To start with, I will not take issue with your analysis of the 82 years AIM-run you have presented. . .its like me going into a boxing ring with Muhamed Ali in his prime years :-)
The issue was not if the 50/50 split at the start can generate [I]reasonable[/I] profits for a particular investment case but that because of our ignorance over the future price developments of any stock the optimum start-split can not be determined. My argument was that any system has that same dilemma for its user, IF that investor wants to use a cash-equity split in his approach.
Besides that, with 1 trade every 3 years even most AIMers will fall asleep at the controls of their machine pretty quickly and wake up, like Snow White, maybe after 7 or more years, having missed 2-1/3 or more trades. Your analysis would appear of little practical use to guide an investor today that has picked a particular stock he likes and that according to his study is about to take off to the Moon. He would most likely be well advised to start with 90/10 Cash Equity Ratio(CER) and disregard your advice that 50/50 is optimum.
I think that you might be saying something quite different than giving an answer to question in the issue at hand: that if one analyses all stock histories and given the certainty that, from a particular starting point, some of them will start rising in value(and maybe stay there or will go down again) and that some will start dropping in value(and may stay there or may start rising again) and that, IF one would have calculated backwards what the optimum stating CER would have been for each stock, that on the average the average of the CERs would probably be close to 50/50. . .some CERs would have been optimum at 90/10 and some would have been optimum at say 20/80, then the average may well come out to be a CER of 55/45.
So, if you assume that all stock pickings will follow the same behavioural pattern as the average pattern then you could advice to start with the 55/45 CER for any stock one would have picked. . .or with a 45/55 CER if THAT was the result of the average behaviour of all the stocks. . . .But not even one stock will follow the average behaviours of all stocks. . .each picking will have it own dynamics, quite different from the average dynamics, so the dilemma remains: because of not knowing how the stock will behave the optimum CER for that stock is not determinable and will most likely not be 50/50, although a 50/50 Start CER would in most cases not result in a disaster, but the same is true for a Start CER = 60/40 or one of 40/60. . . .for a volatile account all of them would likely do OK if the stock does not become worthless.
In practical cases the best one can do is to study the company, its dynamics and consider that in relation to the general economics that are important for that company and then decide what CER might be the best one. Alternatively he might study the price history of the stock he picked and do an optimisation run on it and find out what the optimum CER has to be based on the price frequency update he would like to use. . .daily/weekly/monthly/annual . . . no one would ever pick1 trade in 3 years!.
This detailed approach would at least give a good clue for his starting CER if the investor has noting else to go on. Better yet would be if he figures out the current tendency of the market segment he is investing in and picks his CER on that basis, and do some rebalancing when that is required.
In the end, using Rebalancing on the basis of what happens in the market and how the portfolio is developing makes the starting CER less relevant in the long run anyway. All this means . . .as I see optimum investing. . .that each decision to invest and how to start should be tailored to the specifics of the company or the fund in which is to be invested. A blind 50/50 approach for a start because of the assumption of ignorance with respect to what is going to happen in the future is a poor management tactic.
I feel that your analysis using a 50/50 CER as Starting Shot, however skilful it is executed, has little practical value for the investor that sits on $ 1000000 and wants to know what the Optimum CER should be for his investment in Company XudwRY that he likes for one reason or other.
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