An essential step toward successful investing understands the differences between random and nonrandom occurrences. A random (or a statistically independent) event is an occurrence whose outcome cannot be predicted from preceding events. Examples of random events are the result of a coin toss and the spin of a roulette wheel. For such events, the outcome of any single trial is determined by chance and is impossible to predict. For example, if you toss a fair coin it is impossible to know in advance whether that particular coin will fall heads or tails. The futility of both “it is time to reverse” and “it is running hot” betting systems will become clear if you analyze the game of coin tossing. Each toss has two possible outcomes: heads or tails. When heads occurs, tails cannot, and vice versa. The probability, or likelihood, that a fair coin will fall heads is one-half. This means that, in the long run, you expect half of the outcomes to be heads.
You need to remember two points:
1. It is impossible to predict which outcome will occur on any particular toss.
2. Over many repetitions, about half of the outcomes will be heads and half tails.
If events are random, as in coin tossing or roulette, historical information cannot be used to predict a subsequent event. Are day-today stock price changes random events? If they are, patterns of historical price changes cannot be used to predict the magnitude or direction of subsequent price movements. In addition to randomness, or statistical independence, two important concepts that investors need to understand are expected values and variance. Essentially, these concepts boil down to knowing what to expect and knowing the risk of not getting what you expect. Thus, risk can be defined as unpredictability, or the extent to which results do not match expectations.