{"id":217858,"date":"2025-01-28T11:41:09","date_gmt":"2025-01-28T16:41:09","guid":{"rendered":"https:\/\/ibkrcampus.com\/campus\/?p=217858"},"modified":"2025-01-28T11:41:45","modified_gmt":"2025-01-28T16:41:45","slug":"expected-shortfall-es","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/expected-shortfall-es\/","title":{"rendered":"Expected Shortfall (ES)"},"content":{"rendered":"\n

The article \u201cExpected Shortfall (ES)\u201d was originally posted on QuantInsti<\/a> blog.<\/em><\/p>\n\n\n\n

If you are reading this blog, this means that you are aware of Value at Risk, or simply VaR which is the largest loss that can be incurred by a portfolio with a given confidence level (i.e. a pre-specified probability level).<\/p>\n\n\n\n

However, there is a significant drawback which the VaR as a risk measure carries. In particular, it tells us the threshold of potential loss but not how bad the loss can be beyond that threshold.<\/p>\n\n\n\n

For example, if a portfolio\u2019s 1-day VaR is $1 million at a 95% confidence level, you don\u2019t know how much the loss could be in the remaining 5% of the cases. In addition, it does not account for \u201ctail risk” or extreme events that may lead to larger losses. This brings us to yet another statistical risk measure called Expected Shortfall (ES), which fixes this problem to some extent.<\/p>\n\n\n\n

As seen in the preceding paragraph, to be fully equipped to understand the topic of Expected Shortfall, first one needs to have the knowledge of VaR. What follows is the list of prerequisites needed alongside their descriptions.<\/p>\n\n\n\n

Prerequisites<\/h3>\n\n\n\n
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  1. The introduction to VaR is explained here<\/a>. By reading the referred blog, you will learn how to compute and interpret portfolio VaR, its limitations and advantages in simplest and shortest possible way.<\/li>\n\n\n\n
  2. To get a comprehensive knowledge about VaR and related topics, you can refer to the blog \u201cValue at Risk\u201d. Here you will find a detailed explanation of VaR, its computation in various ways. In addition, this blog provides a coverage of topics like Marginal VaR, Incremental VaR and Component VaR. In short, these VaR tools measure the effects of changing portfolio positions on existing portfolio VaR.<\/li>\n<\/ol>\n\n\n\n

    What is Expected Shortfall (ES)<\/h2>\n\n\n\n

    Simply put, Expected Shortfall is the average loss beyond VaR. It measures the expected loss in the tail of a distribution beyond a certain quantile level (e.g., 95%). It provides insight into the potential losses exceeding the Value at Risk (VaR). Obviously, we specify the confidence level by which ES is computed. Below is the geometric illustration of ES alongside with VaR. Here are the steps for the computation of ES:<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    1. Define Parameters<\/strong><\/p>\n\n\n\n