# Talk:Value at risk

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## Untitled

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

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

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 85.0.247.58 (talk) 11:14, 2 February 2009 (UTC)

## Historical Sim

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 86.154.88.140 (talk) 22:12, 26 February 2008 (UTC)

## Four Parameters?

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)

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)

The normal distribution should be opposed in all its forms! —Preceding unsigned comment added by 81.149.250.228 (talk) 17:12, 22 October 2007 (UTC)

While I understand the point made repeatedly by 81.149.250.228 (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

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
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

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 210.55.180.44 (talk) 02:11, 12 December 2008 (UTC)

## Actuarial calculation of probability of ruin

The relationship between the calculation of the probability of ruin and VaR should be added to the article. —Preceding unsigned comment added by 69.28.232.106 (talk) 18:47, 13 November 2009 (UTC)

## Main use

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?

--90.227.35.146 (talk) 19:52, 3 April 2010 (UTC)

## Clarity on VaR and Time Duration

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.

## Percentile

What is the difference between VaR and percentiles? 184.95.187.124 (talk) 16:22, 21 November 2012 (UTC)

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? 85.40.209.178 (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"

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

"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.