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.