Maximizing Profit Per Hour: A Day Trader's Strategy to Maximize Income

[RogerPN]

A stock day trader has a winning system and he wants to maximize his profit per hour. He has found that when he trades 5 hours a day, 90% of the time he will make 2 points profit or less and 10% of the time he will make more than 2 points profit. He knows that to earn the maximum total amount of profit he will have to trade 5 hours per day, but rather than maximizing his total profit, he wants to make the maximum hourly income.

To do this he plans to trade each day until he hits 2 points in profit, then he quits. His reasoning is that since he is less likely to make more than 2 points a day, he will maximize his return per hour by stopping as soon as he hits his 2 points.

Will his plan work to gain the maximum profit per hour?

 

[EnumaElish]

A stock day trader has a winning system and he wants to maximize his profit per hour. He has found that when he trades 5 hours a day, 90% of the time he will make 2 points profit or less and 10% of the time he will make more than 2 points profit. He knows that to earn the maximum total amount of profit he will have to trade 5 hours per day, but rather than maximizing his total profit, he wants to make the maximum hourly income.

To do this he plans to trade each day until he hits 2 points in profit, then he quits. His reasoning is that since he is less likely to make more than 2 points a day, he will maximize his return per hour by stopping as soon as he hits his 2 points.

Will his plan work to gain the maximum profit per hour?

Since he is maximizing average (per hour) profit, he should stop when marginal profit (from an extra hour) just equals his average profit, which is 2/(hours worked).

 

[RogerPN]

Since he is maximizing average (per hour) profit, he should stop when marginal profit (from an extra hour) just equals his average profit, which is 2/(hours worked).

He never knows for sure what profit, if any will be produced in the next hour, or any hour. All he knows are the probabilities as stated in the original question.

 

[EnumaElish]

You should derive an equivalent relation in terms of expected profit.