A Losing Strategy?

A given strategy gives you x1.2 your original investment 50% of the time and x0.822 your original investment 50% of the time.Note that 1.2·0.822 = 0.98623 which is less than one. So, if you trade this system 100 times with your full equity, assuming you get 50 winning and 50 losing trades, your will end up with a 50% loss, as 1.2^50*0.822^50=0.5.

This is not appealing, is it? But, what happens if you always trade a fraction "f" of your current equity? Look a the graph below, showing the simulated results for 10k experiments:

As in this post, the blue shaded areas correspond to areas including 25%, (darkest), 50%, 75% and 90% (lightest) of the outcomes. The frontiers between areas are 5%, 12.5%, 25%, 37.5%, 62.5%, 75%, 87.5% and 90% percentiles. The solid blue line corresponds to the theoretical case: half of the results lie above and half below this line. The green line is the mean of the outcomes.

It follows, that you may get a final equity E, greater than the initial one Eo. Specifically E>1.016·Eo in 62.5% of the cases if you make each trade with f=0.1, i.e. 10% of our equity.

The following simulation is a similar case where the gains are x1.5 and x0.6575:

Clearly, this might be attractive, depending on your level of risk!