Introduction

In the realm of credit risk assessment, understanding and quantifying the potential loss arising from defaults is crucial for prudent risk management. One of the fundamental measures used to quantify this potential loss is the Expected Loss (EL). Expected Loss provides a comprehensive view of the anticipated credit loss over a given time horizon, incorporating both the likelihood of default and the potential loss given default. In this chapter, we delve into the definition of Expected Loss and explore how it is calculated, shedding light on its significance in credit risk analysis.

Expected Loss (EL)

Expected Loss (EL) is a key metric that estimates the average potential loss that a financial institution may face due to defaults within a specified time frame. It encompasses two critical components: the Probability of Default (PD) and the Loss Given Default (LGD).

Calculating Expected Loss (EL)

Expected Loss is calculated by multiplying the Probability of Default (PD) by the Loss Given Default (LGD), and then by the Exposure at Default (EAD). Mathematically, it can be expressed as:

$$EL=PD \times LGD \times EAD$$

Where:

• $PD$ represents the Probability of Default, which is the likelihood that a borrower will default over the specified time horizon.

• $LGD$ represents the Loss Given Default, which indicates the proportion of the exposure that will be lost in case of default.

• $EAD$ stands for Exposure at Default, representing the total exposure to the borrower at the time of default.

Example: Let’s consider a bank that has provided a loan of $100,000 to a borrower. The bank assesses a PD of 5% for this borrower, and the LGD is estimated at 40%. The Exposure at Default is the full loan amount, i.e., USD 100,000.

Using the formula:

$$EL=PD \times LGD \times EAD$$

$$EL = 0.05 \times 0.40 \times 100,000 = \text{USD 2,000}$$

In this scenario, the Expected Loss for this loan is USD 2,000, indicating the average potential loss that the bank might face due to default.

Significance of Expected Loss (EL)

Expected Loss serves as a valuable tool in credit risk assessment and decision-making. It enables financial institutions to allocate appropriate reserves for potential credit losses, aiding in capital planning and risk management strategies. Additionally, Expected Loss facilitates the evaluation of risk-return trade-offs when extending credit to borrowers with varying levels of creditworthiness.