Questions tagged [value-at-risk]

Value-at-Risk is a family of measures used to help the owner of a position to assess its "worst case value".

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How does Cornish-Fisher VaR (aka modified VaR) scale with time?

I am thinking about the time-scaling of Cornish-Fisher VaR (see e.g. page 130 here for the formula). It involves the skewness and the excess-kurtosis of returns. The formula is clear and well studied (and criticized) in various papers for a single…
Richi Wa
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How to limit the nbr of cross-gamma calculations in a delta-gamma VaR calculation?

Many times, we want to calculate VaR using some parametric approach (delta-normal approximation for instance) when historical simulation or monte carlo are simply to slow. This is fine as long as only the deltas are needed and the instruments are…
Rickard
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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 $$ \sqrt{\frac{df-2}{df}} \times \Sigma{t} \times \mbox{quantitle}(t-\mbox{dist}, 0.01) + \mu $$ (Please excuse the messy formula & the sigma(t)…
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What is the heat-map method of calculating VaR?

I'm familiar with the historical full revaluation, VcV, and Delta-gamma methods, but a client keeps talking about a heat-map method and I'm not sure what he's talking about. Any ideas?
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CVaR reformulation correct?

Conditional Value at Risk (CVaR) is given as: $$CVaR_\alpha(X)=\frac{1}{\alpha}\int_{0}^{\alpha}VaR_\beta(X)d\beta=-E(X|X\leq-VaR_\alpha(X))=-\frac{1}{\alpha}\int_{-\infty}^{-VaR_\alpha(X)}x \cdot f(x)\,dx$$ I am not sure if the last term is correct…
emcor
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Parametric VaR, Normality and Subadditivity

Good evening; I just have a simple question about Value at Risk and the subadditivity property, and I know that it may sound silly I got that, in general, VaR is not subadditive. However, if a portfolio contain elliptically distributed risk factors,…
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Expected Shortfall Formula in terms of P

Let $X$ be a continuous random variable and $Q_x$ is the associated quantile function. Show that expected shortfall $ES_X[p]$ at the confidence level $p$ which is defined as $$ES_X[p]=\Bbb E[X|X\leq Q_x(1-p)]$$ has the representation…
Raveesh
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How to calculate VaR/CVaR for private equity, hedge fund, and alternative investment portfolios?

What is the best method for calculating VaR/CVaR for private equity, hedge fund, and alternative investment portfolios? I have only historical monthly return for them.
pmr
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Understanding VaR rescaling

Assume my portfolio has a current market value of $V_0$, that the daily returns are independent and identically distributed as a normal distribution $N(0, \sigma^2)$ and that there are $N$ trading days in a year. Also, let $\Phi$ denote the cdf of…
augustoperez
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The VaR of a portfolio with Student t returns

A portfolio consists of 300 stocks,150 of A and 150 of B, their annualized covariance matrix is as following: $\begin{pmatrix} 0.09 & 0.018\\ 0.018 & 0.04 \end{pmatrix}$ Thoese two stocks are jointly distributed as Student t with 5 degrees of…
suntoto
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Maximization with risk-neutral investors and VaR constraints

In this paper, the authors make a simple model with: (1) A global bank, who is risk-neutral but has a Value-at-Risk constraint: $$\max_{x_t^B} E_t[x_t^B\prime R_{t+1}]$$ s.t. $$\alpha (Var(x_t^B\prime R_{t+1}))^{\frac{1}{2}} <= 1$$ where…
phdstudent
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Difference in Volatility Calculation from RiskMetrics 1996 to RiskMetrics 2006 VaR

In the original legacy RiskMetrics documentation from 1996, volatility is calculated using a simple exponentially weighted moving average with some decay factor to determine the weights. This would be used in the calculation of volatility for…
beeba
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Parametric VaR with Student-t distribution

Im using VaR to estimate parametric VaR. I have been able to do this using a Normal Distribution, however I want to also do this using a Student t-distribution and I'm unsure how to implement that in Matlab. I have a dataset of portfolio values, I…
Josh.V
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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})\overline{\text{VaR}}^{60}_{t+h},…
dsforecast
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Why is Value at Risk non-negative?

When reading the book of Financial Risk Forecasting, I saw the following example. I am not very clear about two points marked with yellow and green respectively. Regarding the first point marked with yellow color, why $VaR^{1\%}=100$, I think it…
user288609
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