Physics is a science. Math is. Or Biology. Finance is not. Because it deals with the madness of crowds.
> Recipe for Disaster: The Formula That Killed Wall Street
> And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.
> Nassim Nicholas Taleb is particularly harsh when it comes to the copula. "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked," he says. "Co-association between securities is not measurable using correlation," because past history can never prepare you for that one day when everything goes south. "Anything that relies on correlation is charlatanism."
> when people say "finance is science" what they usually mean is "here is the complicated math that proves you can't lose money on this, we've modeled everything"
100% agree. When I was an algorithmic derivatives trader, we joked that the math was there to scare up investors and scare off compliance. Little did we know...
I still remember the days when the 2008 banking crisis was blamed on the mysterious Gaussian copula [0]. This is a much more convenient narrative than saying that the company's leadership was gambling with the company's money, hoping to cash out and leave investors holding the bag.
At least now, title does not go as far as claiming that this is formula that _caused_ the crash, unlike this sensationalist piece[1]. The other popular formula to pick on is Li's Gaussian Copula [2] that did not address tail risks and dynamics of assets' co-dependence.
The important thing to remember is that finance is not physics and any model of reality is just that - model. As long as model's assumptions are close to reality, model works fine. It is failure to understand limitations or when assumptions do not hold any more that led to crash.
Actually the over-reliance of quants on models like Black-Scholes or Gaussian copula is a testament to how well these models work (or should I say worked?) for specific market conditions.
> And yes, in finance, the correlations between asset classes shoot up toward 1 in periods of crisis (black swan event) . Hence, the research for tail-hedging strategies...
Related to what you said here, I was surprised there wasn't a comparison with Vine Copulas in the paper or thread! But this is pretty far outside of my realm of expertise, so maybe it shouldn't be surprising.
"To Wilmott, Gaussian is an example of how dangerously abstract quant finance has become. 'We need to get back to testing models rather than revering them,' he says. 'That's hard work, but this idea that there are these great principles governing finance and that correlations can just be plucked out of the air is totally false.'"
>Lots of people just don't think of financial modeling as a particularly interesting or beautiful area of math
I kind of surprised how those things are frequently mixed together. The math is a science while various industry modelling is an application of the known/established tools/skills. It is like designing a drill vs. actually drilling a hole. (note: i have an MS in Math (3.8 GPA) from one of the top Russian schools)
Your point directly contradicts the conclusions of the paper you linked.
The paper concludes that while there were deficiencies with the modelling method (as there are with any model), input manipulation was at greater fault than inherent failures of the model itself.
"These results support the arguments of Donnelly & Embrechts[4] and Mackenzie & Spears[12], that Li and the Gaussian copula were not to blame for the Crisis...Instead it appears that the gaming of the model beyond its original assumptions, the outsourcing of CDO risk management to credit rating agencies, and the failure to perform holistic risk assessment seem far more to blame."
"The simulation results in this paper show that it is more important to focus on parameter estimation than copula choice. This leads to the observation that when it comes to mathematical financial modelling: in order to avoid a disaster, the cooking is more important than the recipe."
The paper is pointing at one aspect of the modeling (estimating the covariances of the copula), versus another aspect (the copula concept itself). That’s a detail that was very important to the author of the paper, but not to my point.
My point is that mathematical models were indeed being used and followed in this case, and that the issue really was with overextension of the model, and not just generic volatility of any market, as claimed by the GP comment.
Everyone has known for decades that these models (Black Scholes / Gaussian Copula) are wildly inaccurate in the tails. where the real risks live. They are roughly accurate on quiet days. Mandelbrot has been publishing on this since the 1960s! Anyone who pretends to believe these models is running a scam of some kind.
It is true that the GC played a minor role in the recent crisis but Black Scholes did not. See below for details.
The factors in the 2007-2012 crisis:
1. Fraudulent lending practices and falsified loan applications.
2. Excessive borrowings by households fueled by the Fed keeping interest rates too low for too long.
3. Belief that present trends would continue forever and house prices would continue to the moon.
4. Greed blinded people to the risks they were taking.
5. Lax to nonexistent regulation which allowed banks and related organizations to leverage to insane levels. It also allowed companies like AIG to sell insurance that they could not pay off on.
6. Risks were ignored due to perceived government guarantees (Fannie Mae and her ilk).
7. Fraudulently selling subprime toxic garbage as AAA securities. This is where the Gaussian Copula came in. Given known wrong and bogus assumptions (eg that house prices would never fall across the whole USA), it allowed the investment banks to pretend that the top tiers of the subprime securities were AAA ie secure. Internal emails showed they knew they were not really AAA. However the GC was only the vehicle; the underlying problem was fraudulent and criminal intent.
8. Rating agencies were paid large sums of money to rate the toxic waste as AAA. They either knew or did not care that the securities were toxic waste as long as they got the cash.
9. Pension funds and other naive investors believed that the rating agencies and investment banks were not lying when they said the AAA-rated securities were OK.
10. More recently we have seen the crisis in Europe which is the result of the failure to rein in housing bubbles caused by too-loose credit, and by governments which borrowed more than they could afford to pay back, and which made commitments that they could never fulfill (eg excessive pensions).
BS played a role in the near meltdown in 1998 when LTCM went down, and also in the 1987 stock market crash.
In both cases idiots pushed the models outside their sphere of validity. LTCM was leveraged to the hilt and assumed that short term historical correlations would continue to prevail. A cursory examination of history would show this is not the case.
In 1987 a technique called "portfolio insurance" was invented which supposedly allowed the user to simulate a protective "put option" at no cost. Portfolio insurance required selling stocks when the market fell. The BS model assumes infinite liquidity and no price jumps and if these are true PI should work. Again these are not valid assumptions and when the technique was implemented on the overvalued October 1987 market it accelerated and intensified the crash.
Even in physics most models are inaccurate outside a certain range of validity. It requires a degree of honesty and intellectual integrity to refrain from using them when they are not valid. Eg you cannot use Newtonian mechanics at 99.999% of the speed of light.
TL;DR this was not a mathematical mistake - it was fraud.
I know. I read it. My point was that he thinks that because he thinks that Taleb is simply saying 'shit happens'. He's not. We believed in the Gaussian curves and risk measured in standard derivations. We believed VaR and it ate us for lunch. If it's not very useful or original, September would not have proved him out so well.
From the article: "Still others say their models simply failed to predict how the markets would react to near-catastrophic, once-in-a-lifetime financial events like the credit crisis and the collapse of Lehman Brothers."
The fact that they still believe those events were "catastrophic," or "once-in-a-lifetime" means they still haven't grasped the fact that markets aren't Gaussian. As first Mandelbrot, then others showed, financial markets exhibit a much larger number of extreme events than a standard Gaussian distribution. Therefore, any trader that doesn't update his or her models to use a non-Gaussian model won't just be wiped out once. They'll be wiped out again and again as they get blindsided by the "once-in-a-lifetime" price swings that happen to happen every decade or so.
> the Black Scholes model that was developed in 1973 assumes a normal distribution, which is not only wrong
It was better than the vacuum it supplanted. Later iterations replaced constant volatility with a multi-dimensional volatility term and the normally-distributed price-movement assumption with other distributions. Though even through the early 2010s, when I last institutionally algorithmically traded options, the normal variants' speed outweighed the edge-case benefits of e.g. an extreme value theorem curve.
The fascination the popular financial press has with traders delusionally deploying normal distributions is not only wrong, it obscures that the fundamental nature of finance is that of trade-offs, not one right solution.
"Financial Engineering" is discredited and should more discredited.
I'm sure some physics geeks really enjoyed fitting heat equations to financial processes. This exercise ran a foul of the problem that the processes were subject to the normal distribution, were not uncorrelated and had "long tails", etc, etc.. But all these errors were just results of selecting those models which provided actionable data - the markets found those geeks who willing to endorse a dive into reckless asset inflation. This kind of thing has been around since John Law.
The emperor was just as naked five years ago as today. What has changed is what people are willing to see.
Read Nassim Nicholas Taleb. If you're a real geek for this stuff, read Benoit Mandlebrot's financial stuff. HN had a link to Mandlebrot's prediction of the present mess - written in 1998 (when it had almost happened, as opposed to now, when it has happen).
> They might not help you prepare for a black swan type event
at some point probabilistic simulations were all the rage in the financial industry and then the financial crisis happened
it is a fine art to figure out how to elicit the benefits of Monte Carlo simulation to put some structure around the future without falling into a mental trap that blinds you to non-quantifiable scenarios
I am sure you did not understand Taleb at all. Actually I think it is possibly his mistake that he believes common people without n iota of statistics or mathematics can understand it. Let me explain, almost all of the equations that the Bankers used are based on a bell curve for a distributed event funtion. Now its called a bell curve because the be represents the average and assumes that an event of infini value would have zero chance to happen. That is ok general continuous function because that is a theorical contruct; but in a distributed function and which by definition cannot have zero occurance (because it is distributed) and event with infinite value can occur atleast once. The whole base of mathematics, therefore which is being used by the Banks is flawed and should be removed.If you udnerstand this thing, I would say Taleb is to Banking what Einstein was to Physics. He is asking you to change the foundation. Do you understand it? I doubt you do.
> Even if the DS gets close to the money, the massive assumption here is that the underlying money making process is amenable to statistics methodology
Yup.
A famous recipe for rabbit stew starts off "First catch a rabbit ...."
Well, a first recipe for applied math/stat is "First get an application ..."
Still better, pick in a coordinated way the pair of the problem and the method of solution. For business want lots of people/money to have the problem and like the solution. Also want a Buffett moat: Network effect, natural monopoly, a brand name with a lot of power to get and keep customers, maybe some crucial core technology secret sauce difficult to duplicate or equal. Now try to exploit computing and the Internet. Then want LUCK of timing, etc.
Apart from the God-awful layout, the article is pretty light on anything useful or actionable.
> I need merely two variables [...] resulting in a simple yet accurate model.
It's accurate-enough, but not accurate accurate. This is why things like quantum gravity are being researched. Maybe I'm looking too deeply into this analogy, but I think it's a really bad one.
> In highly complex systems such as business, things like butterfly effects can cause massive distortions rendering our models flawed.
Most businesses fail due to a lack of product-market fit. This has nothing to do with chaos theory or initial conditions. In fact, I'd say if you have product-market fit, the market tends to be very lenient of initial conditions.
> In order to perfectly predict the weather, you’d need incredible amounts of data and an equally overwhelming number of data points and then somehow synthesize that into an accurate prediction.
I'm pretty sure that we're still not sure if you can even actually predict the weather -- like, ever (we aren't sure if Navier–Stokes is smoothly solvable in 3D). All these physics analogies are just shallow and inaccurate.
> It’s easy for the takeaway to be human behavior is difficult, business is complex, all data is meaningless, we can’t apply a scientific process at all, let’s wing it. And while there are people who lean heavily on intuition (Gary Vaynerchuk comes to mind) I believe if that’s the takeaway, the pendulum has swung too far out of whack.
I'm not sure why this is "out of whack" -- to me, this seems like a perfectly valid strategy. As I get older, I value intuition more and more. There's a reason Warren Buffet's moniker is the "Oracle of Omaha."
> theory of random walks, risk neutral pricing, and the black scholes option pricing formula to be the most significant findings
Random walks, heck yes! Black Scholes not so much. Its a fantastic toy model, but over all I think, it did more harm than good. People took its thin tail behavior too seriously. There's way too much fluctuation in practice than a Gaussian process would fit/predict.
So I would put it as: mathematically sound enough, empirically not quite so.
Taleb acts as though the finance community doesn't know what a fat tail is, or how to model it. Yes, there are idiotic statistical practices used in the business world (VAR comes to mind) but the best hedge funds employ the types of top mathematics PhDs that understand the concepts and implementation quite well. I've worked with them in the past and it would be a mistake to discard their thinking as trivial or amateurish.
Physics is a science. Math is. Or Biology. Finance is not. Because it deals with the madness of crowds.
> Recipe for Disaster: The Formula That Killed Wall Street
> And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.
> Nassim Nicholas Taleb is particularly harsh when it comes to the copula. "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked," he says. "Co-association between securities is not measurable using correlation," because past history can never prepare you for that one day when everything goes south. "Anything that relies on correlation is charlatanism."
https://www.wired.com/2009/02/wp-quant/
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