VaR and the Black Swan
| Sun Jan. 4, 2009 10:05 AM PST
VaR AND THE BLACK SWAN....Joe Nocera has a good piece in the New York Times Magazine today about VaR, the risk model that established a virtual hegemony on Wall Street before the great financial implosion of 2007-08. Nassim Nicholas Taleb, author of The Black Swan, argues that the fundamental problem with VaR lies not in its technical guts, but in the fact that it's specifically designed to exclude potential catastrophes:
In its most common form, [VaR] measures the boundaries of risk in a portfolio over short durations, assuming a "normal" market. For instance, if you have $50 million of weekly VaR, that means that over the course of the next week, there is a 99 percent chance that your portfolio won't lose more than $50 million.
....VaR is often measured daily and rarely extends beyond a few weeks, and because it is a very short-term measure, it assumes that tomorrow will be more or less like today. Even what's called "historical VaR" — a variation of standard VaR that measures potential portfolio risk a year or two out, only uses the previous few years as its benchmark.
....Yet even faulty historical data isn't Taleb's primary concern. What he cares about, with standard VaR, is not the number that falls within the 99 percent probability. He cares about what happens in the other 1 percent, at the extreme edge of the curve....A good example was a credit-default swap, which is essentially insurance that a company won't default. The gains made from selling credit-default swaps are small and steady — and the chance of ever having to pay off that insurance was assumed to be minuscule. It was outside the 99 percent probability, so it didn't show up in the VaR number. People didn't see the size of those hidden positions lurking in that 1 percent that VaR didn't measure.
Taleb has been making this argument for quite a while, and obviously events have proven him prescient. But I've always had a couple of problems with his critique. First, our current economic crisis isn't really a black swan, is it? Things like this have happened fairly regularly during the past century (and before), on the order of once a decade at least, and maybe more often than that. Pretending that this was a wildly improbable event strikes me as nothing more than a sophisticated version of "nobody could have predicted." After all, if the crash of 2008 really was a one-in-a-hundred (or one-in-a-thousand) event, then it really is true that even reasonable people couldn't have been expected to foresee it.
Second, I've never seen Taleb explain what we should do about this. What's his advice? Here's Nocera: "Taleb likes to say that, as a trader, he has made money only three times in his life — in the crash of 1987, during the dot-com bust more than a decade later and now. But all three times he has made a killing." Fine. He's made money three times in the past two decades. But he knows perfectly well that this doesn't work on a broad scale. Ordinary trading desks have to make daily trades based on evaluation of ordinary risks. That's how global finance gets done. So the question is: given the fact that we need ordinary global finance, and not everyone can just sit around waiting to make a killing on black swans, what should all these ordinary trading desks be doing to protect themselves against possible meteor strikes?
Taleb doesn't seem to say (though maybe he has and I just haven't seen it), but this is what I'd like to hear more about, especially since he seems to have a lot of interesting and perceptive ideas about the behavioral basis of finance and financial crashes. In the meantime, Nocera's article is a good read, even if it doesn't really provide any answers.
UPDATE: Yves Smith pans Nocera's article here. I'm a little puzzled by a lot of what she says, since it strikes me that Nocera wrote at length about topics that she says he ignored, and in no way wound up "defending a failed orthodoxy." But maybe I'm missing something.
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Comments
Submitted by Crissa (not verified) on Sun Jan. 4, 2009 10:05 AM PST.
Do these people even understand what 99% per day means?
It means that you roll the dice each and every day you wake up.
Guess what? You'll probably see that 1% before the year is out.
You'll probably see that 1% before the year is out.
Of course this is true. But at the same time if on the other days of the year all your competitors are making money by pretending the 1% will never show up, by the time it does your prudent strategy will have been run out of business.
The basic answer to this is to regulate the hell out of Wall Street, to the point that we don't encourage the cleverest minds to come there and come up with impenetrably complex rationalizations for doing disastrously wrong things.
If a trading desk is making money trading on a daily basis, then some other trading desk (or a trader without a desk) out there is losing money. There is not enough growth in the economy to help every trading desk turn a profit, considering that huge bonuses and salaries and other expenses have to be met before profits are registered.
Taleb isn't in the business of prescribing a risk methodology for every trader out there. No one can come up with such a methodology given the largely zero sum nature of the trading game (particularly so if you consider the huge bonuses/salaries). If someone is making money, someone else is losing money. Taleb is helpful in realizing that RISK is a real beast. I don't think anyone can eliminate risk from their trading/investing. But realizing that risk exists and developing strategies/tactics will help. There are plenty of hedge funds and traders out there who managed to turn in profits in 2008 -- and that is because they paid attention to RISK. Those who rolled the dice made some great short term profits but eventually lost (e.g all the banks that made great profits for several years only to lose all those profits in one year).
Fund managers are paid to understand and manage RISK. They have to figure it out on their own. Don't expect Taleb or anyone else to come tell you the secret formula to avoiding risk. If someone publishes such a formula, why do we need to pay fund managers to manage our money? Besides, if there is such a magic formula, don't expect it to be published. Use your commonsense and pay attention to risk.
Submitted by Petey (not verified) on Sun Jan. 4, 2009 11:02 AM PST.
"So the question is: given the fact that we need ordinary global finance, and not everyone can just sit around waiting to make a killing on black swans, what should all these ordinary trading desks be doing to protect themselves against possible meteor strikes?"
Traders are free to pursue strategies that work or don't work over the long-term. That's capitalism, and long-term losses are the worries of capital. But systemic controls need to be in place to ensure that leverage doesn't spiral out of control.
This is what folks are referring to when they speak of "regulation of the financial markets."
Submitted by Legacy on Sun Jan. 4, 2009 11:10 AM PST.
Petey: I've written at least a dozen posts making exactly that point. But I'm still curious about what Taleb thinks. Perhaps he has some additional ideas.
Submitted by Maynard Handley (not verified) on Sun Jan. 4, 2009 11:10 AM PST.
I would read Taleb's point as social criticism as much as anything else.
Consider the financial system, US style.
We had some organizations (banks, S&Ls and suchlike) that actually performed a socially useful function. Performing this function required that they limit their risk exposure and be content with a slow, steady return. We also had other organizations (investment banks, trading houses, hedge funds and suchlike) that were basically gamblers. They were (a) not providing an especially useful social function and (b) were in the business of imagining they could make money by being smarter or quicker than the other guy [when, of course, they weren't frauds ala Madoff or doing something illegal ala Boesky].
But, of course, this situation was all changed in the recent past. The banks and suchlike decided they also wanted to make the fancy returns of the gamblers, and they were allowed to get into that game. And now the result is that not only are the socially useful organizations in trouble, but they're so entwined with the socially useless organizations that those also have to be bailed out, all at the courtesy of the US tax payer.
So what are we to make of this. What is Taleb's point? Simple:
There are no free lunches. You can make money, perhaps for years on end, by taking on risk, but the reason people are paying you premiums is on the assumption that one day, when the sky falls, you will pay up and disgorge all those premiums.
This goes to the way we structure society. It's one thing to allow millionaires in hedge funds to gamble away their cash as they wish. It is quite another to structure the entire economy in such a way that when gambling fails the whole machine seizes up. It turns out there was actually a very good reason why retail banking was segregated from investment banking; and, as Taleb would put it, the fact that Phil Gramm couldn't name the particular unexpected event (the "Black Swan") that would cause the whole system to seize up doesn't mean such an event did not exist.
This, moreover, is why saying "First, our current economic crisis isn't really a black swan, is it? Things like this have happened fairly regularly during the past century (and before), on the order of once a decade at least, and maybe more often than that." is not being fully honest.
Yes, things like this used to happen frequently --- because essential financial institutions used to gamble. Then (30s to 70s) they stopped happening --- because essential financial institutions weren't allowed to gamble in this way. Then they started again --- because essential financial institutions were now allowed to gamble again.
Finally "Second, I've never seen Taleb explain what we should do about this. What's his advice?"
Taleb is not in the business of telling you, me, or Goldman Sachs how to gamble. He's not about "how to make a killing in the coming China-dominated years", He is about how to structure society so as to benefit the bulk of its citizens (rather than so as to benefit its 10,000 richest members). What Taleb says we should do about this is simple --- require that essential financial organizations not play the sorts of games that are liable to throw up black swans. If LTCM wants to bet that the price of the Korean Won squared minus the inflation rate of Nigeria is going to go up, they are welcome to do so --- but they are to play this game involving only other similar (non-essential organizations or, perhaps, via contracts that explicitly provide for paying-out and settling every night, or suchlike. Certainly banks (and to a substantial extent traditional insurance companies) are not to be involved.
Submitted by Maineiac (not verified) on Sun Jan. 4, 2009 11:11 AM PST.
As Marcel notes above - Yves Smith tears the article apart.
If I understand Taleb correctly he is not claiming that the meltdown is wildly improbably. What he is saying is that what ever model they are using to measure risk, it fails to fully capture the amount of risk that actually exist. He uses the example of the turkey the day before Thanksgiving. On this day the turkey has the most confidence in its world view. In this case the turkey is Greenspan among others. Taleb is saying we don't have to find a specific problem with any particular way of measuring risk. If a financial wizard seeks to assure us that risk has properly been taken into account, he is wrong. The antidote is to holistically make the financial system more robust.
Kevin,
That's a fair point. However, it's a bit like asking a molecular biologist to not only work out the molecular mechanism underlying a disease, but also get the cure. Taleb does what works for him trading-wise because the absurd excesses and idiotic models and pseudo-science underlying most market trading provide him with a straightforward opportunity. Maybe the real point is that the idea that an economy can make huge amounts of money from moving funds around is itself misplaced. Here in the UK at any rate, things have gotten utterly out of hand. The trading in the city of London has grown larger than the GDP itself. Ultimately however, all the trading strategies are zero sum games (apart from the guys who get the bonuses of course). Taleb's main point (and there's good youtube of an interview he gave to the BBC on this) is that we should be much more honest and humble about how little we actually know. He doesn't claim to have all the answers, he's just astonished at the idiotic nonsense that goes for financial information and journalism, which has been pretty much a tissue of lies, at least since I've been reading it. Sometimes admitting how little we know is the most important thing. Taleb is the only person who has been honest in this way that I'm aware of. I guess journalists and other writers are under too much pressure to come up with bogus explanations. I don't know. For this alone, I salute him.
This stuff is fairly deep in the weeds but here is one presentation of Taleb`s approach & here is Benoit Madelbrot`s take on all this. Mr. Madelbrot agrees with Taleb & put forward ideas (back in the late 1990s) how to do better.
HINT: Don`t trust Gaussian distributions, EVER.
"Fear not the path of truth for the lack of people walking on it." - Robert F. Kennedy
I think the problems arose, because it was possible to construct and solve sophisticated mathematical models involving risk. The problem is what sorts of risk dirtributions, and correlations to put into the model. Since, there was no real way to come up with this data, simple proxies, like historical data, and day to day price volatility were used as a standin for the real thing. Now using proxies and simplifications is a perfectly valid way to do research. It will certainly allow to experiement with systems, and see the sorts of behavior that might arise. But it doesn't offer much insight into the probably effects of whats been left out. Somewhere along the line, the models acquired much more credibility than they deserved. Then the financial system as a whole tried to create the financial equivalent of a perpetual motion machine.
I am reading Taleb right now. I think what he is trying to say, in short form, is that cognitive biases are more insidious than most people realize, and even experts are seriously vulnerble to them. So the bottom line should be, that we need to continually evaluate our assumptions, and ways to coming to conclusions. Otherwise once we let up, we will start making fundamental errors that may produce serious consequences.
> I think the problems arose,
> because it was possible to
> construct and solve
> sophisticated mathematical
> models involving risk.
Or that faster computers and pretty GUIs made it possible to generate so much bafflegab so quickly and forcefully that even hardened financial traders and executives started to believe in it.
My favorite is the corruption of the word "risk" itself, which I have argued over on deLong's site alone has played a big part in the financial disasters of the last 15 years.
Cranky
I think what the New York Post article says is there was a 1% chance of losses and are claiming the perfect storm of the one event out of a 100. Yves Smith is saying its Taleb's view is that chance of failure was in fact about 50-50. The models fail to capture the unknown unknowns.
A post on Taleb etc is in moderation due to multiple links.
Just a heads up & thanks to the mods for keeping the "bad stuff" out.
"Eventually, the truth will emerge. And when it does, this house of cards, built of deceit, will fall." - Robert C. Byrd
From the blog post:
Pretending that this was a wildly improbable event strikes me as nothing more than a sophisticated version of "nobody could have predicted." After all, if the crash of 2008 really was a one-in-a-hundred (or one-in-a-thousand) event, then it really is true that even reasonable people couldn't have been expected to foresee it.
Huh? It doesn't follow that because an event is very improbable, that it can't be predicted. Massive changes in global climate are very improbable, but climate scientists are predicting one will occur soon, and they're probably right. Similarly, recent economic events could have been predicted (and some people did) by simply paying attention to what was going on.
Obviously, there's some correlation in the probability of an event and the ability to predict it (I'm fairly confident that the sun is coming up tomorrow), but it's far from true that "wildly improbable" == "unpredictable".
Submitted by Maineiac (not verified) on Sun Jan. 4, 2009 2:20 PM PST.
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.
"So the question is: given the fact that we need ordinary global finance, and not everyone can just sit around waiting to make a killing on black swans, what should all these ordinary trading desks be doing to protect themselves against possible meteor strikes?"
My best understanding, from reading Taleb, is that you can't ever perfectly know risk; there are always "unknown unknowns" out there; but awareness of that fact leads you to make more conservative decisions than if you deluded yourself into thinking that risk can be accurately measured in any non-Gaussian environment.
My personal suggestion for fixing finance: you should tax leverage. Instituting a progressive tax scale, whereupon investors who borrow money would pay a higher tax than their less leveraged counterparts, would go a long way towards limiting excessive risk-taking.
Orly >"...thinking that risk can be accurately measured in any non-Gaussian environment...."
Actually that doesn`t appear to be what he is claiming. The following is from my Mandelbrot reference above at 2:28 PM.
"The author renders a brilliant critique of modern finance theory. He criticizes all its components, including CAPM, the Efficient Market Hypothesis, and the Black Scholes model as being flawed. All these theories rely on two main assumptions. The first one is that market prices are normally distributed. The author, using price charts, demonstrates that market prices do not follow a normal distribution; but instead a Cauchy distribution...Because the two main assumptions of modern finance are flawed, all related models are flawed as they understate risk. If such models understate risk, they actually overprice stocks and underprice options, and also understate the capital financial institutions should hold to withstand market risk...."
Check out what Mandelbrot says, and Taleb agrees, should be a better way to operate.
I`m not seriously thinking anyone in the business will pay attention to these two of course.
"There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things." - Niccoló Machiavelli
One of my problems with Taleb is that his methodology also uses a model. One of his insights is that thigs at the 99.999999% probility level still happen. People do get hit by lightning. Meteors do fall through people's roofs. His investment strategy is to invest the preponderance of your money in very low risk / very low return investments and lay another small amount on something really bad happening. This is not much more enlightened than investing in blue-chip mutual funds over a long period of time. This strategy also assumes something out of left field will hit most stocks sometimes and wipe out some stocks. But over a range of stocks and over a range of time you avoid getting wiped out while getting decent returns on average.
Taleb plays off the same bell curve, wit the same 99.9999% (black swan) events, but in a diffferent way.
My personal suggestion for fixing finance: you should tax leverage. Instituting a progressive tax scale, whereupon investors who borrow money would pay a higher tax than their less leveraged counterparts, would go a long way towards limiting excessive risk-taking.
I like this idea.
The return on an investment is a random variable, and there are many ways of characterizing the behavior of random variables - expectation, variance, higher moments, VaR, etc. Each of these numbers captures some small aspect of this random behavior. You can play with formulas or have trading heuristics based on whatever measurements you like, but fundamentally the behavior of a random variables is a complex and subtle thing, and something humans have especially bad intuition about.
When engineers design bridges, they don't calculate a single "bridge goodness" number based on some formula no one understands, and then approve the design if that number is high enough. There are experts, who must be certified, who spend time to actually understand the design, it's possible failure modes, etc. Engineers model different aspects of the bridge with computers, they reuse time-tested designs, build scale models, etc. Human intuition just isn't good enough to bet on, and the idea of basing bridge design decisions on a magical single number is absurd.
I read Taleb's critique of modern risk management in this way. Models and associated heuristics are useful insofar as they actually reflect reality. A firm that makes a rule like "We must keep our VaR to be in a certain range" as a shorthand for actually understanding the distribution of the underlying random variable will is making decisions with insufficient information.
The fact that such practices are widespread is not surprising, given how much easier it is to train people to use these tools rather than to find and hire real experts. The fact that we don't consider financial engineering to be in the same vein as structural engineering, where the government actually demands proper risk assessment and mitigation is another story.
Yves Smith's points appear to be (a) distributions are NOT (really really NOT!) Gaussian. (b) that the notion of "variance" of value at risk is not meaningful if the distribution does not have an expected value, e.g. a Cauchy distribution. Is this a fair summary?
I am reluctant to believe that the risk managers of major financial institutions are as foolish with their models as Yves Smith suggests.
Mark Thoma points to James Kwak at Baseline Scenario with more on Nocera's piece, both pro and con.
Bill Arnold >"...I am reluctant to believe that the risk managers of major financial institutions are as foolish with their models as Yves Smith suggests."
How much more financial chaos would it take ?
Seriously you need to consider/remember how Group Think works because this is a prime example of it in action.
*sheesh*
"Against stupidity, the very gods themselves must contend in vain." - Friedrich von Shille
My personal suggestion for fixing finance: you should tax leverage. Instituting a progressive tax scale, whereupon investors who borrow money would pay a higher tax than their less leveraged counterparts, would go a long way towards limiting excessive risk-taking.
I too like this idea, but it should be applied to ALL borrowing. Otherwise, borrowing simply shifts from one place to another. Instead of borrowing 100K in their investment account, a trader would borrow 100K against his home and use those funds to speculate in the stock market.
One should also remember that many home buyers bought more home than they needed because they considered homes as investments instead of merely treating them as a place to live. All the more reason to tax ALL debt at a higher rate.
What are the chances of this happening? 0.00. At this time our tax system actually encourages home buyers to borrow, thanks to the tax deduction on mortgage interest.
Michael Lewis on Taleb and Black-Scholes
http://www.portfolio.com/news-markets/national-news/portfolio/2008/02/19...
Submitted by The Lounsbury (not verified) on Mon Jan. 5, 2009 11:29 AM PST.
Drum, you still don't quite understand what Taleb means by a black swan. He means an un-thought of event; that financial markets are subject to crises, and a crisis arrived is not the 'black swan' - rather the specific entry point of the failures was not thought of (by many); e.g. the risk models that - based on historical data - did not integrate an all US real estate market melt down. It is not the rarity of the event as such, that Taleb labels black swan, but an event that is not conceived of. Although he also makes the point that risk models seem to systematically under estimate "large events."
Insofar as there is a take away, it is risk managers in financial institutions need to be aware of the apparent systematic error and treat it more successfully AND regulators as well (e.g. Basel II and internal modelling standards).
Submitted by The Lounsbury (not verified) on Mon Jan. 5, 2009 11:34 AM PST.
Of course Yves makes the point in the post that awareness in theory exists, but incentivisation (I rather like the CV put...) is another matter.
