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44 HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 2.1 A continuous distribution is a series of infinitely thin binsdata with more bins. That is, they would look pretty much the same graph-
ically. However, using fewer bins does reduce the information content of a
distribution. Likewise, using more bins increases the information content
of a distribution. If, rather than recording the finishing position of the pole-
position horse in each race, we record the time the horse ran in, rounded to
the nearest second, we will get more than 10 bins, and thus the information
content of the distribution obtained will be greater.
If we recorded the exact finish time, rather than rounding finish times
to use the nearest second, we would be creating what is called acontinu-
ousdistribution. In a continuous distribution, there are no bins. Think of
a continuous distribution as a series of infinitely thin bins (see Figure 2.1).
A continuous distribution differs from adiscretedistribution, the type we
discussed first, in that a discrete distribution is a binned distribution. Al-
though binning does reduce the information content of a distribution, in
real life it is often necessary to bin data. Therefore, in real life it is often
necessary to lose some of the information content of a distribution, while
keeping the profile of the distribution the same, so that you can process the
distribution. Finally, you should know that it is possible to take a continu-
ous distribution and make it discrete by binning it, but it is not possible to
take a discrete distribution and make it continuous.
When we are discussing the profits and losses of trades, we are essen-
tially discussing a continuous distribution. A trade can take a multitude of
values (although we could say that the data is binned to the nearest cent).
In order to work with such a distribution, you may find it necessary to bin
the data into, for example,$100-wide bins. Such a distribution would have