ANALYTICAL TOOLBOX: Probability of Profits in Practice
September 21, 2006
The settings for the Probability of Profits tool favor strategies that benefit from sideways movement, but also allow for moderately bullish or bearish outlooks. This makes sense when you consider the calculation makes use of a future mean value that is equal to the current’s day close. When the user changes the future mean value or the volatility outlook, other strategies become eligible for review.
Future Mean Value
In August we reviewed graphs for various S&P 500 Index (SPX) measures, including thirty years worth of daily closing values. The resulting histogram had a significant number of observations in the lowest end of the scale. Rather than this long review period, let’s look at a timeframe that is more consistent with equity option holding periods. Figure 1 displays closing data in histogram form for stock XYZ over a period that is slightly longer than seven months.
Figure 1: Closing Value Histogram for Seven Months – Stock XYZ Statistica
Basic statistical measurements for the data are included with the chart heading. The closing price for the first day was 79.09 and is the input number for the future mean value. However, the actual mean value for the seven months of data was 81.90—3.6% higher than the assumed value. How would this affect the results? (Note: The price movement that generated this data is displayed in a chart at the end of the article.)
The analysis date is Jan 2nd and an August butterfly strategy is evaluated using 1 long 75 strike call, 2 short 80 strike calls and a long 85 strike call. The following two graphs are generated using the 100-day SV. The first uses 79.09 as the future mean value and yields a Probability of Profit of 20.9 while the second uses 81.90. The Probability of Profit of result is also calculated as 20.9.
Figure 2: Standard Deviation Price Projection @ 79.09 Optionetics Platinum
The 1 SD band shifts upward, but still encompasses the same area of profitability. While the future mean value is important, it does not necessarily have to be exact to provide reasonable results. The more important factor is an outlook for the security that is well suited for the tool and a strategy that matches it.
Figure 3: Standard Deviation Price Projection @ 79.09 Optionetics Platinum
Does this mean that when your trade’s zone of profitability falls within 1 standard deviation band the position will be profitable? Does a certain value for the Probability of Profits guarantee results? The answer is no to both, but the point of the exercise is to show you how historical data is used to project future prices and how this compares to actual results.
It’s important to understand how the tool assumptions and user-defined changes impact probability results. Such an understanding should help you determine which changes are rational and which will provide results that fit the model, but are not realistic. As is, the tool is best applied to strategies that rely on sideways movement. Continued review of different examples should provide the user with additional insight to the challenges faced when trying to apply the tool to a directional strategy.
Trade Example
It’s early September and volatility seems low considering we’re entering a relatively busy and uncertain time for the markets. Although the seasonal bias is downward, both the S&P 500 (SPX) and the leading exchange traded fund [ETF] that tracks it—the SPDRS S&P 500 (SPY)—are in upward trends. A trader may consider a straddle position to capitalize on a strong upward or downward movement in the ETF, an increase in volatility or both.
Using Optionetics Platinum we’ll review a trade using Dec 130 options for SPY, with a trade initiation date of 9/8/06. Recall a straddle uses a long call and a long put with the same strike price and expiration month to take advantage of a strong move upward or downward. The maximum risk for the position is the maximum debit, the breakeven to the upside is the strike price the initial debit and the breakeven to the downside is the strike minus the initial debit. The maximum reward is unlimited to the upside and limited, but high, to the downside (since SPY can only technically fall to zero).
Figure 4: Risk Analysis for SPY Dec 130 Straddle Optionetics Platinum
Figure 5: Risk Graph for SPY Dec 130 Straddle Optionetics Platinum
The probability of profit with 0 days left and a statistical volatility of 10.21 is 29.85. Clicking on this value brings you to the probability calculator. Using the default entries, we obtain the graph in Figure 5 that displays +/- 1SD levels and +/- 2 SD levels approximately 100 days out (trade days is 98 days).
Figure 6: Standard Deviation Price Projection for SPY Dec 130 Straddle Optionetics Platinum
Although almost the entire area between the two breakeven points falls within the red curve (+/- 1 standard deviation), the Probability of Profits value is relatively low at 29.85. That is because a straddle requires directional movement outside of the breakeven points. You must keep in mind the type of strategy you are evaluating when using the probability function.
The downside breakeven of 122.50 is just below the -1SD red band, but most of the prices within the 1SD curve represent some level of losses for the position. There is a good deal of price movement that can take place without the breakeven levels being reach. In addition, it appears that 122.50 is a lower support area for the ETF, with that level holding recently in June and July.
The trader may wish to see if price reaches this point and re-evaluate a straddle since strong movement away from this level is reasonable from a technical standpoint—price should move strongly upward if this intermediate term support holds and down strongly if it fails.
Summary
The Probability of Profit uses historical price, volatility and time data to create a very large number of potential price paths going forward a set number of days. The equation that serves as the basis for the probability calculation is:
Probability of Profit = # of Profitable Trades / Total # of Trade Simulations
Optionetics Platinum actually makes use of the lognormal properties of the distribution to calculate this value by measuring the area under the curve that is generated by historical data. There is an upward bias to the distribution results because price cannot fall below zero. Probability of Profit data is initially fed into the program using the closing price of the underlying security, one of five volatility measures and time to expiration for the strategy evaluated. The results are provided in chart form for ease of use and a more intuitive understanding of the price movement needed to garner profits.
Since the calculation is generated with the assumption that today’s closing price is the future mean value for the stock and that volatility will remain the same, the analysis favors sideways strategies. The trader can change the future value assumption, but should only do so when there is a valid rationale for it. When viewing the graph generated by the statistical analysis, the trader must be aware of price points or ranges that result in a profitable position. Directional trades will require movement that is centered by some value other than the current day’s close. In addition, more volatile conditions can both help and hinder profitability and the user should consider this when reviewing the output for the tool.
Copyright© 2006 Optionsanalysis, Inc. and Optionetics, Inc. All Rights Reserved.
To access other articles written by Clare White, please click here.
Clare White, CMT
Contributing Writer and Options Strategist
John Broussard
Optionetics Platinum Developer
Optionetics.com ~ Your Options Education Site
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