What is Positive Expectancy?
Positive expectancy sounds like something a motivational speaker would talk about or a psychiatrist. In fact, there are some people that use the term for those reasons. This article is about using the term in the context of Forex trading strategies, STATISTICS, and MATH. One of the major advantages from using an automatic Forex trading system is built in discipline that maintains a high POSITIVE EXPECTANCY that can lead to large profits. Positive expectancy defined in its most simple form, is that on the average, there is a probability that you will make more money than you will lose.
If the Forex trader gets nothing else from this article the MOST IMPORTANT POINT that must be understood is that WITHOUT POSITIVE EXPECTANCY in any Forex trading system automatic or otherwise, there are no money management procedures or trading techniques that will prevent you from losing all your money.
Most traders confuse positive expectancy with the probability of winning. Forex traders and especially Forex system developers love to brag that their system "picks winners 97.3% of the time", and fall for the easy but incorrect logic and "feeling" that a high percentage of wins means a high profit. Sadly, this is NOT TRUE! Winning 97.3% of the time will not generate Forex profits if the 2.7% of losing trades wipe out your account. Confusing win probability with positive expectancy is what ultimately leads to Trader's Ruin.
Trader's Ruin is the mathematical certainty that over time the trader will lose all his money to the market if he trades without positive expectancy. Many very successful traders and auto Forex trading systems have a win probability of about 40%, with a high positive expectancy that returns huge profits.
If an automatic currency trading program wins 9 out of 10 times (90% wins!), and the average win is $10 but the average loss is $100 - that system has a negative expectancy and will lose money!
If an automatic Forex currency trading system wins once every 20 trades (5% wins!), losing an average $5 each losing trade but makes an average $100 on each win, that system has positive expectancy and over the long run will make money.
Did that tie your brain in a knot? Let's explain a little further.
To be able to say an automatic Forex trader, or any system, has positive expectancy means that on average the system will make more money than it loses. On any given trade, it may win or it may lose, but the average over time and many trades is profitable. This should include costs and slippage and be measured over an absolute minimum of 30 to 100 trades, preferably many more.
This analysis assumes the Forex trader and the Forex trading tool are properly capitalized and the trades are properly sized to reasonably ensure the system will survive the inevitable periods of losses.
"Properly capitalized" means you have enough money in your account that you can make properly sized trades and survive long enough for the average returns to grow your account. If the account is too small, it is much more likely a run of losses will wipe you out before you have time to generate profits.
"Properly sized" trades means that the average size of expected profit on any trade is large enough to cover expected average losses plus trading costs and still have positive expectancy.
"Exit loss" will be defined for this article as the amount the trade will be allowed to move against us before it is "stopped out" by our stop loss setting and we exit the trade. This applies to both winning and losing trades.
"Costs" in Forex trading are usually in the form of "bid/ask" spreads, Forex brokerage fees or commissions are usually small or non-existent. There are still real costs that figure into the expectancy of the system.
"Slippage" is defined as the difference between the price a trader expected to pay when a trade is ordered and the actual price paid. The Forex market is always moving and if the market moves against our trade, the time between our contract order and when it is executed in the market may allow the price to change. A good Forex automated trading system has an average known slippage value figured into the system also.
To make this easier to understand, let's put some numbers to it. These are simplified examples to illustrate the concept and the numbers may or may not match real FX trading strategies.
If my automatic Forex trading system follows a set of rules that allows an exit loss of $10 before it is stopped out, and my costs are $10, and my "slippage" averages $5 then my average loss will be: $10 exit loss + $10 costs + $5 average slippage = $25 average loss per losing trade. These trades are generally trades that immediately move against the trader.
If the trader executes each trade at $1000/trade and if my Forex trading system has an average winning trade of $50 (which includes the $10 exit loss), after costs and slippage we have $50 -$10 -$5 = $35 profits.
Now all we need to figure out our expectancy is to know our probability of a winning trade. Let's start with a system that has a 50% chance of winning. So this system has the same winning average over time as flipping a coin.
The Expectancy Equation
Pp = Probability of Profit
Ap = Average Profit
Pl = Probability of Loss
Al = Average loss
Expectancy = (Pp x Ap) - (Pl x Al)
In our first case:
Pp = 0.5
Ap = $35
Pl = 0.5
Al = $25
Expectancy = (0.5 X $35) - (0.5 X $25)
= ($17.5) - ($12.5) = $5
So this system trading at $1000 per trade has a positive expectancy of $5 per trade when traded over many trades. The profit of $5 is 0.5% of the $1000 that is at risk during the trade.
Now let's examine how our Forex trading techniques, rules, and behavior can affect our profits. First let's pretend we have experienced a run of losses and we are low on money because we are not properly capitalized. What happens if we lower the amount of money at risk and only trade $500 per trade? This cuts our profits in half but does not affect costs and slippage. An average winning trade is now $25, after costs and slippage we have $25 -$10 -$5 = $10 profits. This is a big hit to profits, but it is still a profit... right?
If we examine our expectancy our numbers look like this:
Pp = 0.5
Ap = $10
Pl = 0.5
Al = $25
Expectancy = (0.5 X $10) - (0.5 X $25)
= ($5) - ($12.5) = -$7.5 !!!
This system trading at $500 per trade can be expected to lose money on the average of $7.50 per trade.
NEGATIVE EXPECTANCY ! By trying to conserve money we have ensured that we will lose money! This illustrates the importance of having a properly capitalized account for the size of our trade, and the importance of watching the effect of costs and slippage. Trading many small trades can push a good Forex trading system into negative expectancy with costs and slippage.
Let's now make a different assumption, let's double our trade size and start our trading at $2000 a trade (assuming our account is properly capitalized to do this). An average winning trade is now $100, after costs and slippage we have $100 -$10 -$5 = $85 profits.
Pp = 0.5
Ap = $85
Pl = 0.5
Al = $25
Expectancy = (0.5 X $85) - (0.5 X $25)
= ($42.5) - ($12.5) = $30
We doubled the amount of capital at risk, but it has increased our net average profit per trade by SIX TIMES! The percentage gain is also increased to 1.5%, an increase of profit per dollar risked by THREE TIMES. This is a very good result.
Let's examine one more case and double our trade amount again to $4000 a trade (assuming again our account is properly capitalized to do this). An average winning trade is now $200, we are assuming costs for this remain the same traded as one lot, after costs and slippage we have $200 -$10 -$5 = $185 profits.
Pp = 0.5
Ap = $185
Pl = 0.5
Al = $25
Expectancy = (0.5 X $185) - (0.5 X $25)
= ($92.5) - ($12.5) = $80
Another nice average profit per trade. We doubled the amount of capital at risk again, but this time it has only increased our net average profits by 2.67 times. The percentage gain is also increased to 2.0%, an increase of profit per dollar risked of only 1/3 of the previous increase. From this point on, increasing the size of our trade, assuming that fees and slippage stay the same, has only a small, gradually diminishing effect on our trade efficiency as it gets larger and larger. Gross and net profits will increase, but the average percent return on our capital at risk will stay about the same.
The examples above are simplified to make the arithmetic easier and to illustrate the concepts. Lot size, leverage, and many other factors complicate the equations in real world trading but the basic concepts remain the same. Without positive expectancy, the trader is assured of losing his money.
This demonstrates that the small Forex trader needs to carefully examine his trading techniques and exercise "iron willed discipline" in his trading to ensure that he can effectively "stay in the game". Trying to do "on the job" Forex training while making small timid trades with a "too small" account is not a way to "increase or protect your money," in fact it may be the sure way to Trader's Ruin.
The joy of automated Forex trading systems and mechanical trading software is that it enforces trading discipline that keeps losses small, and lets winning positions run with built in positive expectancy. It is Forex made easy. There are websites that do online reviews of several automated systems that have the capability to do simulated Forex trading online, on a Forex demo account, so that the average trader can test them for 60 days with no risk and each has a 100% money back guarantee. Many offer suggestions for the best Forex broker compatible with their online Forex trading platform and offer full support for setting up your Forex demo account.
The beginning trader, just learning Forex trading, can learn a tremendous amount just from the running the demo accounts and can learn which is the best Forex system trading software for his or her goals. Rather than spend money on Forex training, a currency trading seminar, or trying to create your own FX trading strategies and implement them, the astute trader can let the experts do that and just test their work for profitable results. Then sit back and watch the Forex autotrading robots make money while you relax and rake in the profits.
Positive expectancy sounds like something a motivational speaker would talk about or a psychiatrist. In fact, there are some people that use the term for those reasons. This article is about using the term in the context of Forex trading strategies, STATISTICS, and MATH. One of the major advantages from using an automatic Forex trading system is built in discipline that maintains a high POSITIVE EXPECTANCY that can lead to large profits. Positive expectancy defined in its most simple form, is that on the average, there is a probability that you will make more money than you will lose.
If the Forex trader gets nothing else from this article the MOST IMPORTANT POINT that must be understood is that WITHOUT POSITIVE EXPECTANCY in any Forex trading system automatic or otherwise, there are no money management procedures or trading techniques that will prevent you from losing all your money.
Most traders confuse positive expectancy with the probability of winning. Forex traders and especially Forex system developers love to brag that their system "picks winners 97.3% of the time", and fall for the easy but incorrect logic and "feeling" that a high percentage of wins means a high profit. Sadly, this is NOT TRUE! Winning 97.3% of the time will not generate Forex profits if the 2.7% of losing trades wipe out your account. Confusing win probability with positive expectancy is what ultimately leads to Trader's Ruin.
Trader's Ruin is the mathematical certainty that over time the trader will lose all his money to the market if he trades without positive expectancy. Many very successful traders and auto Forex trading systems have a win probability of about 40%, with a high positive expectancy that returns huge profits.
If an automatic currency trading program wins 9 out of 10 times (90% wins!), and the average win is $10 but the average loss is $100 - that system has a negative expectancy and will lose money!
If an automatic Forex currency trading system wins once every 20 trades (5% wins!), losing an average $5 each losing trade but makes an average $100 on each win, that system has positive expectancy and over the long run will make money.
Did that tie your brain in a knot? Let's explain a little further.
To be able to say an automatic Forex trader, or any system, has positive expectancy means that on average the system will make more money than it loses. On any given trade, it may win or it may lose, but the average over time and many trades is profitable. This should include costs and slippage and be measured over an absolute minimum of 30 to 100 trades, preferably many more.
This analysis assumes the Forex trader and the Forex trading tool are properly capitalized and the trades are properly sized to reasonably ensure the system will survive the inevitable periods of losses.
"Properly capitalized" means you have enough money in your account that you can make properly sized trades and survive long enough for the average returns to grow your account. If the account is too small, it is much more likely a run of losses will wipe you out before you have time to generate profits.
"Properly sized" trades means that the average size of expected profit on any trade is large enough to cover expected average losses plus trading costs and still have positive expectancy.
"Exit loss" will be defined for this article as the amount the trade will be allowed to move against us before it is "stopped out" by our stop loss setting and we exit the trade. This applies to both winning and losing trades.
"Costs" in Forex trading are usually in the form of "bid/ask" spreads, Forex brokerage fees or commissions are usually small or non-existent. There are still real costs that figure into the expectancy of the system.
"Slippage" is defined as the difference between the price a trader expected to pay when a trade is ordered and the actual price paid. The Forex market is always moving and if the market moves against our trade, the time between our contract order and when it is executed in the market may allow the price to change. A good Forex automated trading system has an average known slippage value figured into the system also.
To make this easier to understand, let's put some numbers to it. These are simplified examples to illustrate the concept and the numbers may or may not match real FX trading strategies.
If my automatic Forex trading system follows a set of rules that allows an exit loss of $10 before it is stopped out, and my costs are $10, and my "slippage" averages $5 then my average loss will be: $10 exit loss + $10 costs + $5 average slippage = $25 average loss per losing trade. These trades are generally trades that immediately move against the trader.
If the trader executes each trade at $1000/trade and if my Forex trading system has an average winning trade of $50 (which includes the $10 exit loss), after costs and slippage we have $50 -$10 -$5 = $35 profits.
Now all we need to figure out our expectancy is to know our probability of a winning trade. Let's start with a system that has a 50% chance of winning. So this system has the same winning average over time as flipping a coin.
The Expectancy Equation
Pp = Probability of Profit
Ap = Average Profit
Pl = Probability of Loss
Al = Average loss
Expectancy = (Pp x Ap) - (Pl x Al)
In our first case:
Pp = 0.5
Ap = $35
Pl = 0.5
Al = $25
Expectancy = (0.5 X $35) - (0.5 X $25)
= ($17.5) - ($12.5) = $5
So this system trading at $1000 per trade has a positive expectancy of $5 per trade when traded over many trades. The profit of $5 is 0.5% of the $1000 that is at risk during the trade.
Now let's examine how our Forex trading techniques, rules, and behavior can affect our profits. First let's pretend we have experienced a run of losses and we are low on money because we are not properly capitalized. What happens if we lower the amount of money at risk and only trade $500 per trade? This cuts our profits in half but does not affect costs and slippage. An average winning trade is now $25, after costs and slippage we have $25 -$10 -$5 = $10 profits. This is a big hit to profits, but it is still a profit... right?
If we examine our expectancy our numbers look like this:
Pp = 0.5
Ap = $10
Pl = 0.5
Al = $25
Expectancy = (0.5 X $10) - (0.5 X $25)
= ($5) - ($12.5) = -$7.5 !!!
This system trading at $500 per trade can be expected to lose money on the average of $7.50 per trade.
NEGATIVE EXPECTANCY ! By trying to conserve money we have ensured that we will lose money! This illustrates the importance of having a properly capitalized account for the size of our trade, and the importance of watching the effect of costs and slippage. Trading many small trades can push a good Forex trading system into negative expectancy with costs and slippage.
Let's now make a different assumption, let's double our trade size and start our trading at $2000 a trade (assuming our account is properly capitalized to do this). An average winning trade is now $100, after costs and slippage we have $100 -$10 -$5 = $85 profits.
Pp = 0.5
Ap = $85
Pl = 0.5
Al = $25
Expectancy = (0.5 X $85) - (0.5 X $25)
= ($42.5) - ($12.5) = $30
We doubled the amount of capital at risk, but it has increased our net average profit per trade by SIX TIMES! The percentage gain is also increased to 1.5%, an increase of profit per dollar risked by THREE TIMES. This is a very good result.
Let's examine one more case and double our trade amount again to $4000 a trade (assuming again our account is properly capitalized to do this). An average winning trade is now $200, we are assuming costs for this remain the same traded as one lot, after costs and slippage we have $200 -$10 -$5 = $185 profits.
Pp = 0.5
Ap = $185
Pl = 0.5
Al = $25
Expectancy = (0.5 X $185) - (0.5 X $25)
= ($92.5) - ($12.5) = $80
Another nice average profit per trade. We doubled the amount of capital at risk again, but this time it has only increased our net average profits by 2.67 times. The percentage gain is also increased to 2.0%, an increase of profit per dollar risked of only 1/3 of the previous increase. From this point on, increasing the size of our trade, assuming that fees and slippage stay the same, has only a small, gradually diminishing effect on our trade efficiency as it gets larger and larger. Gross and net profits will increase, but the average percent return on our capital at risk will stay about the same.
The examples above are simplified to make the arithmetic easier and to illustrate the concepts. Lot size, leverage, and many other factors complicate the equations in real world trading but the basic concepts remain the same. Without positive expectancy, the trader is assured of losing his money.
This demonstrates that the small Forex trader needs to carefully examine his trading techniques and exercise "iron willed discipline" in his trading to ensure that he can effectively "stay in the game". Trying to do "on the job" Forex training while making small timid trades with a "too small" account is not a way to "increase or protect your money," in fact it may be the sure way to Trader's Ruin.
The joy of automated Forex trading systems and mechanical trading software is that it enforces trading discipline that keeps losses small, and lets winning positions run with built in positive expectancy. It is Forex made easy. There are websites that do online reviews of several automated systems that have the capability to do simulated Forex trading online, on a Forex demo account, so that the average trader can test them for 60 days with no risk and each has a 100% money back guarantee. Many offer suggestions for the best Forex broker compatible with their online Forex trading platform and offer full support for setting up your Forex demo account.
The beginning trader, just learning Forex trading, can learn a tremendous amount just from the running the demo accounts and can learn which is the best Forex system trading software for his or her goals. Rather than spend money on Forex training, a currency trading seminar, or trying to create your own FX trading strategies and implement them, the astute trader can let the experts do that and just test their work for profitable results. Then sit back and watch the Forex autotrading robots make money while you relax and rake in the profits.
About The Author: Ben Theranbak is an avid student of history, economics, statistics and the markets. He has an MBA, an MS in Aeronautical Engineering and is a graduate of the Naval War College. A former Naval Aviator, Ben is a skydiver and world traveler. Get a FREE report on a SPECIAL new development in FOREX trading at his website at http://trueairspeed.ws This site also offers reviews of several of the best available FOREX automatic trading systems that offer fully automated trading capability along with the ability to fully test the systems using Demo accounts or paper trading for a full 60 days along with full, unconditional 100% money back guarantees.
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