Questions tagged [cvar]
The cvar tag has no usage guidance.
38
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Efficient frontier plot including Mean-Variance and Mean-CVaR frontiers
I am trying to compare the outcomes of a Mean-Variance and Mean-CVaR Optimization approach. I succeeded in plotting the efficient frontiers + tangency portfolios for both cases. Does anyone know how ...
2
votes
1
answer
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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 + \...
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3
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0
answers
204
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Large deviations theory in finance
In probability theory, the theory of large deviations concerns the asymptotic behavior of remote tails of sequences of probability distributions.
A related post says:
Large deviations theory is ...
- 2,815
1
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2
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161
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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-...
- 2,815
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1
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133
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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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206
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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 ...
- 349
1
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1
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104
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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.). ...
- 161
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89
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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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4
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1
answer
2k
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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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95
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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 ...
1
vote
1
answer
560
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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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2
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740
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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 ...
- 33
0
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1
answer
345
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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)?
$$
Can ...
- 33
3
votes
1
answer
254
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CVaR formulation
I am a research intern and I am working on a topic about a profit maximization of a risk-averse newsvendor by using Conditional Value-at-Risk.The problem is that I found different expressions of CVaR. ...
1
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1
answer
131
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Why no median-CVaR optimization for portfolios?
Question
Since CVaR is a concept that can be applied to all probability distribution, even if they do not follow normal distribution, I thought CVaR should be more concerned with median, not the ...
- 520
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1
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106
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Backtesting EGARCH-NIG CVaR in R
I fitted an EGARCH model with a NIG distribution to a series of returns.
Using the following link I tried got how I should calculate the CVaR of the model
http://r.789695.n4.nabble.com/CVaR-with-NIG-...
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0
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44
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Which performance evaluation measure to assess "Connectedness Matrix" based porfolios?
1. Question
Which performance evaluation measure would be best to assess the portfolios built on 'connectedness matrix'? The connectedness matrix is the concept introduced in the academic paper "...
- 520
2
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0
answers
170
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Methods for calculating Expected shortfall
Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each
with a face value of $100. Assume:
each bond is priced at 90 dollars
each bond has a 4% probability to default within 1 year
...
- 71
1
vote
0
answers
95
views
Mean-cVaR model: How can one include transaction cost
$$
\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^{} ...
- 1,585
2
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1
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130
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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 ...
- 131
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2
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511
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)+...
- 129
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1
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117
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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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3
votes
1
answer
90
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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4
votes
2
answers
451
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 ...
- 129
6
votes
1
answer
736
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:
$$P_{\text{CVaR}} = \arg \min_w \text{VaR}_\alpha+\frac{1}{(1-\beta)S}\...
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296
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Berkowitz test for CVaR backtesting
I want to test CVaR using the Berkowitz test (focus on the left tail). I have a couple of doubts:
Do I need to transform only actual losses that are above CVaR;
In the first transformation, whether ...
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139
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How to derive the limit of ratio between VaR and CVaR?
I know if $X \sim N(\mu,\sigma^2)$, then $VaR_{\alpha}(X) =\mu + \sigma\Phi^{-1}(\alpha)$ and $CVaR_{\alpha}(X) = \mu + \sigma \frac{\phi(\Phi^{-1}(\alpha))}{1-\alpha}$
But how to evaluate $\lim_{\...
user28045
2
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1
answer
260
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Questions about VaR and CVaR. Is there any relation between $VaR_{\alpha}(X)$ and $VaR_{\alpha}(-X)$, or $CVaR_{\alpha}(X)$ and $CVaR_{\alpha}(-X)$?
I have some questions when dealing with Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).
Is there any relationship between $VaR_{\alpha}(X)$ and $VaR_{\alpha}(-
X)$, or $CVaR_{\alpha}(X)$ ...
- 47
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1
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580
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Confidence Interval on Monte-Carlo-CVaR
I use the Monte-Carlo Simulation for the computation of VaR and CVaR and wish to compute the 95% Confidence Interval of my result(not the confidence level of VaR). In the case of VaR this is simple ...
- 522
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181
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Question on Rockafellar's Paper for optimisation of CVaR
In Rockafellar and Uryasev's Paper about CVaR Optimisation they showed in Equation (17) that using Monte-Carlo-Simulation one can use $$\tilde F_{\beta}(x,\alpha)=\alpha+\frac{1}{q(1-\beta)}\sum_{k=1}^...
- 522
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2
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350
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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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1
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0
answers
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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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258
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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 ...
- 31
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1
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154
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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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1
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1
answer
3k
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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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1
answer
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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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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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2k
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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 ...
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