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To properly develop my trading strategies I need to find a way to calculate maximum theoretical income made from trading time series with perfect accuracy (i.e. trading while holding 'crystal ball' and knowing future) with given trading fees.

So, let's say formally, I'm looking for an algorithm, at which..

Input data:

  • Historical time series 'T' (may be stock/asset/index/whatever tradeable)
  • Fee rates (constant % per each trade)
  • Initial capital (I don't think positions will depend on it though)
  • bool:short positions available (optional, only long if not)

Output data:

  • Theoretical maximum profit made up of trading 'T'
  • Every long and short 'ideal' position (and their closings, of course) made up of such algorithm
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The book Modeling Maximum Trading Profits with C++: New Trading and Money Management Concepts covers exactly what you're trying to do, based on the idea of Robert Pardo's "perfect profit" described thus:

"Perfect profit is a theoretical measure of market potential. It is the total profit produced by buying at every valley and selling at every top that occurs during a historical period of market history. This is obviously impossible in practice, therefore the name perfect profit. Because of the method of calculation, perfect profit will constantly grow from the beginning of the historical test period to its end. (p. 204)"

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