Risk denotes the probability of an outcome, when an individual places an investment of value in the path of forces outside their control. Straightaway the madness of this practice is revealed, yet the pages of history are littered with those that have brought about the greatest advances mankind has ever made in return for risking something of value.
It may be interesting to note that the volatility of the recent global financial crisis saw the advent of many newcomers onto the BRW Rich List in 2008, and the contention that risk is defined by the market falling is not to the point. Today, due to the very existence of derivatives such as options, swaps and forward rate agreements, an individual can direct risk and return to almost every possible market contingency, regardless of the volatility exhibited.
The Bell Curve represents a distribution of events, with the ‘bell’ representing those events that are most likely; events that are in close proximity to present market price. These resemble at-the-money options.
As we get further away from conditions prevailing at the time, the likelihood of particular events occurring will not only decrease, but will decrease in probability at an increasing rate. These less likely events take their place along the tapering edges of the bell, extending to both extremes. A pricing model attributes time value in this very fashion.
The standard deviation is the unit used to measure the probabilities transgressed from the status quo, to the market price when a particular event occurs. These measured intervals decrease in size, as the two poles of this dimension are approached; the difference between a movement of one standard deviation and two standard deviations will be far greater than that of seven deviations and eight standard deviations.
Primarily, this is due to the fact that there is little difference between probabilities that are small with other probabilities of that class, and similarly, little difference between probabilities that are high with members of that class also. They are described at a high level of abstraction that classifies them broadly as ‘high’ or ‘low’ probability.
However, when events of low probability are compared with those that are of high probability, a happening may be for example, said to be effected by a movement across seven standard deviations. In this event it is a rare occurrence indeed. When volatility is high, it is useful to note that not only are the entire bell and its tapered edges lifted higher on the plane, but the edges of the bell, move closer in gradient to the body. In higher volatility, this is directly due to the indiscriminate application of an increased probability in all possible events. The opposite will be found in low volatility with in this case, the actual bell of the curve becoming much smaller.
Accordingly, a matrix of probabilities is able to be placed in perspective.
Heavily reliant on reason, the contention that price and quality are inexorably attached is well founded in history. Even more so in perfect markets, at very least we can state with confidence that low risk and high risk are not uniformly priced. While the perception of value is a personal value judgment, what is most definite is that markets provide returns that are commensurate with the risk undertaken.
Consideration of the capital needed to fund a position, and also a variety of possible market outcomes must firmly occupy the consciousness of every trader. Insight into one’s own ability to function under the weight of risk is also crucial to profitability, as decision making needs to be carried out as free of subjective influences as possible. At any length, a good rule of thumb will be to allow 25% of risk capital to remain free for unexpected contingencies.