Introduction

In the realm of credit risk assessment, understanding the mean and standard deviation of credit losses assumes paramount importance. These statistical measures provide insights into the central tendency and dispersion of credit loss outcomes, allowing institutions to gauge potential risks and make informed decisions. In this chapter, we will delve into the estimation of the mean and standard deviation of credit losses, assuming a binomial distribution. This distribution model is particularly relevant in scenarios where there are two possible outcomes - defaults and non-defaults. Let’s explore how these measures can help us comprehend credit risk more effectively.

Estimating Mean of Credit Losses

The mean of credit losses represents the average loss that an institution can expect over a defined period. In the context of a binomial distribution, it is calculated using the following formula:

$$\mu = PD \times EAD$$

where:

• $\mu$ refers to Mean of Credit Losses
• $PD$ refers to Probability of Default
• $EAD$ refers to Exposure at Default

Here, the Probability of Default (PD) signifies the likelihood of a credit event occurring, and Exposure at Default (EAD) represents the amount of exposure at the time of default. This formula helps institutions anticipate the average credit loss they may face.

Estimating Standard Deviation of Credit Losses

The standard deviation of credit losses indicates the extent of dispersion or volatility around the mean credit loss. It is calculated as follows:

$$(\sigma)=\sqrt{PD \times EAD \times LGD} $$

where:

• $\sigma$ refers to Standard Deviation
• $PD$ refers to Probability of Default
• $EAD$ refers to Exposure at Default
• $LGD$ refers to Loss Given Default

Here, Loss Given Default (LGD) signifies the proportion of exposure that would be lost in the event of a default. The standard deviation provides valuable insights into the potential range of credit losses, helping institutions assess the risk associated with credit exposures.

Example: Let’s consider a financial institution with a portfolio of loans. The institution estimates a Probability of Default (PD) of 5%, an Exposure at Default (EAD) of USD 1,000,000, and a Loss Given Default (LGD) of 40%. The mean and standard deviation of credit losses can be calculated as follows:

• Mean of Credit Losses: $\mu = 0.05 \times 1,000,000 = \text{USD 50,000}$

• Standard Deviation of Credit Losses: $\sigma = \sqrt{0.05 \times 1,000,000 \times 0.40} ≈ \text{USD 632.45}$