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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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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 ...
Leboea Polinyane's user avatar
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Coherent risk measure

One of the characteristics of a Coherent risk measure is Positive homogeneity (ref, ...
Bogaso's user avatar
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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 ...
CLARA.19's user avatar
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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 ...
CLARA.19's user avatar
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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 ...
charelf's user avatar
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Conditional Value at Risk using GARCH models

In this paper:
Barbab's user avatar
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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 + \...
BlueRedem1's user avatar
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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 ...
Manish 's user avatar
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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 ...
Marco Aurélio Guerra's user avatar
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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/...
develarist's user avatar
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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 $P(S_t\leq x)=1-a$ ($a:$...
actuarialboi9's user avatar
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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 ...
Richard Hardy's user avatar
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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 $F_X(a-)<1$....
Wombat's user avatar
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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 ...
chocolatekeyboard's user avatar