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Mathematical Expectation in Trading Systems-Must read

  
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Here is a brief lesson in how mathematical expectation works.

On the roulette wheel there are 36 numbers, double zero, and the blank. That makes 38 spaces to bet on. Each bet costs $1 to play. The winner pays $35. To calculate the mathematical expectation of the roulette wheel you do the following:

Multiply the probability of winning by what you win when you win. And from that, you subtract the probability of losing by the cost of each bet. The difference is the mathematical expectation. If it’s positive, it’s a fair bet. If it’s negative, you don’t play.

[(1/38) x (35)] – [(37/38) x (1)] = mathematical expectation of playing roulette.

(35/38) – (37/38) = (-2/38) or (-1/19).

So in the case of the Roulette wheel, the best bet is not to play. The problem is playing Roulette is fun! Most professional money handlers don’t find losing money fun. And that’s the difference between the professional and an amateur.

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“The mathematical expectation of the speculator is zero.” -Louis Bachelier was a French mathematician who was, well after the fact, credited with founding the Efficient Market Thesis. In 1900 Bachelier published his Ph.D thesis titled “The Theory of Speculation.” In his paper, Bachelier discussed the use of Brownian motion to evaluate stock prices. Unfortunately, his thesis was “not appropriately received”, which resulted in academic black-balling and the concept being buried for more than sixty years.

Almost sixty-five years later Professor Eugene Fama from the University of Chicago was officially credited with developing the Efficient Market Thesis after publishing his Ph.D thesis. His paper was titled “The Behavior of Stock Market Prices.” The core tenet of his paper and the Efficient Market Thesis is that an investor “cannot consistently achieve returns in excess of average of market returns on a risk-adjusted basis, given the information that is publicly available at the time the investment is made.”

Is it not somewhat ironic that the determination of who founded the Efficient Market Thesis was not efficient?”

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