Jacob Bernoulli, the famous Swiss mathematician, is best known for his introduction of the theorem known as the law of large numbers. Wikipedia defines the law of large numbers as “a theorem in probability that describes the long-term stability of the mean of a random variable. Given a random variable with a finite expected value, if its values are repeatedly sampled, as the number of these observations increases, the sample mean will tend to approach and stay close to the expected value (the average for the population).”

In other words, since the probability of flipping a coin and seeing a head (or tail) is 50%, the more we flip the coin, the more we will see the frequency of heads or tails approach 50%. Also, the expected value (50%) becomes more reliable the more we flip.

In his book “Against the Gods”, Peter L. Bernstein points out where Bernoulli performed various studies using marbles to conclude that a sample of 25,500 trials was necessary to achieve what he called “moral certainty.” Moral certainty he defines as a 2% chance of error.

He understood that the Law of Large Numbers is very important because it stabilizes long term outcomes for random events. In Las Vegas a player may beat the table in a given day, but eventually, whatever edge is built into the game will dominate, the more the game is played.

Is this true of trading systems though? I don’t think so.

First, there are big differences in reliability when testing such things as trading concepts and coin tosses. In the “real world” there are few longer term trading systems that can even produce 25,000+ trades as a sample size. Even if we could, Bernoulli had the advantage of working with a closed sample (5,000 marbles). Traders take in new data every day as new trades surface. This is the equivalent of throwing more marbles in the jar, perhaps even different colored marbles. Although a back test with 5,000 trades is likely to be more reliable than one with 200, it still has limitations that should be viewed with skepticism.

Tweet This Post

“We can’t always take advantage of a particular period. However, in an uncertain world, perhaps the investment philosophy that makes the most sense, if you study the implications carefully, is trend following. Trend following consists of buying high and selling low. For 19 years, we have consistently bought high and sold low. If trends were not the underlying nature of markets, our type of trading would have very quickly put us out of business. It would not take 19 years or even 19 months of buying high or selling low ALL of the time to bankrupt you.

Nevertheless, trends are an integral, underlying reality in life. How can someone buy high, sell low, and be successful for two decades unless the underlying nature of markets is to trend? On the other hand I’ve seen year after year, brilliant men buying low and selling high for awhile successfully and then going broke because they thought they understood why a certain investment instrument had to perform in accordance to their personal logic.”

Tweet This Post

Ed Seykota in the book, “Market Wizards,” writes, “Systems trading is ultimately discretionary.  The manager still has to decide how much risk to accept, which markets to play, and how aggressively to increase the trading base as a function of equity change.  These decisions are quite important, often more important than trade timing.”

It seems most sophisticated traders are aware of the fact that a system needs to be properly quantified and tested before trading. The sample size of the trades needs to be large. These traders are familiar with the terms of curve fitting and optimization. I wonder, however, how many traders continue to study the model as they trade their equity. How many understand the logic behind the entries, stops, exits, and money management techniques. How many are adjusting position size to meet expanding and contracting volatility and changes in market correlation.

Seykota also points out in the book, “Market Wizards,” that at times, “The markets shift from trending to non-directional price action.  These systems become unprofitable and under-capitalized. The trader without experience will be shaken out. Longevity is the key to success.”

It is this discretionary knowledge that examines the risk and helps build one’s confidence. Without this understanding, doubt will come into play and longevity compromised. A draw-down will inevitably force a decision based on emotion and not sound trading principles.

It is in our human nature to prefer pleasure, and avoid pain.  In spite of our natural instincts, good trading sometimes requires us to act against our natural inclinations. We must do what is necessary, not what is comfortable.

Tweet This Post