Probability Theory: A Winning Bet

By Wagner, Gregory E. | Modern Trader, September 2001 | Go to article overview

Probability Theory: A Winning Bet

Wagner, Gregory E., Modern Trader


While most traders are familiar with multiple sophisticated methods of forecasting market turns, the understanding of chance is quite ancient. Using risk control ultimately can determine your trading success.

All traders have losses. Only good traders take small losses quickly, and it is this ability more than anything else that separates winners from losers in commodity futures trading. Yet, systematic risk control programs too frequently are assigned a secondary role in favor of analytical techniques. The reason is as clear as the answer to the following question. Which is more fun, designing a system to identify potentially profitable trades or designing a risk control system?

No one needs to sell the need for quantitative analysis. The prevailing faith in mathematical formulas and models is powerful. From simple moving averages to the sophistication of the Black-Scholes option-- pricing model, it is presumed orderliness can be extracted from the inherent chaos of price discovery. However, the array of readily available number-crunching processes used today are deployed mainly in search of profitable trades, not in the area of equity risk management.

Yet, the same mathematical theories on which traders consistently rely to bolster trade selection confidence can be of equal or greater value in constructing a practical foundation for handling the financial risks of futures trading.

Perhaps the most valid guidelines for actively incorporating equity risk management principles into a personal trading plan are embodied in probability theory. As theories go, probability theory is rather sound. After all, Las Vegas was built and continues to flourish based on probability theory.

An understanding of risk The organized historical roots of probability theory began with the French philosopher and mathematician Blaise Pascal. Pascal, prompted through correspondence with a part-time gambler, became intrigued by the challenge of winning in games of chance. According to Pascal, his ambition was "to reduce to an exact art, with the rigor of mathematical demonstration, the incertitude of chance, thus creating a new science which could justly claim the stupefying title: the mathematics of chance."

Pascal's seminal work on probability theory, Traite' du Triangle Arithmetique, which contains what is known as Pascal's Triangle (see "Monsieur Pascal's wonderful triangle," right) was discovered only after his death in 1662 and published three years later. Indeed, Pascal could be regarded as the father of equity risk management. Why he chose not to make public his work while alive is fittingly a matter of speculation.

However, before Pascal took up the challenge of how to win in games of chance, a much less sophisticated form of probability theory existed in primitive societies in the form of divination techniques. Dreams, omens, etc., were interpreted deterministically; the event was thought to produce the outcome. Because the stakes were survival in a subsistence economy, not simply making a few dollars, the outcome was simple. The event would or wouldn't happen.

Non-number divination techniques functioned as crude decision-- making shortcuts. Trying to establish a probability ahead of time and then work around the perceived odds, whether good or bad, has a long history. Although seemingly unsophisticated, that is probably the actual unorganized historical origin of probability theory - it is based in the most fundamental of human needs to provide guidance in a primitive and seemingly unpredictable environment.

Through the work of Pascal and others, probability theory has evolved into a broadly useful and mathematically systemized tool. Pascal pioneered an area in probability known as binomial distribution while working on the odds involved in coin tossing; we'll examine these to illustrate the self-evident and motivational risk management principles. …

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