Option Investor

Options 101 - Knowledge Yields Success!

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Volatility Basics

Over the past few weeks, we have made a number of references to volatility in stock prices and the fact that it can often be very difficult to predict. Traders without knowledge of the way volatility and probability affect option values and potential risk-reward have little chance of surviving in the derivatives market, thus it seems appropriate to review this subject for those who are serious about achieving long-term success.

Volatility is one of the most important factors in option trading because it measures the amount by which the underlying asset fluctuates in a given period of time. Before you can estimate the future volatility of an issue, or the potential for an issue to reach a certain price, you must understand how a stock's movement is quantified from a statistical standpoint. Historical volatility is calculated by using the Standard Deviation of an underlying asset's price changes (from close of trading each day) for a certain time period. By definition, standard deviation of a collection of numbers is the square root of the difference between the mean of the squares of the numbers and the square of the mean of the numbers. In simpler terms, the standard deviation is basically the "mean of the mean," and it can often help you find the story behind the historical data. To better understand this unique concept, you must learn more about what statisticians call "normal" distribution, which is the elementary component of most probability calculations.

Probability: A Way to Measure Uncertainty

The great philosopher Aristotle once said, "The probable is what usually happens" and that statement was never more accurate than with derivatives trading. In fact, the early Greeks were well known for their knowledge of arithmetic and logic but despite this early understanding, the modern study of probability did not begin in earnest until a few hundred years ago when the great French mathematicians Pascal and Fermot discussed numerical theories related to games of chance. In the current era, probability theory is an integral component of statistical mathematics and it is used in a variety of applications across a range of industries. As traders, the area we need to focus on is how probability distributions are utilized in financial markets and risk management to forecast future events.

In the simplest terms, probability is the likelihood of a given event's occurrence. Taken one step further, probability theory is a branch of mathematics that studies the likelihood of occurrence of random events in order to predict the future behavior of defined systems. For the laymen, the easiest way to understand probability is with some simple experiments such as flipping a coin or rolling dice. Calculating probable outcomes in a coin toss is relatively simple because there are only two possible outcomes - heads or tails - and one or the other must occur. At the same time, each flip of the coin is an independent event and the outcome of one trial has no effect on future results. Some people mistakenly believe that a number of consecutive outcomes makes it more likely that the next toss will result in a different results, however that assumption is a fallacy. No matter how many times the coin flip ends with heads or tails, the probability that it will be one or the other on the next toss is always 1/2 or 50%.

Although the coin-toss experiment provides an excellent example of probability in our every-day lives, it is woefully inadequate for illustrating a complex system with a large number of potential outcomes. For this type of analysis we need to view a probability distribution: a curve that shows all the values that the random variable can take and the likelihood that each will occur. As you may know, a bell curve is one way to illustrate a distributional model for univariate data. Univariate data consist of samples or measurements of a single quantitative variable such as a stock or option price. A fundamental reason for studying this type of data is to characterize its movement or distribution. This involves comparing how the data is distributed with regard to standard distributions, especially the normal distribution. A normal distribution of data means that most of the examples in a set of data are close to the "average," while relatively few examples tend to one extreme or the other. If you depicted normally distributed data on a graph, it would look something like this:

Normal Distribution Chart:

The x-axis (the horizontal one) is the value in question, and the the y-axis (the vertical one) is the number of data points for each value on the x-axis. Not all sets of data will have graphs that look this perfect. Some will have relatively flat curves, while others will be steeper. Sometimes the mean will lean a bit to one side or the other. However, all normally distributed data will have something like this same bell-curve shape. The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. When the examples are fairly tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the curve is relatively flat, that suggests a relatively large standard deviation in the data. Computing the value of a standard deviation is complicated but here what a standard deviation represents graphically:

Standard Deviations Chart:

One standard deviation away from the mean in either direction on the horizontal axis (the red area on the above graph) accounts for somewhere around 68% of the possible outcomes in this group. Two standard deviations away from the mean (the red and green areas) account for roughly 95% of the outcomes. Three standard deviations (the red, green and blue areas) account for about 99% of all the possible outcomes. If this curve were flatter and more spread out, the standard deviation would have to be larger in order to account for the number of possible outcomes. That is why the standard deviation can tell you how spread out the results in a set are from the mean.

You might wonder why this information is important and the answer is simple: The knowledge of probability theory can be used to determine the likelihood of a particular issue trading above or below a specific number or within a given profit range. While this information can be derived through a complex study of historical data, it is much easier to use a simple probability calculator (preferably, a "monte-carlo" style calculator) to make this forecast. Of course, the fact that it "should" remain in a particular range doesn't mean it will and that's the reason traders have to learn to manage losing plays effectively - so they don't create catastrophic draw-downs on one's portfolio.

Some Volatility Guidelines

Volatility is the most important variable in valuing an option, and it also a necessary component in assessing the probability of a successful outcome in a specific position. But, as you have learned by now, the future volatility of the underlying issue is usually a very difficult value to accurately determine. Professional traders use several different timeframes to assess a stock's potential movement. In most cases, the 20-day historical volatility (hv) provides a reasonable projection of the short-term volatility of any instrument. But, for longer-term strategies, the 50-day and 100-day historical volatility values should be compared with the near-term numbers to identify any changes or disparities in the recent character of the issue. As you would expect, a sizable move in the underlying instrument, due to an earnings report or an unexpected event, can produce catastrophic losses, even in a limited-risk position such as a spread. With that in mind, it's crucial to make a volatility estimate prior to selecting the expiration month for a spread and for most traders, 20-day, 50-day, 90-day and 1-year periods are adequate timeframes to evaluate the magnitude of future movement that can be expected over the life of an option.

Comparing historic volatility to implied volatility helps a trader determine whether options are cheap or expensive. Implied volatility (iv) is a theoretical value designed to represent the volatility of the underlying security based on the price of the option and the most common way to use this component is to observe an average of some past period of time, such as a 100-day moving average. Experienced traders also use an adverse volatility estimate, based on historical volatility, in order to provide a more conservative appraisal of an option's true value. By definition, implied volatility is a mathematical measure of the relative cost of an option, and it is largely based on the historical volatility of the underlying issue. In reality, the implied volatility of an option is mostly determined by market expectations of the underlying security. When evaluating historical and implied volatility for specific option trades, it is best to use the most conservative values in pricing calculations. For example, if you are going to sell an option, use a high estimate, perhaps the maximum value of the most common (20, 50 and 100 DMA) short-term volatility data. With that approach, the current price of the option will have to be inflated for the premium to appear "overpriced." In contrast, if you plan to engage in a strategy where you expect the underlying issue to be active, then a low volatility estimate (the minimum of the 20, 50, or 100 DMA) would be more appropriate. Using that technique, the option will look "cheap" only when it is relatively inexpensive, based on historical stock movement.

Theory Versus Reality

It should be obvious by now that volatility is an important piece of the trading puzzle, not only for assessing an issue's potential for price movement but also for analyzing an option's fair value. Although prices for exchange-listed options are established in the marketplace by computerized pricing models, buyers and sellers do exert a strong influence on actual market values. More importantly, pricing models are based upon the mistaken assumption that all stock price movement is "random." Clearly, there are many stocks that are moving in well-defined price trends, as opposed to moving randomly, and if you can identify those stocks whose price trends are likely to continue, you can achieve an edge against the option-pricing model. Much of our effort at the Option Investor Newsletter is devoted to finding stocks that exhibit such trends, so our subscribers can profit from buying undervalued options, selling overvalued options, or initiating limited-risk spreads on these issues.

Trade Wisely!

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