This is very common formula used in terms of portfolio analysis.

The formula for expected rate of return

Where Ri is the return from stock under state i, pi is the probability that states i occurs and n is the number of possible states.

Now, How can we use this formula in our trading system to find expected return.

For example you have system A, where you use stop loss @ 10 points & Take profit @ 20 points. Winning rate of your system is 50% .

So your expected return for the system would be,

in this case,

( 0.50 * (-10)) + (0.50*20) = 5 points

So if you make 20 trades per month with 1 standard lot ($10 per point, in case of Forex trading), then your expected rate of return in this case will be, (5 * 10) * 20 = $ 1000.

Above picture is a screenshot of my calculator, which I made using the formula.

Here is another way of calculating expected return with perfect lot size with the help of "Multiple Losing Streak Probability Calculator".

Here you just need to add the consecutive loss manually from the "Multiple losing streak calculator" & this calculator will automatically calculate ideal lot size & expected return with it. Here trial trade can be use as total number of trade in a given period of time. Say 45 trades in a month. All custom able according to the need of a trader, including the average SL & TP.

You can use multiple system for finding total expected return.

In that case the general formula is ,

The formula for expected rate of return

**E (R) = ∑ R**_{i}p_{i}Now, How can we use this formula in our trading system to find expected return.

For example you have system A, where you use stop loss @ 10 points & Take profit @ 20 points. Winning rate of your system is 50% .

So your expected return for the system would be,

**(probability of loss * Stop loss ) + (probability of win * take profit)**in this case,

( 0.50 * (-10)) + (0.50*20) = 5 points

So if you make 20 trades per month with 1 standard lot ($10 per point, in case of Forex trading), then your expected rate of return in this case will be, (5 * 10) * 20 = $ 1000.

Click to view large |

Here is another way of calculating expected return with perfect lot size with the help of "Multiple Losing Streak Probability Calculator".

Click to view large |

You can use multiple system for finding total expected return.

In that case the general formula is ,

E(R

_{x}) = (R_{1}x P_{1}) + (R_{2}x P_{2}) + (R_{3}x P_{3}) + …….+ (R_{n }x P_{n})
You can add Standard Deviation & variance for further analysis in case of multiple systems return analysis.

Here is another example of using same formula for binary option trades,

Here is another example of using same formula for binary option trades,

Considering 21 trading days in a month.

Here Average Risk amount is actually the total profit/loss divided by the total number of trades. You can do the calculation by yourself if you have an account statement already or any trade samples available to count expectancy.

Suppose you have trading system, considering all brokerage cost or spread, it have average profit of 15 pips, average loss of 7 pips, winning probability is 60% & average risk per trade is 10 pips, under any given number of trades. Then Expectancy would be 4.52 pips. That means under a certain sample size, it has an expectancy of making 4.52 pips with each trade.

Average risk is the amount of pips you put as stop loss when you enter trade, divided by the no of trades. I have shown it here in terms of pips. You can use it with monetary value also for any market.

Good luck!

**Updated**[27/3/2016]**:**There is another version of it, formula taken from Van Tharp's Position Sizing book. It can be use for monetary value of trades.

**Expectancy = [{(Average Profit)*(Probability of winning)} - {(Average Loss) * (Probability of Losing)}]/Average Risk Amount**Here Average Risk amount is actually the total profit/loss divided by the total number of trades. You can do the calculation by yourself if you have an account statement already or any trade samples available to count expectancy.

Suppose you have trading system, considering all brokerage cost or spread, it have average profit of 15 pips, average loss of 7 pips, winning probability is 60% & average risk per trade is 10 pips, under any given number of trades. Then Expectancy would be 4.52 pips. That means under a certain sample size, it has an expectancy of making 4.52 pips with each trade.

Avg Win in pips | Avg Win Rate | Avg Loss in Pips | Avg Loss Rate | Avg Risk | Expectancy |
---|---|---|---|---|---|

15 | 60% | 7 | 40% | 10 | 4.52 |

Average risk is the amount of pips you put as stop loss when you enter trade, divided by the no of trades. I have shown it here in terms of pips. You can use it with monetary value also for any market.

Good luck!

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