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Trades needed for confidence

StatisticsHard

Each trade has independent P&L with mean $0.5$ and standard deviation $10$ . What is the smallest number $n$ of trades for which the expected total P&L is at least $2$ standard deviations of the total above $0$ ?

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Hint

The mean of the total grows like $n$ , but its standard deviation grows like $n$ .

Solution

The total over $n$ trades has mean $0.5 \times n$ .
Its standard deviation is $10 \times n$ .
We need $0.5 \times n \geq 2 \times 10 \times n$ , which simplifies to $n \geq 40$ .
Squaring gives $n \geq 1600$ , so the smallest value is $1600$ .

Answer: $1600$

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