# Questions tagged [value-at-risk]

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### VAR interpretation

I definitely struggle to understand the following interpretation of VAR (value at risk) provided by Jorion $$VAR(c)=E[X]−Q(X,c)$$ where $X$ is a random variable, $E[X]$ its expected value, $Q(X,c)$ ...
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### Calculate Value at Risk for floating rate note

Consider a floating rate note: nominal: € 100 000 000 coupon period: annualy remaining time to maturity: 7 years and 3 months The coupon amounts to 3.3%, the current 3M-money market rate amounts to 3....
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### Calculate VaR using method of historical simulation

A bank invests € $1.000.000$ in a hedge fund. The last 500 daily returns can be taken from a database. The worst 20 returns are -4.58 -2.95 -2.95 -2.93 -2.17 -2.08 -2.06 -1.98 -1.94 -...
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### Do the minimum VaR and minimum ES portfolios lie on the mean-variance efficient frontier?

The mean-variance efficient frontier holds the minimum variance portfolio, but in the graph above it shows that the minimum VaR (Value-at-Risk) and minimum ES (CVaR) portfolios (expected shortfall/...
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### VaR and Expected Shortfall for Geometric Brownian Motion

Given that $dS_t=\mu S_tdt+\sigma S_tdW_t$ ,a risk free rate r and defining Value at Risk and Expected Shortfall as $VaR_{t,a}=S_0e^{rt}-x$ where $x$ is the amount such that $P(S_t\leq x)=1-a$ ($a:$...
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### Value at Risk under increasing function

There is an exercise I struggle to solve. I hope you can give me a hint. Let X be random variable taking values in $I\subset \mathbb{R}$. I have to show that the Value at Risk is invariant under any ...
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### Decomposition of Contribution to Variance

$C$ is a $N\times N$ covariance matrix of stock returns. Assuming $w$ is a vector of positions in each asset, the total variance of the portfolio is $$w^TCw$$ The contribution to total variance of the ...
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### How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk and Conditional Tail Expectation?

How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk and Conditional Tail Expectation????
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### What is the differential Value-at-Risk?

I am currently working on a Machine Learning Project, implementing portfolio optimization algorithms according to different risk measures. I have found sufficient information on Sharpe Ratio ...
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### Cornish Fisher VaR Parameters Calibration

I am trying to calculate Cornish-Fisher (modified VaR), but I am in a trouble because when I am reading some articles, some authors calculate the Cornish-Fisher expansion taking parameters S and K, as ...
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### Univariate Portfolio Analysis

We want to form 10 portfolios based on the level of VAR (99%) for equity data over a 30 year period. Portfolio 1 is the portfolio of stocks with the lowest value-at-risk and Portfolio 10 is the ...
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### Backtesting conditional VaR

I'm writing a thesis about conditional VaR of Standard & Poor's 500 index. I have fitted my log-returns with GARCH(1,1)-proces and then made some conditional VaR-forecast (500 observations) with ...
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### Variance minimization vs. Value at risk

When computing Minimum Variance Hedge Ratios as explained f.e. in Hull (2012) the goal is to select a hedge ratio such that the variance of the portfolio is minimized. My question is now what are the ...
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### CRRA Ultility， simple question

for CRRA, does increasing gamma leads to increase in risk-aversion? Looking at the curve, I think increasing gamma leads to less in risk-aversion (since the risk preimum is less). But in terms of ...
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### Determining Value at Risk of a Poisson distribution

If my discrete random variable had a poisson distribution with both moments say equal to 10, how can I find the Value at Risk for a 95 percent confidence interval? I have seen that I need to ...
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### How do you calculate value at risk on a portfolio of fixed income instruments

I'm curious about this question both for a parametric "Delta" style approach and a Monte Carlo full revaluation approach and I will lead one question into the next. Taking the "Delta" approach first. ...
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### How are non-equity derivatives handled in monte carlo Value at Risk simulations

If you have a portfolio of stocks and options it's straight forward enough to generate correlated stock paths and evaluate the positions at the end of the time horizon, but what do you do if your ...
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### Incremental/marginal contribution to VaR in a simulation setting

Estimating marginal contributions to VaR in a simulation setting is apparently quite difficult (see e.g. this blog post) due to issues with sampling variability. My question is whether the following ...
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### portfolio return, sharpe ratio and value at risk

Can you please help me to confirm if my calculations are correct or need improvement, or (too simplistic...) : - portfolio return, - portfolio standard deviation, - portfolio sharpe ratio - ...
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### How accurate is the square root of time rule for VaR for a portfolio containing several different types of instruments

Assuming that your value at risk model is based on normality assumptions, e.g. using a Delta-Gamma normal model does the approximation hold perfectly for a portfolio of stocks and options? What about ...
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### Lognormal asymmetry implication on Value at Risk

To examine the Value at Risk implications for a portfolio consisting of a spot and futures time series I have generated a 1-day monte carlo simulation. I was long in the spot and short in the future (...
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### Value at Risk (VaR): Normal distribution with gamma distributed volatility

If I was to do a 99% VaR calculation on a portfolio with normally distributed returns $\mathcal{N} (\mu,\sigma)$, the 99% VaR would be $\mu - 2.33\sigma$. Instead of having a constant volatility, let'...
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### Correlation in GARCH model

I don't think I have ever come across the concept of stochastic correlation so I imagine it's not very widespread, but I had the idea to implement a Monte Carlo VaR model for a portfolio of stocks by ...
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### How does delta-gamma VaR work in practice and when can it be preferable to Monte-Carlo VaR?

So I will start off by just stating my understanding of the two methods through some examples and lead that into my question. Hopefully it is correct but if not then perhaps the answer to my question ...
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### Value at Risk for portfolio with different maturities

I am new to StackExchange and relatively new to quantitative finance. I work at a commodity trading company and we have an extensive portfolio of futures and options on commodities (traded on the CME, ...
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### Can value at risk be computed using downside deviation?

Value at risk is usually computed with a regular standard deviation. But can it be computed using downside deviation (semi-deviation) instead? Particularly if I want to consider a Var that includes ...
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### 99.97% Percentile VaR Approximation

I have been working with a group which references a 99.97% 10-day VaR figure. They calculate this value via a 99% 1-day historical simulation over 500 days and then scale it under the assumption of a ...
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### Interpretation of $\alpha$ (confidence level) in mean CVaR optimization

How are an investors risk preferences related to $\alpha \in (0,1)$ in a mean CVaR optimization? Would a risk averse investor choose a higher value of $\alpha$, and if so why? My understanding is, ...
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### Analytical portfolio optimization for VaR under multivariate normality

Given a set of assets with returns following a multivariate normal distribution with a known mean vector and a known covariance matrix, $$r \sim N(\mu,\Sigma),$$ I want to find optimal portfolio ...
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### Absolute and Relative Value at Risk

Is it correct to calculate the VaR as 99% max between loss and profit. E.g. if 99% VaR on the loss side of the distribution is -100, and on the positive side of the distribution there is a value ...
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### Stop-Loss strategies

Does anyone know some bibliography about the problems or limitations of using Stop-Loss strategies in a portfolio? Let me explain better: for example you can have a portfolio of 30 stocks from ...
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### Backtesting a stock scoring model

I'm working on a simple stock scoring model consisiting of 3 factors: 1.market cap 2.liquidity of the stock 3.the value at risk we defined 3 intervals for each factor and we assigned the ...
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### Portfolio optimization w.r.t. value at risk: introductory or survey references

I am looking for references introducing the problem of portfolio optimization when the target characteristic is value at risk. A textbook treatment would be great. Surveys on the topic are also ...