# Questions tagged [value-at-risk]

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### Value-at-Risk "hiding risk in the tail" and diversification?

I have a question regarding Value-at-Risk and diversification? When one says that VaR "hides the risk in the tail", does one mean that if we for instance look at VaR at level p=0.05 say, we might get ...
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### Value-at-Risk Calculation with respect to the Capital Requirements

I want to calculate the Value-at-Risk at date $t$ in such a way that I minimize the capital requirements given as \begin{align} \text{CR}_{\,t+1\,:\,t+250} = \sum_{h=0}^{249}\max\left( -(3+k_{t})\...
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### Value-at-Risk of the sum of three independent lognormal random variables with different confidence level

there are three Business units in a firm, each has operational VaR value which are independent from eachother. the quantile for each opVaR is different from the others. can I simply add the VaRs to ...
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### Empirical distribution function of overlapping time series data

If we model asset return volatility for periods of more than one (say more than one day) there is the square-root rule which holds true under some assumptions. The situation is more tricky if we look ...
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### What is the difference between these two Expected Shortfall definitions?

I have come across different ways expected shortfall is defined. e.g. $$ES_a(X)=\frac{1}{1-a}\int_a^1VaR_b(X)db$$ and $$ES_a(X)=\frac{1}{a}\int_0^aVaR_b(X)db$$ e.g. on Wikipedia's article. Are these ...
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### Quantiles, Value-at-Risk and log normal random walks…

Sorry, that's probably quite a bunch of silly questions, but I just got lost a bit and need to dot all the i's and cross some t's :). Let's say we have a series of returns (like this one we may get ...
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### How to extrapolate VaR?

I have a model predicting 1-day VaR. How does 1-year VaR follow from it? Shall I just multiply by 365 or another method?
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### Portfolio VaR with Copula?

Let the portfolio be given by: $$X=X_1+X_2$$ $(X_1,X_2)$ are dependent through a Copula function $C(u_1,u_2)$, such that the joint distribution is given by: $$F(x_1,x_2)=C(F(x_1),F(x_2))$$ What is ...
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### Overlapping Value-at-Risk Backtest Data an Issue?

My understanding of VaR model back testing is thus: ~~ t: Calculate daily VaR using look back data over n past days t+1: Compare daily return against VaR, record breach if one occurred, repeat ...
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### Does one use the covariance or correlation matrix in cholesky decomposition to generate correlated samples

Can we interchangeably use Cholesky decomposition of covariance and correlation matrix to generate simulations? If not, in which situations do we use one or the other and why? Thanks in advance.
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### Difference between VaR and credit VaR?

Quick question: is there a difference between credit VaR and VaR or are they the same thing?
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### Estimation of Empirical Expected Shortfall of a heavy tailed distribution

Assume that you have a portfolio for which you have estimated a parametric model to the underlying instruments, but the distribution of the portfolio as a whole is too complicated to compute ...
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### Comparing Backtests of Value-at-Risk and Expected Shortfall

My goal is to test if ES (CVaR) empirically is a better risk measure than VaR for a set of given variables (assumed underlying distribution, confidence level, sample size) for different asset classes. ...
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### Value-at-Risk formula when using skewed-t distribution

I am trying to find a formula for the skewed-t VaR. For example the VaR formula for a t-distribution is $$\sqrt{\frac{df-2}{df}} \times \Sigma{t} \times \mbox{quantitle}(t-\mbox{dist}, 0.01) + \mu$$...
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### Determining the portfolio return distribution to calculate CVaR/ES

I'm trying to do a portfolio optimization with an expected shortfall constraint. For this, it is necessary to know the distribution of expected portfolio returns. When doing this empirically, my plan ...
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### Market risk stress testing?

I am doing a research for a paper for market risk stress testing. In fact I found some information on the web about this important topic such as: Stress Testing from Art to Science Stress Testing ...
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### Fitting distributions to financial data using volatility model to estimate VaR

I want to fit a distribution to my financial data using a volatility model to estimate the VaR. So in case of a normal distribution, this would be very easy, I assume the returns to follow a normal ...
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### Value at Risk Monte-Carlo using Generalized Pareto Distribution(GPD)

I have created a VBA program to calculate VaR by using Monte Carlo, I have simulated Brownian Motion. This method might be ok for 100% equity portfolio, but let's say this portfolio may have fixed ...
The parametric VaR is defined as follows: $$VaR=Z_a*Vol$$ Is this the best way to interpret how much risk is being taken on for a particular asset? How does one interpret volatility on its own if ...