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I'm tempted to supplement my Lazy Quote Diary: This Should Never Have Happened with a couple of quotations on "Value at Risk" from Taleb's Dynamic Hedging (1997). His basic thrust is that VaR is a rule of thumb used by traders to quickly estimate the proper size of a hedge for a single instrument, and that it should not be taken as a measure of risk for whole portfolios, which is precisely what has happened (Basel II has made VaR the cornerstone of risk management in banking). In fact, there are good mathematical reasons not to use VaR for portfolios.
The Value-at-Risk

Below is a presentation of a risk management method that, like portfolio insurance, can only work if a small number of people are using it. It is a paradox ... that states that it can only work (and succeed) if it is unsuccessful

"Porfolio insurance" was a financial product which caused a liquidity hole in 1987. Essentially, the way this insurance was constructed it caused larger positions to be taken in stocks than would otherwise have been, when  people tried to get out of the positions as prices started going the wrong way it snowballed out of control.
The VaR can present some useful short-term hedging tools for traders... However, it led to seriously disputed applications by risk management firms that led (perhaps innocently) their customers to believe they possessed tools to summarize the overall market risks for a position, a unit, a department, or an entire firm, in one simplified numerical exposure, without standard error.
So VaR was already "seriously disputed" as a risk measure before 1997.
The idea of disclosing the overall exposure as one simple quantity appeals to most corporate board members and regulators, many of whom are uninitiated into the nuances and complexities of financial market risks. They can easily be impressed by the "scientific" tools used.

... Critics of VaR (including the author) argue that simplification could result in such distortions as to nullify the value of the measurement. Furthermore, it can lead to charlatanism. Lulling an innocent investor or business manager into a false sense of securitycould be a serious breach of faith. ...

In brief, it cannot be used to say "Within 99.7% (or within 90% or something of the sort), you are not expected to lose in the next month more than 1 million dollars". The innocent treasurer or company official would believe himself to be listening to a scientific statistic similar to statistics on airplane crashes. It could, however, be used to say: "You are expected to lose no more than 100,000 dollars within the next two hours with a 66% accuracy, provided that you do not try to liquidate your position and the other similar firms do not have the same portfolio."

After discussing various shortcomings of VaR when large deviations are involved, he concludes
The VaR provides an admirable short-term hedging tool but is by no means a risk management device
Under "dangers of generalized use" he discusses how
the fact that such a system became a benchmark would cause a snowball effect.

... In a schematic world of a small numner of homogeneous leveraged players, everyone would end up with close to the same portfolio constitution and weights owing to the diversification scheme (optimal portfolio) ... They would all ivest more lulled with the knowledge of being comfortably diversified asthey were properly taught by the risk management consultant.

...

Assume that the price of A went down. Assume that the volatility of A increased. To maintain a constant VaR ... the operator would have to sell some stocks of B and C. The quantities, though small, would be enough to push prices lower and make operators race each other to the state of near-bankruptcy. ... An interesting parameter in hedges is that they only work when they are not identified as hedges by the multitude. If most other similar institutions needed to act in a similar manner in similar circumstances, there would be a dynamical system traders would need to account for.

And then the punchline
The market will follow the path that will thwart the higher number of possible hedgers.


We have met the enemy, and he is us — Pogo
by Carrie (migeru at eurotrib dot com) on Wed Feb 13th, 2008 at 05:23:18 PM EST
[ Parent ]
So what you're essentially saying (or quoting Taleb as saying) is that the stock market can only be modelled as long as most players on it - as measured by their dollars, not their noses - are ignorant of the models used.

Somehow, this strikes me as a fact that should not be surprising. After all, if the market works, and everyone has access to the same information, future value should already be incorporated into share price - so in order to do better than betting on horses, you need to be better at predicting the future value than the other players.

So, are these people betting on horses, or do they think everyone else are suckers, or have I missed something in my analysis?

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Wed Feb 13th, 2008 at 05:54:04 PM EST
[ Parent ]
<physics>Think of it as a condensed-matter phase transition between a weakly-coupled regime and a strongly-coupled regime (or one with long-range correlations - probably strongly coupled via duality). Linear (mean-field) techniques to describe the environment of a single component of the sytem are appropriate when the back-reaction of a single element on the hole system is negligible. But in the strongly-coupled/long-range-correlated regime different kinds of techniques are needed even to describe the local environment, because of backreaction.</physics>

We have met the enemy, and he is us — Pogo
by Carrie (migeru at eurotrib dot com) on Wed Feb 13th, 2008 at 06:51:33 PM EST
[ Parent ]
I'm sure that description would be very helpful if I'd had condensed-matter physics. Unfortunately, I've dabbled in x-rays and quantum computing more than condensed matter.

What I hear you saying is that they assume that stuff happening on the other side of the market is only weakly correlated with the stuff that happens to their portfolio. And that assumption turned out to be Very Wrong.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Thu Feb 14th, 2008 at 09:07:11 AM EST
[ Parent ]
Checking that there's a small door out of a theatre that allows you to get out at any time won't help you much when fire has started and everybody is trying to get out through that single small door...

Un roi sans divertissement est un homme plein de misères
by linca (antonin POINT lucas AROBASE gmail.com) on Thu Feb 14th, 2008 at 10:39:44 AM EST
[ Parent ]
You watch the show from that doorway so you can make them all pay to get out.

Signed: Bill Gates

by afew (afew(a in a circle)eurotrib_dot_com) on Thu Feb 14th, 2008 at 10:53:39 AM EST
[ Parent ]
After one year of working closely with a large var system and the underlying portfolio, I conclude that it is a rather good risk management tool.

That is, when it is properly implemented (full MC) and with a sensible model. We only got a few backtesting exceptions above the norm (when major US banks had dozens since the beginning of the crisis).

VaR (and CVaR ideally) does tell you that you are at risk, and how much risk, it does not tell you how to cut that risk without materializing the loss if your market isn't deep enough - VaR analyzes market risk, not credit risk or liquidity risk. Confusions on the aim of the indicator are due to over-hyping and marketing by gurus and software vendors.

And lastly, VaR applies to trading portfolios, not to investment portfolios. And all the significant losses in this crisis happened in banking portfolios, except for the Kerviel case. VaR isn't even computed on banking portfolios (buy and hold, whether direct or indirect through SIV, of crappy assets like CDO's and RMBS, which are meant to take direct exposure and are not hedged because they are not supposed to default, hedge not being available on the required notionals anyway, or if "available", it's bogus, see monolines).

Pierre

by Pierre on Thu Feb 14th, 2008 at 01:19:54 PM EST
[ Parent ]
I understand what you're saying and that's the way it's supposed to work in theory, but then how do you explain all these 50-year events and 11- or 23-sigma moves, and so on?

We have met the enemy, and he is us — Pogo
by Carrie (migeru at eurotrib dot com) on Thu Feb 21st, 2008 at 04:25:47 AM EST
[ Parent ]
I don't explain these. The market is not log-normal. It may even follow a diffusion law where no moment exist and sigma is moot or infinite. That does not undermine the VaR concept. It does mean that the common MC VaR computed with a set of normally distributed shocks is an optimistic approximation of the market risk. It does not preclude the use of MC VaR with a set of Levy-distributed or fractal shocks (although practical calibration issues have so far precluded real-life adoption, banks R&D are still working on it, guys next door to me).

It does degrade the accuracy of VaR through prices and/or greeks used in VaR and derived by means of log-normal resolution of stochastic equations, or MC diffusions. For equities, volatility smiles etc are some sort of built-in-pricer fixes, though ugly. Younger derivatives markets (CDS anyone ?) may have a bigger accuracy problem. Although nothing impossible to overcome.

My feeling is, these present short-comings are (quite) well understood in (some) (french) risk management. The US do seem to have a huge problem with it. Presently writing an article on this, but it will be company-copyrighted material ("you address the shortcomings faster if you buy my consulting", no shit).

Pierre

by Pierre on Thu Feb 21st, 2008 at 11:51:51 AM EST
[ Parent ]

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