## Solving for how many trades/day to achieve a certain % of profitable days

### Solving for how many trades/day to achieve a certain % of profitable days

Hello Bloxillians, I have a question and I was wondering if some mathematically gifted members might lend a hand in solving it. If I have a daytrading system that has a win rate of 25% and the average wins are 3.8 times the size of the average loss, how many completed trades would I need to make each day in order to achieve a percentage of, let's say, 65% profitable days. Thanks, The Zoop

### Re: Solving for how many trades/day to achieve a certain % of profitable days

It seems to me that you can't set out to measure that without making some kind of an assumption about the trader's position sizing algorithm. To name one famous example, if you have an infinite bankroll then "Martingale" betting, where you double your bet after a loss, might be worth considering.

So I made an assumption: it would be instructive to assume that the trader's position sizing was algorithm X.

Then I coded up a little bitty Monte Carlo simulation using perl. Instead of simply simulating ($WIN / $LOSS) = 3.8, I simulated four different values of the ratio ($WIN / $LOSS). Yes, 3.8 was one of the four ($W/$L) ratios simulated.

Each trade had a 25% probability of being a winner, and the serial correlation coefficient was zero. I simulated ten thousand trading days, with "T" trades per day, where T varied from one trade/day to Many trades/day.

The results are shown below. As you would expect, all curves start at 25% of days profitable, because at one trade per day and 25% winning trades, it must be true that 25% of days are profitable. 25% of TRADES are profitable, and trades are the same thing as days when T=1 trade per day.

Then as the number T of trades per day increases, you move from left to right along the horizontal axis of the chart. There is a very interesting sawtooth action in the data, and this is real. It's not an artefact of simulation, it's not a bug in the pseudo-random number generator. It's built into the problem statement itself, and all correct solutions will include it. Readers can have some fun thinking about this on their own. If it's driving you crazy, simulate the situation either with a computer or with pencil and paper and dice. After a few dozen trades you'll probably get a Eureka moment.

It's also interesting that changing the ($WIN / $LOSS) ratio has an effect, but it's not gigantically bigger than the sawtooth effect inherent in the problem itself.

I have deliberately removed the numerical labels from the plot axes. This reminds readers that their programmers do perform a valuable job; your programmer deserve every penny you're paying her. Without programmers you wouldn't be able to create these kinds of plots and obtain these kind of Eureka insights. So go talk to your programmer right now and thank her for the great job she's doing. And pay her on time.

Maybe another reader might be willing to donate two or three (wo)man-hours of their programming staff, to write, debug, and run a program which answers this question.

So I made an assumption: it would be instructive to assume that the trader's position sizing was algorithm X.

Then I coded up a little bitty Monte Carlo simulation using perl. Instead of simply simulating ($WIN / $LOSS) = 3.8, I simulated four different values of the ratio ($WIN / $LOSS). Yes, 3.8 was one of the four ($W/$L) ratios simulated.

Each trade had a 25% probability of being a winner, and the serial correlation coefficient was zero. I simulated ten thousand trading days, with "T" trades per day, where T varied from one trade/day to Many trades/day.

The results are shown below. As you would expect, all curves start at 25% of days profitable, because at one trade per day and 25% winning trades, it must be true that 25% of days are profitable. 25% of TRADES are profitable, and trades are the same thing as days when T=1 trade per day.

Then as the number T of trades per day increases, you move from left to right along the horizontal axis of the chart. There is a very interesting sawtooth action in the data, and this is real. It's not an artefact of simulation, it's not a bug in the pseudo-random number generator. It's built into the problem statement itself, and all correct solutions will include it. Readers can have some fun thinking about this on their own. If it's driving you crazy, simulate the situation either with a computer or with pencil and paper and dice. After a few dozen trades you'll probably get a Eureka moment.

It's also interesting that changing the ($WIN / $LOSS) ratio has an effect, but it's not gigantically bigger than the sawtooth effect inherent in the problem itself.

I have deliberately removed the numerical labels from the plot axes. This reminds readers that their programmers do perform a valuable job; your programmer deserve every penny you're paying her. Without programmers you wouldn't be able to create these kinds of plots and obtain these kind of Eureka insights. So go talk to your programmer right now and thank her for the great job she's doing. And pay her on time.

Maybe another reader might be willing to donate two or three (wo)man-hours of their programming staff, to write, debug, and run a program which answers this question.

### Re: Solving for how many trades/day to achieve a certain % of profitable days

LOL Try never as your expected return is negative. You are expecting to make 95 cents per dollar risk. Not to say you won't have positive runs on occasion but clearly it is a losing proposition.

### Re: Solving for how many trades/day to achieve a certain % of profitable days

ZOOPY12: " ... a win rate of 25% and the average wins are 3.8 times the size of the average loss ..."

IRVLLC: "... your expected return is negative. You are expecting to make 95 cents per dollar risk. Not to say you won't have positive runs on occasion but clearly it is a losing proposition."

SLUGGO: Let's try an example with 4 trades. 25% of them (1 trade out of 4) are winners, and 75% of them (3 trades out of 4) are losers. If Trader Thelma risks 100 Chinese Renminbi per trade, she loses (3 x 100) Renminbi on the three losing trades, and she wins (1 x 3.8 x 100) Renminbi on the single winning trade. So her net result after 4 trades is +80 Renminbi. This is a gain of 20 Renminbi per 100 Renminbi risked. ("20 cents per dollar"). Something is wrong with your arithmetic, IRVLLC.

IRVLLC: "... your expected return is negative. You are expecting to make 95 cents per dollar risk. Not to say you won't have positive runs on occasion but clearly it is a losing proposition."

SLUGGO: Let's try an example with 4 trades. 25% of them (1 trade out of 4) are winners, and 75% of them (3 trades out of 4) are losers. If Trader Thelma risks 100 Chinese Renminbi per trade, she loses (3 x 100) Renminbi on the three losing trades, and she wins (1 x 3.8 x 100) Renminbi on the single winning trade. So her net result after 4 trades is +80 Renminbi. This is a gain of 20 Renminbi per 100 Renminbi risked. ("20 cents per dollar"). Something is wrong with your arithmetic, IRVLLC.