# Reasoning behind multiple names for the equivalent risk measures AVaR/ETL/ES/CVaR

Doe's any one know the history behind, or background of the multiple naming conventions for the equivalent risk functions. Different quant authors prefer using different names, does any one know why? which came first? why do some quants prefer one over the other. What is the history behind all of this.

ES - expected shortfall
CVaR - conditional value at risk
AVaR - average value at risk
ETL  - expected tail loss

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Possibly the biggest road block to learning statistics are the varied and nonsensical naming. “[...]bad names reflect (or even result in) difficulties in understanding.” Hurst, Joseph, colours and noises: The importance of names in an important natural behaviour, Demetris Koutsoyiannis itia.ntua.gr/getfile/792/1/documents/… – montyhall Mar 15 '13 at 5:40

No specific history. I'm not aware who introduced this measure initially. Most probably it came up as an example in the research papers on coherent risk measure. All names make sense to some extent:

Expected shortfall - as it's an expectation of losses
Conditional Value at Risk - as it can be written as $E[X |X >VaR_α(X)]$, i.e. conditional expectation
Average value at risk - as it can be written as $\frac{1}{1-\alpha}\int_{\alpha}^1VaR_{\beta}(X)d\beta$, which is essentially an average Expected Tail Loss - as it's expectation calculated in the tail of loss distribution

It's also sometimes called Tail VaR.

Personal preferences of people are usually based on their favorite risk management reference book.

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I have also seen (in rough decreasing importance order): Mean excess loss, Tail conditional expectation and the variant C.T.E., Tail mean, Mean shortfall...

AVaR doesn't seem as common as the other three you mentioned.

Acerbi&Tasche 2002 discuss the difference between CVaR and ES. In practice there's little mention on reasons for each choice and rarely any differences have a significant role so that all variants become equivalent. The different naming flavours mostly originate historically from various areas: very roughly (from my concentrated and relatively limited sample) CVaR seems more en vogue among economists&traders, ES among risk managers, ETL among "statisticians", TVaR in econometrics, CTE among actuaries etc...

For other formulations of ES check also spectral and distortion risk measures.

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