Platinum offers different probability tools that enable traders to gain perspective on future security moves given past performance. As the mandatory statement goes, past performance does not guarantee the future, but it certainly offers a bit of a reality check when considering price expectations for option strategies. Getting the most out of the tools requires a basic understanding of the assumptions made when implementing them and playing around a bit.

The Platinum tools appear with search results when finding trades, as a stock chart option, with risk graph results for individual trades and when launching the Probability Calculator from the risk graph. They include:

• Odds
• Probability of Profit
• Kelly Bet Fraction
• Standard Deviation Bands
• Probability Cones
• Probability Calculator

Basic Probability Assumptions

The probability tools in Platinum make use of assumptions similar to those used in the Black-Scholes Option Pricing Model for European Style options, published by Fischer Black and Myron Scholes. These include in statistical language:

1. Security returns follow a normal distribution
2. Volatility remains constant
3. The expected mean return for the security is zero

While it’s not critical to understand the nitty-gritty of why these statistical concepts were selected or apply, it is important to understand how they impact probability tool results. Hopefully the explanations and impact that follow are as quick and painless as possible.

Security returns follow a normal distribution

When you plot security returns on a histogram, you will find many follow the Bell curve distribution if you have sufficient data. Returns are used in place of prices because price cannot go below zero, something that’s useful so you can apply different statistical techniques.

The only problem with this approach is that returns may exhibit fat tails, meaning you don’t have nice symmetry for the Bell curve. Instead there are more results grouped in the histogram bars at either end of the data plot than what you’d expect. This translates to a higher number of extreme positive and negative returns in the stock market.

Using Worden Brothers daily data from 1/1/1980 through 8/6/2008 for the Dow Jones Industrial Average (INDU) to display returns, the histogram in Figure 1 shows a normal curve around the data. Hopefully you can see there are also a reasonable number of values extending the extremes.

Figure 1: Dow Jones Industrial Daily Returns using Histogram from Statistica (1/1/1980 – 8/6/2008)
(click here for larger view)

In the stock market there are times when strong positive or negative returns occur—it’s probably safe to assume some days from October 1987 appear on the left side histogram. So if you use a tool that applies a more symmetrical curve, even if it’s flatter (less volatile) or more peaked (more volatile), there are going to be days in the stock market that move outside of the range captured by the curve. It doesn’t mean you can’t use the tool, it just means a probability result doesn’t equate to a sure thing.

Volatility remains constant

Platinum obtains probabilities by running a very large number of trials and collecting the results from those trials. Rather than using some random number to map out potential price paths for the security, it makes use of volatility values such as the 100-day statistical volatility [SV] or a user defined value (i.e. an implied volatility).

Using the Probability Cone feature on stock charts as an example, a chart with 30 future days calculates a statistically valid daily return for Day One based on the volatility value selected and adds this to yesterday’s closing value. To calculate Day Two in the cone, Platinum calculates another statistically valid daily return based on the same volatility value and adds it to the Day One value obtained.

Figure 2 displays an SPY daily chart using Platinum and the Probability Cone feature. The red cone will capture 68% of the future price paths generated using the approach described while the blue cone captures 95% of them.

Figure 2: SPY Price Chart backdated to December 2007 with a 250 Future Day Probability Curve

The 100-day SV was used to create Probability Cones 250 days forward. Since there is price data for a portion of the period, that information is also displayed. A majority of the data fits within the blue cone, while a smaller percentage is also captured in the red cone. As expected, the potential price range increases as you go out further in time.

The expected mean return for the security is zero

Note how the cones in Figure 2 are centered by a horizontal line drawn from the last close available (in Dec 2007). This chart was drawn using than assumed mean return of 0. In Figure 3, the same horizontal line is drawn; however, the cones are constructed with a user-defined mean return for SPY of 8%. As a result they are skewed upwards creating a higher price range for each day’s expected closing value in the future.

Figure 3: Same SPY Price Chart with a Predicted Rate of Return of 8%

Since there’s been a bearish market in place since the Dec 2007 closing date used in this example, a larger number of actual prices fall below both the red cone and blue cone range.

What’s the Point?

You can gain a much better grasp of how different inputs impact the Platinum Probability tools by playing around with Probability Cones using historical data. Select different Stock Date settings by changing the date in the upper right hand corner to include:

1. Days that appeared at the bottom or the top of major trends
2. Days that followed wide ranging, volatile trading periods
3. Days that were part of a quiet trading period

In addition, vary the chart settings to the left of the chart and observe the impact to the probability cones and the chart price scale.

Figures 4 & 5 also make use of the current 100-day SV on the back-test date and a 0% predicted rate of return, but are initiated on different days. Figure 4 was drawn on 8/5/08 while the Figure 5 chart was drawn using the July 14^th low. What type of strategies (bullish, bearish or neutral) might the trader be considering on July 14^th?

Figure 4: SPY Price Chart drawn on August 5^th, 2008 with a 100 Future Day Probability Curve

The cones are also used on the Probability Calculator which is used to calculate the Probability of Profit value found on the Risk graph page of Platinum. It uses the price range bounded by the future day cone that corresponds with the option expiration date for the nearest expiration month in a strategy. Profitability is based on how these values translate to gains or losses for the trade on that day.

Consider the impact of implementing a bearish strategy with a predicted rate of return of 0% on July 14th based solely on a Probability of Profit value greater than 50%. Even though we may look back in 100 days and find that most prices fall within the blue cone region of the chart in Figure 5, it doesn’t guarantee profits for the strategy. Note the SPY price scale difference for the two charts.

Figure 5: SPY Price Chart drawn on July 14^th, 2008 with a 100 Future Day Probability Curve

These examples only scratch the surface for a discussion on the Platinum Probability tools, but hopefully they help provide some initial steps for you to take to better grasp them. For some more detailed explanations, check out the Analytical Toolbox articles from August & September of 2006 written with John Broussard.

Another great resource for improving your understanding of the underlying statistics for option pricing and the probability tools is the Platinum Help Guide. Two books referenced in the guide you may want to consider for a deeper understanding are Jerry Marlow’s Options Pricing Black-Scholes Made Easy and Sheldon Natenberg’s Option Volatility & Pricing.

To access other articles written by Clare White, please click here.

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