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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Expected shortfall ： ウィキペディア英語版 Expected shortfall Expected shortfall (ES) is a risk measure, a concept used in finance (and more specifically in the field of financial risk measurement) to evaluate the market risk or credit risk of a portfolio. It is an alternative to value at risk that is more sensitive to the shape of the loss distribution in the tail of the distribution. The "expected shortfall at q% level" is the expected return on the portfolio in the worst $q$% of the cases. Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), and expected tail loss (ETL). ES evaluates the value (or risk) of an investment in a conservative way, focusing on the less profitable outcomes. For high values of $q$ it ignores the most profitable but unlikely possibilities, for small values of $q$ it focuses on the worst losses. On the other hand, unlike the discounted maximum loss even for lower values of $q$ expected shortfall does not consider only the single most catastrophic outcome. A value of $q$ often used in practice is 5%. Expected shortfall is a coherent, and moreover a spectral, measure of financial portfolio risk. It requires a quantile-level $q$, and is defined to be the expected loss of portfolio value given that a loss is occurring at or below the $q$-quantile. == Formal definition == If $X\; \backslash in\; L^p(\backslash mathcal)$ (an Lp space) is the payoff of a portfolio at some future time and then we define the expected shortfall as $ES\_\; =\; \backslash frac\backslash int\_0^\; VaR\_(X)d\backslash gamma$ where $VaR\_$ is the Value at risk. This can be equivalently written as $ES\_\; =\; -\backslash frac\backslash left(E(\backslash \; 1\_\})\; +\; x\_(\backslash alpha\; -\; P(\backslash leq\; x\_))\backslash right)$ where $x\_\; =\; \backslash inf\backslash$ is the lower $\backslash alpha$-quantile and is the indicator function. The dual representation is :$ES\_\; =\; \backslash inf\_\}\; E^Q()$ where $\backslash mathcal\_$ is the set of probability measures which are absolutely continuous to the physical measure $P$ such that $\backslash frac\; \backslash leq\; \backslash alpha^$ almost surely. Note that $\backslash frac$ is the Radon–Nikodym derivative of $Q$ with respect to $P$. If the underlying distribution for $X$ is a continuous distribution then the expected shortfall is equivalent to the tail conditional expectation defined by $TCE\_(X)\; =\; E(X\; \backslash leq\; -VaR\_(X))$.〔(【引用サイトリンク】title=Average Value at Risk )〕 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". Expected shortfall can also be written as a distortion risk measure given by the distortion function 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Expected shortfall」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.