Love the typo... :-)

Nocera is on target with the criticisms of VaR, although not complete. There are both practical and epistemological problems with VaR.

First is the presumption of a normal distribution, which is likely to be inaccurate. Any skew or kurtosis makes VaR extremely suspect.

Second is the reliance on historical data, even comprehensive data, in terms of defining the distribution, simply because it doesn't include things that COULD happen, but simply haven't yet. This becomes more a problem of human imagination than of math. Consider this: you could buy waterfront real estate in Florida, and consider yourself prudent to buy hurricane insurance etc. But what if a hurricane(s) thoroughly total Florida and the entire Eastern Seaboard. Then you have a small but potential risk of the insurance company being insolvent. But that is rarely considered. And that leads to the third risk.

Third, within that 1% threshold there is a lot of bad stuff, much of which is existentially threatening in nature. It's one thing to say that you have a 1% chance of losing $50 million in one day. But its another to say that you have a 0.5% chance of losing $5 billion. The problem is that the risk there, but if you stop at 1%, then you don't know where your real "risk" is. As with the previous example, there may be a 1% risk of your house being totaled, but where is the risk of the whole insurance framework collapsing?

And fourth, as an adjunct to the second, the past may not be prologue. Not only can things happen which have never happened before, but the fact that the rules of the game change introduce a whole new set of probabilities to deal with. When people only had rifles to play with, even the presence of a million rifles represented a 0% risk of ending the world. However, a few hundred ICBMs raise that risk considerably, making past probabilities irrelevant and dangerous. Put another way, every time you introduce a new financial instrument into the system, you have no idea how its going to interact with the existing environment, especially under stress situation, correlations very much tend to go to 1.

So essentially, the problem is that we can't know what we don't know. So not only is VaR weak, but we don't even have the first clue as to what might be an alternative. One idea might be to avoid existential risk completely, but that might prevent a lot of economic activity from taking place. And not everybody can buy insurance or else those who are selling it will be crushed in the event something actually happens. Ultimately, it will require that we show more imagination as to what CAN happen in a bad world, not assume that we can diversify risk away, and realize that much of the game is living to play again tomorrow.

Juan del Llano: thanks, fixt. It took me forever to spot it.

(In the first line, I wrote 'bogs'.)

Anytime I see an economics article, I tend to head to Big Picture, Economist's View, Calculated Risk, Naked Capitalism, and Paul Krugman's blog for more expert commentary.

All that said, I really want to see a nice virtual wrestling match between Yves and Paul regarding Obama's stimulus plan that Paul condones with the stated fear that the stimulus will be insufficient and Yves who has tended to be more cautious if not outright against it.

I don't recall seeing probability distributions referred to as "abnormal" before. That was amusing.

I'd tend to use non-normal in my papers.

I think that the critiques of the risk modeling methodology are very general ones, applicable to almost any effort to apply probability and statistics to a real problem for which a lot of empirical data is available that calls out for quantitative approaches.

I have looked at the RiskMetric's 1996 paper, and the models appear to be quite a reasonable and informed. Just as the linear models for stress calculations for the design of bridges and skyscrapers and airplanes and spaceships do not apply when things break, the RiskMetric's models were quite deficient in face of the financial industry meltdown. It's not the fault of the models or even the modelers but of the users of the model who were ignorant of the models' limitations.

like a drunk looking for the keys he dropped when he got out of his car under the light across the street because that's the only place where he can see what's on the ground.

But the Law of the Lamppost is often a useful(sometimes, the only) way forward.

From a comment over at Keven Drum's new house:

==========
As an example ask a financial wizard to compute the risk of failure of a triple A rated bond. They can give you an answer to so many decimal places. Now, ask what is the chance that BB bonds are being rated AAA. The answer is that their risk model does not include that possibility, they answered the question with the assumption that triple A bonds are rated correctly. Now construct a complex financial model with thousands of such assumptions, the 99% answer is nonsense.

Posted by: Maineiac on 01/04/09 at 5:20 PM
===========

That hits a key point IMHO.

Cranky

“”This becomes more a problem of human imagination than of math.””

My take on derivatives has turned into an intuitive approach to “Derivatives are an always risk management system”.

Funny, but as one reads about derivatives the so called opportunities and risk involved from the operations of derivative in this white collar environment reaches out to an inevitable chaos, uncertainty, unknown added with rules of imagination.

Seems after one runs out of cash it leaves a money manager with no recourse but to deal in derivatives. So we have probable Ponzi trading without money till contracts are cashed in.
What was really funny to me was an article with the term “essentials” of the derivative. This is the real free market, but here, new types of bandits operate.

Check out what I paraphrase below from one of the descriptions of the derivative market, and it’s been around apparently for decades. There are a ton of descriptions and that’s the problems “There are no rules”.

“The nature of derivatives essentially means that the opportunities for trading this type of investment are limited only by the imagination. The other side of this is that someone interested in entering the derivatives trading market needs to either have a trusted financial representative, or learn as much about the business as possible”.

Which, for me, is way necessary considering the best imagination wins.

“NATURE OF DERIVATIVES IS BY IMAGINATION” yikes…what if your imagination is completely wrong. Like wrong way Bush and Company. Does that mean you can run to the Federal Reserve board of Andrea Mitchell of MSNBC, wife of former federal reserve board chairman Allen Greenspan to find out how much time will it take to get that free money tax payer loan that guarantees profit before Obama get into Office? The corruption connection at MSNBC is guaranteed.

So we can not blame it on Clinton, maybe blame it on Reagan and his partner Bush One, ha, ha…what the Republican Party always claimed at the time; the best thing to do was let the free market do it, remember Newt Gingrich always “whaling” about the free market .

Here, likely the Bush bots don’t want to be blamed for the economic aids disease that kills a five hundred and ninety six trillion dollar failing free market that needs the treasury printing presses running max to print up your tax dollars at a rate that can exhaust our paper and ink let alone have any asset value. Sheesh.

Its no wonder the big banks don’t want anyone to know where the bailout money goes. My personal opinion is that real huge amount of tax payer money is buried in national security secrets too. For reasons Bush and Company didn’t want America to know the horror that was looming for years Bush kept trillions of dollars in transactions secret.

Bush’s legacy; America’s culture of corruption in crime beyond comprehension.

> George P:
> And fourth, as an adjunct to the second, the
> past may not be prologue. Not only can things
> happen which have never happened before, but the
> fact that the rules of the game change introduce
> a whole new set of probabilities to deal with.

and

> gregor:
> the RiskMetric's models were quite deficient in
> face of the financial industry meltdown. It's
> not the fault of the models or even the
> modelers but of the users of the model who were
> ignorant of the models' limitations.

Yeah, except that these financial meltdowns are not exactly rare or unknown events, nor is the expansion of the bezzle until the principals of the financial world are raking off huge sums: these things have been occurring with a period of about 20 years since large-scale finance was invented in the 1500s (and who knows - maybe before that too) and since 1988 have been happening regularly every 7 years. That isn't exactly an unquantifiable black swan of "risk".

Cranky

This is why 'in god we trust' is found on our money.

As Bernard Gilroy pointed out, what's the alternative to VaR? Its imperfections, I think, are overrated.

The purpose of capital regulation (or capital) is not to protect banks from all states of the world. Capital regulation exists to draw a line. Within the states of the world contemplated by capital regulation, banks are supposed to protect themselves. However, when the system is slapped by the fat tail, the regulator is supposed to step in. Capital regulation is supposed to make regulatory interventions rare, but is not supposed to provide a 100% safety blanket.

The imperfections of VaR are therefore fairly unimportant. The important issues: was enough capital required? Why did everybody fail to see why a real estate crash (which was anticipated) would produce such a meltdown?

The law of the lamp post (sometimes it's the only light you've got) fails when there are incentives to toss things away from the light. This was part of the Nocera article -- if the rules explicitly ignore the 1%, and reward the 99%, and you can make the 99% look better by worsening the 1% -- well heck, we can probably devise a financial instrument that does that. And what results, is a distinctly non-normal distribution of risk.

Saying that the law of the lamp post is the only thing you've got goes under the heading "necessity, the tyrant's plea".

The rule in pretty much the rest of the engineering field is: if you don't have the tools to analyze some new method, then don't use that method, or at most use it with incredible circumspection. Financial engineering, derived as it is from economics (linear utility functions measured in cash, perfect information, and so many other assumptions as to be effectively uncountable) seems to be about assuming that the world will magically conform to your simplest models, just as long as you can make lots of money for a little while.

Mathematics never lies, but liars can do mathematics. Therefore, the failure has been on the human side- The computer is merely a TOOL. As they say "Garbage in- Garbage out"

There's only one major problem with this post: saying that there are two "different fundamental problems" with VaR.

Saying that you assume that reality is like a fair coin toss, with equal probability of two possibilities, MEANS (=is mathematically equivalent to) that you can expect a normally distributed probability of outcomes.

Hilz, I love your stuff, but you are missing something in the math. If I have a coin and toss it 100 times, and record the number of heads, it'll be between 0 and 100 - probably close to 50. If I repeat the exercise, and graph all the results, over time it will be normally ("bell-shaped") distributed, centered on the 50. The two criticisms are the same criticism, it appears, from your description.