Expected Loss and Unexpected Loss
We will cover following topics
Introduction
Expected losses provide a foundation for proactive risk management, while unexpected losses underscore the importance of resilience in the face of unforeseen events. Distinguishing between expected and unexpected losses is crucial for allocating capital and resources effectively. While expected losses guide day-to-day risk management, unexpected losses highlight the potential impacts of severe events that might challenge an organization’s stability.
By comprehending these concepts and their implications, organizations can build robust risk management strategies that address both the predictable and the unforeseen events.
Expected Loss
Expected loss refers to the anticipated average loss that an organization or investor can foresee based on historical data, statistical analysis, and probabilities. It’s a predictable outcome that forms the foundation of risk management strategies. The formula for calculating expected loss is:
$$EL = PD \times LGD \times EAD$$
where:
- EL = Expected Loss
- PD = Probability of Default
- LGD = Loss Given Default
- EAD Exposure at Default
Example of Expected Loss in a Retail Business: Consider a retail business that sells goods on credit. This means customers can take the goods and pay at a later date. This business is exposed to the risk that some customers may not pay their debts, resulting in bad debt.
Historical Data Analysis:
The business has been operating for five years and has collected data on credit sales and defaults. On average, the business has $1,000,000 in annual credit sales. Historical data shows that 2% of these credit sales result in defaults.
Calculating Expected Loss Components:
- Probability of Default (PD): Based on historical data, the PD is 2% or 0.02.
- Loss Given Default (LGD): If the business expects to recover 20% of the defaulted amounts through collections or collateral, the LGD is 80% or 0.80.
- Exposure at Default (EAD): Assuming the total annual credit sales are exposed to default risk, the EAD is $1,000,000.
Calculating Expected Loss:
$$EL= PD \times LGD \times EAD = 0.02 \times 0.80 \times \text{USD 1,000,000} = \text{USD 16,000}$$
This calculation indicates that the retail business can expect to lose $16,000 annually due to customer defaults. This expected loss can be accounted for as a bad debt expense on the income statement and can be factored into the pricing strategy of the goods sold.
Example of Expected Loss in a Bank: Consider a bank that issues a $500,000 loan to a business. The bank assesses the risk of default and calculates the expected loss using the following data:
- Probability of Default (PD): The bank estimates a 5% chance (0.05) that the business will default on the loan.
- Loss Given Default (LGD): The bank expects to recover 50% of the loan amount through collateral, so the LGD is 50% or 0.50.
- Exposure at Default (EAD): The loan amount is $500,000.
Calculating Expected Loss:
$$EL= PD \times LGD \times EAD= 0.05 \times 0.50 \times \text {USD 500,000} = \text{USD 12,500}$$
This means the bank expects to lose $12,500 if the business defaults on the loan. The bank can use this information to set interest rates, decide on loan terms, and determine the amount of capital reserves needed to cover potential losses.
Management of Expected Losses
Both the retail business and the bank can take steps to manage and mitigate these expected losses:
Retail Business:
- Implement stricter credit checks before offering credit terms.
- Diversify the customer base to reduce the impact of individual defaults.
- Increase prices slightly to cover potential losses.
Bank:
- Charge higher interest rates for higher-risk loans.
- Require more collateral to reduce LGD.
- Diversify the loan portfolio to spread risk.
By understanding and managing expected losses, businesses and financial institutions can better navigate financial risks and ensure long-term stability and profitability.
Unexpected Loss
Unexpected loss refers to losses that go beyond the expected or predicted losses. It is often challenging for firms to estimate unexpected losses because they are “unexpected” by definition.
Example: Continuing with the previous example, imagine that the bank’s statistical model predict an expected loss of USD 200,000. However, due to an economic downturn, the actual loss from defaults turns out to be USD 500,000. The unexpected loss in this case would be 500,000−200,000 = USD 300,000.