## 2011/01/24

### The Financial Modellers' Manifesto

Paul Wilmott and Emanuel Derman, both quant gurus, wrote and signed what they call The Financial Modeller’s Manifesto in 2009. It is modelled after The Communist Manifesto written by Marx, which I find quite ironic.

Before we get onto the manifesto, I want to mention some things about the people behind it. Derman started off in South Africa, studying at the university of Cape Town, just as I did (although he got a PhD in theoretical physics). In a sense, therefore, he is a role model for me.

Wilmott started the Certificate in Quantitative Finance, a six month course. He is editor-in-chief of Wilmott magazine and has a quantitative finance forum and recruitment organisation run under his name (some hubris here?).

Both warned against the risk of misusing mathematical models long before the crisis (though I know quotes have a way of being taken out of context).

What I like about the manifesto
1. It is honest.
2. It is written in a colloquial style, making it more accessible and emotive.
3. The oath will always be relevant as it contains timeless principles.
4. It is a call to action.
5. It draws the crucial distinction between physics and financial mathematics.

What I dislike
1.   There are too many specifics. CDOs might not exist in twenty years, making the manifesto applicable mostly to the present (with the exception of the oath).
2. There is too much jargon.
3.  The authors claim no responsibility. They are reacting to everyone else’s mess.
4.  It is too informal, making it harder to take seriously.
5.  It does not advise on how to fulfil its demands.
6.  Discussions about whether the Black-scholes model is good or not are not really relevant.
7.  It was written after everything it says had already become obvious.

What we need
We need clear guidance for future quants and a way to hold them accountable. The manifesto points in the right direction. It gives a useful oath, and by adjusting the first line to make it more formal (perhaps, “I know the world of finance does not function according to exact mathematical laws”) it could become something quants can put on plaques and recite as they get their qualifications.
But we need more. We need a code of ethics or a code of conduct for quants. Not a one page document that reads more as an article than anything else, but something substantial with a gravity that weighs on your conscience. More than that, though, we need people to ascribe to this code. That is, we need a professional body for quants that police their behaviour and set best practices. I find myself wondering whether actuaries can do this. We already have professional conduct standards (lacking only in specifics that will apply to quants). The creation of a quantitative finance specialisation for actuaries would allow quants to practice as actuaries and thus they would be held to these standards.
The problem is actuarial training is ill-suited to providing the kind of (highly mathematical) skills that quants need (I know this from unfortunate experience). The alternative is to create a professional body for quants alone, but this may involve a lot more work and may take years to be accepted. The public would appreciate it, I think. Throughout the financial crisis they have heard only horror stories of quants and such a large step would certainly help assuage fears, and, I think, result in more responsible practices.
Some references:

Wikipedia:
• Wikipedia, 2011a. Emanuel Derman. Wikipedia. Available at: http://en.wikipedia.org/wiki/Emanuel_Derman [Accessed January 22, 2011].
• Wikipedia, 2011b. Financial Modelers’ Manifestor. Wikipedia. Available at: http://en.wikipedia.org/wiki/Financial_Modelers’_Manifesto [Accessed January 22, 2011].
• Wikipedia, 2011c. Paul Wilmott. Wikipedia. Available at: http://en.wikipedia.org/wiki/Paul_Wilmott [Accessed January 22, 2011]
The actual manifesto:
• Wilmott, P. & Derman, E., 2009. Financial Modelers’ Manifesto. Paul Wilmott’s Blog. Available at: http://www.wilmott.com/blogs/paul/index.cfm/2009/1/8/Financial-Modelers-Manifesto [Accessed January 23, 2011].
The professional conduct standards of the Institute of Actuaries in the UK:

## 2011/01/17

### The Crystal Ball

Nassim Taleb, in his books The Black Swan and Fooled by Randomness, argues vehemently against predictions as they can be dangerous, blinding us to other outcomes, having us make decisions based on poor (or no) information. In the 25-year special edition of The Economist a wonderful piece of irony unfolds. Taleb himself, unfathomably, makes some predictions for 2036. On page 90 there is an article Future imperfect which analyses the Economist’s record at making predictions. And for the grand finale, the magazine provides a set of financial forecasts for 2011 for various industries and countries.
I was surprised to find Taleb had written such an article. When at first I saw, quite accidentally during a Google search, that someone claimed he had made such predictions, I thought it was a joke. But there the article is, in the The Economist. I am still not convinced that perhaps Taleb is not the one playing the prank on The Economist and its gullible readers.
The first article mentions Taleb; forgets to mention Taleb would have abhorred all the predictions mentioned (whether they came true or not). The set of 2011 figures are the kinds of things Taleb most wants us not to predict: GDP and inflation (population is also included, but this is arguably more predictable). The errors in such predictions are large. What use are the numbers if we can place no confidence in them?
Taleb’s predictions are
1.       City-states will prevail rather than nation-states
2.       Currencies will either not exist or be pegged to a standard
3.       No more large, debt-laden, listed companies
4.       Most technologies more than 25 years old will survive and most of the younger ones will be dead
5.       There will be biological and electronic pandemics
6.       Religion will experience a revival
7.       Science will produce few gains in non-linear domains
8.       Academic economics will be regarded with disdain
This is a very eclectic mix of predictions, is it not? As with many predictions, I suspect it is really just a wishlist (with the possible exception of point 5). From this angle point 6 is very interesting. Taleb’s books are secular and he has remained very obscure regarding his feelings on religion. Would he like a revival? I would. But that is drifting off topic.
Taleb bases these predictions on the premise that one will expect a system that relies too heavily on prediction to break eventually and 25 years is a long enough time. I agree with TechnoOccult that the link between this premise and the predictions is threadbare at best. I would very much like to know the logic Taleb is using. I am worried that he has lost his objectivity. A podcast I heard a few months ago contained a ranting Taleb with little thought that he might not always be right.
The future is filled with black swans, by definition unpredictable. Every one of these predictions could, in principle, be thrown off by a well-placed black swan. Is this not what Taleb warned us against? We are not just talking about a system breaking; we are speculating about how and what will take its place. Perhaps Taleb is becoming overconfident, fooling himself into thinking that he is cultivating his deep-seated insecurity, while making ever bolder ideological statements. I would be truly sad if this is the case. Of course we need to wait 25 years to see if he is right, by which time we might be eulogising him.
Some references
Taleb’s books:

• Taleb, N.N., 2007a. Fooled by Randomness 2nd ed., Penguin.
• Taleb, N.N., 2007b. The Black Swan, Penguin

The TechnoOccult article (which for some reason only mentions five predictions) that alerted me to all this:

• Finley, K., 2010. 5 Predictions from Nassim Taleb for 2036. TechnoOccult. Available at: http://technoccult.net/archives/2010/11/29/5-predictions-from-nassim-taleb-for-2036/.

The podcast I mentioned:

• EconTalk, 2010. Taleb on Black Swans, Fragility and Mistakes. Library of Economics and Liberty. Available at: http://www.econtalk.org/archives/2010/05/taleb_on_black_1.html.

## 2011/01/02

### Latex in Blogger

I have searched many many hours for a good way to display maths in Blogger. I have found no perfect solution yet. My current solution (used in my previous post) is to use the Codecogs engine. I place an image tag in the html that points to the engine and which contains my latex code, as in this example

<img src="http://latex.codecogs.com/png.latex?F(x) = 1 – \left(\frac{k}{x}\right)^a" />

which gives

$F(x) = 1 – \left(\frac{k}{x}\right)^a$

I do not like the dependence on an external server (which may shut down in the future). If anyone has a better solution please let me know.

### Power laws: Mandelbrotian is the new Gaussian?

Benoit Mandelbrot, the pioneer of fractals, died last year. I only found out months later. His death should have been announced as a great tragedy to the whole world. Mandelbrot I also only recently found out also made contributions to financial mathematics. I would like to discuss one aspect, which may not be original Mandelbrot, but which Taleb names after him.

The old
It has been well publicised that normal distributions do not work. At least they do not work for modelling financial markets. It is my impression that, despite knowing this, everybody continued to use them. Because the quants, the people who were supposed to ‘know’ said it was okay, the normal distribution became a kind of placebo.

These methods have, however, always had their critics. Taleb (who wrote Fooled by Randomness and The Black Swan) is one of them. The latest financial crisis proved them right. But still, the normal distribution is what everybody knows, and I think it will take a while before ‘better’ practices become widespread.

The new
One alternative to normal distributions that has been suggested, and which Taleb argues we should use, albeit with caution, is that of power laws. He calls such distributions Mandelbrotian, to challenge the conventional Gaussian. Power laws have, of course, been around for a very long time (they are hardly new). Zipf’s law is a specific example in the field of linguistics that was proposed in 1935 and the specific example we will be looking at was researched even earlier. I am not quite sure how much work on power laws has been done in terms of financial markets nor am I certain exactly what Mandelbrot’s contribution was.

Power laws are interesting creatures, showing themselves seemingly everywhere. They occur in nature where they give the frequency of different sizes of earthquakes, of the sizes of craters on the moon and the extinctions of species. These are some examples mentioned by John Gribbin in his book Deep Simplicity.

Things such as the distribution of city sizes and the disparity of wealth also seem to follow power law distributions. The ubiquity of this distribution not only in nature, but in human behaviour, makes it seem like some kind of universal law (which we cannot help but obey). Such an interpretation should be avoided of course. With interest in power laws high, you are more likely to hear about confirming evidence (this is what people will be looking for). Eventually we will find important examples that are not governed by power laws or we may find the power law distribution is a poorer estimate than some other law.

Definition
There is a general definition of a power law distribution, but I will merely define a special case, the Pareto distribution which has the distribution function
$F(x) = 1 – \left(\frac{k}{x}\right)^a$

with support x > k and a > 0. There is a more general definition for which some of the properties I discuss below would only hold asymptotically. The Pareto distribution is also the source of the infamous 80-20 or Pareto law (not really a law). I have yet to establish exactly how this was derived but watch this space.

Why power laws are cool
Self-similarity
They display self-similarity. Self-similarity is a property of fractals (remember that Mandelbrot is famous for his work on fractals). Taleb calls these distributions scalable (as opposed to the normal distribution, which is not scalable). It follows from the following property:
$Pr(X > tx) = t^{-a} Pr(X > x).$

So, for example, if a = 1, doubling x always lowers the probability of seeing a higher value by half. This also demonstrated by the fact that if you fix a new minimum wealth level you get a Pareto distribution with the same exponent:
$Pr(X > x | x > x_m) = \left(\frac{x_m}{x}\right)^a$

More concretely, if X represented wealth levels, the inequality among the rich would be the same as that among the poor. So if your wealth is x_m, half the population will have twice that wealth, and half of them four times that and so on.

Infinite moments
For certain (common) cases they have infinite variance or even infinite mean. For a <= 2, the variance is infinite. For a <= 1, so is the mean. In these cases we will not be able to rely on the Central Limit Theorem (or the Law of Large numbers in the second case). This makes the maths harder and moves us irrevocably away from normality.

Fat tails
They have fat tails. This means that extreme values are more likely than for the normal distribution. The structure of the tails is given by the self similarity of the distribution as shown earlier. For the normal distribution doubling the wealth level would lower the probability of higher observations by much more than half and much more rapidly further up the tail we go.

Estimation difficulties
They are hard to fit. Determining the exponent to use is apparently not easy and the resulting distribution is very sensitive to use. Taleb gives a good illustration.

Can they help us?
The danger is that everyone will jump on the new bandwagon. I can see the headlines twenty years from now. Math whizzes cause greatest financial crash in history. Math models fail us again. These Mandelbrotian distributions are just another fraud. Taleb warns that we cannot model everything, that even appropriate mathematics is of but limited use. In any event we should use models with caution. I am very interested in how far we can take them. I am definitely not yet done with power laws. Expect more posts on this topic.

Some references