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Questions tagged [var]

Value at Risk, a widely used risk measure of the risk of loss on a specific portfolio of financial assets.

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22 views

Simulation VaR and CVar assuming Normal Distribution

Am I missing something? Currently implementing a VaR and CVaR measure assuming normality of wealth value. after executing the following script, VaR is always greater than CVaR, as expected, but ...
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23 views

VaR calculation using excel gives different value than VaR using R at all c values except at c=0.5

This is VaR calculation in excel using variance-covariance method. This is VaR calculation in R. ...
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1answer
35 views

Calculating Value-at-Risk for difference between two assets / series

I'm working on a 'portfolio' comprised of, say, £100 long in Asset A and £200 short in Asset B. In reality it is a holding in A and an obligation to pay B (think a retirement plan with a single pool ...
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2answers
54 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)+...
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27 views

How to fit and test VaR in R

I have estimated the below model with gjr-garch11 gjrgarch11n.spec = ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder=c(1,1)), mean.model = list(armaOrder=c(1,0), include.mean = TRUE), ...
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2answers
32 views

Parametric VaR assumption question

Why do you have to make a correlation matrix when calculating the parametric value at risk, if one of the assumptions for this method to work is that the assets of the portfolio must be independently ...
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1answer
50 views

VaR for Options portfolio

I'm asked to estimate VaR for Options portfolio. Firstly, I wanna try to estimate VaR for AAPL stock european call option using Historical Simulation but I can't find any Historical Data. I tried ...
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1answer
95 views

Mean - Value at Risk optimization portfolio

so I'm intrested in building a process that computes the optimal portfolio selection based on asset using the framework of return maximization and VaR (montecarlo simulation) minimization. So far I ...
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1answer
46 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 (...
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62 views

Gonzalo Granger and Hasbrouck Information Share

I am trying to implement the two methods for price discovery following this paper Price Discovery in CDS and Bond Markets. I allready looked for implementation and based my work on this R project ...
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0answers
65 views

Value at Risk of a Portfolio

I am currently practicing for my Risk Management exam in July but my lecturer is of no help and my colleagues and I have no idea on how to proceed with this question. The past exam papers have similar ...
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2answers
65 views

Calculation VaR on long term period

I'm calculating VaR numbers from historical data for a single instrument (it's plain vanilla, not a derivative) and receive such variables: I could provide necessary data, and formulas but I guess ...
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0answers
27 views

Modelling approaches for interest rate risk in the banking book (IRRBB)

I am having a hard time researching papers that deal with the measurement of market risk in the banking book. The trading book as I see it is similar to asset management and as the name says the ...
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1answer
71 views

Understanding example on VaR

Trying to understand the example below on VaR in Wikipedia. I don't really understand how the 1% VaR is being defined here. Firstly, shouldn't it be 1% Var is 100 since its the amount her looses? And ...
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73 views

Monte Carlo simulation based VaR: daily vs annual parameters

I am given the initial price, annualized return, and volatility of a security. I am trying to calculate annualized VaR using Monte Carlo simulation approach. To do this I will use the following ...
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2answers
142 views

The BISAM fat-tailed volatility model vs EWMA volatility model

Came across the following marketing material where the company called BISAM (FactSet) aka FinAnalytica (?) has developed following fat-tailed volatility model: $$ r_{t} = \mu + \epsilon_{t} $$ $$ \...
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1answer
388 views

Difference between Delta-Gamma and Delta-normal method for VaR

I was reading the differences between Delta-Gamma and Delta-normal method for VaR. One of the difference I found is mentioned below, but I can't understand it's importance. Can anybody please explain ...
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1answer
113 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 ...
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2answers
89 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 $w$:...
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0answers
41 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. ...
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1answer
104 views

Modelling operational risk for Basel pillar 2 (internal model for OpRisk VaR)

I am somewhat familiar with OpRisk for pillar 1. As far as I know OpRisk for pillar 1 will be replaced by standard approaches soon. So what is left is proper modelling in pillar 2. What are best ...
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1answer
557 views

EWMA VaR, code from Quant Risk

I am currently attempting to improve my python and understanding of VaR. I have been using the website Quant Risk: http://www.quantatrisk.com/2015/12/02/student-t-distributed-linear-value-at-risk/. ...
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78 views

Moving window forecasting in Eviews

I have estimated a VAR model with three variables: rate of prices inflation, rate of unemployment and Federal Funds rate (quaterly data, 1960-2000) . I want to do pseudo out-of-sample forecasts (...
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66 views

Calculating the 6-month VaR and expected shortfall from the 3-month values

I have this problem that I'm not really sure how to crack. Recall that the log return $X_t$ of a portfolio at time t is defined as $$X_t = log(V_t) - log(V_0)$$ Where V denotes the value of the ...
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1answer
180 views

PRIIP Category 3 Curves

Good evening, I've tried searching similar posts, but most are unanswered or in a more advanced step than what I'm trying to achieve. I've managed to do the boostrap method for spot prices ...
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2answers
552 views

Value at Risk - Long/Short position

I have a simple question on the VaR for a portfolio that consists of a long and short position. Say I have a portfolio consisting of the following positions: long 1000 shares of stock X short 1000 ...
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99 views

Parametric VaR of a portfolio of a stock and an option on that stock

I understand how to calculate the parametric VaR of a stock and an option separately. But I don't understand how one can calculate the VaR of a portfolio of a stock and an option on that stock using ...
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37 views

VaR of future foreign currency income stream

Assume I have a series of future incomes in a single foreign currency. How do I calculate the total VaR for this forex risk using the volatility method? My first thought was that I could simply add ...
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0answers
18 views

Adding Correlation do Parametric VaR

I have a quite simple spreadsheet where I do parametric VaR by doing the following: Pt+1 = P + (P x Volatility x norm.inv(alfa;0;1)) For this step I am not worried about assuming normality of ...
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0answers
255 views

Value at risk - correct way to calculate the PnL for backtesting

I have a single security in amount $X_t$, for instance 100 shares of some security, where t denotes the day. The returns are calculated $r_t = ln(P_t / P_{t-1})$, where P denotes the price of the ...
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1answer
360 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{...
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59 views

How to derive the limit of ratio between VaR and CVaR?

I know if $X \sim N(\mu,\sigma^2)$, then $VaR_{\alpha}(X) =\mu + \sigma\Phi^{-1}(\alpha)$ and $CVaR_{\alpha}(X) = \mu + \sigma \frac{\phi(\Phi^{-1}(\alpha))}{1-\alpha}$ But how to evaluate $\lim_{\...
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1answer
106 views

How to regard foreign currency forward as foreign and domestic bonds on VaR

In John Hull's book Options, Futures and Other Derivatives 9th page 507 We want to calculate the VaR of a ...
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1answer
74 views

Covariance Interest Rate Risk Time Series

Apologies in advance if this question has been asked already. I am estimating basis risk for different term points in the curve. Imagine i have three time series (1-month, 3-month, 1-year). I ...
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1answer
68 views

VaR estimation when returns are not independent, e.g. ARCH

Time series of returns, $r_t$, in finance are often modeled with some type of conditional heteroskedasticity model, e.g. ARCH(1): $$r_t = \sigma_t z_t$$ $$\sigma_t^2 = a_0 +a_1 r_{t-1}^2$$ where, ...
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1answer
170 views

expected shortfall as unconditional expectation

Acerbi has several backtests for expected shortfall. The second backtest is based on this equality Does anybody know how to derive this equality? Can anybody explain, why it makes sense, especially ...
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1answer
118 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 ...
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1answer
252 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 ...
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1answer
86 views

How to forecast Value-at-Risk in R with different assumptions?

I'm calculating 1-day parametric VaR estimates under the assumption that the returns are distributed as a generalized error distribution. I have the historical observations of the returns, obtained ...
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1answer
684 views

Risk neutrality correction for Monte Carlo Bootstrapping according to PRIIP regulation for products of category III

The PRIIP (packaged products) regulation prescribes Monte Carlo bootstrapping simulation for calculation of VaR for products of category III (non-linearly leveraged products). The idea is based on ...
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1answer
384 views

Backtesting Value at Risk. With kupiec test

I have a certain problem with backtesting calculated earlier Value at Risk. I've got calculated daily VaR with historical simulation method for stocks. I've used two values of alpha 0.05 and 0.1. Now,...
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1answer
477 views

Expected Shortfall Basel III style: what is the idea?

I would like to do a qualitative question about the Expected shortfall in the Basel 3 document. First of all let me introduce few definitions. Suppose to have a portfolio $P$ depending on a family ...
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1answer
202 views

Difference between the Basel IRB and the Vasicek formula

The well known Basel IRB formula is as follows: $${\displaystyle K=LGD*\left[N\left({\sqrt {\frac {1}{1-R}}}*G(PD)+{\sqrt {\frac {R}{1-R}}}*G(0.999)\right)-PD\right]}$$ where the term below is the ...
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41 views

Value at Risk relative changes

I have this portfolio: Long position : 3 milions € in USD , 7 milions € in AUD Short position: 10 milion € in SEK Risk factors are foreign exchange rates (returns). I have problem with relative ...
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3answers
530 views

Can a VaR equivalent Volatility (VEV) be negative?

As from title, can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative?
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2answers
647 views

non-subadditivity of VaR

I have been reading up on VaR and get very confused by the subadditivity concept. On wikipedia, it says "VaR is not subadditive: VaR of a combined portfolio can be larger than the sum of the VaRs ...
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2answers
342 views

It is possible to carry out the Component VaR decomposition through non parametric methodologies?

I would like to know if it is possible to break down the VaR risk (using historical and Monte Carlo methodology) among the portfolio assets just like the Component VaR concept in the parametric ...
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156 views

Traffic Light Approach

I recently came across this term "Traffic Light Approach" in the parlance of Back testing and Model Validation. I don't understand it very clearly. I googled a bit, dint find anything very ...
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2answers
307 views

Fixed Income VaR: Yield Vol vs Cash Flow Mapping

I have come across two ways of measuring VaR for Fixed Income instruments thus far: Express the volatility in of basis points and the position in terms of sensitivity to a 1 basis point movement in ...
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1answer
119 views

Implied volatility in parametric VaR

I'm calculating 1-day parametric VaR estimates for a stock index under the simple assumption that the returns are normally distributed. My question is, what is your opinion of using a volatility index ...