## Risk/Reward, Win/Loss and losing streaks

## Risk/Reward vs. Win/Loss

Quite often people talk about risk/reward ratios they prefer to trade. For example some prefer to trade with risk/reward 1:2 or to risk $100 to make $200, some prefer 1:3 or to risk $100 to make $300. Based on preferred risk/reward ratio it is possible to calculate win/loss ratio needed to stay profitable. The formula is 1/(risk_reward + 1). For 1:2 it would be 33% which means one needs to hit winning trades at least 1/3 of time to stay profitable. Which makes sense, if you lose $100 twice and make $200 you stay break-even and if you win more times than that you stay profitable. The relationship can be easily plotted like this

## Losing streaks

Now novice trader might find a trading system which wins 30% of a time with risk/reward 1:3 and might expect to make $3,000 over 100 trades by risking $100 and expectation of $300. So how much capital do you need to trade this strategy? Some might say you can have 5-6 losing trades in a row or a drawdown of $600 and then come back. Not so fast. If you apply simple math. Trader should absolutely expect to hit 13 losing trades in a row or $1,300 drawdown over 100 trades and he is not prepared to handle it look for different strategy. The formula for probability of number of losing trades is quite simple. You take probability of loss (70% in our case) and multiply it by itself. For 13 trades it would be 70% * 70% * 70% * 70% ... = 1% which means out of 100 random sequences of trades at least 1 would consist of all losing trades. Relationship between win/loss ratio and at least 1 expected losing streak length can be plotted like this:

As you can see from the chart above even for 50/50 trading system a trader should expect to hit at least one streak of 7 losing trades in a row out of 100 trades which has nothing to do with quality of his trading system.

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