Technical Analysis Archive

The Aroon indicator is a conceptually simple technical indicator. Developed in 1995, it is newer than many of the more popular technical indicators. But for some reason, not all charting web sites offer the Aroon indicator. Yahoo! Finance doesn’t offer it. Neither does CME Group. Two charting web sites that do are Stockcharts and Barchart.

Calculation of the two outputs of the Aroon indicator, and involves only a single parameter, a span parameter specifying the number of bars over which to calculate the indicator. The most common setting is 25 days. The formulas are:

Occasionally, people will subtract from to calculate the Aroon oscillator, which varies from -1 to 1.

A look at the historical 5-day close-to-close returns following 25-day Aroon crossovers on non-penny American stock prices from Yahoo! Finance reveals 5-day returns with geometric averages of 0.039% for positive crossovers and 0.020% for negative crossovers. It doesn’t look very promising so far, but we’ll take another look at the Aroon indicator in the future.

In a recent post, I suggested that Bollinger bands *might* be useful in a trading strategy by themselves but warned that it could be risky. Let’s take a look….

If you had made a trade in the past 30 years based solely on a high Bollinger band reading, more often than not, the stock price would have risen in five days. But if you had invested all of your money in several trades that way in sequence, odds are, you would have lost money! How is that possible?

It’s simple: When you lose money on the stock market, you have to make a larger percent gain in order to make back your money. If you have a 25% loss, you need a 33% gain just to break even. Three 25% gains are more than wiped out by a single 50% loss.

This chart was prepared by calculating the geometric average of all possible 5-day changes from close to close in the Yahoo! Finance stock market historical data available on January 13, 2011 across bins of 0.1 deviations (eliminating any stocks that had ever traded below $1). While it implies that stocks that are far below their lower Bollinger bands may be profitable short-term purchases, some care should be taken in interpreting this chart, as it may understate the risk for purchases. In addition, this chart should not be used as a substitute for simulation, and past performance is not always an indicator of future results.

A new investor cannot spend much time reading about how to time trades without reading about Bollinger Bands. While rarely discussed in academic research, Bollinger Bands are the most popular volatility model. The notion is simple: Calculate the average closing price and its standard deviation over a series of sliding windows, each one covering a fixed number of bars. Find the upper and lower bands by adding and subracting a multiple of the standard deviation from the average stock price, and BAM! You have Bollinger Bands.

This procedure has some appeal to many people who have had a little training in statistics. It resembles the widely-taught procedure for calculating confidence intervals on a normal distribution.

There are, however, a few problems with the analogy of Bollinger Bands and normal confidence intervals:

1. Stock prices do not really follow a normal distribution. They more nearly follow a log-normal or even a Levy distribution. Sometimes, people use log Bollinger Bands to partially compensate for this deficiency, but that is uncommon.
2. Stock prices show a high degree of autocorrelation. Ordinarily, we would expect that the price today would be highly correlated with the price tomorrow–and that the price tomorrow would be highly correlated with the next day’s price. This violates a key assumption used for calculating ordinary normal confidence intervals, i.e. that all samples are independent.
3. It isn’t clear what would be indicated if the stock price crosses a Bollinger Band. Does it indicate that the stock price has reached an improbable level and that regression towards the mean is to be expected? Or does it indicate that there has been a shift in the mean?
4. Bollinger Band calculations use the population standard deviation rather than the sample standard deviation. Common wisdom from introductory statistics classes would suggest using the sample standard deviation and the t-distribution within a normality framework.

Of course, it is a bit unfair to apply these criticisms to Bollinger Bands without noting that the same criticisms can be applied in varying degrees to a wide array of volatility models. And it is worth considering that given the popularity of Bollinger Bands, they affect investor behavior, causing forseeable price shifts. In the next article in this series, we will empirically examine the historical behavior of stock prices with relation to their Bollinger Bands in popular configurations.