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May 18, 2007

Defending an argument against VaR

A recent article published on RiskCentre news from the author IRA staff on the subject 'Will Basel II finally discredit VaR' left me shocked and raised an eyebrow, actually both of them shot up. This journal critiques some of the assertions that were made against a backdrop of logical thought but before we begin I have to state one theme left me slightly disappointed. When someone slings hard unjustified criticism against a maxim but does not offer an alternative we are left with little option but to diffuse some of the affirmations into the pool of white-noise. All that said, being a dedicated risk professional I feel it my duty to at least point out another light on the hill in the relative risk world of darkness.

This is where it started:

[AUTHOR IRA STAFF] <<< Where we asserted that the use of risk pricing tools such as Value at Risk or 'VAR' models and other types of statistical routines arguably amplified the effect of excess liquidity, boosting the throughput of the Wall Street vastly expanding the pool of risk for end-users.>>>>

Firstly before we refute this, what is VaR?

Value at Risk or VaR is a measure of potential loss from an unlikely adverse event in a normal everyday market environment. It is an expensive measure of risk because it focuses on the worst case event (the tail of the loss curve) and thus in our simple definition alone we would realize that the use of VaR is likely to reduce liquidity or funds available for investment because a larger holding of capital for potential loss would be required by the institution when the institution focuses at the end of the curve rather than the body or mean.

After some debate the article then accepted this point and followed on with ...

[AUTHOR IRA STAFF] <<< To review, VAR models summarize the expected maximum loss (or worst loss) over a target horizon within a given confidence interval. To us, this is an elegant way of saying "I don't know. >>>

Lets be totally real here, a spiritually centred person is aware of this and so is the wise investor. We simply don't know the future and this conundrum has been plaguing man since he realised that some inkling into what might happen can be derived by speculating on outcomes from past events with the same properties. Surely this insight is far better than no perception at all however the argument is actually more profound than this. Assume for example we did know what is going to happen without question of doubt and there was no such thing as chance, then one could argue does opportunity exist at all? To engage in opportunity is to invest a resource into an entity which has potential to move past its current position to a higher one and the steeper the potential the higher the return. Now remove that tensile gap and the price will flatten for everything that is instantly available without limit has little value be it important or not. VaR is the worst case scenario of this tensile gap so it makes a conservative estimate on what could go wrong and that surely has to be the most sane approach to any investment strategy. VaR departs us from our own myopic delusional sentiment and brings all estimates to a single view of exposure.

Looking at the next argument from the article

[AUTHOR IRA STAFF] <<< The trouble with VAR models is that the methodology says nothing about specific risks regarding specific transactions, yet provides risk practitioners with the false impression that the particular risk has been measured >>>

This is not true, the technique for deriving VaR is through the use of variance/covariance, Monte Carlo or historical simulation and it involves using historical data which in our above example is the set of circumstances on a current investment position and the potential for these prices to move away from what we believe or want. These inputs are often combined in different ways depending on the method so that an estimate of a particular percentile of the loss distribution, typically the 99th percentile of loss is created. Now after these calculations only the foolish analyst would throw away his data, equations, documented techniques and workings. What is false about the risk measure is that the 99th percentile of loss is quite improbable and sanely conservative but still VaR should not be expressed alone, it should be justified like any estimate and back tested for accuracy.

Then like many authors with an agenda they made a set of convoluted linguistic twists so that the reader would land at a point where the contraction and change in article direction would be lost. The sad result was the following statement:

[AUTHOR IRA STAFF] <<< Simply stated, if the overall risk calculated in the VAR model appears to be low, then additional risk may be taken >>>

Hang on its the worst case loss, its the 99.9th percentile position, how can that be low however the author did introduce an interesting concept. To be concise the insertion of the word 'additional' is impacting in a risk measure. 'Additional' lends us to believe that each marginal choice in a network of risk based decisions actually has the propensity to conceal the real potential loss from the starting position of an investment. That is, it is a human tendency of error to forget the tally of wins and losses when a goal seems ever so close especially when we just read our risk profile over a short stint in time.

The article did stipulate a real fact in respect to Pillar III, thank the world of regulation for that.

[AUTHOR IRA STAFF] <<< Pillar III of Basel II, the requirement for market discipline, where banks will be compelled to publicly disclose and benchmark the efficacy of VAR models against their actual results, including public 'mark-to-actuals' results for VAR, Defaults, Loss Given Default and Exposure at Default, etc. Will Pillar III ultimately be the undoing of VAR? >>>

What worries me however is that the US regulators are yet to fully adopt an approach for Basel II, landing between the first version of the accord and some advanced standard approach. Really the advantages of Pillar II and III are probably a long way off for US bankers even though Pillar II and III could seriously assist in publishing the true volatility US institutions are exposing themselves to.

Now to finish up the author stated the following:

[AUTHOR IRA STAFF] <<< Just as global regulators are enshrining VAR as the centerpiece of the Basel II regime, markets may demonstrate that this method of measuring risk is entirely useless >>>

VaR is not new to the 'global' banking community and just because regulation is adopting what most investment institutions are using will not demonstrate that this measure of is risk is entirely useless. My dear people, financial institutions have been using VaR to explain the Greek measures of market risk for sometime. VaR simplifies the varied measures of this exposure type so that expressions of threat can occur in a transparent manner. In my opinion, this is overstated and a touch sad. Its authoritarian sounding no doubt about that and it may just fool some, confuse the masses perhaps, but without an alternative and with assumptions missing I have to rebuke that VaR is entirely useless.

Posted by CausalEvents at May 18, 2007 11:28 PM

Comments

Dear Mr. Davies,

it seems to me that there are two weak spots in your defense of VaR that might be quite common in the Risk community. I don't think that VaR is entirely useless because of these, but I would like to address them.

1: "Value at Risk or VaR is a measure of potential loss from an unlikely adverse event in a normal everyday market environment." As far as I am aware of, VaR does not address unlikely adverse events, but the normal losses in normal every day market environments.

2 "VaR is the worst case scenario" Here you address the IRA quote regarding "VAR models summarize the expected maximum loss" I personnally like Jim Christians remark: "In reality, VAR only tells you how small a loss can be". A 99% VaR tells you that approximately 3 times a year your los will be bigger. Not how much bigger.

In my understanding VaR does definitely not address extreme events, and other measurements do much better in the fat tail areas.

Posted by: Johan Steunenberg at May 24, 2007 03:36 AM

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