Real trading is based on a stream of returns, continuous numbers, not coin flips. We manage these streams by building a probability matrix. The best way to do this is to bin our data.
First, we calculate the range of the data and create bins. We then calculate our joint probability tables. We will use the equity curves of three different systems. “Data bins” (below) is an example from chapter four of Vince’s book, “The Leverage Space Trading Model.”
The first step in building a joint probability table is to process the equity data into differences. Next, we break the period difference into bins. The max, min and range are needed to do this:
We decide to make five bins for each system’s results. The bins do not have to be equally spaced, but we will do so to simplify our example. Here are the bins:
Each bin is represented by its mid-point. We then record the number of actual occurrences for each of the combinations between the three systems. The actual number of records and the number of occurrences are used to calculate the probability of each combination.
In real data sets, over longer holding periods such as monthly or yearly, we often have many combinations without any occurrences. We can address this by adding additional data or by replacing some of the lower performing cases with worst-case scenario, black swan scenarios. We also must figure how many holding periods these black swans should last so we can create multiple records to simulate a real event. If we test over 10 to 20 years of data, it’s important to do this because there likely will be a black swan case in the data set.
In our example, we have 13 data records, but 125 combinations across the five bins. This gives most individual records very small probability. Our next step is to condense the table to only combinations with supporting cases (see “Joint scenarios”).
Because many of our possible cases did not occur in our data set, we remove these cases from the joint scenarios table. So, our table has been pared down to only 12 rows, not our original 125 possible combinations. We then set n = 12 for calculation purposes. At this point, we have all of the information we need to perform the Leverage Space calculations.