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Questions tagged [cvar]

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How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk?

How to prove the following relation of Conditional Value-at-Risk $\text{CVaR}_{\alpha}(X)$ and Value-at-Risk $\text{VaR}_{\alpha}(X)$, \begin{equation} \text{CVaR}_{\alpha}(X) = \text{VaR}_{\alpha}(X)+...
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References for Risk Adjusted Portfolio Optimization

I'm trying to formulate BL portfolios which use Mean VaR, Mean CVaR optimization to calculate risk-adjusted equilibrium returns. Can someone point me to any references on this topic? I'm looking for ...
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1answer
76 views

How to calculate $\frac{\partial\ \text{CVaR}_{\alpha}(\min(X,d))}{\partial d}$ and $\frac{\partial\ \text{VaR}_{\alpha}(\min(X,d))}{\partial d}$?

How to calculate $\frac{\partial\ \text{CVaR}_{\alpha}(\min(X,d))}{\partial d}$ and $\frac{\partial\ \text{VaR}_{\alpha}(\min(X,d))}{\partial d}$? Here, $\text{CVaR}$ is short for Conditional Value-...
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1answer
67 views

How to minimize $CVaR_{\alpha}(\min(X,d))$, where $X$ is a random variable and d is the decision variable?

How to solve the following problem, $$ \min_{d \in \mathbb{R}^{+}} \text{CVaR}_{\alpha}(\min(X,d)) $$, where, X is a random variable whose distribution function $f_{X}(x)$ is given and $d$ is the ...
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What's the advantages of $EVaR$ over $CVaR$?

$CVaR$, which is short for Conditional Value-at-Risk, has long been accepted by both academe and practice as a good coherent risk measure. Entropic value-at-risk ($EVaR$) is a comparative new coherent ...
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30 views

Proper Equity and FX CFD Long-Short portfolio proportions definition

I am very new to Quantitative Finance, although I have somewhat experience in trading CFDs. I am trying to create a Market Risk Management Tool in Excel VBA that should calculate CVaR of a mixed ...
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1answer
156 views

Rockafellar-Uryasev mean-CVaR optimiztion

In Rockafellar-Uryasev 2001 paper (http://www.ise.ufl.edu/uryasev/files/2011/11/CVaR1_JOR.pdf) the mean-CVaR optimization can be written as a linear programming optimization problem as: $$P_{CVaR} = \...
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115 views

Berkowitz test for CVaR backtesting

I want to test CVaR using the Berkowitz test (focus on the left tail). I have a couple of doubts: Do I need to transform only actual losses that are above CVaR; In the first transformation, whether ...
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How can I randomly pick entries in a .gdx file in GAMS?

As the title states, how can I randomly pick say $5$ entries (say bond names or dates) from a gdx file BondIndexData.gdx found at https://www.gams.com/latest/finlib_ml/libhtml/finlib_BondIndex.html?
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Given $(1+\rho)E[X] \leq CVaR_{\alpha}(X)$, what is the relationship between the positive coefficient $\rho$ and the confidence level $\alpha$?

If the following equation holds, $$ (1+\rho)E[X] \leq CVaR_{\alpha}(X) $$ what is the relationship between $\rho$ and $\alpha$?
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Scenario Generation in GAMS

Suppose we have the dataset from https://finance.yahoo.com/quote/%5EIXIC/history?period1=1068652800&period2=1510502400&interval=1wk&filter=history&frequency=1wk which consists of ...
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How to derive the limit of ratio between VaR and CVaR?

I know if $X \sim N(\mu,\sigma^2)$, then $VaR_{\alpha}(X) =\mu + \sigma\Phi^{-1}(\alpha)$ and $CVaR_{\alpha}(X) = \mu + \sigma \frac{\phi(\Phi^{-1}(\alpha))}{1-\alpha}$ But how to evaluate $\lim_{\...
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68 views

How to calculate the distortion function for EVaR?

As defined in Entropic Value-at-Risk: A New Coherent Risk Measure (reference) (wiki) by A.Ahmadi-Javid, the entropic value-at-risk (EVaR) of $x\in L_{M^{+}}$ with confidence level $1-\alpha$ is: $$...
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1answer
143 views

Questions abut VaR and CVaR. Is there any relation between $VaR_{\alpha}(X)$ and $VaR_{\alpha}(-X)$, or $CVaR_{\alpha}(X)$ and $CVaR_{\alpha}(-X)$?

I have some questions when dealing with Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Is there any relationship between $VaR_{\alpha}(X)$ and $VaR_{\alpha}(- X)$, or $CVaR_{\alpha}(X)$ ...
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1answer
210 views

Confidence Interval on Monte-Carlo-CVaR

I use the Monte-Carlo Simulation for the computation of VaR and CVaR and wish to compute the 95% Confidence Interval of my result(not the confidence level of VaR). In the case of VaR this is simple ...
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1answer
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Question on Rockafellar's Paper for optimisation of CVaR

In Rockafellar and Uryasev's Paper about CVaR Optimisation they showed in Equation (17) that using Monte-Carlo-Simulation one can use $$\tilde F_{\beta}(x,\alpha)=\alpha+\frac{1}{q(1-\beta)}\sum_{k=1}^...
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2answers
215 views

How to calculate the distortion function for CVaR?

Can anyone give me some hints as to how to prove that $$g(x) = \begin{cases} \frac{x}{1-\alpha}, &0 \leq x \leq 1-\alpha\\ 1 , &1-\alpha \leq x \leq 1 \end{cases}$$ ...
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How to understand quadratic finance or practice of Value-at -Risk(VaR)

We define the following notions for a jointly normally distributed random vector $P=(P_1,...,P_n)$ with f the density function. $$\mu=\int_{-\infty}^{\infty}(x_i-\mu_i)f_i(x_i)dx_i$$ $$\sigma^2_{ij}=...
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Non-parametric estimator - CVAR / Expected shortfall

Is the estimation of the CVAR using known non-parametric methods (histogram , kernels) is different than the estimation of any other R.V.? If the answer is yes, then I am interested to know whether ...
3
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1answer
120 views

VaR calculation accuracy/comparison/effectiveness through different R packages

My question is what would be the better( in terms of estimation accuracy) method of VaR calculation among below two:, also any small code snippet will be great as a starting point for me. 1st method: ...
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1answer
1k views

Calculate CVaR for a portfolio

I would like to calculate the Conditional Value at Risk for a portfolio. To be honest, I'm trying for a few days to find an example to calculate for an entire portfolio, not just for one security and ...
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1answer
1k views

Elicitability of risk measures

I read that CVaR (Conditional Value-at-Risk, also Expected Shortfall), satisfies coherence, but not Elicitability. On the other hand, VaR satisfies Elicitability, but not coherence. What is ...
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73 views

how to find CVaR/AVaR for triangular fuzzy no

While going through different methods of risk measure i came across AVaR/CVaR, while i was calculating AVaR/CVaR in credibilistic environment using VaR, i got stuck in the calculations eg. For ...
4
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1answer
709 views

Portfolio optimization with Portfolio CVaR Constraint

I wanted to optimize a portfolio based on a portfolio-wide CVaR constraint (i.e. $CVaR_p \leq 0.08$). Unfortunately, I only find solution that minimizes the entire CVaR of the Portfolio. Do you mind ...