Questions tagged [value-at-risk]
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183
questions
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57 views
Estimating VaR of bond due to changes in the US yield curve
I am attempting estimate the 99% 10-day VaR of an investment grade bond due to changes in the US yield curve. The data provided is the daily prices of the bond over time. In addition I have the Daily ...
0
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1answer
41 views
Is scaling the standard deviations in the VaR formula (parametric) equivalent to scaling the VaR figure at the end?
I have come across people calculating parametric VaR who scaled the standard deviations by say square root of 10 to scale up to a 10 day horizon.
Elsewhere I have seen textbooks suggesting that it is ...
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0answers
38 views
LogNormal VaR Formula Risk Metrics
https://web.mst.edu/~huwen/teaching_VaR_Weiqian_Li.pdf
On page 6, the paper above mentions RiskMetrics would use the following VaR formula:
...
1
vote
1answer
66 views
VaR and Expected Shorfall estimations with negative shape parameter of a GPD (Extreme Value Theory )
So im trying to replicate an code from the Quantative Risk Management Book (https://github.com/qrmtutorial/qrm/blob/master/code/09_Market_Risk/09_Standard_methods_for_market_risk.R). But when i try a ...
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34 views
Implications of modeling operational risks without frequency distribution
When modeling operational risk, the Loss Distribution Approach (LDA) is widely used. Usually, we model the loss frequency distribution and the loss severity distribution and then aggregate both to ...
1
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1answer
78 views
Optimal Portfolios with Skewed and Heavy-Tailed Distributions
I am learning about portfolio theory and been using Markowitz. I wondered, however, if I can use distributional and asymmetric information of the returns to solve the problem. For instance, I have a ...
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26 views
VAR Monte Carlo GBM vs Selecting Normal Dist Returns
I am running a VaR calculation and have seen two ways of doing it in several places online.
One simply assumes normal distribution of returns and selects n number of returns from the normal ...
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0answers
85 views
Interpretation of Value at Risk
Let $X$ be a Loss random variable (Positive values of X represents Losses) and let $p \in (0,1)$. I know that the Value at Risk at level $p$ of $X$ is defined as:
$$VaR_p(X) = inf{\{x \in \mathbb{R} : ...
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1answer
65 views
Calculating the Value-at-Risk when changing the confidence level
If I have a VaR estimate at a 95% confidence interval is 10, how do I calculate the approximate level of the VaR if the confidence level was raised to 99%, assuming a one-tailed normal distribution?
1
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1answer
60 views
VAR interpretation
I definitely struggle to understand the following interpretation of VAR (value at risk) provided by Jorion
$$VAR(c)=E[X]−Q(X,c)$$
where $X$ is a random variable, $E[X]$ its expected value, $Q(X,c)$ ...
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49 views
Calculate VaR using method of historical simulation
A bank invests € $1.000.000$ in a hedge fund. The last 500 daily returns can be taken from a database. The worst 20 returns are
-4.58 -2.95 -2.95 -2.93 -2.17 -2.08 -2.06 -1.98 -1.94 -...
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3answers
194 views
Do the minimum VaR and minimum ES portfolios lie on the mean-variance efficient frontier?
The mean-variance efficient frontier holds the minimum variance portfolio, but in the graph above it shows that the minimum VaR (Value-at-Risk) and minimum ES (CVaR) portfolios (expected shortfall/...
2
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1answer
154 views
VaR and Expected Shortfall for Geometric Brownian Motion
Given that $dS_t=\mu S_tdt+\sigma S_tdW_t$ ,a risk free rate r and defining Value at Risk and Expected Shortfall as
$VaR_{t,a}=S_0e^{rt}-x$ where $x$ is the amount such that $P(S_t\leq x)=1-a$ ($a:$...
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1answer
105 views
Is there Cornish-Fisher volatility, given that there is Cornish-Fisher Value-at-Risk?
The Cornish-Fisher expansion is used to approximate the quantile $q_\alpha$ of a return distribution in order to extend the traditional Value-at-Risk (VaR) measure
$$VaR = \mu(X) + \sigma(X) q_\alpha $...
0
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1answer
60 views
Someone help me understand why for portfolio variance or Parametric Value at Risk we have to compute the covariance matrix?
I understand that portfolio variance is computed through $w'Cw$, where w is the vector of weights, $C$ being the covariance matrix. However, what I don't get is this: why can't this portfolio variance ...
1
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1answer
143 views
Code (Python or R) references for operational risk models (AMA/COM)
I have to build an operational risk model and to be compliant with Basell II and III regulations I thought of using AMA (Advanced measurement approach) or COM (change of measurement).
We have no ...
1
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1answer
50 views
A simple question about VaR estimation
"A 99% VaR using 1,000 (simulation) replications should be expected to have only
10 observations in the left tail, which is not a large number. The VaR estimate
is derived from the 10th and 11th ...
1
vote
1answer
82 views
Mean-EVaR efficient frontier
Entropic Value-at-Risk (EVaR) is an alternative and more efficient risk measure than conditional Value-at-Risk (CVaR). EVaR serves as an upper bound to both VaR and CVaR.
Below is a graph of the mean-...
1
vote
1answer
100 views
Does Value-at-Risk have any mathematical equivalence to copulas?
Portfolio Value-at-Risk estimated using the copula approach often just means generating artificial data sampled from a parametric copula('s joint multivariate distribution) as a model fit over the ...
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0answers
43 views
Multi-period Basel/Vasicek formula
I need to apply Basel/Vasicek formula to a 20-years horizon, both from a 20-years cumulative perspective and year-on-year basis.
Please find below the formula of the Basel Capital (ie. unexpected loss)...
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31 views
Covariance of Individual Return and Portfolio Return
Hi guys,
Is it possible to get the covariance between the individual return and portfolio return given the correlation matrix, volatility matrix, weights matrix and return matrix?
I know how to get ...
0
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1answer
130 views
MonteCarlo Value at Risk for a bonds portfolio
As mentioned in the title, I am trying to calculate MC VaR for a portfolio consisting entirely of bonds.
I already modeled the zero curve using Vasicek and Cox,Ingersoll & Ross models.
Next steps ...
-1
votes
1answer
55 views
Good ways to select best decision among N decisions, each with a profit/loss distribution? [closed]
I'm working on a problem where an asset owner (e.g., owner of a factory, power plant, etc.) can take a number of possible decisions (say 10). Each of those 10 decisions entails certain actions, but ...
1
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1answer
64 views
Do stationary prices need to be differenced for VaR?
I have a time series of electricity futures prices that I have shown to be stationary via the Augmented Dickey Fuller test (alpha = 0.05). Does that mean that, in calculating their individual values-...
0
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1answer
48 views
Can I say VAR is a prediction report?
We use Algorithmics RiskWatch where portfolios are analyzed by VaR over scenarios. Can I say that they are predictions reports? or descriptions reports?
0
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1answer
284 views
Correct way to calculate interest rate volatility for risk calculations
I'm trying to include interest rate derivatives in some Value at Risk calculations and am having trouble getting trustworthy values. My current approach is to look at the appropriate risk factor for ...
1
vote
1answer
98 views
Delta-normal VaR of portfolio of stock and call option
I have to calculate the 10-day 99% VaR of a portfolio that consists of a portfolio of 260 stocks of a company $K$ and that is short 500 call (European) options of the same company.
I know that the ...
6
votes
1answer
245 views
Optimizing a portfolio whose risk is target expected shortfall
I want to maximize the return of a $n$-asset portfolio under known risk:
$$\max_{\{w \in \mathbb{R}^{n}|w_{1}+...+w_{n}=1\}} \; \mathbb{E}\left[\sum_{i=1}^{n}w_{i}R_{i}\right]$$
under the constraint
$$...
1
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1answer
51 views
Value at Risk under increasing function
There is an exercise I struggle to solve. I hope you can give me a hint.
Let X be random variable taking values in $I\subset \mathbb{R}$. I have to show that the Value at Risk is invariant under any ...
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0answers
165 views
Decomposition of Contribution to Variance
$C$ is a $N\times N$ covariance matrix of stock returns. Assuming $w$ is a vector of positions in each asset, the total variance of the portfolio is
$$w^TCw$$
The contribution to total variance of the ...
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0answers
23 views
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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58 views
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 ...
2
votes
1answer
76 views
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 ...
0
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0answers
100 views
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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0answers
39 views
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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0answers
18 views
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 ...
4
votes
1answer
80 views
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 ...
1
vote
1answer
170 views
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 ...
0
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2answers
214 views
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. ...
0
votes
1answer
55 views
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 ...
2
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1answer
76 views
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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222 views
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
- ...
1
vote
1answer
270 views
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 ...
1
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0answers
25 views
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 (...
1
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1answer
160 views
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'...
0
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1answer
479 views
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 ...
4
votes
1answer
174 views
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, ...
1
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0answers
52 views
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 ...
4
votes
1answer
300 views
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 ...
4
votes
1answer
258 views
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 ...
