New approaches to volatility

By Thomas Stridsman
Although it might seems as if every stone has already been turned in the search for better analysis tools, a little logical thinking and experimentation can point you in the direction of more practical and useful trading techniques.

Just as “Baseline basics” (Active Trader, July 2010) and “A baseline trend strategy” (Active Trader, Aug. 2010) explored the advantages and disadvantages of different price “baselines” (moving averages, center lines, moving medians, and estimated modes), there are ways quantitative analysts in general — and system traders in particular — can expand their understanding of how to better estimate volatility and market momentum.

Probably the best-known volatility indicators in the financial world are standard deviation (calculated for a given period — days, weeks, hours, etc.) and average “period” range (the price distance between a period’s highest price and its lowest price). Period range is often calculated using the so-called “true range,” which incorporates the previous period’s closing price (if it is outside of the more recent period’s (bar’s) range, making the true range the slightly wider of the two calculations because it includes any gaps between bars. This article will use the standard period range calculation.

Two other volatility calculations that might be better choices for traders are absolute deviation and absolute momentum. Let’s start by comparing standard deviation and absolute deviation.

Two ways to deviate
Standard deviation is usually calculated around an average, which in the world of technical analysis would be a moving average of closing prices. The formula measures the distance between each price observation and the average price, squares these numbers so they are all positive, adds them together, divides this result by the number of price observations minus one, and then calculates the square root of this result.

Standard deviation = √∑(x – M)² / (N – 1)

Where:

x = individual price observation
M = sample mean
N = number of observations

Squaring all the price-average differences to make them positive has a drawback, however: It makes the standard deviation calculation rather sensitive to large outliers (a price that is significantly different from most other observed prices within the sample). For example, if most of the daily price-average differences in a 10-day sample are small but one or two are exceptionally large — which would occur if there was a one- or two-day price spike — the resulting standard deviation might give the impression of higher volatility for this period that wasn’t really representative of the entire period.

The absolute deviation addresses this problem by calculating the absolute value of the price-average differences rather than squaring them. This might make it a better choice for system developers because it is less sensitive to outliers, and is therefore a more stable measure and better able to result in more robust systems. The absolute deviation formula is:

Absolute mean deviation =
Abs(x – M) / N

Where:

Abs = absolute value
x = individual price observation
M = sample mean
N = number of observations

Although both formulas measure deviations relative to the mean (average) price — the most common approach in trading — this isn’t always the best way. Any of the four baseline prices could be used for calculating these deviations; the one that should be used is the one that currently best describes the central (equilibrium) price, around which the period’s fluctuations take place.

Table 1 compares the average 15-day absolute deviation and standard deviation values for crude oil (CL) futures using the four different baselines, from April 1990 to May 2010. Notice the absolute deviation is consistently lower than the standard deviation — in part because it is less sensitive to large outlier values, which probably makes it preferable to standard deviation for measuring volatility in a trading system.



Also notice how the deviations based on the center line and estimated mode are larger than those using the mean and median. This is because prices are typically not perfectly normally distributed, but instead are skewed either higher or lower, forcing the center line and the estimated mode outside and on either side of the mean and median lines. This will result in more large price deviations relative to each line, creating a higher volatility value.

If the challenge is to pick as the baseline that best describes the central tendency of the data and best fits with the true, unknown distribution, maybe the answer is to pick none of them. Range volatility might make a better alternative.

For the complete article, see the September 2010 issue of Active Trader magazine. Click here to subscribe.



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