Have you ever wanted to know what the probability of success is for a given trade?  The Probability Calculator is a web based tool that allows you to calculate the mathematical probability of certain prices being achieved during a given time period.  This allows you to check how realistic your expectations are with respect to given price moves.  Given an underlying price, future volatility, and time period, this tool will instantly calculate the first, second, and third deviation price movement, both to the downside and the upside.

You can also add a target price and the program will tell you the probability of the asset being above or below that price on your target date.  Add a price range, and the program will tell you the probability of being below the lowest price target, above the highest price target, and the chance of finishing between those two target prices by your target date.
Of special interest to option traders, the program will also tell you the probability of the underlying touching your target price(s) anytime during the time period you choose.

An example of the Probability Calculator, with all fields filled in, is shown in Figure 1

Figure 1: Example calculating the probabilities of price movements of a stock

There are a number of fields that you are required to fill in before any values can be calculated.  A change in any one of these will affect the probability values that are displayed in the lower section.  Let’s look at each input field in detail.

Type of Asset
Click on the down arrow to see three choices in the drop down menu - Stock, Index or Future.  Simply choose the appropriate one for the asset you are interested in.

Current Price
Here you should input the current price of the underlying stock, index, or future you are interested in.  The calculator uses your information to create a lognormal distribution of prices that will be centered on the price you input here.

Future Date/Days Ahead
Only one of these two fields needs to be entered.  If you input a specific expiration date, the number of days is automatically calculated and displayed.  If you input the number of days, the Expiration Date field will automatically be populated.  The longer the time period until expiration, the wider the lognormal distribution and standard deviations will be, since you are giving more time for the underlying price to move.

Future Volatility
All other things being equal, increasing the volatility input here will increase the range of probable future prices, while a lower volatility number will decrease it.  The volatility number that is required for this field is a percentage, normalized to one year.

Knowing what to input into this field is the usually the most difficult decision users of this probability calculator have.  What should be input in this field is the expected future volatility of the asset.  Naturally, no one knows exactly what the volatility of an asset will be in the future.  But there are a couple methods we can suggest you use to find an appropriate number.

Most options software (including OptionVue 5 of course) as well as the best online brokers calculate and display Statistical Volatility, the actual volatility of the asset and the implied volatility of each individual option.  Either could be used.  The "purest" method of measuring volatility is by statistical analysis of the recent price history of the asset itself.  However, implied volatility is usually considered to be a better indication of future volatility, because options are priced to reflect the market’s expectations for the future.  If you choose to use the implied volatility of an individual option, the at-the-money call option in the near-term month is probably your best choice.

Dividend Yield
This is an optional field, used for stocks and indexes.  It is optional because many stocks, and all futures, do not pay dividends.  The field asks you to input an annualized percentage yield.  It would be best to use the future dividends that will be paid.  That is not usually known, but the history of past dividends is usually a reliable guide.  All the major free financial websites calculate and display the dividend yield for indexes and stocks that pay dividends.

You can also calculate the annualized percentage yield yourself by looking up the past dividend pattern and payouts.  For example, GE paid a dividend each quarter of $0.28.  So in one year it paid out 4 x $0.28 = $1.12.  Divide that by the current stock price of $37.14 and you would get an annualized dividend yield of 3%.

Risk-Free Interest Rate
Another optional field is the interest rate.  In this field you should input the current quoted interest rate on a US Treasury bill, note or bond that most closely corresponds to the length of the period being analyzed. This field defaults to 2%, although it has been changed to the current one month T-Bill rate of 3.0% in the example shown.

Once you have these fields filled in (or at least all the required fields) click the Go button.  The section entitled “Price at Each Standard Deviation” will fill in.  There will be a price shown at one, two and three standard – both to the upside and downside.  This would be a good time to discuss the distribution these results are based on, the significance of the standard deviation numbers, and how they should be interpreted.

Lognormal Price Forecasting and Standard Deviations
Studies have shown that stock price changes are very close to being lognormally distributed over time.  This means, for one thing, that the chances of a stock doubling in a period of time are equal to the chances of the stock dropping to half its price during the same period.  (That is very different from saying the chances of a stock rising 5 points are equal to the chances of it dropping 5 points, which would be a normal distribution).

Standard Deviation, from statistics, is a tool for measuring how widely a set of numbers deviate from their mean.  It is computed by taking the square root of the sum of the squares of the differences from the mean.  The 1st standard deviation represents a 68% chance of being between the one standard deviation numbers (represented by the -1 and +1 boxes).  The chances of being between the two 2nd standard deviation prices is 95%, and the chance of being between the two 3rd standard deviation numbers is 99%.

Seeing the likely distribution of future prices allow you to see just how realistic your price targets are.  It is important to remember that these are numbers calculated using statistical methods.  The Calculator does not know about any news or events may be happening on any individual asset.  It does not know, for example, that there was just a takeover bid on the company, that they just reported great earnings, or that there was a failure of the soybean crop in Brazil.  So if you know that something unusual is happening that will affect the price of an asset, please take that into account and do not blindly follow the numbers that come up in this calculator.

First Target and Second Target
Below the risk free interest rate, there are two more optional input fields available that will be of special interest to option traders - First Target and Second Target.  Here you enter one or two prices and the program will show you the probability of finishing below, between, or above these prices as well as the probability of ever touching these prices.

If you enter only a single price in the First Target box and click Go, the program will display the probability (in percentages) in the three fields relevant to a single price target: Probability of finishing below lowest target, ever touching lowest target, and finishing above highest target.

The probability of finishing below and above a single target must add up to 100%.  These two numbers tell you what the odds of finishing above and below a price, important information to have when considering a specific strike price for a trade.  Those selling options in the hopes they will expire worthless will find this very useful.  For those considering a directional trade, such as the purchase of an option, the probability of ever touching the price will probably be of the most interest.

If you input a second target, the program then shows you the chance of ever touching both the lower and higher targets.  It will also show the probability of ever touching both the lower and higher targets anytime between today and the chosen date.  You will also get one additional field filled in, the probability of finishing between these two target prices.  For a price range, adding the probability of finishing below the lowest target, above the highest target, and finishing between the two targets add up to 100%.

We mentioned earlier that all the standard deviation numbers are based on the lognormal distribution and statistical methods.  The chances of finishing below, above, and between any price target(s) are also calculated using this same lognormal distribution.  However the values displayed for ever touching a price target are calculated differently – here it uses a Monte Carlo calculator.  Each time you click “Go”, it runs through 1,000 simulations based on your inputs and gives you the percentage of time it hit that target.  That means there can be some minor variation in these numbers each time you run it.

The probability calculator can enhance your ability to calculate the probability of success for a given trade.  The ability to see the probability of the underlying price ever touching one of your target price(s) is of special interest to option traders when choosing which strike price to use.  And seeing the mathematical odds of certain prices being achieved during a given period of time allows you to check how realistic your price expectations are whenever you are considering a prospective trade.

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