# 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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### 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 + \...
56 views

### 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 ...
40 views

### Computing the marginal expected shortfall (MES)

I found the following Matlab code to compute the marginal expected shortfall (MES). I understand the code but the mathematical part is not clear to me. More specifically, I don't understand these two ...
77 views

### 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 ...
282 views

### 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/...
255 views

### 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 $P(S_t\leq x)=1-a$ ($a:$...
225 views

### 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 ...
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 $F_X(a-)<1$....