Fat tails, long-term autocorrelation, discontinuities in price changes, divergent variances.

Aside from missing those observable features of the data, the theory is missing much about market agents: herding and contagion, information asymmetries, slow convergence to equilibrium, non-normally distributed errors, heterogeneous strategies and objectives, interaction effects, confirmation bias.

I'm just repeating Taleb, and his mentor Mandelbrot, of course:

https://www.amazon.com/Black-Swan-Improbable-Robustness-Frag...

https://www.amazon.com/Misbehavior-Markets-Fractal-Financial...

Not sure why I get downvoted

http://www.amazon.com/The-Misbehavior-Markets-Financial-Turb...

This is not at all surprising. Statistics isn't the right tool for financial analysis... it's just the best tool that we have. Incredibly unlikely statistical events happen all the time in finance.

A great read on an alternative view on the topic of using statistics for finance is The (Mis)Behavior of Markets by Benoit Mandlebrot [1]. It's very well written, basic enough for most to comprehend and first book on finance I read in college (before I went on to major in finance + math).

The aforementioned book has some very interesting notions with Trading Time being my favorite. Basically one can near-perfectly "forge" financial data with fractal objects called "financial cartoons" [2]. The objects are composed to two distinct fractals - one for price vs trading time and another for trading time vs clock time [3]. The latter rescales the volatility seen former, either compressing or expanding it. Rescaling volatility isn't a new idea, but it was a parallel "discovery".

There has been some work on figuring out how to use Fractal Geometry to analyze financial time series data but it's still in its infancy. The problem is figuring out how to transform the data into the fractals domain + figuring out what the results from a fractal based analysis would mean for forecasting future events. I've been working on these problems for many years (in earnest in college and as a hobby thereafter) but made little true progress.

[1] http://www.amazon.com/The-Misbehavior-Markets-Financial-Turb...

[2] http://classes.yale.edu/fractals/randfrac/Market/Fake/Fake.h...

[3] http://classes.yale.edu/fractals/randfrac/Market/TradingTime...

That's what's really going on, it's a great way to make some quick money. But if you were to ask the standard free-market ideology side of it can always be mustered - "we're just trying to get the pesky and inefficient government out of markets so they can 'function better'", despite the efficacy such claims proving incredibly dubious over the last few decades and even more doubtful when empirically tested [1].

[1] http://www.amazon.com/The-Misbehavior-Markets-Financial-Turb...

Game theory is ultimately a drastic oversimplification (a model) of human agency. It happens to coincide with certain popular simplifications nicely, but ultimately it's flawed. In situations where it tries to prove either cooperation or competition is the superior behavior it often sets up its actors in such a way that it begs the question (the answer is baked into how the variables are set up and how the agents are made to optimize those variables). I wouldn't take it too seriously as an authority on ethical questions. It's most useful as a model to reason about average outcomes in a limited set of situations. It tends to get into trouble elsewhere [1]

[1]: http://www.amazon.com/The-Misbehavior-Markets-Financial-Turb...

The (mis)Behavior of Markets, A Fractal View on Risk, Ruin, and Reward by Benoit B. Mandelbrot and Richard L. Hudson.

You may enjoy this book if you are interested in Financial Markets, have some knowledge of Efficient Market Theory, and aware of existence of Fractal Geometry.

http://www.amazon.com/The-Misbehavior-Markets-Financial-Turb...

It's strange how I can read an article in The Economist about Benoit Mandelbrot's "multidisiplinary" approach that makes almost no mention of his work on Economics.

To be fair, most of the stuff that isn't pretty pictures goes past me. However, one thing he did do was completely eliminate the validity of the (Nobel-prize winning) Black-Scholes model.

So we have E. Fama (another Nobel prize winner) with his efficient market hypothesis, stating that in a perfectly rational market, prices are random. The loophole for economic theorists, and the basis for Black-Scholes, was that price variances were thought to be predictable. Prices were random, but their fluctuations were generally not, and could be modeled as a Gaussian distribution. Mandelbrot suggested that this a soothing inaccuracy: prices were capable of varying much more wildly than that. He suggested that a Pareto distribution was more accurate.

So then we have one of the more fundamental problems in Economics: it is not a science. It's more of a cult for math geeks, in my opinion. If you can't prove that markets follow a Pareto distribution (implying an unpredictably-random price volatility), then why should economists listen to you? Black-Scholes gives them partial results, and that's better than nothing, right?

Right?

B. Mandelbrot: The Misbehavior of Markets: A Fractal View of Financial Turbulence http://www.amazon.com/Misbehavior-Markets-Fractal-Financial-...

Market prices as fractal patterns? Where have I seen that before?

Ah, yes, here: http://www.amazon.com/Mis-Behavior-Markets-Fractal-Reward/dp...