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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understanding Value-at-Risk correclty

The are several types how to calculate the VaR. I am focussing on the method of calculation the VaR in percentage. $VaR=I*z*std*\sqrt{t}$ This gives the VaR in €. I have the z-value, the daily ...
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32 views

Approximation of portfolio VaR (after mapping) when Delta and Gamma both equal zero

As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form : $$V(S) = S^3 - 30S^2 + 300S + 150$$ with current value $S = 10$. $S$...
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How to add Risks-Not-In-VaR (RNIV) to VaR under Basel III

I am trying to generate/prove the magnitude of the over-conservativeness of the regulatory VaR (internal models) under Basel III against what a more accurate VaR would be. However, I can't seem to ...
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42 views

How can I manually calculate the VAR of a call and put portfolio?

How would I solve the following question? Im unsure how to estimate the stock price using MCS.
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30 views

A quick and dirty loss distribution and Credit VaR

I need to create a loss distribution for a credit portfolio as the first steps to estimate the portfolio Credit VaR. I have historical monthly account snapshots (payment history) of all accounts ...
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77 views

1 day VaR vs 10 day VaR

Even while using historical simulation VaR, 1 day VaR is converted into 10 day VaR by multiplying 1 day VaR by Sqrt(10) for regulatory reporting purposes. What are the underlying assumptions for ...
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1answer
102 views

VaR equivalent volatility meaning

I have a hard time with interpreting VeV. I mean - I see its just standard deviation derived from Cornish-Fischer VaR, but I don't really know how to interpret it. The formula for VeV is: ...
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Compute the VaR from NPV (Net present value)? [closed]

A client is evaluating an investment in Indochina requiring an initial expenditure (period 0) of 10,000, and which then in periods 1 and 2 gives a benefit V1 and V2. Assume that the discount rate to ...
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Do correlated assets affect the price of a portfolio of derivatives?

I need to compute the value at risk of a given portfolio as an exercise for a class at university but I have trouble understanding how correlated assets affect the price of the portfolio. Could you ...
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1answer
44 views

GJR-GARCH model using garchFit function

I'm trying to use the garchFit function described here in order to define a GJR-GARCH model to estimate volatility and then forecast VaR. I tried using ...
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68 views

Monte Carlo VaR w/ Multivariate Normal vs. Parametric

In Aladdin's Monte Carlo VaR, the default setting for the joint distribution of factor returns is multivariate normal. Given that normal distributions do not capture the fat tails seen in empirical ...
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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 ...
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117 views

What should the half-life be in EWMA when calculating VaR from EWMA?

If we want to calculate an $x$-day VaR ($x$ is some time period in days) from an Exponentially Weighted Moving Average (EWMA) of vector of returns, what should the half-life in the decay factor in ...
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99 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 \...
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71 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 ...
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RiskMetrics VAR calculations and conditional distribution of sum of log returns

According to Tsay's book in Chapter 7, for the Risk Metrics model: A nice property of such a special random-walk IGARCH model is that the conditional distribution of a multiperiod return is ...
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64 views

Value at Risk Calculation

In historical simulation VaR, if we have stale data for some of our risk factors, which means daily returns on a particular risk factor is 0 on multiple occasions. Is there any way to solve this other ...
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50 views

GARCH(1,1) and Value at Risk: Rolling window or non-overlapping samples

Currently studying on financial risk management. I want to test different methods of VaR estimation. I want to model volatility using a GARCH(1,1) model. My question is what should the size of the ...
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1answer
68 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 ...
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1answer
76 views

How long is considered `long-term'?

For a project I am doing I need to simulate the balance sheet of a pension fund. In order to do so I also need to simulate euro inflation. Since my inflation data is non-stationary, I model it using ...
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68 views

Extreme Value Theory for Value-at-Risk: Advantage versus historical simulation?

I started researching this topic and it is well covered in the literature. My understanding is that it uses a historical time series of returns of a given set of stocks and represent such ...
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61 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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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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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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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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152 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
65 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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89 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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91 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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49 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
82 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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164 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
156 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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2k 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
123 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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96 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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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
118 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
921 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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1answer
231 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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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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154 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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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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1answer
697 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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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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121 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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87 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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77 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
181 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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159 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 ...