Introduction

Understanding the recovery rate and its implications is crucial for evaluating the potential losses associated with loans and credit assets. The recovery rate signifies the portion of the outstanding loan that a lender can recover in the event of default. This chapter delves into the intricacies of recovery rate definition, its calculation, and its role in determining the expected loss from a loan.

In the landscape of credit risk, the recovery rate holds a pivotal role in gauging the potential losses that lenders might face. While assessing credit risk, it is vital to not only understand the probability of default but also to quantify the potential losses that may arise from defaults. The recovery rate addresses this aspect by providing insights into the salvage value of credit assets post-default. In this chapter, we will delve into the concept of recovery rate, explore its calculation, and connect it to the calculation of expected loss from a loan.

Recovery Rate

The recovery rate is defined as the percentage of the loan’s principal amount that a lender is able to recover after a borrower defaults. This recovery process might involve selling collateral, liquidating assets, or pursuing legal action. In a scenario where the recovery rate is higher, lenders have a better chance of recouping their losses in case of default.

Calculating Recovery Rate: The recovery rate is typically expressed as a percentage, ranging from $0 \%$ to $100 \%$. To calculate the recovery rate, one can use the following formula:

$$\text { Recovery Rate }=\frac{\text { Recovered Amount }}{\text { Total Outstanding Loan Amount }} \times 100 \%$$ Where:

• Recovered Amount: The amount recovered from the defaulted loan through asset liquidation or collateral sale.
• Total Outstanding Loan Amount: The original principal amount of the loan.

Expected Loss Calculation

The expected loss from a loan is the average amount a lender can expect to lose in the event of default. It takes into account both the probability of default and the potential loss given default (LGD). The formula to calculate expected loss is as follows:

$$\text{Expected Loss} = \text{Probability of Default} \times \text{LGD}$$

Where:

• Probability of Default: The likelihood that the borrower will default on the loan.
• LGD (Loss Given Default): The proportion of the loan that is not recovered after default, i.e., (1 -Recovery Rate).

Example: Let’s consider a loan with an outstanding amount of USD 100,000 and a recovery rate of 60%. If the probability of default is 10%, the expected loss can be calculated as follows:

$$\text{Expected Loss} = 0.10 \times (1 - 0.60) \times 100,000 = \text{USD } 4,000$$