Questions tagged [cvar]

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Mean-EVaR efficient frontier

Entropic Value-at-Risk (EVaR) is an alternative and more efficient risk measure than conditional Value-at-Risk (CVaR). EVaR serves as an upper bound to both VaR and CVaR. Below is a graph of the mean-...
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1answer
85 views

Estimating CVaR for non-Gaussian distributions

Calculating CVaR needs Gaussian distribution, however, what if the distribution is not Gaussian? Or the distribution is unknown? Can I use many Dirac Delta functions to estimate a distribution and ...
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137 views

CVar optimization algorithms

An alternative measure of losses to Var, with more attractive properties, is Conditional Value-at-risk or CVar which is also called Mean Excess Loss, Mean Shortfall, or Tail Var. CVar is a more ...
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1answer
61 views

When is the VAR equal to the CVAR

After running an optimisation using a quadratic utility (CRRA) function I calculate an CVAR that is equal to the VAR especially for very small risk-aversion levels ($\gamma$=1 and $\gamma$=2 e.g.). ...
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18 views

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

How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk and Conditional Tail Expectation????
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65 views

CVaR portfolio optimization with risk aversion parameter

I'm trying to implement the Rockafellar's function described in this paper http://past.rinfinance.com/agenda/2009/yollin_slides.pdf with a risk aversion parameter for my thesis. The function to ...
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1answer
508 views

CVAR alternatives for optimization

Are there some alternatives to the CVaR measure for portfolio optimization, which are easier to implement for ex. with a linear program? They can be just approximations of CVaR or measures ...
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0answers
50 views

Expected Shortfall for ARMA-GARCH Model

I need to find an analytical solution for the 99% confidence expected shortfall (CVaR) for a long position of 100 dollars at time $t$ for an asset with returns modeled by an ARMA(1,1)-GARCH(1,1) model ...
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1answer
271 views

Manually calculating and backtesting VaR and CVaR from DCC-GARCH R

I estimated a GARCH fit to the log returns of three series (CAC 40, a french real estate index and french T10 bond yield series) using rugarch. I then manually ...
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2answers
281 views

CVaR is concave risk measure or convex?

I see in pflug modeling and measuring risk book, CVaR is concave... But the other book definate cvar is convex... If assume cvar is concave, then cvar optimization problem give us a global optimal ...
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1answer
63 views

Subadditivity of cvar(R)، R is random vector

$R=(R_1,\ldots,R_n)$ is random vector in $L^1(\mathcal{R}^n)$. Then is it true that $$ \operatorname{Cvar}(R_1+ \cdots + R_n) \le \operatorname{Cvar}(R_1) + \cdots +\operatorname{Cvar}(R_n)? $$ Can ...
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1answer
163 views

CVaR formulation

I am a research intern and I am working on a topic about a profit maximization of a risk-averse newsvendor by using Conditional Value-at-Risk.The problem is that I found different expressions of CVaR. ...
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1answer
79 views

Why no median-CVaR optimization for portfolios?

Question Since CVaR is a concept that can be applied to all probability distribution, even if they do not follow normal distribution, I thought CVaR should be more concerned with median, not the ...
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1answer
54 views

Backtesting EGARCH-NIG CVaR in R

I fitted an EGARCH model with a NIG distribution to a series of returns. Using the following link I tried got how I should calculate the CVaR of the model http://r.789695.n4.nabble.com/CVaR-with-NIG-...
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0answers
39 views

Which performance evaluation measure to assess “Connectedness Matrix” based porfolios?

1. Question Which performance evaluation measure would be best to assess the portfolios built on 'connectedness matrix'? The connectedness matrix is the concept introduced in the academic paper "...
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0answers
124 views

Methods for calculating Expected shortfall

Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each with a face value of $100. Assume: each bond is priced at 90 dollars each bond has a 4% probability to default within 1 year ...
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69 views

Mean-cVaR model: How can one include transaction cost

$$ \min \delta CVaR - (1-\delta) \sum_i^{n} \mu_i x_i \\ \sum x_i = \sum x^{old}_i \\ Losses(s) = \sum x_i - \sum_i^{n} (R(s,i))x_i \\ VaRDev(s) = Losses(s) - VaR \\ CVaR = VaR + \frac{\sum_s^{} ...
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1answer
105 views

Why Can I not estimate a CVAR from Heston Model

I fit the parameters of Heston model, using option data for SPX. Now I have the process S and P 500 is expected to follow. I make 100,000 simulations of this process and then calculate the expected ...
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2answers
238 views

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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1answer
103 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
80 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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1answer
209 views

What are 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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1answer
466 views

Rockafellar-Uryasev mean-CVaR optimiztion

In Rockafellar-Uryasev 2001 paper the mean-CVaR optimization can be written as a linear programming optimization problem as: $$P_{\text{CVaR}} = \arg \min_w \text{VaR}_\alpha+\frac{1}{(1-\beta)S}\...
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249 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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121 views

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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1answer
217 views

Questions about 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
492 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
129 views

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
286 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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102 views

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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0answers
222 views

Non-parametric estimator - CVaR / Expected shortfall

Is the estimation of the CVaR using known non-parametric methods (histogram, kernels) different than the estimation of any other R.V.? If the answer is yes, I am interested to know whether there are ...
3
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1answer
144 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
2k 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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0answers
85 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 ...
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1answer
1k 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 ...