ATR, Volatility and Standard Deviation

ATR, Volatility, and Standard Deviation…OH MY!

by Jared Levy

Tue, 01 Sep 2009 11:02 CDT

Related Symbols: SPX DJIA

 With regard to the title of this article, I thought it was appropriate to bring my three favorite words (besides “It’s Raining Men”) back for September. Many traders, including myself, have the feeling that September will bring not only volatility, but negative price action to the marketplace. In fact, the markets, on average, are down between 0.5% and 1.0% in September, according to Stock Trader’s Almanac.

Whatever your opinion, having a firm grip on these concepts is an integral part of not only setting realistic expectations for your trading and spotting anomalies, but possibly (and perhaps more importantly), finding a reasonable stop loss level in your trade.

All three of these measurements are somewhat related, but each is expressed in slightly different ways and interpreted differently. For most of us “home-gamers,” we are not going to use ultra-complex mathematical models to find precise deviations for a stock’s “normal” patterns as a means of finding some sort of volatility arbitrage and trying to capture it.

More likely, we are using these observations as a means to identify “realistic” and relatively abnormal occurrences in either an option’s pricing or a stock’s behavior.

Let’s start with volatility. First off, there are several types, so for this example I’ll just use historical (observed) and implied. Historical volatility is an annualized number expressed in percentage terms telling us how much a stock has moved in the past.

Volatility helps us gauge a stock’s behavior and gives us a benchmark, so to speak, when examining a potential trade strategy and setting profit targets and stop losses. Volatility is typically measured using close-to-close prices as the inputs for finding deviation or volatility.

Using close-to-close observations helps to “normalize” the intraday noise that tends to occur in the marketplace. Plus, it’s quite cumbersome to take every single price movement into consideration to compute volatility. Although with today’s technology, that is certainly possible and I know that certain market participants use that data.

For example, if I said a stock was moving on a 40% volatility and the stock was trading at $100.00 per share, that means it would be realistic for the stock to move either 40% higher (($40.00) or 40% lower ($40.00) about 70% of the time (this is where standard deviation comes in …).

Now, on to standard deviation. As a professional market maker, my options and decisions on trades were based upon how volatile a stock is, was, or will be in the future. By definition, standard deviation is a measure of the variability or dispersion of a statistical population, a data set, or a probability distribution. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

To simplify, standard deviation is the annualized expected movement (expressed in whole dollars), using the current stock’s price as the mean, while plugging in the observed volatility. So if the current stock price was $100.00 and we were using an observed volatility of 40%, one standard deviation over a year’s time would be $40.00 up or down, and this distribution would occur about 70% of the time.

What are the Chances?

• 1 St. Dev = 68.3% chance the stock will stay within plus or minus 1 standard deviation.
• 2 St. Dev = 95.4% chance the stock will stay within +- 2 standard deviations.
• 3 St. Dev = 99.7% chance that the stock will stay between +-3 standard deviations.

Obviously, it’s all about the input. If you are using 40% as your volatility measurement and you are taking your measurements right after March 2009, your observed volatility may be high and you may be expecting too much movement out of your stock. If, however the markets have been quiet for some time and you use that measurement, your calculations may be low.

This ambiguity is what makes the marketplace work and is also why there is NO perfect answer. For me, I like to use a blend of both the historical volatility as well as the implied volatility of the options to generate my forward-looking volatility calculations.

By the way, to determine the daily expected volatility of a stock, take your annual volatility number and divide by 16 (the square root, roughly, of the number of trading days in a year). That will be your daily average % volatility.

Now, on to ATR. ATR stands for average true range or average trading range. ATR measures the average dollar movement of a stock over different time periods, typically taking 14 periods into account. It also measures more than close-to-close pricing.

ATR takes the LARGEST movements into account, which enables the trader to get a closer look at the true recent behavior of the stock he or she is trading. I use ATR as a quick confirmation of a stock’s over bought or oversold condition.

I also use this as the outer edge of where I would place my stop- loss or profit target or as an entry for a reversion to the mean trade. For instance, if a stock or index has exceeded its daily ATR and I see a chart pattern that looks attractive for entry, I may enter long or short then cover once the stock has hit its “normal” 1 standard level. As most times, ATR will be greater than daily standard deviation.

Just some thoughts!

Closing with another favorite three-word phrase of mine: “Keep selling, Mortimer” 🙂