The fraction of the defaulted claim that is ultimately recovered determines how severe the loss is, given that default has occurred.

Two quantities must be kept distinct. The recovery rate describes the proportion of the exposure recovered. Loss given default (LGD) describes the proportion not recovered. Both require a clearly stated exposure denominator and a consistent treatment of costs and timing. The default probability is a separate input: it is not part of either ratio.

Definition: Let $E$ be the exposure being measured at the time of default, and let $R$ be the recovery amount measured on a consistent basis. The recovery rate is $R/E$. The loss amount is $E-R$, and loss given default is $(E-R)/E$. When recoveries are bounded between zero and the exposure, the recovery rate and LGD are each between zero and one.

The exposure $E$ should be stated in the problem or specified by the analyst. It is the claim amount used as the denominator for this calculation; it may include principal, accrued interest, or other amounts only if the stated measurement convention includes them. The later calculation of exposure at default addresses how an exposure may be estimated for a position. Here, treat the default-date amount as given.

From Gross Proceeds to Measured Recovery

A creditor may receive several cashflows after default. A practical recovery measure generally considers the value available to satisfy the claim, rather than treating every dollar collected as a dollar of recovery. For example, legal and servicing expenses incurred to collect a debt reduce what is available to the creditor. If the measure is stated on a net basis, subtract those costs before calculating the ratio.

Timing also matters. A nominal recovery collected several years after default is not economically equivalent to the same amount collected immediately. For a present-value measure, discount each recovery and each relevant cost to the default date using the specified effective annual rate $i$. If $R_t$ is a net cash recovery at time $t$ years after default, its default-date value is $R_t v^t$, where $v=1/(1+i)$. Use nominal totals instead when the question explicitly asks for an undiscounted recovery measure.

\text{Recovery rate}=\frac{\text{recovery amount on the stated basis}}{\text{default-date exposure on the same basis}}

The numerator and denominator must refer to compatible claims and valuation dates. A ratio can be misleading if, for instance, the numerator is discounted to the default date but the denominator is a later balance, or if costs are deducted from one component but not another.

Worked Example: Net Recovery After Collection Costs

A hypothetical lender has a claim of $E=\$250{,}000$ when a business defaults. It receives $\$92{,}000$ from collateral and $\$31{,}000$ from a later liquidation distribution. Workout costs are $\$8{,}000$. Calculate the net recovery amount, recovery rate, and LGD on an undiscounted basis.

Method. Add the cash proceeds, deduct the specified costs, and compare the resulting net recovery with the default-date exposure. This avoids the common mistake of reporting gross receipts as the creditor’s recovery.

Step 1: Total gross proceeds. \[ \$92{,}000+\$31{,}000=\$123{,}000. \]

Step 2: Net recovery. \[ R=\$123{,}000-\$8{,}000=\$115{,}000. \]

Step 3: Recovery rate. \[ \frac{\$115{,}000}{\$250{,}000}=0.46=46.00\%. \]

Step 4: LGD and loss amount. \[ \text{LGD}=1-0.46=0.54=54.00\%,\qquad \$250{,}000-\$115{,}000=\$135{,}000. \]

Check. The recovery and loss amounts sum to the exposure: $\$115{,}000+\$135{,}000=\$250{,}000$. The ratios also sum to 100.00%: $46.00\%+54.00\%=100.00\%$.

Why Recovery Rate and LGD Are Complements

On a common measurement basis, the recovery rate and LGD are two descriptions of the same division of the exposure: the recovered portion and the unrecovered portion. This identity is useful both for calculation and for checking a result.

Define the loss amount.
For exposure $E$ and recovery $R$, the loss is $E-R$, provided $R$ is measured as the amount that reduces the claim.

Divide by the same exposure.
LGD is $(E-R)/E$, while the recovery rate is $R/E$. Both use the same default-date exposure as denominator.

Simplify.
$(E-R)/E=E/E-R/E=1-R/E$. Since $R/E$ is the recovery rate, $\text{LGD}=1-\text{recovery rate}$.

Result: When loss and recovery are defined on the same basis, $\text{LGD}+\text{recovery rate}=1$. In amount terms, $E-R+R=E$. If the amounts or valuation bases differ, this check may fail because the inputs are inconsistent.

This derivation also explains why LGD is a conditional severity measure: it describes the loss fraction given default. It does not say how likely default is. Combining severity with default likelihood to calculate expected credit loss is a separate step.

Collateral and Seniority

Collateral can support recovery by giving a creditor rights to the proceeds from specified assets. It does not guarantee recovery of the full claim. Asset values can fall, liquidation can take time, and legal or sale costs can reduce proceeds. The relevant collateral amount is the value actually available to satisfy the claim under the stated assumptions, not automatically the asset’s estimated market value.

Seniority determines the order in which competing claims receive available value. In a simple liquidation waterfall, higher-priority claims are paid before lower-priority claims. A junior creditor can therefore have a low recovery even when the estate has substantial value, if senior claims absorb that value first. Conversely, the recovery of a senior claim is not necessarily complete if proceeds are insufficient to satisfy it.

The following example assumes one senior claim is secured by all net liquidation proceeds and the junior claim receives only what remains after the senior claim is paid. Actual legal arrangements can be more complex, so the priority assumptions must be read carefully.

Worked Example: A Priority Waterfall Changes Recovery

A hypothetical borrower defaults with a senior secured claim of $\$360{,}000$ and a subordinated claim of $\$240{,}000$. The collateral sells for $\$300{,}000$, and liquidation costs are $\$30{,}000$. Under the stated arrangement, all net collateral proceeds go first to the senior claim; the junior claim receives any remaining proceeds. Calculate each claim’s recovery rate and LGD.

Method. Determine net proceeds first, then allocate them in priority order. A common mistake is to divide the net proceeds proportionally between claims even though the problem specifies a priority waterfall.

Step 1: Net proceeds available. \[ \$300{,}000-\$30{,}000=\$270{,}000. \]

Step 2: Allocate to the senior claim. The senior claim is $\$360{,}000$, which exceeds the $\$270{,}000$ available. It therefore receives all $\$270{,}000$, leaving nothing for the junior claim.

Step 3: Senior recovery rate and LGD. \[ \text{Recovery rate}_{\text{senior}}=\frac{\$270{,}000}{\$360{,}000}=75.00\%, \qquad \text{LGD}_{\text{senior}}=25.00\%. \] The senior loss is $\$360{,}000-\$270{,}000=\$90{,}000$.

Step 4: Junior recovery rate and LGD. The junior claim receives $\$0$: \[ \text{Recovery rate}_{\text{junior}}=\frac{\$0}{\$240{,}000}=0.00\%, \qquad \text{LGD}_{\text{junior}}=100.00\%. \] Its loss is $\$240{,}000$.

Check. Total loss is $\$90{,}000+\$240{,}000=\$330{,}000$. Total exposure is $\$360{,}000+\$240{,}000=\$600{,}000$, and total net proceeds plus losses equal exposure: $\$270{,}000+\$330{,}000=\$600{,}000$.

Recovery Timing and Present Value

A recovery measure should state whether it is nominal or discounted. The choice affects the measured recovery rate and LGD, even when the cash amounts are unchanged. Discounting is especially relevant when comparing recoveries with a default-date exposure: it places later cashflows on a common date with that exposure.

For the calculation below, assume $i$ is an effective annual rate and that the stated net recoveries are received at the end of the indicated years. The example uses that rate as the specified discount basis; it does not imply that every recovery analysis must use the same rate.

R_{\text{PV}}=\sum_t R_t v^t,\qquad \text{recovery rate}_{\text{PV}}=\frac{R_{\text{PV}}}{E},\qquad \text{LGD}_{\text{PV}}=1-\frac{R_{\text{PV}}}{E}

Worked Example: Discounting Recoveries at Different Dates

A hypothetical creditor has a default-date exposure of $\$200{,}000$. It expects net recovery cashflows of $\$84{,}000$ at the end of year 1 and $\$63{,}000$ at the end of year 2. Assume an effective annual discount rate $i=5\%$. Calculate the present-value recovery rate and LGD at default. Round dollar amounts to the nearest cent and percentages to two decimal places.

Method. Discount each net cashflow separately to default, add the present values, and divide by the default-date exposure. The common mistake is to use the undiscounted total while describing the result as a present-value measure.

Step 1: Discount factor. \[ v=\frac{1}{1.05}=0.95238095\ldots \]

Step 2: Present value of each recovery. \[ \$84{,}000v^1=\frac{\$84{,}000}{1.05}=\$80{,}000.00, \] \[ \$63{,}000v^2=\frac{\$63{,}000}{1.05^2} =\frac{\$63{,}000}{1.1025}=\$57{,}142.86. \]

Step 3: Total present-value recovery and recovery rate. \[ R_{\text{PV}}=\$80{,}000.00+\$57{,}142.86=\$137{,}142.86, \] \[ \text{recovery rate}_{\text{PV}}=\frac{\$137{,}142.86}{\$200{,}000}=68.57\%. \]

Step 4: LGD. \[ \text{LGD}_{\text{PV}}=100.00\%-68.57\%=31.43\%. \] The corresponding present-value loss is $\$200{,}000-\$137{,}142.86=\$62{,}857.14$.

Check. The recovery rate and LGD sum to 100.00%, and the present-value recovery plus present-value loss equals the stated exposure. Without discounting, the cash recoveries total $\$147{,}000$, or 73.50% of exposure; that is a different, nominal measure.

Common Calculation Traps

A reliable calculation begins by identifying the claim, measurement date, and recovery convention. The following errors can produce plausible-looking but inconsistent percentages:

Using the wrong denominator. Divide by the exposure specified for the default event, not by the collateral value, total borrower assets, or a later balance unless the question explicitly defines that basis.
Counting gross proceeds as net recovery. Deduct costs that the stated measure treats as reducing recovery. Do not subtract them twice if the supplied recovery is already net.
Ignoring payment priority. Allocate proceeds according to the stated seniority and security terms before calculating each creditor’s ratio.
Mixing nominal and present-value quantities. Discount cashflows when a present-value measure is requested, and keep the denominator on a compatible date and basis.
Confusing severity with likelihood. LGD is the loss fraction given default. It is not the probability of default and does not by itself measure expected loss.

Under a convention in which recovery is limited to the claim and costs are included consistently, recovery rate and LGD lie between 0% and 100%. If a calculation produces a recovery above 100%, check for mismatched dates, accrued amounts, duplicated proceeds, or a numerator and denominator defined on different bases. A stated convention may sometimes permit recoveries to exceed the measured claim; in that case, report the result under that convention rather than silently forcing it into the 0%–100% range.

Key takeaway: State the default-date exposure, define which proceeds and costs count as recovery, and specify whether amounts are discounted. Then calculate recovery rate and LGD from that same basis and verify that the recovered and unrecovered portions reconcile to the exposure.

Check Your Understanding

For each problem, state the recovery basis before calculating. Answers are provided for checking.

A hypothetical claim is $\$180{,}000$ at default. The creditor receives $\$54{,}000$ from a guarantor and $\$36{,}000$ from collateral. There are no additional costs, and amounts are undiscounted. Find the recovery rate, LGD, and loss amount. (Answer: recovery rate $=50.00\%$; LGD $=50.00\%$; loss $=\$90{,}000$.)
A defaulted claim is $\$320{,}000$. Gross proceeds are $\$150{,}000$, and collection expenses of $\$10{,}000$ are deducted from recovery. On an undiscounted basis, calculate net recovery, recovery rate, and LGD. (Answer: net recovery $=\$140{,}000$; recovery rate $=43.75\%$; LGD $=56.25\%$.)
A senior claim of $\$250{,}000$ and a junior claim of $\$150{,}000$ share a liquidation estate. After costs, $\$220{,}000$ is available. All proceeds go first to the senior claim. Find each claim’s recovery rate and LGD. (Answer: senior recovery rate $=88.00\%$, LGD $=12.00\%$; junior recovery rate $=0.00\%$, LGD $=100.00\%$.)
A creditor’s default-date exposure is $\$100{,}000$. Net recoveries of $\$42{,}000$ and $\$33{,}075$ arrive at the ends of years 1 and 2, respectively. With effective annual $i=5\%$, calculate the present-value recovery rate and LGD. (Answer: present-value recoveries $=\$40{,}000+\$30{,}000=\$70{,}000$; recovery rate $=70.00\%$; LGD $=30.00\%$.)
A claim of $\$500{,}000$ has gross recoveries of $\$260{,}000$ at default and $\$126{,}000$ at the end of year 1. The year-1 recovery has a $\$21{,}000$ collection cost paid at the same time. For a present-value measure using effective annual $i=5\%$, calculate recovery rate and LGD. (Answer: net year-1 recovery $=\$105{,}000$; present-value recovery $=\$260{,}000+\$100{,}000=\$360{,}000$; recovery rate $=72.00\%$; LGD $=28.00\%$.)

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