Questions tagged [value-at-risk]
The value-at-risk tag has no usage guidance.
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How does CVaR change when the mean and variance of the loss distribution change?
I have a CVaR constraint in my optimization problem and I want to change the mean and standard deviation of loss distribution during each iteration. How can I get the new CVaR based on the old CVaR ...
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VaR of ARCH model
Consider the following:
$r_t = \theta r_{t-1}+u_t$
$u_t=\sigma_t\epsilon_t$
$\sigma^2_t=\omega+\alpha u^2_{t-1}$
$-1<\theta<1,\omega>0,\alpha \in(0,1)$
What is the 99% 2-day VaR of a ...
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1answer
44 views
Value-at-risk and Equity delta
How to validate value-at-risk calculation on an equity portfolio using equity sensitivities? I don't have trouble doing that for rates instruments or options but I don't know which underlying risk ...
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32 views
Monte Carlo VAR with differente asset classes
I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is ...
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1answer
26 views
Scenario generation for Value at risk: How to interpret the scenarios
This is a a simple and rather pratical approach and not theoretical. Let's assumes I have generated 250 scenarios for a given fixed portfolio. Hence we assume that the asset returns can result in 250 ...
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1answer
58 views
Computing Montecarlo VaR for a single asset
I'm trying to understand the procedure to compute the Value-at-Risk for a single asset by implementing the Montecarlo technique.
Here it follows the procedure step-by-step in 5 points:
selecting the ...
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1answer
75 views
Variance-Covariance VaR: how to get the volatility?
Because the variance-covariance VaR assumes that the returns are normally distributed, in theory it is easy to get VaR by simply finding the mean and the volatility (standard deviation) of the ...
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1answer
51 views
Delta-Gamma VaR question on inputs (do I need only one delta or the delta for the past 500 days?)
When calculating a VaR using the Delta-Gamma approach, I am supposed to use this formula:
∆(V) = Delta * ∆(X) + 0.5 * Gamma * ∆(X)²
where:
∆(V) = change in value of the asset in portfolio
∆(X) = ...
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2answers
60 views
Procedures to follow when VaR model fails backtest
I was wondering what the correct procedure is to follow when a VaR model fails a backtest (either conditional coverage and/or independence tests)?
Assuming I am restricted to using a historical VaR ...
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2answers
64 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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0answers
53 views
Pricing default risk in cryptos
I'm looking to figure out how to price "insurance" against a counter-party defaulting in an OTC cryptocurrency transaction. I think the first measure would be to calculate VaR? I'm planning on ...
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1answer
56 views
Value at Risk for normal r.v. with shock (regimes)
I am struggling to understand how was this simple Value-at-Risk calculated. It's Example 1 in Daníelsson, Jón, et al. "Fat tails, VaR and subadditivity." Journal of econometrics 172.2 (2013): 283-291 (...
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35 views
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
81 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
113 views
How to compute a single Value-at-Risk (a single quantile) of portfolio returns taking into account correlation between individual returns?
Introduction
My goal is to retrieve a single Value-at-Risk (VaR) of a N(0, H) random variable $X$ at the $\alpha \in (0,1)$ confidence level where H is a known d-dimensional positive definite matrix ...
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28 views
Hedger's utility function associated with minimizing value at risk
What must be the general shape of a hedger's utility function if the hedger is minimizing value at risk?
What is a simple example of such a utility function?
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33 views
Does it make sense to simulate from the multidimensional GBM?
Suppose I have times series data on 3 assets and I do $N$ simulations (GBM) first for each of assets individually and then from a multidimensional GBM since their log-returns are correlated (I use ...
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1answer
113 views
Volatility scenario generation for value-at-risk
I have the following problem: For a single name plain vanilla equity option calculate 1y VaR for given confidence level.
Is there any state-of-the-art or current market practice known on how to ...
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1answer
130 views
Negative VaR equivalent Volatility (VEV) and its meaning?
Can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative and what does it mean if it has a negative value?
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1answer
46 views
What is the relationship of Value-at-Risk of a random variable $X$ and a constant $D$ $VaR_{\alpha}(min(X,D))$and $VaR_{\alpha}(X)$?
Suppose $X$ is a nonnegative random variable and $D$ is a constant, what is the relationship of $\text{VaR}_{\alpha}(min(X,D))$ and $VaR_{\alpha}(X)$? Here, $VaR$ stands for Value-at-Risk as,
$$
VaR_{\...
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1answer
69 views
Value at Risk for a plain vanilla interest rate swap
Hello I have question regarding the computations of the Value at Risk for a plain vanilla interest rate swap (i.e. same currency and fixed-for-floating).
I have a data set consisting of the Swap ...
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1answer
73 views
Value-at-Risk and dividend payments
How should dividends be considered when computing Value-at-Risk for a stock portfolio using Historic data.
To simplify let's consider a very simple portfolio of one long position on a stock. My VaR ...
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19 views
Difference between Standard VaR and VaR with partial set of Risk Factors
Ciao,
I'm working on VaR and Expected Shortfall and this question came out.
For a given portfolio VaR can be computed w.r.t. all the risk factors or just for a subset. Infact you can decide to 'freeze'...
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139 views
Delta- Gamma approximations for VaR
I was reading Delta- Gamma approximations for VaR from Phillipe Jorion-Value at Risk 3rd edition, I got stuck here, how do they derive equation $10.10$ from $10.9$.
Also in eq. $10.9$ they have ...
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0answers
18 views
Definition of μ in Parametric Absolute Ex-Ante Risk
Parametric Value at Risk (of an investment fund) depends on the Gaussian Distribution and comes in two forms; Relative VaR (ie relative to the mean) and Absolute VaR. Both are calculated as ...
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1answer
93 views
VaR of long options
I just had a chat with a risk manager who thinks that the daily VaR of a long option with a maturity under three months should be 'Premium of the Option' / 20 (assuming twenty days in a month)
...
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0answers
44 views
How can I find what Loss Given Default to use
I want to come up with the appropriate loss given default for a commodity derivative in my CVA calculation. would anyone know where I can find this information?
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Do they apply any weights to asset PnLs before arriving at Pflio PnL in HVaR Computation?
My current understanding is; Eg: If you have 2 assets in your pflio
1.the assets are mapped to risk factors.
2.Historical Shocks are applied to risk factors and the assets are valued again.
3....
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1answer
112 views
What is the name of this VaR calculation strategy?
Here's a question on a passage from this paper I'm reading. Here's the quote:
Given the vector of portfolio weights $w$, and the estimate of the
conditional variance, $\Sigma_{t,k}$, the ...
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1answer
115 views
Risk Management methods for Stock portfolio with ~30 stocks
What is ideal Risk Management method/methods s for stock portfolios with 25-30 stocks and around 50.000 USD invested in those stocks. Every stock bought will be kept in the portfolio for 1 to 12 ...
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2answers
91 views
Assigning Global VaR to portfolio members
Assuming that I calculate a parametric VaR of a portfolio with 3 assets, and I need to assign the amount each asset (equity) contributes to the VaR.
Lets say that:
$C$: Is the correlation matrix
$w$:...
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30 views
Choosing the DoF for a t-copula when copulafit doesn't work
I'm currently writing my Master thesis where I investigate some different methods of dimension reduction regarding Value at Risk for very large equity portfolios.
My current data set contains of 5000 ...
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1answer
97 views
Calculating Value at Risk (VaR) of a Stock position assuming geomtric brownian motion (GBM)
I want to calculate the VaR for a long position (S) in stockprices after one year. Therefore i tried two methods:
analytical solution: $VaR = S\cdot p_0\cdot \sigma_d \cdot \Phi^{-1}(1-\alpha)\cdot \...
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0answers
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VaR decomposition of non-normal portfolio by g-and-h distribution
According to Doowoo Nam (2013), VaR of non-normal portfolio returns approximated by g-and-h distribution can be decomposed pretty much in the same way as the VaR of a portfolio with normal returns. ...
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83 views
Backtesting VaR
I just started reading about Value at Risk and there were a few questions that were brought to me as I was fiddling with it in R. Suppose my time series that is ...
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1answer
190 views
Intuitive explanation for expectiles
I am looking for an intuitive explanation for expectiles.
Here is a link to a paper about expectiles:
Bellini and Di Bernardino: Risk Management with Expectiles, European Journal of Finance, May ...
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1answer
186 views
Can portfolio Value-at-Risk be calculated analytically for multivariate t-distributed returns?
It is widely known that VaR is generally not sub-additive in all but the most restrictive cases (typically when a Gaussian return distribution is assumed, which fails when it matters the most).
...
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1answer
130 views
Risk Compensation
I try to understand the different ways to compensate for risk.
In the CAPM, when we plot the excess return against the risk, we find that portfolios of interest lie on the efficient frontier (i.e. ...
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0answers
66 views
Calculate VaR using the extreme value theory
I am trying to calculate the Value at Risk for different models. But I am now confused for some reason. Could you please help me?
I calculate the 1% and 5% VaR (so negative numbers) and I am also ...
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1answer
63 views
Calculate standard deviation from the value at risk
I have the following data:
VaR
VaR%
Expected return
Am I right to think that I would be able to derive standard deviation from this?
Using the formula: VaR%= ER-(zscore*SD), I should be able to ...
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1answer
466 views
Ratio between Expected Shortfall and Value at Risk for $t$-distribution
If $X$ is a random variable with $t$-distribution of parameter $\mathcal{v}$, how can I prove that
$$
\lim_{\alpha \to 1^{-}} \frac{\mathrm{ES}_{\alpha}(X)}{\mathrm{VaR}_{\alpha}(X)} = \frac{\mathcal{...
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1answer
70 views
What's the relationship between $VaR_{\alpha}(X)$ and $VaR_{1-\alpha}(X)$ if the probability distribution function is not symmetric?
If the probability distribution function $f(x)$ is not symmetric, is there any relationship between $VaR_{\alpha}(X)$ and $VaR_{1-\alpha}(X)$?
Here, $VaR$ is defined as
$$
VaR_{\alpha}(X) := \inf\...
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1answer
452 views
VaR : Student-t GARCH
I have a question on the VaR estimation via the student t GARCH model.
Under this framework, the one day ahead VaR estimate is calculated by the following formula:
$$VaR_{p}=\mu_{t+1}+\sigma_{t+1}\...
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1answer
152 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
131 views
VaR Backtesting. High frequency of exceedances
I'm preparing for thesis defense and I've got simple question connected with Value at Risk backtesting. Portfolio VaR was calculated using historical simulation approach (250 days and 500days) and ...
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1answer
303 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
471 views
Backtesting Value at Risk. With kupiec test
I have a certain problem with backtesting calculated earlier Value at Risk.
I've got calculated daily VaR with historical simulation method for stocks. I've used two values of alpha 0.05 and 0.1. Now,...
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1answer
109 views
testing stressed VaR
How can you compare stressed VaR estimates?
What are statistical tests for assessing the quality of stressed VaR estimates?
I think the VaR Coverage test for example by Christoffersen (1988) would ...
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1answer
276 views
Why do regulators assume a risk-neutral world?
It is clear that when pricing derivatives we do this in the risk-neutral measure for known reasons.
In the calculation of the VaR equivalent Volatility (VEV) in the KID-SRRI calculation (see page 9 ...
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2answers
901 views
non-subadditivity of VaR
I have been reading up on VaR and get very confused by the subadditivity concept.
On wikipedia, it says "VaR is not subadditive: VaR of a combined portfolio can be larger than the sum of the VaRs ...
