Questions tagged [value-at-risk]
The value-at-risk tag has no usage guidance.
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2answers
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Value-at-Risk theory papers
I am looking for some papers related to the value-at-risk theory. I would like to focus on mathematical aspects of VaR. I would like to read something about modern approaches to VaR (maybe using ...
2
votes
1answer
56 views
Historical VaR for shares in foreign currency
I'm currently studying John Hull's [1] example on historical value at risk for portfolio consisting of four stock indices.
In this example Hull converts the prices of the stock indices to the home ...
2
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1answer
112 views
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 ...
1
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0answers
38 views
Does it make sense to subtract VaR from spot shocks?
I have a model to compute the Event Risk (in dollars) from a shock to the spot price of an asset. I also have the 10-day VaR PnL for the same assets returns. These two numbers are then aggregated to ...
3
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1answer
91 views
Value-at-Risk for a portfolio model with Gearing
My models:
Say I want to construct a portfolio so I maximize my expected return while keeping my risk (measured by Value-at-Risk) lower than my risk target.
$$\max \sum x_i \mu_i \\
VaR_{0.05} \leq \...
2
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0answers
55 views
Methods for calculating Expected shortfall
Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each
with a face value of $100. Assume:
each bond is priced at 90 dollars
each bond has a 4% probability to default within 1 year
...
4
votes
1answer
98 views
How do I compute Value at Risk of a European call option?
Consider a European call option on a non-dividend paying stock, where the
option has strike K = 100 and expiry T = 0.25, i.e. the option expires 3
months from now. The option is on a single share. The ...
0
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0answers
26 views
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 ...
2
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0answers
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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 ...
1
vote
1answer
49 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 ...
1
vote
0answers
41 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 ...
0
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1answer
38 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 ...
1
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1answer
60 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 ...
0
votes
1answer
140 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 ...
0
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1answer
104 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) = ...
0
votes
2answers
64 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 ...
2
votes
2answers
68 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)+...
2
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0answers
54 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 ...
1
vote
1answer
58 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 (...
0
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0answers
36 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 ...
0
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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-...
1
vote
1answer
118 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 ...
1
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0answers
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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?
0
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0answers
37 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 ...
2
votes
1answer
138 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 ...
1
vote
1answer
156 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?
1
vote
1answer
47 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_{\...
2
votes
1answer
97 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 ...
1
vote
1answer
79 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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0answers
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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'...
0
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0answers
163 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 ...
0
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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 ...
1
vote
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
46 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?
1
vote
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 ...
1
vote
1answer
118 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 ...
1
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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
$w$:...
0
votes
1answer
126 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 \...
2
votes
0answers
42 views
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. ...
2
votes
1answer
212 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 ...
3
votes
1answer
212 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).
...
4
votes
1answer
133 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. ...
1
vote
0answers
67 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
66 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
542 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
$$
\lim_{\alpha \to 1^{-}} \frac{\mathrm{ES}_{\alpha}(X)}{\mathrm{VaR}_{\alpha}(X)} = \frac{\mathcal{...
0
votes
1answer
76 views
What's the relationship between $VaR_{\alpha}(X)$ and $VaR_{1-\alpha}(X)$ if the probability distribution function is not symmetric?
If the probability distribution function $f(x)$ is not symmetric, is there any relationship between $VaR_{\alpha}(X)$ and $VaR_{1-\alpha}(X)$?
Here, $VaR$ is defined as
$$
VaR_{\alpha}(X) := \inf\...
1
vote
1answer
522 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}\...
1
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1answer
156 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
142 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 ...
4
votes
1answer
348 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 ...
