A ratio of averages is not the same as an average of ratios

Here is a sample of a question we get frequently from users.

Q. The Average Ratios of Gross Profit/Loss and Average Win/Average Loss that
NST is providing on the (ALL INSTRUMENTS AVERAGE) ((AVG)) report are not
correct. I don’t know whether the inputs or the outputs are wrong, but
something is awry.

I note on the examples provided with NST that the ratios are correct, but it
appears that only one stock (rather than a basket of stocks) was tested.
Have you looked at the numbers across a back-tested basket of stocks to see
if the values reported in the (ALL INSTRUMENTS AVERAGE) ((AVG)) report are
accurate?

A. We can see where your confusion may come from: a ratio of averages is not
the same as an average of ratios. Here is an example of two symbols (MSFT
and AAPL) on the chart:

Symbol: MSFT AAPL Average (across all symbols)

Gross profit: $3.195 $0.00 $1.5975

Gross Loss: $4.20 $0.57 $3.385

Ratio GP/GL: 0.76 0.00 0.38

In this example, the average ratio 0.38 is NOT a result of division of 1.5975 by
3.385, but rather an average of 0.76 and 0.00, i.e., (0.76+0.00)/2=0.38.

So, any ratio found on the ALL INSTRUMENTS AVERAGE report is the result of
averaging corresponding ratios of each individual symbol on the chart, and
not a ratio of two averages from the ALL INSTRUMENTS report.

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