Modern economics and investment analysis had their beginnings with the theories of the mathematical physicist, John Von Neumann, in the early 1900’s.  The early work in these fields assumed that the actors were rational, something which more modern finance has finally scrapped.  Along with that axiom, it was also assumed that games, including investment, were fair games.

A fair game is one in which a player has an equal chance of winning and losing.  This concept also led to the introduction of Gaussian Normal probability distributions (the famous bell-shaped curves), into finance, as they are symmetrical, conforming with equal probability of winning or losing.  Another convenience of Gaussian distributions is that they can be completely described by two parameters: the mean and the variance of the distribution.

There is an a priori reason to expect that the distributions of investment would not be Gaussian: technically, one can win an unlimited amount, so, positive returns could be unlimited, while losses (at least for unlevered investment) are limited to 100 percent of your investment.

The fair game theme also leads to assumptions of efficient markets, which are markets in which you cannot earn abnormal returns because that would not conform to fairness.  Fairness in the sense of efficient markets means beating the general market.  In that sense, the zero of the game is recalibrated to return on the market, and you have an equal chance of doing better or worse than the market.

In truth, people are not rational, markets are not really efficient, and investment is not a fair game.  We should already have a clue for that in looking at all of the people who get paid money to be in the investment business.  Of course, many of the people who are in the investment business are actually paid for marketing, not investing, so, we should already realize that people in the investment business make use of psychology, in marketing, to take advantage of the fact that people are not rational.  For those who are truly professional investors, barriers to entry, in terms of ability, capital, knowledge, etcetera, serve to create market inefficiencies, which professionals take advantage of.  Connecting with the efficient market theories, professionals have or develop information and process it more quickly than the man-on-the-street, which gives them an advantage and which turns investment into an unfair game.  They also use other tactics, like stop loss orders, portfolio diversification, limiting capital committed to one position, to also make the game unfair by biasing their aversion to loss.  They also primarily deal in arbitrages, many of which are completely riskless.

More rigorous mathematical financial analysis began in the 1950’s, when the Von Neumann methods were applied to find minimal variance (the measure of risk) portfolios. Then, in the 1970’s, the capital asset pricing model was developed, and, in the mid-1970’s, stochastic processes, which are, basically, the calculus of Gaussian distributions, were applied to develop the Black-Scholes options model, and the pursuit of that line of investigation continues into today.  Another school of investigation, behavioral finance, began in the 1980’s, and its focus has been on the irrationality of people in games.

A final aspect of the Gaussian distribution, which finally led the rational the mathematical school to realize that distributions in investment are not Gaussian, is that 99.9% of all possibilities lie within three standard deviations of the mean.  After the stock market crash of 1987, it was pointed out that a crash of that magnitude, under perfect Gaussian statistics, could only happen once in 3 billion years.  And, thus, began the search for better fit distributions, skewed to one side, and the fair game hypothesis was finally dethroned.