# 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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### Understanding intuition behind in-elicitability "problem" of expected shortfall

Keeping related questions in mind (ES not elicitable), I am trying to understand the intuition behind the "problem" driven by the expected shortfall (ES) not being elicitable with four short ...
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### How can I apply the GARCH-MIDAS model to the FTSE MIB using the CPU as an explanatory variable?

I am trying to understand how climate risk impacts the financial market and I am calculating VaR and ES. I am applying the GARCH-MIDAS model to the FTSE MIB, using the Climate Policy Uncertainty Index ...
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### Approximating Distortion Risk Measures by the Sum of their CVaRs

Can you please cite me to the paper that prove the theorem that any distortion risk measure can be approximated using the sum of its CVaRs? Someone said it is Axiomatic Characterization of Distortion ...
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### Coherent risk measure

One of the characteristics of a Coherent risk measure is Positive homogeneity (ref, https://en.wikipedia.org/wiki/Coherent_risk_measure). ...
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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 https://faculty.washington.edu/ezivot/econ589/acertasc.pdf 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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### 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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1 vote
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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 (https://github.com/qrmtutorial/qrm/blob/master/code/09_Market_Risk/09_Standard_methods_for_market_risk.R). 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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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 $F_X(a-)<1$....