William Eckhardt – The Mathematical Trader (Math Trading Strategies)

Last Updated on April 18, 2023

William Eckhardt is an American investor, commodities and futures trader, and fund manager. Eckhardt was one of the pioneers of quantified and mathematical trading and used some of the theories that later were popularized by Nassim Nicholas Taleb. William Eckhardt was interviewed by Jack Schwager in New Market Wizards.

Eckhardt is also known for taking the opposite bet of Richard Dennis in the famous Turtle Trader Experiment (see more of that below).

This article looks at the trading career of William Eckhardt, and we end the article by taking some of the most interesting quotes from Jack Schwager’s interview.

William Eckhardt’s life and trading career

He began investing in 1974 after he finished his four years of doctoral research at the University of Chicago in mathematical logic. However, Eckhardt never completed the Ph.D. program in mathematics, admitting that he left graduate school for the trading pit after an unexpected change in thesis advisors. Although he left academia prematurely, William had published several papers in academic journals. He was an avid reader of Benoit Mandelbrot, the mathematician that also had a huge influence on Nassim Nicholas Taleb.

William spent his early trading years on the floor. He eventually abandoned this activity-filled arena for a more analytical approach — system-based trading. For over a decade, he recorded success trading his own account, primarily based on the signals he got from the models he developed but supplemented by his own market judgment.

From 1978, he averaged better than 60% per year in his own trading, with 1989 as the only losing year, until the mid-1990s.

In describing his trading approach, William Eckhardt explained:

Basically, I would buy when weak hands were selling and sell when they were buying. In retrospect, I’m not sure that my strategy had anything to do with my success. If you assume that the true theoretical price is somewhere between the bid and the offer, then if you buy on the bid, you’re buying the market for a little less than it’s worth. Similarly, if you sell on the offer, you’re selling it for a little more than it’s worth. Consequently, on balance, my trades had a positive expected return, regardless of my strategy. That fact alone could very well have represented 100% of my success.

He found the Eckhardt Trading Company (“ETC”) in 1991 as an alternative investment management firm — specializing in trading global financial futures and commodities. The firm managed over $1 billion in managed accounts – both domestic and offshore products. The firm’s clients include corporate, private, institutional investors, and funds of funds.

In 1993, his article Probability Theory and the Doomsday Argument was published in the Philosophical Mind journal. The follow-up article A Shooting-Room view of Doomsday was also published in the same journal in 1997.

He believed that the correct application of statistics and mathematical models was a key concept for successful trading. But, he highlighted the problems in using these concepts, saying that “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.” Please read the quotes further below in the article to get a better understanding of Eckhardt’s theories.

Before he founded ETC, William was also involved in the Turtle Trading Experiment, organized by his partner and friend, Richard Dennis. The objective of the experiment was to judge a philosophical disagreement between the two partners — that is, to determine if the skills of a successful trader could be reduced to a set of rules. The experiment was a huge success. Novice traders ended up making $100 million. William Eckhardt, who believed that trading couldn’t be taught, lost his bet to Dennis.

Other famous traders and their trading strategies

William Eckhardt trading strategy quotes:

To get a better understanding of William Eckhardt’s mindset, please read the following quotes:

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


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


Price distributions have more variance than one would expect on the basis of normal distribution theory. If the variance is not finite, it means that lurking somewhere out there are more extreme scenarios than you might imagine (later called tail risk)….any classically derived estimate of risk will be significantly understated.


There are a lot of pitfalls in designing systems. First of all, it’s very easy to make postdictive errors.


Seven or eight is probably too many. Three or four is fine. (Discussing the number of parameters in a strategy.)


As a general rule, be very skeptical of your results. The better a system looks, the more adamant you should be in trying to disprove it.


When the human eye scans a chart, it doesn’t give all data points equal weight. We tend to form our opinions on the basis on the basis of these special cases. Thus, even a fairly careful perusal of the charts is prone to leave the researcher with the idea that the system is a lot better than it really is.


The human mind was made to create patterns. It will see patterns in random data. The human mind will tend to find patterns where non exist.


Buying on a retracement is psychologically seductive because you feel you’re getting a bargain versus the price you saw a while ago.


I think these indicators are nearly worthless (about RSI and stochastics).


I haven’t seen much correlation between good trading and intelligence. Average intelligence is enough. Beyond that, emotional makeup is more important. This is not rocket science.


One common adage on this subject that is completely wrongheaded is: You can’t go broke taking profits. That’s precisely how many traders do go broke.


The success rate of trades is the least important performance statistic and may even be inversely related to performance.


Natural instincts will mislead us in trading. Therefore, the first step is succeeding as a trader is reprogramming behavior to do what is correct rather than what feels comfortable.

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