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Optionetics Platinum offers a variety of tools for analysis of options and potential trades. Between the sheer number of these tools and an individual’s natural tendency to look at a limited number of them (victims of habit), it seems necessary to dedicate a few Analytical Toolbox articles to this powerful platform. The remaining August and September articles will be focused in this area. If you are not a Platinum user, stay with it—the content will cover a variety of statistical and analytical techniques that could still very well add value to your trading.

Probability of Profit Intro

When discussing the Kelly Bet Fraction a couple of weeks ago, the Probability of Profit was referenced in the Optionetics Platinum website as: “the probability that the predicted stock price falls within the option trade''s profit regions. The predicted stock price distribution is computed by projecting the stock price randomly into the future using the SV (statistical volatility).” More on this definition in a moment, but for now let’s back up a bit.

First, it’s appropriate to start a discussion on probability of profit with reminding readers of two key concepts often repeated in Optionetics’ materials: 

Statistics is a tool traders have at their disposal to evaluate potential trades, the effectiveness of a system and portfolio performance. It’s useful in option analysis, as well as technical and fundamental analysis. When an individual performs a review on the top 10 stocks from a fundamental scan that produced a list of 100 stocks, he or she is using the statistical concept deciles, whether this is done intentionally or not.

A further review is completed on a scan shortlist because the individual recognizes that this step is just one in a process to help improve portfolio results. Trades are not immediately taken on the shortlist because a top decile approach doesn’t represent a “holy grail” to profits. Similarly, the probability of profits discussion that follows does not guarantee performance results. It represents another tool that is readily available to Platinum users and perhaps less accessible—but valuable—to non-Platinum users. By truly understanding the function of the tool, a trader can make the most of it in their own trading.

Probability Review

When using statistics, the individual generally takes a meaningful sampling of data then makes certain observations about the entire population using calculations from the subset. There is no causation assumed (i.e. this x happened because of y) and no concrete conclusion drawn. Statistics is much more vague than the typical math we encounter day to day.

Probabilities are derived from an event with different outcomes and used to measure the likelihood of events happening in the future. The toss of a coin provides a nice example because there is only one of two outcomes possible and each separate coin toss represents an independent event. Here are the rules: flip a fair coin 1000 times and when heads appears you win a $1, tails you loose $1. The expected Probability of Profit for heads is as follows:

A less onerous way to put this is:

So the Probability of Profit = ~500 heads/1000 = 0.5.

Note the Probability of Profit calculation is shown as an approximation. It’s an average value (=mean) we expect to obtain if we keep repeating sets of 1000 tosses of a coin. Although the topic of odds will be discussed further in a different article, it bears mention here. The Odds of Success for this wager is determined by calculating expected gains and dividing it by expected losses. In the example:

Again, the value obtained is an approximation and it’s what we expect to see if we continually toss a coin 1000 times and log the results. This does not mean in round 558 of tossing a coin 1000 times that we will absolutely realize such results. The Odds of Success calculation, like Probability of Profit, is simply a means of measuring expectations based upon past performance.

Given Odds of Success = ~$500 wins / ~$500 losses = 1:1, 50% of the time we expect to win. The odds are such that we put up a dollar to win a dollar. What happens to our Probability of Profit and Odds of Success if the heads payoff is changed to $2 while the loss remains $1?

Probability of Profit

• # of Heads Possible / Total # of Tosses
• (½ * 1000) / 1000
• 500 / 1000 = 0.50

The Probability of Profit remains the same, however, the Odds of Success changes:

Odds of Success

• 1 chance in 2 for $2 gain (1000 times) / 1 chance in 2 for $1 loss (1000 times)
• ½ * ($2) * 1000  /  ½ * ($1) * 1000
• ~$1000 wins / ~$500 losses = 2:1

The Probability of Profit remains the same, however, the Odds of Success changes:

50% of the time we expect to win, but the payoff is such that we put up a dollar for the potential to win two dollars. Our odds are now better at 2 to 1.

Kelly Bet Fraction Application 

For those interested in the Kelly Bet Fraction [KBF] that was introduced a couple of weeks ago, we have the following result given Probability of Profit = 0.5 and Odds = 1:1 or Odds = 1,

KBF = 100 * { [ ( Probability of Profit * (Odds + 1) ) – 1] / Odds ) = 100 * [ (0.5 * 2) – 1] / 1 = 0

This means there is no investment over the long run that can make an even-money coin toss increase your profits. However, when odds = 2:

KBF = 100 * [ (0.5 * 3) – 1] / 2 = 25%

This means at each coin toss invest 25% of your current stake to grow your profits optimally.

Probability of Profits Extended to Options Trades

The Optionetics Platinum analysis platform includes a few probability calculations; some are behind the scenes while others are more interactive with the user. In this article series we’ll discuss:

When considering option applications, what is one alternative available for data sampling? Ideally, the notion of past price movement comes to mind. Options analysis makes use of statistical volatility, a calculation that measures the speed of change in prices based upon some set interval (i.e. days, weeks, years, etc.) over a past number of periods (i.e. 10, 20, 500, 100, …).

Statistical volatility for options—also known as historical volatility—uses a standard deviation calculation and annualizes that result. This means that although a variety of time intervals may be reviewed, the end value can be compared to other SV values because it is standardized over a year. A trader uses SV to compare the relative volatility of different underlying securities, with higher SV values associated with more volatile securities. In terms of its application to probabilities, past price movement represents a series of events in which we base our future expectations.

Now let’s move to an option trade. We are in the movie "Ground Hog Day" and we can place the same trade each morning on the same day with the same start conditions but the stock thereafter each day will behave differently. So we try the same trade 1000 times.

Each trade that ends in a profit, we count and add the profits to a Pile of money we call "Profits". We put losses in the pile of money labeled "Losses" and count them. We compute the following parameters based on the 1000 events we accumulated: 

That’s basically all there is to it. How does Platinum perform 1000 trades? Platinum replaces the stock price at option expiration at the end of each of the 1000 trades with a statistical distribution of the future stock price at option expiration. The stock price in the future is assumed to have a statistical distribution based on its current SV value. This approach includes many underlying assumptions about the stock''s future prices. A book that goes into great detail of Probability of Profit is Jerry Marlow’s "Options Pricing Black-Scholes Made Easy."

Platinum computes the probability the stock will be between two values using the statistical distribution and looks at the Risk Curve. If the Risk Curve says "Profit" those probabilities are put in the "Profit" pile. Otherwise they go into the "Losses" pile. When all stock prices have been checked, the probabilities in the "Profit" pile are summed to give the Probability of Profit. Odds are computed similarly. 

Probability Calculator

Probability Calculator is a tool for finding future stock price probabilities. It finds and displays probability text values and charts the stock and probability data. Input data can be for a specific stock symbol or generic user values. A new feature in Platinum''s Probability Calculator, not found in most other probability calculators, is you can enter the stock''s future rate of return or enter a future expected stock price. A future expected stock price could come from ProfitSource and Elliott wave analysis, for example.

There two ways to find the Probability Calculator:

1. Create Trades > More Tools > Probability Calculator, and
2. Settings > General Settings > Display Probability of Profits, Odds

In the Risk Graph (I or II), you then click the Probability of Profit value at expiration.

Platinum''s Probability Calculator does a complete statistical analysis of what happens if the future stock price is reached statistically. Probabilities are found for ending between targets (like the breakevens in a collar or calendar spread), ending above targets, (like the call breakeven) or ending below targets in credit spreads. An example with charts is shown below.

The input and output parameters for Probability Calculator are:

• Stock Symbol - Enter a stock symbol. It defaults to the stock symbol used in the prior web page or trade. If you change the stock symbol, click the green CALCULATE button to refresh the page with that stock's values.
  
• Stock Price - The stock's close value. The value will change if the web site data updates. If you edit the stock price and change it, it will no longer be affected by the web site updates.
  
• Stock Predicted Rate of Return - Enter the stock's expected future rate of return. Or enter the future expected mean value of the stock price. The TAPP price from ProfitSource, for example could be this future expected price. Another possibility is the center max profit value of a collar, calendar spread or butterfly trade. When you change either entry and click elsewhere on the page, the rate of return and future mean value are recomputed to sync up.
  
• Probabilities Computed At - Enter a future date or days into the future. When you change either entry and click elsewhere on the page, they are recomputed to sync up once you click the CALCULATE button.
  
• Volatility Type - Click an IV or SV volatility radio button and that number is loaded into Volatility. If you don't click User Defined then the volatility number can change with each web site data update.
  
• Volatility - The annual volatility used to form the stocks log normal statistical distribution.
  
• Annual Interest Rate - The web sites interest rate.
  
• Annual Dividend Rate - The stock's dividend rate.
  
• First and Second Price Target - Probabilities are found as to whether the stock ends above, below or between these targets. The first target must be greater than the second target.
  

The user’s output variables are as follows: 

• Future stock price at each standard deviation - The 1 2 and 3 standard deviation values of the future stock at the input future days. 
  
• Probability of future stock price - The probabilities the stock meets the criteria shown at the input future days.

Let’s analyze a trade with the Probability Calculator. The trade is an Iron Condor with 38 days to go. 

Figure 1:  Probability Calculator Inputs & Outputs, courtesy Optionetics Platinum

Figure 2: Price Chart with Standard Deviation Bands & Trade Risk Graph, courtesy Optionetics Platinum

We click the linked Probability of Profit number in the related Risk Graph (at 0 days) and get the data shown in the first chart (Figure 2). Based upon historic data, the stock is assumed to move sideways. The probability the stock falls between the trade breakevens at expiration is 46%. The stock closed at 42.66 and we note the condor profit center is above this level. A trade is reasonable if our future expectation for the stock is bullish.

The Probability Calculator opens in a new window with input data coming from the trade. Trade breakevens become the Probability Calculator''s targets. If the trade has only one breakeven, the breakeven becomes target 1 and the Probability Calculator''s 2nd target is changed to 90% of the breakeven. The Risk Graph''s "trading days to expiration" are converted to Probability Calculator''s "Future Days." The trade''s underlying stock symbol becomes the Probability Calculator''s stock symbol. The following charts are generated using these initial parameters for the trade. 

Figure 3: Price Chart with Standard Deviation Projections & Target Probabilities, courtesy Optionetics Platinum

The best-case scenario for the position is a future mean stock value centered in the Condor at 47.5. We now want to evaluate this probability given the past movement in the underlying. The value is then input into the Probability Calculator’s "Stock Mean at Future Date" a new results generated. 

The new standard deviation projections chart is shown in Figure 4, with the future stock price distribution is now centered at the Iron Condor breakevens. Assuming a reasonable future mean value for the price projection, the probability we will end between the breakevens has increased to 60%.

Figure 4: Price Chart with Revised Standard Deviation Projections, courtesy Optionetics Platinum

This Probability Calculator example actually incorporates the Probability of Profits application, but is also available through other Platinum tools. Although the information provided warrants further discussion, the volume of material covered to this point makes it difficult. We will re-visit this topic next week.

Summary

This is another one of those series that will build upon previous topics—but it is nearing the end of summer and we need to once again sharpen skills. The tools shown in this article make use of statistical volatility to identify price projections if the movement in the underlying remains similar to the past and to calculate probability of profits for an option position. As with any other statistical application, there are a variety of assumptions made when using past data to predict future performance.

Remember that we are discussing tools. While applying statistics to security prices there are no guarantees. However, such an approach remains rational for a trader to review. Nothing replaces the need for effective risk management in your trading.

To see the other articles by Clare White, please click here.


Clare White, CMT 
Contributing Writer and Options Strategist
and John Broussard                                   
Optionetics Platinum Developer                
Optionetics.com ~ Your Options Education Site

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Recent Articles by Clare White and John Broussard, Optionetics.com

• September 28, 2006
  ANALYTICAL TOOLBOX: Trade Odds
• September 21, 2006
  ANALYTICAL TOOLBOX: Probability of Profits in Practice
• September 14, 2006
  ANALYTICAL TOOLBOX: Two Keys to the Probability Calculations
• September 7, 2006
  ANALYTICAL TOOLBOX: Future Prices & Standard Deviation Bands
• August 24, 2006
  ANALYTICAL TOOLBOX: Probability of Profit