Anyone who has been forced to take Statistics 101 in high school or in college has probably been exposed to a discussion of the odds of getting a head or a tail when flipping a coin. Extensive experiments have documented that no matter how many times you flip a coin, there is always a 50-50 chance of getting a head or a tail. If you toss ten straight heads in a row, you still have a 50-50 chance of getting a head on the eleventh try.

This axiom is the cornerstone for the concept of normal distribution of random events. For example, let’s flip a penny 225 times — 15 separate series of 15 tosses each. The theoretical results follow:

Each time this experiment is repeated, the results may or may not be repeated. However, the majority of time, very similar results will result.

Specifically, the results most often — assuming the coin used is properly balanced – will be in the middle of the spectrum. It would be very unusual (32,000:1) to get 15 straight heads or tails, or only one or two tails and the rest heads, or all heads and no tails. Normal distribution describes what is likely to occur when random events occur. Charting this on a graph generates the well-known bell-shaped curve.

An additional assumption is made, namely that when the normal distribution concept is applied to the “random price action,” one needs to use lognormal distribution. This skews the results to the positive side of the mean to account for inflation and the unlikely event of a commodity price going to zero. Making this adjustment to the curve produces a bell-shaped curve leaning slightly to the right.

The bell-shaped curve is the distribution curve. The one produced by flipping a coin repeatedly is “normal” or moderate in appearance, but the shape can change. Erratic data produces a flat arc because the data points are scattered. Data representing a slow moving futures market result in a curve that is very steep or narrow, since the data points are close together.

The key concept is that the flatter the shape of the distribution curve, the more volatile is the market being evaluated. Plotting price changes for various markets to generate distribution curves is important so traders can quantify market volatility. Once this is done, it gives traders the ability to make statistically valid estimates of what price moves can be expected from these markets.

Underline the words “statistically valid estimates of what can be expected.” This is the best a trader can do when he is attempting to forecast futures prices. On average, or normally, he will be correct, but this doesn’t guarantee that he will always be right. It’s inevitable that he will still experience losses.

Hopefully, it will put the odds in the trader’s favor, giving him an edge. It should provide an excellent insight into market volatility, allowing him to answer questions like:

How much of a price move can I expect?

What are the chances of this market making a limit move?

Can I expect a certain futures or stock to make enough of a move during the life of the option I plan to buy to make a profit on the option?

This type of analysis provides educated guesses to these questions. It is the basis behind the computer programs that calculate the theoretic value of options, as an example. By running these formulas, the programs rank the option alternatives telling traders which ones are underpriced or overpriced.

What this analysis does not do is tell us which way a market will move. Don’t forget, we are discussing volatility of what has been classified as RANDOM moving markets. The trader should be able to figure the statistical odds of a market making a $2.00 move over the next 35 days — but will it be up or down?

But that information won’t come from this type of analysis. The answer – or, more correctly, the best estimate — must come from other types of analysis, such as fundamental or technical.

Once a trader has an opinion of whether he is facing a bull or bear move, he turns to volatility research to determine the expected volatility of the market(s) under consideration.

The next step is to calculate the probability of the anticipated price projections.

The distribution curve provides a graphic representation of the distribution of random price action. It is now necessary to quantify the data so projections can be made.