Theoretically (EMH), No trading or active management is profitable consistently over time as all of those opportunities have already been exploited.
In practice: If you reduce the problem to a gambling problem.
- Equity of K
- Txn cost of C
- Stock S
- with Price at each point of time Pt
- X - Quantity of Shares Bought
- Target Threshold = TT
- Target Price = Pt + TT
- Stop Threshold = ST
- Stop Price = Pt - ST
Case 1. Assume C = 0, TT = ST
Enter at at Price Pt (Long at Pt)
Max win = TT
Max Loss = ST
Risk to Return ratio = 1
The probability that makes this gamble a fair bet is 50% (prob that each side is hit first).
Case 2. Assume C = C
Max win = TT -2C
Max loss = TT + 2C
Risk to Return here is (TT-2C)/(TT+2C) < 1 for any positive C
So your probability to win needs to be large enough such that p(win)(TT-2c) -((1-p(win))(TT+2C)>1
which simplifies to
2p(win)TT-TT-2C > 1
Recall P(win) here is bounded by 1.
Certainty Case P(win) = 1
2TT-TT-2C > 1
TT-2C > 1
This must hold for profitability, this long expression implies that when you win you get The threshold less transaction costs.
Now to solve for the probability that which the game is fair
2p(win)TT-TT-2C = 1
The probability of you being right MUST be greater than (1+TT+2C)/2TT.
1/2 + C/TT +1/2TT
Where C/TT is the ratio of cost to win.
So the marginal probability over 50% in a 1 to 1 bet is equal to the ratio of Cost to win, + 1/(2*TT)
Some toy numbers from IB. if C = 2.50 (fx trade cost)
1/2 + 3.50/2TT
So the probability of you winning is equal to 1 half + 3.50/2TT, where 2TT is the threshold.
As you see here you will need to be more accurate than 50%, assume that TT = 10$
gives you a "fair game" probability of 67.5%, meaning to actually make money you need to be more than 67.5% accurate. An interesting fact is if TT was 175$
1/2+3.50/350 = 51%, however the market probably does not move far enough to generate these types of profits per trade as the WIDER your target the closer the probability goes to 50% assuming fixed transaction costs.
So The lesson from this is if you aren't accurate, Have a WIDE target (in a 1 to 1 bet) as your chance of being wrong is lower, however your losses as a % of equity can be higher, given that people are more risk averse and do not have infinite capital the MAX DD's may not be tolerable.
Now with the specific case you mentioned of day to close.
1/2 + C/TT +1/2TT
The level of gains possible must be unrealistically high relative to transaction costs for it to be profitable.
Therefore unless you have a serious edge over the market, chances are you will not be profitable.