• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
  • Skip to footer
Finance Train

Finance Train

High Quality tutorials for finance, risk, data science

  • Home
  • Data Science
  • CFA® Exam
  • PRM Exam
  • Tutorials
  • Careers
  • Products
  • Login

Expected Loss, Unexpected Loss, and Loss Distribution

Risk Management

This lesson is part 3 of 6 in the course Foundations of Credit Risk Modelling

While the terms expected loss and unexpected loss are commonly used in risk management, it is important to have a clear understanding of what they actually mean.

In general, expected loss as the name suggests is the expected loss from a loan exposure. On the other hand unexpected loss is the loss that exceeds the expectations.

Expected Loss
In statistical terms, the expected loss is the average credit loss that we would expect from an exposure or a portfolio over a given period of time.

The expected loss is measured using the following formula:

Portfolio Expected Loss: The total expected loss of a portfolio will simply be the summation of expected losses of individual assets. This is because the mean of the sum is the same as the sum of the mean.

Since the expected loss is what a business expects to lose in a year, the business will generally have budget for it and the losses can be borne as a part of the normal operating cash flows.

Unexpected Loss
The unexpected loss is the average total loss over and above the mean loss. It is calculated as a standard deviation from the mean at a certain confidence level at a certain confidence level. It is also referred to as Credit VaR.

A business will safeguard itself from unexpected losses by allocating capital.

Unlike expected loss, the expected loss of a portfolio is not calculated by adding the unexpected loss of individual assets. This is because unless there is perfect correlation, the standard deviation of sum will not be the same as the sum of standard deviation.

The unexpected loss of a portfolio at a 99% confidence level will be expressed as follows:

UL99% = D99% – EL

Where D99% represents the 99% Var Quantile.

If the 99% VaR level is $200m and the expected portfolio loss is $50, then the unexpected loss will be $150m.

The unexpected loss of a portfolio will be expressed as follows:

UL (Portfolio) = \sum UL_i \rho_i

Apart from the expected and unexpected losses, there are also catastrophic losses, which are covered by insurance.

The Credit Loss Distribution

The following diagram shows the credit loss distribution.

 

 

Characteristics of Credit Loss Distribution

The credit losses distribution has three key characteristics:

  1. It is not symmetrical. There is a limited upside because the best scenario is when there is no loss. However, there is extremely large downside, that is, the losses can be huge.
  2. It is highly skewed. The distribution is more concentrated toward small losses, with very few chances of large losses.
  3. The distribution has heavy tail, i.e., the probability of large losses reduces very slowly.
Previous Lesson

‹ Exposure, Default and Recovery Rates

Next Lesson

Understanding Recovery Rates ›

Join Our Facebook Group - Finance, Risk and Data Science

Posts You May Like

How to Improve your Financial Health

CFA® Exam Overview and Guidelines (Updated for 2021)

Changing Themes (Look and Feel) in ggplot2 in R

Coordinates in ggplot2 in R

Facets for ggplot2 Charts in R (Faceting Layer)

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Primary Sidebar

In this Course

  • What is Default Risk?
  • Exposure, Default and Recovery Rates
  • Expected Loss, Unexpected Loss, and Loss Distribution
  • Understanding Recovery Rates
  • Factors Affecting Recovery Rates
  • Using Beta Distribution for Estimating Recovery Rates

Latest Tutorials

    • Data Visualization with R
    • Derivatives with R
    • Machine Learning in Finance Using Python
    • Credit Risk Modelling in R
    • Quantitative Trading Strategies in R
    • Financial Time Series Analysis in R
    • VaR Mapping
    • Option Valuation
    • Financial Reporting Standards
    • Fraud
Facebook Group

Membership

Unlock full access to Finance Train and see the entire library of member-only content and resources.

Subscribe

Footer

Recent Posts

  • How to Improve your Financial Health
  • CFA® Exam Overview and Guidelines (Updated for 2021)
  • Changing Themes (Look and Feel) in ggplot2 in R
  • Coordinates in ggplot2 in R
  • Facets for ggplot2 Charts in R (Faceting Layer)

Products

  • Level I Authority for CFA® Exam
  • CFA Level I Practice Questions
  • CFA Level I Mock Exam
  • Level II Question Bank for CFA® Exam
  • PRM Exam 1 Practice Question Bank
  • All Products

Quick Links

  • Privacy Policy
  • Contact Us

CFA Institute does not endorse, promote or warrant the accuracy or quality of Finance Train. CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.

Copyright © 2021 Finance Train. All rights reserved.

  • About Us
  • Privacy Policy
  • Contact Us