Analysis of Trading Systems Outcomes

I was reading a forum post, and a gentleman asked this question: "If one can predict [the] market daily movement 55% of time correctly, for example, SPY movement, how to profit it ?".

In fact, one  should some preliminary questions. A first question whether the abovee method is profitable, because the above quote did not include the loss and gain involved with the 55% probability of success. Let us assume that W is the win amount, L is the loss amount. A prerequisite to profitability is for the quantity  W*.45 + L*0.55  to be positive.

Assuming that the above quantity is positive, one then needs to know the draw down. Let us denote by D, the draw down (for instance D= 24%). To apply proper risk management, one needs to put at work an amount of capital such that at most 2% is lost on a single trade (central limit theorem). To take into consideration the drawdown D, the 2%, and to apply central limit theorem properly,  this means that at most 1/12 of one's capital can be used as the dollar value of a single trade. This implies that the the quantity, W.045+L*0.55 needs to be divided by 12, if it were computed under assumption of full usage of capital. This leads to the amount one may  make on single a trade on average.

Once one does the above calculations, one would get the percentage return on a single trade (projected to the full amount of account size), and since only one trade can be made at any given time and   there can be periods of time when no trades can be placed, the annualized return must be less than the annualized return corresponding to the quantity: (W*.45 + L*0.55)*(D%/2%).

We are not done yet, the trader also needs  to be aware of the probability of ruin, which is always non-zero. The probability of ruin cannot be reduced to zero because the trade outcome is not certain.

One should not forget to reduce the returns to take into account the risk free rate of return, the cost of commissions, and also one's time and other resources devoted to trading. One should also allocate an amount of money to trading mistakes, cost of shorting stocks or using leverage, and the like.

If one runs the numbers one may actually find that the returns are much lower than one may have expected at the beginning.,