Questions tagged [cvar]
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28
questions
0
votes
1answer
37 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 ...
0
votes
1answer
40 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 ...
3
votes
1answer
120 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. ...
0
votes
0answers
29 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 ...
2
votes
1answer
35 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-...
2
votes
0answers
34 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 "...
2
votes
0answers
83 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
...
1
vote
0answers
56 views
Mean-cVaR model: How can one include transaction cost
$$
\min \delta CVaR - (1-\delta) \sum_i^{n} \mu_i x_i \\
\sum x_i = \sum x^{old}_i \\
Losses(s) = \sum x_i - \sum_i^{n} (R(s,i))x_i \\
VaRDev(s) = Losses(s) - VaR \\
CVaR = VaR + \frac{\sum_s^{} ...
2
votes
1answer
91 views
Why Can I not estimate a CVAR from Heston Model
I fit the parameters of Heston model, using option data for SPX. Now I have the process S and P 500 is expected to follow. I make 100,000 simulations of this process and then calculate the expected ...
0
votes
0answers
64 views
Simulation VaR and CVar assuming Normal Distribution
Am I missing something?
Currently implementing a VaR and CVaR measure assuming normality of wealth value.
after executing the following script, VaR is always greater than CVaR, as expected, but ...
2
votes
2answers
102 views
How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk?
How to prove the following relation of Conditional Value-at-Risk $\text{CVaR}_{\alpha}(X)$ and Value-at-Risk $\text{VaR}_{\alpha}(X)$,
\begin{equation}
\text{CVaR}_{\alpha}(X) = \text{VaR}_{\alpha}(X)+...
0
votes
1answer
92 views
How to calculate $\frac{\partial\ \text{CVaR}_{\alpha}(\min(X,d))}{\partial d}$ and $\frac{\partial\ \text{VaR}_{\alpha}(\min(X,d))}{\partial d}$?
How to calculate $\frac{\partial\ \text{CVaR}_{\alpha}(\min(X,d))}{\partial d}$ and $\frac{\partial\ \text{VaR}_{\alpha}(\min(X,d))}{\partial d}$?
Here, $\text{CVaR}$ is short for Conditional Value-...
3
votes
1answer
79 views
How to minimize $CVaR_{\alpha}(\min(X,d))$, where $X$ is a random variable and d is the decision variable?
How to solve the following problem,
$$
\min_{d \in \mathbb{R}^{+}} \text{CVaR}_{\alpha}(\min(X,d))
$$,
where, X is a random variable whose distribution function $f_{X}(x)$ is given and $d$ is the ...
0
votes
0answers
108 views
What's the advantages of $EVaR$ over $CVaR$?
$CVaR$, which is short for Conditional Value-at-Risk, has long been accepted by both academe and practice as a good coherent risk measure. Entropic value-at-risk ($EVaR$) is a comparative new coherent ...
2
votes
1answer
295 views
Rockafellar-Uryasev mean-CVaR optimiztion
In Rockafellar-Uryasev 2001 paper (http://www.ise.ufl.edu/uryasev/files/2011/11/CVaR1_JOR.pdf) the mean-CVaR optimization can be written as a linear programming optimization problem as:
$$P_{CVaR} = \...
1
vote
0answers
215 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 ...
0
votes
0answers
113 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_{\...
2
votes
1answer
181 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 $CVaR_{\alpha}(X)$ ...
3
votes
1answer
412 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 ...
3
votes
1answer
100 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 $$\tilde F_{\beta}(x,\alpha)=\alpha+\frac{1}{q(1-\beta)}\sum_{k=1}^...
5
votes
2answers
256 views
How to calculate the distortion function for CVaR?
Can anyone give me some hints as to how to prove that
$$g(x) = \begin{cases}
\frac{x}{1-\alpha}, &0 \leq x \leq 1-\alpha\\
1 , &1-\alpha \leq x \leq 1
\end{cases}$$
...
1
vote
0answers
92 views
How to understand quadratic finance or practice of Value-at -Risk(VaR)
We define the following notions for a jointly normally distributed random vector $P=(P_1,...,P_n)$ with f the density function.
$$\mu=\int_{-\infty}^{\infty}(x_i-\mu_i)f_i(x_i)dx_i$$
$$\sigma^2_{ij}=...
2
votes
0answers
199 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
votes
1answer
130 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: ...
1
vote
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 ...
2
votes
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 ...
1
vote
0answers
77 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
votes
1answer
863 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 ...
