Talk:Expected shortfall

Inconsistencies with VaR article

The notation presented in this article is confusingly inconsistent with that in the [VaR article](https://en.wikipedia.org/wiki/Value_at_risk). In particular, the VaR article, alpha is the 'significance' (so the probability is 1 - alpha), but in this article, alpha is not really clearly defined but is eventually revealed to be the probability for the worst loss:

> informally, and non rigorously, this equation amounts to saying "in case of losses so severe that they occur only alpha percent of the time, what is our average loss".

I think it should be decided whether to use alpha or (1 - alpha), but this has to be consistent over the two very closely related articles. And in any case, the explanation of alpha should not be left to that informal 'footnote'. Perhaps that 'footnote' should be moved to the top of the section? It is by far the most useful part of the article.

46.208.237.130 (talk) 22:55, 4 June 2024 (UTC) I don't think it's even consistent within this article. In the 'Optimization of expected shortfall' section alpha seems to have switched to 1-alpha with no explanation at all. At the top of the article, with the dual representation, alpha -> 0 would correspond to optimizing over all probability measures, but in the optimization section, if alpha = 0, the measure p is still very much in play.

Terrible Article

Would just like to state that this is a terrible article. I have no idea how to calculate expected shortfall even after reading this entry multiple times. Someone needs to show the working in example two so that people actually have some clue where the numbers came from. This unsigned comment was entered at 00:30 on 2008 January 25 by 128.12.72.119.

I tried to address this (legitimate) criticism. Encyclops (talk) 01:11, 26 January 2008 (UTC)

Difference not clear

We know that there is a difference between Expected Shortfall and CVar. In this article seems to be the same. [Unsigned comment by 189.60.201.90]

According to Acerbi and Tasche (2002), On the coherence of Expected Shortfall, [1] page 5 "We will see below (Corollary 4.3) that the Expected Shortfall is in fact identical with CVaR".

The concepts were developed separately but turned out to be identical. There may be people who use the terms in a different sense and if so it would be good to mention the different definition in the article. But AFAIK at this stage it has been clarified that ES and CVaR are identical.Encyclops (talk) 15:49, 13 April 2010 (UTC)

That reference is broken. Actually, there are several definitions for ES and CVaR which are in some (see non-continuous) cases NOT identical! Acerbi and Tasche make reference to Uryasev. He again does define ES and CVaR differently, e.g. [2] (page 17). So I guess, since there is no agreement on how to deal with this difference, I suggest to mention the discrepancy (sorry for my poor english). — Preceding unsigned comment added by 129.132.156.131 (talk) 07:33, 19 April 2012 (UTC)

Merge with expected value?

The two concepts are different. If a portfolio has a value of 0 or 2 with 50-50% probabilities, its expected value is 1. However its q-expected shortfall with q=50% is 0. (Koczy 13:49, 28 July 2007 (UTC))

Right, completely different things. Do not merge. Encyclops 22:51, 28 October 2007 (UTC)

WikiProject class rating

This article was automatically assessed because at least one WikiProject had rated the article as stub, and the rating on other projects was brought up to Stub class. BetacommandBot 16:24, 9 November 2007 (UTC)

Expected Shortfall vs. Tail Value at Risk

In some places (e.g. Appendix A of http://ec.europa.eu/internal_market/insurance/docs/2006-markt-docs/2534-06-annex-cea_en.pdf) expected shortfall is given as the same name as tail value at risk. Should a note of this be made on the page? AVaR and TVaR are very closely related as is. Zfeinst (talk) 21:39, 3 February 2011 (UTC)

Yes, I think if a synonym is mentioned in an official or widely read document (regulations, Basel Committee, major journals, etc.) it should be mentioned here. It is confusing that there are so many related terms, but Wikipedia can help to clarify the relationships. Encyclops (talk) 22:06, 3 February 2011 (UTC)

Expected Shortfall v.s. Conditional VaR

The definition of Expected Shortfall should be different to Conditional VaR, so they should not be the same. CVaR with p-quantile should be defined as below: CVaR_p = -inf{(E(X - s)^- /(1-p)) - s, s belongs to real number} 144.214.103.169 (talk) 07:49, 2 March 2012 (UTC)

If you go to [3] section 4 (page 14) you will see that CVaR is also referred to as expected shortfall in the literature, and the representation you give is equivalent to the others (where you can explicitly solve for the minimizing 's'). Zfeinst (talk) 15:51, 2 March 2012 (UTC)

Too technical and advanced

This article is far too technical for most people. You don't need to use the 'Radon-Nikodym derivative' to explain ES, it is a relatively simple and intuitive concept. This article is at Maths Ph.D. level, there needs to be an explanation at the bank manager level. 74.108.41.188 (talk) 00:11, 18 May 2012 (UTC)

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Is the expected shortfall a positive or negative quantity?

Under the Formal Definition heading, two allegedly equivalent definitions of expected shortfall are given. If I'm not mistaken, the first of these two (defined as an integral over VaR) implies that expected shortfall is a negative number, whereas the second (defined as, essentially, a conditional expected value) implies that expected shortfall is positive? Which of these two is correct? 78.145.67.66 (talk) 15:18, 23 November 2024 (UTC)