Volatility is commonly used as a measure of risk for systems and understanding risk adjusted returns is required for longevity in trading. There are various ways to calculate risk adjusted returns, each with pluses and minuses. Having a basic understanding of these pluses and minuses helps you select the best measure for your needs while also highlighting shortfalls to keep in mind. This is particularly important for option traders who rely on volatility as part of their edge.

This first article in the series provides different views of system returns as background for comparing risk-adjusted returns.

System Volatility

Volatility measures how dispersed returns are from an expected (average) value. The standard deviation of returns can be calculated using spreadsheet software to obtain the system's volatility, along with average, median, maximum and minimum values. Systems with a mean and median value that are close together will likely have less outliers, or big winning/losing trades, contributing most of the profits or losses for a system. It also suggests the returns are less dispersed, but you need to consider the actual standard deviation as well. Unfortunately, just viewing the numbers can be less than informative.

First, table 1 provides spreadsheet stats for the system which includes 90 trades. The system seeks to profit from reversion to the mean characteristics for stocks over the short-term and is a long only approach. It is based on James Altucher's QQQQ Crash System1 which uses Bollinger Bands [BB] to signal trading opportunities. These particular results were back-tested trades for Home Depot (HD) with BB settings of 10-days for the simple moving average and 1.75 standard deviations for the bands. Note that a filter was also added for these results.

Table 1: Stats for HD Altucher Crash System

Two possible reasons a median result (think middle result) is higher than the average result include: 1) an outlier or outliers to the downside are bringing down the average or 2) there is just a higher number of trades above the average level.

Other calculations you can make on this base data to assess applying the system include probabilities that negative returns will be within certain levels. Assuming a normal distribution of returns, 1SD, 2SD and 3SD can be subtracted from the mean returns to obtain 68%, 95% and 99% probabilities shown in Table 2.

Table 2: Probability of Larger Losses

Figure 1 provides a scatter plot of the returns for 90 trades and can be more helpful than deciphering statistics. The linear regression line that is sloping slightly downward to the right suggests conditions that are moderately less well suited to the system in more recent trades or the system's edge is less effective as time passes.

Figure 1: Scatter Plot for HD Altucher Crash System

The line remains above the zero level, but it excludes commissions and slippage. Staying with the data we have, what about the account equity that results from progressing through these trades? Is it possible a series of losses in a bear market would put a halt to it before too much time passed? I'll premise that with anything is possible, but it's best to view an equity curve to get a sense of reality. Figure 2 provides an equity curve that assumes a starting value of $1,000. There was no interest accrued over the period of time the system was out of the market, which was a majority of the time.

Figure 2: Equity Curve for HD Altucher Crash System

What if the worst-case scenario prevailed and we re-sort the trades in ascending order so that the worst trades came first and best trades came last? Figure 3 re-draws the equity curve with this assumption. It appears the data suggests risk of ruin is not likely; however, it starts with a 50% drawdown and as a result less equity accrues.

Figure 3: Worst-Case Scenario Equity Curve

As a final consideration, is the assumption of a normal distribution of returns acceptable? To assess this, a histogram of returns was created using twelve 2% intervals. By viewing the histogram provided in Figure 4, it does appear that a bell curve can be drawn around the bars so the statistics used are valid. As always, it doesn't mean the statistics guarantee future profitability.

Figure 4: Histogram of Returns Using 2% Intervals (Interval 1: -0.10% to -0.08%)

It is interesting to note that the outliers were more on the positive end, along with a greater concentration trades above average (47 of 90 trades).

Summary

If the system data you view does not provide you with a good sense of how individual trade results are impacting the overall results or if the typical trade seems to be capitalizing on an edge, consider downloading the trades to a spreadsheet so you can get some different views of them. Doing this a few times will likely help you feel more comfortable with the system performance data you typically assess. It may also give you the confidence to stick with a reasonable system that has a run of losses or dropping a sub-standard one before the first signal.

1 Altucher, J. (2004). Trade Like a hedge Fund. Hoboken, NJ: John Wiley& Sons, Inc.

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Clare White
Contributing Writer and Options Strategist
Optionetics.com ~ Your Options Education Site
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