Talk:Value at risk

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Is the VCV matrix the same as the covariance matrix used in the VCV model? This point needs to be clarified - Gauge 22:52, 20 Aug 2004 (UTC)

Signs Error[edit]

It seems to me the formula in calculation part (2) subsection (iii) should be: VaR = V_p * (mu - sigma*z). Else a portfolio with positive mean is penalized. You can still throw a minus sign in front if you prefer to think of VaR in terms of loss rather than dollars at risk.

Mistake in Graph[edit]

There is a mistake in the graph!! The VaR is 1.07 Mio EUR, since this is the difference between the current value and the minimum value with a probability of 95%! —Preceding unsigned comment added by (talk) 11:14, 2 February 2009 (UTC)

Historical Sim[edit]

just me or does the historical sim section say assume 2.33 Sig for a 99% distribution --assuming gaussian surely? —Preceding unsigned comment added by (talk) 22:12, 26 February 2008 (UTC)

Four Parameters?[edit]

The article says VaR has four parameters but then lists only three, and goes on to talk about two? Is there a missing parameter or should this just say three/two parameters. Hull says two parameters (currency is ignored since you can just change that at spot).

VaR(A+B) > VaR(A)+VaR(B)[edit]

It is stated in the article that it is impossible to construct two portfolios so that VaR(A+B) > VaR(A)+VaR(B). I have an article of Jón Daníelson [Journal of Banking & Finance, 2002, 26(7), 1273-1296] stating that there are Portfolios which have this property. Has somebody some knowledge? (I am no finance expert myself, so please forgive if it is a stupid question).

Rpkrawczyk 15:13, 19 January 2007 (UTC)

Sure. Take two bonds which are independent and default by some horizon with probability 0.03. Now make three portfolios; portfolio A invests $1 in bond #1, portfolio B invests $1 in bond #1, portfolio C invests $1 in bond #1 and $1 in bond #2. 95% VaR(A) and 95% VaR(B) both equal $0 -- because 95% of the time the bonds lose no money. 95% VaR(C) = 95% VaR(A+B) = $1 > 95% VaR(A) + 95% VaR(B). (P(no defaults = 0.9409, P(1 default) = 0.0582, P(2 defaults) = 0.0009)
What I'm wondering is why reference the paper as "Artzner et al" when many people coming here won't know the full authorship; and, the paper is high-profile enough to warrant mentioning all authors (Artzner, Delbaen, Eber, and Heath)--Cumulant (talk) 13:59, 20 January 2008 (UTC)

This page is a disgrace[edit]

The normal distribution should be opposed in all its forms! —Preceding unsigned comment added by (talk) 17:12, 22 October 2007 (UTC)

While I understand the point made repeatedly by (I have read Mandelbrot's book about markets too), it seems his additions are non-encyclopedic in the nature. If only someone could elaborate on VaR criticism even more and in the encyclopedic manner... for the time being I dare to revert page once again. Ruziklan 08:14, 23 October 2007 (UTC)
If you have read the book, you should write on the Normal Distribution article. Refer to the talk section titled Mandelbrot. Nshuks7 (talk) 10:31, 7 December 2007 (UTC)
Taleb's article in LSE ([1]) states two problems which can be included in this section:
1. Measuring probabilities of rare events requires study of vast amounts of data. For example, the probability of an event that occurs once a year can be studied by taking 4-5 years of data. But high risk-low probability events like natural calamities, epidemics and economic disasters (like the Crash of 1929) are once a century events which require at least 2-3 centuries of data for validating hypothesis. Since such data does not exist in the first place, it is argued, estimating risk probabilities is not possible.
2. In the derivation of VaR normal distributions are assumed wherever the frequency of events is uncertain. (needs improvement)Nshuks7 (talk) 17:33, 7 December 2007 (UTC)

Extensive rewrite[edit]

The main things I did in this rewrite were to:

  1. Add sources in a consistent format, and link sources to specific material in the article
  2. Distinguish between risk management and risk measurement
  3. Distinguish between risk measure and risk metric
  4. Add a history section
  5. Bring in both some older and newer sources to give a broader picture of the concept

AaCBrown (talk) 19:07, 19 October 2008 (UTC)

Bank Robbery Example[edit]

I'm not really a fan of the bank robbery example. It remains equally likely that a given branch will be robbed, the probability of robbery of an individual branch does not change as the network size changes. The risk to the bank as a proportion of it's size won't change. More relevant to this point is the correlation in risks, if you have 2 branches right next to each other if one gets robbed it is likely that the branch next to it will be robbed, enlarging the VaR above the sum of the VaRs.

The switching of spending from insurance to security is more reflective that as scale increases some operations become more economically efficient and as such to obtain an optimial portfolio, that minimises cost for a given level of risk, a rebalancing of options will occur. If you have 100 branches it might be cheaper to have a security team and insurance (on a per branch basis) then the same option with just one branch. Am I right? Or just a giant noob? —Preceding unsigned comment added by (talk) 02:11, 12 December 2008 (UTC)

Actuarial calculation of probability of ruin[edit]

The relationship between the calculation of the probability of ruin and VaR should be added to the article. —Preceding unsigned comment added by (talk) 18:47, 13 November 2009 (UTC)

Main use[edit]

The current version of the article states that VaR has five main uses in finance: risk management, risk measurement, financial control, financial reporting and computing regulatory capital. I'm not sure about that. In my opinion VaR has only one use; and it is risk measurement. Risk measurement is, in turn, used for several purposes; such as risk managment, financial control, financial reporting and regulatory capital. Is there a need to make a distinction between the use of VaR on the one hand and the use of risk measurement on the other?

-- (talk) 19:52, 3 April 2010 (UTC)

Clarity on VaR and Time Duration[edit]

Suppose you say that the 5% one-month VaR is $1 million. There seems to be an ambiguity out there in papers that describe VaR about how this is interpreted, in which I've seen two implied definitions, namely:

  1. There is a 5% probability that the portfolio will drop in value by $1 million from today's value at some point during the next one-month duration.
  2. There is a 5% probability that the value of the portfolio one month from today will be less than $1 million.

If anything, this article seemed to imply the second definition, although I felt it did not clarify this precisely. The only mathematical statement was simply the definition of a fractile, with no mention of time. In some other papers I've been exposed to, it seemed like VaR was defined the first way, and it was that sense of the maximal loss over the duration that seemed to distinguish it from the older, simpler, and more familiar concept of a fractile or percentile.

I came to this article hoping that this distinction would be clarified, but felt that it was not. So at this moment, I'm left wondering about which is the "correct" definition of VaR.

The precise definition could be clarified if it the time were made explicit. For a T-duration VaR at 1-\alpha level, let L^t denote the loss at time t in the future. Then the two possibilities would be:

  1. \text{VaR}_{\alpha,T}=\inf\{l\in \real: P(\text{max}\{L_t:0 \leq t \leq T\}>l)\leq 1-\alpha\}
  2. \text{VaR}_{\alpha,T}=\inf\{l\in \real: P(L_T>l))\leq 1-\alpha\} —Preceding unsigned comment added by Ldc (talkcontribs) 16:44, 19 May 2010 (UTC)

Inconsistent example image at beginning[edit]

The article starts out by saying that a VaR of $1 million means that a loss of $1 or more will occur 1 day in 20. It then has an image showing the 10% fractile of a normal distribution, where the x-axis is labelled "Portfoliowert" -- which is German for "portfolio value". The image indicates that the VaR is 0.82 MioEuro. But that value would be a profit, not a loss. It appears that the sign is inconsistent here. In the image, the values to the left of zero would be losses, so if we said the VaR is 0.82, it would mean we'd be indicating -0.82 on the x-axis of the image, not +0.82 where the fractile line is drawn.

This is further emphasized in the last paragraph of the Details section:

Although it virtually always represents a loss, VaR is conventionally reported as a positive number."

Given that, the VaR in the image should be labelled as "VaR = -0.82 Mio EUR". It would be even better if the graph were re-done with the bell curve to the left of the origin (reflected around the origin from what is there now) and with the axis labelled "portfolio loss" rather than "portfolio value" (portfoliowert). —Preceding unsigned comment added by Ldc (talkcontribs) 03:12, 20 May 2010 (UTC)

A few answers[edit]

I did the last major rewrite of this article. Since then, changes "larger" to "smaller" in: "A common complaint among academics is that VaR is [not] subadditive.[4] That means the VaR of a combined portfolio can be [larger/smaller] than the sum of the VaRs of its components." Later TheEnamem deleted the "not". The original statement is correct. Academics complain that VaR is not subadditive, that is they complain that the VaR of a portfolio can be larger than the sum of the VaRs of its components. In general the risk of a portfolio is less than or equal to the sum of the risks of its components. This is usually true of VaR as well, but need not be. So the first edit is a clear error. The second made the two sentences consistent, so was well-intentioned, but has to be reversed as well. I'll fix that. doesn't like the bank robbery example, but I'm not sure of the objection. The idea is to show that a non-subadditive measure can make sense to a risk manager. It's true that the "risk" of bank robberies in some sense goes down as the institution gets larger, that is the standard deviation of daily robbery losses divided by total bank assets declines. Robberies get more predictable. On the other hand, robberies will increase VaR more in a large institution than a small one. Academics usually object to this as a contradiction. But in terms of how you deal with the risk, it makes sense that a large bank would treat robberies statistically, a medium-sized bank would treat them as exceptional events and a single-branch bank would insure against them. I'll look over the example to see if I can make it clearer. wants to relate VaR to risk of ruin. There is a literature that discusses both concepts, but I don't think there's any simple, clear relation that belongs in this article. thinks there is one use of VaR and four applications. I would agree if there were one way to compute VaR, and then four different types of decisions made from the same number. But I think that's not the case, that there are five uses, each with its own calculation method and goals. I'll see if I can make this more clear.

The time duration is a good point, and one that there is disagreement about. I'll try to come up with a mention for this.

I agree the picture is not a good representation of VaR and is inconsistent with the text. I'm not good with pictures, I hope someone else can fix this.

Okay, I did it myself, but I'm not particularly proud of the result. Someone with some talent could do a better job.AaCBrown (talk) 15:04, 21 June 2010 (UTC)

—Preceding unsigned comment added by AaCBrown (talkcontribs) 15:08, 20 June 2010 (UTC)

Has this article been subverted by a cult?[edit]

This article contains a great deal of editorializing based on non-peer reviewed 'literature'. Preposterous statements such as the following do not belong here, and certainly not in the history section:

"The crash was so unlikely given standard statistical models, that it called the entire basis of quant finance into question" —Preceding unsigned comment added by Peter.cotton benchmark (talkcontribs) 02:09, 8 October 2010 (UTC)

online VaR calculator[edit]

Hi All. During the past few days I have been trying to add an external link to an online tool that calculates Historic VaR for a set of sp500 stock chosen by the user. This link has been removed repeatedly by the moderators. I would like to open a discussion on this topic due to my deep conviction that this is a value added tool to the user community. Here are my main reasoning points: 1) this is a unique online tool lets the users monitor live the var of their portfolio 2) is on topic and provides a live experience for those that have never been confronted with this risk management method. 3) the other existing external link applies the parametric approach to calculate the var, this one uses a historic simulation approach that is potentially more accurate. A previous discussion with Kuru resulted in the understanding that this external link could be maintained. Here is the link — Preceding unsigned comment added by Indoorworkbench (talkcontribs) 07:59, 4 April 2011 (UTC)

Negative VaR[edit]

The explanation of the negative VaR seems inconsistent to me. Shouldn't it read "a one-day 5% VaR of negative $1 million implies the portfolio has a 5% chance of making less than $1 million over the next day" (instead of more)? I.e., referring to the sketch, shouldn't the VaR be usually located to the left of the peak, irrespective of whether it is positive or negative? -- (talk) 14:57, 3 January 2012 (UTC)


What is the difference between VaR and percentiles? (talk) 16:22, 21 November 2012 (UTC)

This article has a hole[edit]

This article seems to do an acceptable job of talking about organizational and surface quantitative details. But the problem is that there seems no discussion or link to one of how the underlying model is constructed. What I would like to know is not only how VaR is phrased, like as a positive or negative number, or the controversy surrounding the use of VaR in financial institutions, but also how the underlying model of probabilities is arrived at from past data. Is VaR just, say, a kind of regression? What is the mathematical technique used? (talk) 00:43, 27 November 2012 (UTC)

VaR is a function, the negative quantile function to be more precise. If you knew the underlying distribution of the returns then it is simply finding the quantile. As for how VaR is used in practice, I can imagine a section on it but even that you would probably find unsatisfying since Wikipedia is not a textbook. The purpose of the page should be on VaR, not on instruction on how to calculate in practice (other than brief overview of methods, mainly done by referencing other pages I think). How do other's feel about a new section for this purpose? Zfeinst (talk) 04:58, 27 November 2012 (UTC)

Title should be "Value at Risk", not "Value at risk"[edit]

As is shown by the article's consistent use of the capital R in "Value at Risk" and "VaR", this is a technical term with established capitalization. That established capitalization should appear in the title as well. I wonder if someone who works on this page could move the article to "Value at Risk" while making the current title a redirect? Duoduoduo (talk) 16:53, 1 July 2013 (UTC)

I do not like these additions[edit]

"It is also possible to define VaR as the risk measure which calculates the maximum loss expected (or worst case scenario) on an investment, over a given time period and given a specified degree of confidence."

The main reason is all VaR writings emphasize that VaR is NOT a worst case scenario. This is a common and major confusion. Beyond that, this is simply a less precise repitition of the definition in the deleted paragraph. What does "maximum loss expected" mean? The "risk measure" can't "calculate" anything.

Also, it's not a minor edit to replace the definition.

"Thus, VaR is a piece of jargon favored in the financial world for a percentile of the predictive probability distribution for the size of a future financial loss. In other words if you have a record of portfolio value over time then the VaR is simply the negative quantile function of those values."

The two parts contradict, the first claims VaR is a percentile of a predictive distribution, the second that it is a historical measurement. Both of these are possible ways to construct a VaR system, but neither are the definition of VaR, which does not assume a probability distribution. VaR is non-parametric and defined only operationally, there is a property that a system must have to be a VaR system. How that system is constructed is unrelated to the definition.

Both additions are unsourced.

I am going to undo these, unless someone objects. AaCBrown (talk) 21:16, 10 October 2013 (UTC)

VaR risk measurement section[edit]

I believe the information in the "VaR risk measurement" section may be inaccurate.

The original text suggests that because Value at Risk is a measurement of loss, and since losses across a business can be aggregated to determine total P&L, VaR is also additive. This is incorrect. Risk exposures in separate divisions may hedge or neutralize each other when considered in aggregate. IE - If Portfolio X is long 50 EUR Puts @ 6/30/14 while Portfolio Y holds the same position short would result in zero exposure, not in the exposure of Portfolio X + Portfolio Y.

The second paragraph touts VaR as a "distritubtion-free metric", meaning it doesn't need a probability distribution to make any statistical assumptions on the behavior of the data. This is only true for non parametric VaR models. Parametric and semi-parametric VaR models, on the other hand do apply distributional assumptions to the data.

I therefore will remove the language, unless anyone objects. Thank you. — Preceding unsigned comment added by InsideNoize333 (talkcontribs) 02:50, 21 June 2014 (UTC)