Given a single technical
analysis indicator (TAI) such as the Moving
Average Convergence Divergence (MACD) indicator when it signals
a buy it is either right (the stock goes up) or wrong (the stock
goes down). If the MACD has a 50% accuracy rate then a buy signal
has a 50% chance of being correct.
If you use MACD and the Detrended
Price Oscillator (DPO) together (and the DPO also has a 50%
accuracy rate) and they both provide a buy signal, what is the probability
that the stock will rise?
p = probability
50% is represented here as a fraction ½
Success means the stock went up
Failure means the stock didn't go up (went down or stayed
the same)
Unity is 100%, meaning it comprises all the possibilities of success
and failure
Unity = p(Success) + p(Failure)
Rearranging the equation
p(Success) = Unity - p(Failure)
Substituting 1 (as in 100%) for Unity and expanding p(Failure)
p(Success) = 1 – p(Failure(MACD)) x
p(Failure(DPO))
Why is p(Failure(MACD)) multiplied by p(Failure(DPO))? If the
stock goes down and they both predicted a rise then both had to
be wrong. How could one be wrong and the other right if the stock
rose? If both predict a rise, then both have to be wrong for the
stock not to rise.
Substituting values into the formula and solving
p(Success) = 1 – ½ x ½
p(Success) = 1 – ¼
p(Success) = .75 or 75%
So two indicators, each with a 50% chance of success, when taken
together, create a combined indicator (DPO and MACD) with a 75%
chance of success. Good, but can we do better?
First, the MACD and DPO have success rates better than 50%. Our
testing has found successful prediction rates between 70% and 80%.
For conservative projections we'll use the lesser value.
Second, we use more than two TAI. Say the third one is the Triply
Smoothed Exponential of Log of Closing Price (TRIX). It too
has a successful prediction rate between 70% and 80%.
So, if all three indicates indicate a price rise, what is the probability
that they are correct?
Unity = p(Success) + p(Failure)
p(Success) = Unity - p(Failure)
p(Success) = 1 – p(Failure(MACD)) x p(Failure(DPO)) x p(Failure(TRIX))
p(Success) = 1 – (3/10 x 3/10 x 3/10)
p(Success) = 1 – 27/1000
p(Success) = .973 or 97.3%
This is a key to the success of Positive Territory, finding the
right combination of technical analysis indicators with a high predictive
accuracy to increase the overall probability of successfully predicting
a price rise in the short term.
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