
Introducing the Precision Probability Index PPI
Indicator and user function for Tradestation
Computing the exact probability of one data set being higher than another data set any number of days or bars into the future with 100% Mathematical accuracy
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© Roger Medcalf 2005  2011 ... You may not reprint text or images without permission 

Questions
Take a look at the chart below. There are three circles shown A B C from left to right.



It would be nice to know these exact mathematical probabilities before placing a trade
Answers





Precision Probability Index PPI (Crossing above or below 50% line gives early warning of changing conditions)


Interpretation of above example. This is computing the probability of a 4 period weighted average being above a 35 period average 1 bar into the future with exaggeration set to x 2. If a 4 period average is above a 35 period average its considered to be in an uptrend with a long position being the best option. However with the Precision Probability Index the chances of your trade being good or bad is accurately displayed in one simple output number. Instead of guessing, now you will know exactly. This is true, you have my word on it. The formula uses the probability density function which is used to compute option prices. Instead of using the current price and the "strike" price used in option terminology I have used three dynamics sets instead of a two. Volatility being one of these, affects the probable future outcome, as when volatility is high the odds of a price moving a large amount is increased which obviously results in a much closer to 5050 probability outcome. Conversely if the short period average is way above the long period average accompanied by low volatility then we have a much higher probability of that condition staying the same which gives a 8020 type situation.


Now for some stark truthful realities 

Please take part in this little one minute experiment. Plot a typical stock, future or forex chart in realtime, daily, or any time frame you like, then plot a 7 day weighted average and a 12 period weighted average on the data. Now look at the differences between the averages and try to figure out what you consider the usual maximum and minimum probabilities that the 7 period average will be above the 12 period average one day or bar into the future. Take your guess then scroll down.


If you have guessed 20%80% or 30%70% you will get a nasty shock. 

The reality of trading Forgive me for dampening your enthusiasm, but with a 7 period and 12 period moving average system looking ahead one bar into the future the highest probabilities likely to achieve are not much better than a 49%  51%. The truth is not always pleasant to know, but read on, its gets better. Once you factor in costs for dealing, you will be lucky to ever get better than 50% odds (even money) More than 95% of all price action will be contained within a 2% difference in odds. Now that really pours cold water on people who think they have a "sure thing". One could argue this point and claim to have better odds than that, but in the undisputable truth of maths odds are odds and nobody can argue with maths. If you knew with 100% certainty that Warren Buffet will buy 10 million shares every day for the whole month and there would be no sellers at all, you could perhaps claim to have better odds than stated above.


Now for something a little better 

Please take part in another little one minute experiment. Plot a typical stock, future or forex chart in realtime, daily, or any time frame you like, then plot a 40 day weighted average and a 80 period weighted average on the data. Now look at the differences between the averages and try to figure out what you consider the usual maximum and minimum probabilities that the 40 period average will be above the 80 period average one day or bar into the future. Take your guess then scroll down.


If you have guessed 20%80% or 30%70% you will still get a nasty shock, but the situation is improving 

The Precision Probability Index gives you the edge Now you can see the scale runs from 46.5% up to 52.5% giving a 5% range. This is enough to give a slight edge to a traders statistics, and all that has been done is using longer period moving averages in the calculations. 40 period and 80 period. If a long trade was taken when the odds were at 52.5% then the trader will know with very high probability that in a year with one thousand trades he will have had 525 winning trades and 475 losing trades. If each loss was $1000 and each win was $1000 then the end result would be $525,000 minus $475,000, giving a profit of $50,000. In reality the results would be much better as the losers would be cut early and the winners would be run until the odds changed to below 50%. Even if the average winning trade is only 20% bigger than the average losing trade then we end up with profits of ($525,000 x 1.2)  $475,000 = $155,000 As this information sinks into your mind...


Now for something much more interesting 

The Precision Probability Index is versatile and tells the 100% mathematical truth (Exaggeration factor must be set to zero) Now you can see the scale runs from 46.5% up to 55% giving a 8.5% range. This is enough to give a much bigger edge to a traders statistics, and this time the difference between the two prices used has been increased. The two period moving averages in the calculations are 12 period and 100 period. Simply because these have more potential to be vastly different in value, one attains a much clearer picture of the odds for making trades.


The Precision Probability Index reveals hidden patterns that you don't see any other way Study the example below carefully. The plot is more jagged now as I have set the short period to 1 the long period is 100. You will obviously see the rise above 50% on the left of the chart, but what else do you see? Take a good look


If you are observant you may have noticed just above the white 50 line that the price is getting supported each time the probability up hits around 51% Now you can see the hidden patterns that are created by the quiet traders. You can see they are seeking opportunities to buy when the odds are in their favour AND when the trend is still classified as being up. This is rather uncanny to observe and makes one think that the institutions with all their quantitative analysts are using something similar to PPI to call their trade entries.


The Precision Probability Index reveals price support areas in trends Now you can clearly see the support area at the 50% line. The example is using 12 bars into the future to calculate the values. In this type of signal the trigger is given when the probability falls (gently) to the 4951% region then begins rising again. This is seen most clearly with 1 short period and large long periods (100 in this case)


The Precision Probability Index reveals price resistance areas in trends 

In the above example, you can clearly see the resistance areas encountered around the 50% line. The example is using 1 bar into the future to calculate the values. In this type of signal the trigger is given when the probability rises (gently) to the 4951% region then backs away downward again. This is seen most clearly with 1 short period and large long periods (100 in this case)  
The Precision Probability Index becomes a Market tracker type decision maker 

This example demonstrates the extreme versatility of PPI. The lengths are period 15 and 50, but the main change is the exaggeration factor input setting has been raised to 3, so therefore the indicator is no longer telling complete mathematic truth as the probabilities are exaggerated. The main turning points are easily seen as the averages converge and diverge which create instant changes in the probability rates with virtually no lag. Note: As exaggeration factor is increased, the PPI becomes closer to a binary output. ( 100 or 0 ) This is yet another very useful feature as a trend definition indicator as shown in the chart below but with exaggeration factor elevated to 5 times.


The Precision Probability Index can be tuned to become a DSP binary trend indicator (100 or 0) 

The example above is using exaggeration factor 5 and as the exaggeration factor increases, more clear hidden patterns begin to emerge, I doubt it is possible that anybody could ever ask for a more crystal clear indication of a trend changing direction. Please remember that exaggeration factors that are not 0 do not give exact mathematical probabilities. The variation of the factor is designed to add further dimensions of the use of this product.


The Precision Probability Index becomes a Market tracker Those of you who are old enough may remember the software platform which ran in DOS mode and was called Indexia. People mainly bought this Indexia research package because it came with an excellent indicator called Market Tracker. This was the creation of South African technician Jeremy Duplessis who I met a few times. The indicator was a probability model with a large amount of smoothing. As Indexia is no longer available, those who miss using Market tracker could begin to feel at home with Precision Probability Index. In the example below we can see a plot which has a very strong resemblance to it.


The Precision Probability Index becomes a sinusoidal plot with a signal line The setting called signal line can be enabled by typing TRUE or FALSE into the indicator properties box. The dotted grey line is the same plot as the yellow line but has more smoothing added to it which creates a lag effect. The crossing of the PPI above the signal line can give timely warnings of a change in direction.


Precision Probability Index uses the following seven inputs for maximum user flexibility.


PPI can gives you all this versatility of usage


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Disclaimer please read carefully  
All the indicators, functions, signals and formulas available from PrecisionTradingSystems have been selected for their high levels of efficiency as trading tools. However this does not guarantee success when using them on all markets you choose to trade in. Risk of losses are high with even the best systems, and a good understanding of risk control mechanics is required before using any products you have received from PrecisionTradingSystems. You are responsible for ensuring all precautions have been taken in your trading decisions and PrecisionTradingSystems cannot be help responsible for any losses you may incur while using its products. These products and formulas are designed for Traders who have several years experience of trading, if you do not consider yourself in this category then please invest some time to study your methods carefully before risking any money.


RISK DISCLOSURE 

HYPOTHETICAL PERFORMANCE DISCLOSURE 
Hypothetical performance results have many inherent limitations, some of which are described below. no representation is being made that any account will or is likely to achieve profits or losses similar to those shown; in fact, there are frequently sharp differences between hypothetical performance results and the actual results subsequently achieved by any particular trading program. One of the limitations of hypothetical performance results is that they are generally prepared with the benefit of hindsight. In addition, hypothetical trading does not involve financial risk, and no hypothetical trading record can completely account for the impact of financial risk of actual trading. for example, the ability to withstand losses or to adhere to a particular trading program in spite of trading losses are material points which can also adversely affect actual trading results. There are numerous other factors related to the markets in general or to the implementation of any specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results and all which can adversely affect trading results.
