Over the New Year break I read the illustrated Cartoon Guide to Statistics which was great to go over the basics of classical statistics, and the format makes it easy to pick it up for a few minutes reading. I have also been recommended, and bought Statistics Unplugged – which deals with the same topics more in depths. But to be honest it still sits untouched on my desk…

Another area of statistics which very often comes up in the context of *serious* trading system development is **Robust Statistics**. I have not found a good book to leave *unread* on my bookshelf on Robust Statistics yet so I’ll have to make do with with an *unused* bookmark on the wikipedia article ;-)

Anyway, Bill Eckhardt is a succesful automated trend follower with a strong background in Mathematics (although he apparently never finished his PhD – abandonning his studies for the trading pits). He was also Richard Dennis partner in the Turtle Trading experiment. I re-read his interview in New Market Wizards where he emphasises on a few concepts such as understanding statistics, bet size, and even psychology.

Here are some interesting inssights from the book interview (starting pg 107):

– Statistics are an important element of mathematics for trading:

– “The analysis of commodity markets is **prone to pitfalls in statistical inference**, and if one uses these tools without having a good foundational understanding, it’s easy to get in trouble.”

– “Classic Statistics work well if you are correct about data distribution assumptions. Because distributions are pathological, **we need robust techniques**”

– “define what you mean by robust?

A robust statistical estimator is one that is **not perturbed much by mistaken assumptions** about the nature of the distribution.”

– He mentions the concept of infinite variance in market prices distribution and particularly **Mandelbrot** and his precursor work on this topic.

– Traders should be **more conservative in risk control** than might be implied from statistical interpretations using normal distribution

– **Less degrees of freedom is better** – a degree of freedom is a parameter that produces a different system for every value (e.g. length of Moving Average in crossover systems).

– Chart patterns do not work

– Wished he’d **focus more on money management** at the start of his trading career (and mentions that in trading, Money Management is the most tractable problem, mathematically speaking)

– Mentions Utility functions and states that **all the utility functions used in his risk management model are bounded**. He takes the example that if utility functions were unbounded, there would be an amount for which a billionaire would be willing to bet his whole net worth at the flip of a coin.

– Interesting remark about bet size: if you plot system performance against bet size, you obtain a curve in the shape of a **rightward-facing cartoon whale**, going up in a straight line before dropping dramatically.

– “Trading size is one aspect **you dont want to optimize**: the optimum comes just before the precipice. You want to be at the left of the optimal point, in the high zone of the straight curve”

– Gives his point of view on psychology and trading.

Milktrader// Feb 8, 2010 at 7:02 amHe has hit it on the head. Markets do not conform to Gaussian distributions because they lack stationarity. They are also not iid (independent and identically distributed). Treating them as such only leads to trouble. I’m also impressed with the reference to Mandlebrot, who is the father of chaos theory.

Another area that may be worth pursuing is machine learning, which is the other side of the statistics coin. Inferential statistics and neural network predictions both attempt the same thing, but use different terms and techniques to arrive at their answers.

RiskCog// Feb 10, 2010 at 12:05 amA good book for some practical statistical theory such as robust estimators and interpolation is Numerical Recipes. Old books are available online: http://www.nr.com/oldverswitcher.html

See chapters 3, 5, 14, and 15

Also, a body of theory that is rich with applications for speculators is Robust Non-Linear Control Theory.

Jez// Feb 11, 2010 at 3:24 amThanks for the recommendation RiskCog! I’ll check them out

Correction// Feb 17, 2010 at 1:38 amWilliam Eckhardt does not have a PhD in Mathematics.

http://en.wikipedia.org/wiki/William_Eckhardt_(trader)

Maybe that is exacty why he is such a successful trader!

Jez// Feb 17, 2010 at 4:12 amThanks “Correction”… ;-)

I updated the post – although I tend to take wikipedia info with a pinch of salt (I recently found out by way of experiment that you dont even need a login to it to change the pages!)

I guess the fact that he does not mention PhD on his fund website is a good enough double-check confirmation…

In any case, thanks for taking the time to point to that factual mistake – and I would tend to agree with you on the fact that NOT getting a PhD is probably a favourable factor to trading success ;-)

brmr// Mar 15, 2011 at 2:34 amJez,

Bill Eckhardt is almost close to completion of his Phd when he left and joined Richard Dennis according to his interview in Futures Mag (2/28/20011).

“As I recall more than half the course revolved around developing the right attitude, guarding against debilitating emotions, how to think about risk, and how to handle success and failure. Teaching the turtle system itself doesn’t take very long”

” We spent a lot of time talking about our theories on how to control risk; that was actually the bulk of the course. Attitude, emotional control, discipline; those things are harder to teach. All the turtles learned the system and learned the strategy; that was the easy part, but some of them brought the right attitude and right mental set to it and they prospered and became very rich”

His order of importance as stated was Psychology (attitude),risk control (money management) and methods. Quite similar to what Seykota and Tom Basso suggested in their interviews