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Questions tagged [cvar]

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5
votes
1answer
350 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}\...
5
votes
2answers
262 views

How to calculate the distortion function for CVaR?

Can anyone give me some hints as to how to prove that $$g(x) = \begin{cases} \frac{x}{1-\alpha}, &0 \leq x \leq 1-\alpha\\ 1 , &1-\alpha \leq x \leq 1 \end{cases}$$ ...
4
votes
1answer
426 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 ...
4
votes
1answer
899 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 ...
3
votes
1answer
104 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}^...
3
votes
1answer
124 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. ...
3
votes
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 ...
3
votes
1answer
131 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: ...
2
votes
2answers
114 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)+...
2
votes
1answer
187 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 $CVaR_{\alpha}(X)$ ...
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 ...
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 ...
2
votes
1answer
38 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
37 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
85 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 ...
2
votes
0answers
201 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 ...
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 ...
1
vote
0answers
25 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 ...
1
vote
1answer
70 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 ...
1
vote
0answers
57 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
vote
0answers
222 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 ...
1
vote
0answers
93 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}=...
1
vote
0answers
79 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 ...
0
votes
1answer
43 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 ...
0
votes
1answer
94 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-...
0
votes
0answers
30 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 ...
0
votes
0answers
114 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 ...
0
votes
0answers
116 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_{\...
-1
votes
0answers
31 views

What will be the best risk measure for a mixed portfolio?

How can I calculate the risk for the mixed portfolio (bonds and equities)? I would like this to be a single number (say, cVaR of the portfolio). How can I integrate liquidity and credit risks of the ...