Profitable ETF trading strategies: reflection theory and its implications on back testing
A simple explanation of reflection theory comes from the mathematical field of set theory and statistics. The theory can be made as complex as you want it to be, based on your interest in statistics and math, but the essence of it is intuitive and has some interesting insights for back testing your systems in the stock market.
To begin with, the reason we conduct back testing is to ensure that our intuitive insights, which are triggered by enthusiasm and emotion in our pattern matching brain, may actually have some objective truth to them when subjected to rigorous analytical confirmation.
The manner in which we conduct back testing and the assumptions that we used to drive the analytical engine are all important when it comes to having reliability and confidence in the results. If you start with a bad set of assumptions, then even the most perfectly applied back testing technique will come up with invalid and unsupportable conclusions.
Back testing is like logic and deduction in that sense. If you start with bad information, you can be perfectly logical but come up with conclusions that are logically sound and don’t work in the real world.
Reflection theory suggests that in normally distributed populations, that for a sufficiently large population there will be subsets which have the same characteristics as the larger population from which they are drawn. This leads you to conclude that the inferences you draw on samples can be applied with great degrees of confidence to the behavior of the population at large.
At the simplest level, if you believe that the market returns are normally distributed, then you can take samples at will and data mine them for relationships between variables of your choosing and then apply any edges that you find to the broader population with great confidence.
Everything we know about the distribution of stock market returns, though, is that they are not normally distributed and that therefore great care must be taken in your sampling technique and in your out of sample testing for validation for any rule set that you propose to put real money on.
There are proponents of the idea that the market is so abnormally distributed that there is ian irreducible chaotic nature about the market which should put an upper limit on any risk you propose to take, no matter what the statistical evidence from back testing suggests.
The short answer to this is: place your confidence wisely and always have an out. Never be the first mouse, unless you have to be, and remember that there are no old, bold mountain climbers.