Questions tagged [expected-shortfall]

Expected shortfall (a.k.a. expected tail loss or conditional VaR) at $q\%$ level is a risk measure defined as the expected return on the portfolio in the worst $q\%$ of cases.

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Coherent risk measure

One of the characteristics of a Coherent risk measure is Positive homogeneity (ref, ...
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Why is the expected shortfall not elicitable? [duplicate]

Can someone pls provide an intuitive explanation of why expected shortfall is not elicitable and thus why it is challenging to backtest it? I have read the following clear definition of elicitable ...
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Proof for expected shortfall sub additivity

I found on pag 5 the proof about the sub additivity of expected shortfall. I understood the demonstration on the whole, but I would like to ...
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compute Expected Shortfall / Conditional VaR from distribution

I want to compute the Expected Shortfall from a distribution of returns. I have no closed solution for my distribution of returns, so I wonder if I can simply compute ES by taking the mean of all the ...
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Conditional Value at Risk using GARCH models

In this paper:
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Showing that the shortfall-to-quantile ratio of a normal distribution goes to one

I dont get why $$\lim_{x \to \infty} \frac{\mu \{1 - \Phi(x)\} + \sigma \phi(x)}{(\mu + \sigma x) \{1 - \Phi(x)\} } = \lim_{x \to \infty} \frac{1}{1 - \sigma \frac{1 - \Phi(x)}{(\mu + \...
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Calculation of Expected Shortfall using IMA Approach ( FRTB)

I am trying to calculate the Expected shortfall of a FX portfolio through IMA Approach of FRTB in excel . I have used several combinations in excel to get the liquidity horizons and then calculate the ...
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VaR and Expected Shorfall estimations with negative shape parameter of a GPD (Extreme Value Theory )

So im trying to replicate an code from the Quantative Risk Management Book ( But when i try a ...
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Do the minimum VaR and minimum ES portfolios lie on the mean-variance efficient frontier?

The mean-variance efficient frontier holds the minimum variance portfolio, but in the graph above it shows that the minimum VaR (Value-at-Risk) and minimum ES (CVaR) portfolios (expected shortfall/...
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VaR and Expected Shortfall for Geometric Brownian Motion

Given that $dS_t=\mu S_tdt+\sigma S_tdW_t$ ,a risk free rate r and defining Value at Risk and Expected Shortfall as $VaR_{t,a}=S_0e^{rt}-x$ where $x$ is the amount such that $P(S_t\leq x)=1-a$ ($a:$...
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Minimizing variance vs. expected shortfall: distributions where the difference is salient

In portfolio theory in finance, given a set of $n$ assets to choose from, one often selects portfolio weights so as to maximize expected return and minimize some measure of risk, e.g. variance or ...
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Expected Shortfall monotonicity

I have to show monotonicity for a more general case than the expected shortfall. I have to show that $E(X|X \geq a) \geq E(X|X \geq b), \forall a,b \in \mathbb{R}$ so that $a\geq b$ and $F_X(a-)<1$....
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Calculating Expected Shortfall of combined portfolios

So I am reading lecture notes here: The example is this: We have two independent portfolios of bonds. They both have a ...
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