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@exsoldier No particular distribution was used, just pseudorandom % change in assets value from within a given range, e.g. -5% to +7%. So each value from that range is equally probable. This was not meant to be academic research but please let me know what distribution could best mimic stock...

@ianamol Buying the dip is not my cup of tea, it's interesting though

@hummel2 Good point, I forgot about that. I have account with several brokers so that I can minimise or even almost eliminate the commission paid, depending on what I'm buying. In the US the commissions are lower, but in Germany you could have access e.g. to eToro, DeGiro or Firstrade (US broker)

@how2101 Thank you. I wrote an update to answer your remarks.

@jalp2016 I clarified a couple of things in the post to answer your comments. Thank you for valueble remarks. Here I used random data just to show the idea but of course historical stock data would be much, much better. I'm working on that.

UPDATES (17-09-2020): Instead of replying to each of you individually, here are my comments and corrections (thank you for valuable comments): From your comments I see the post turned out to be a bit misleading: the DCA and modified DCA do indeed perform better than lump sum investing, but in...