What is Positive Expectation?
Positive expectation sounds like something a motivational speaker or psychiatrist would talk about. In fact, there are some people who use the term for those reasons. This article is about the use of the term in the context of Forex trading strategies, STATISTICS, and MATHEMATICS. One of the main advantages of using an automatic Forex trading system is a built-in discipline that maintains a high POSITIVE EXPECTATION that can lead to big profits. Positive expectation, defined in its simplest form, is that, on average, there is a probability that you will win more money than you will lose.
If Forex trader gets nothing more from this article, the MOST IMPORTANT POINT to understand is that NO POSITIVE EXPECTATION in any automated or other Forex trading system, there are no money management procedures or trading techniques that will Don’t lose all your money. .
Most of the traders confuse the positive expectation 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”, falling for easy but incorrect logic and the “feeling” that a high percentage of profit means a big profit. Unfortunately, this is NOT TRUE! Winning 97.3% of the time will not make a profit in Forex if 2.7% of losing trades kill your account. Confused odds of winning with positive outlook is what ultimately leads to Trader’s Ruin.
Trader doom is the mathematical certainty that, over time, the trader will lose all his money in the market if he trades without a positive expectation. Many very successful Forex traders and automated trading systems have a winning probability of around 40%, with high positive expectation leading to large profits.
If an automated forex trading program wins 9 times out of 10 (90% win!), and the average win is $10 but the average loss is $100, that system has negative expectation and will lose money!
If an automated Forex currency trading system wins once every 20 trades (5% win!), loses an average of $5 for each losing trade but generates an average of $100 for each win, that system has a positive expectation and, In the long run, it will generate money.
Did that tie your brain in a knot? Let’s explain a little more.
Being able to tell that a Forex auto trader, or any system, has a positive expectation means that, on average, the system will make more money than it loses. On any given trade you can win or lose, but average over time and many trades are profitable. This should include costs and slippage and be measured in an absolute minimum of 30-100 trades, preferably many more.
This analysis assumes that the Forex trader and Forex trading tool are properly capitalized and trades are of adequate size to reasonably ensure that the system will survive the inevitable periods of loss.
“Adequately capitalized” means that you have enough money in your account to be able to make appropriately sized transactions and survive long enough for average returns to grow your account. If the account is too small, a series of losses is much more likely to wipe you out before you have time to make a profit.
“Appropriately sized” trades means that the average size of expected profit on any trade is large enough to cover average expected losses plus trading costs and still have a positive expectation.
The “exit loss” will be defined for this article as the amount the trade will be allowed to move against us before it is “stopped” by our stop loss setting and we exit the trade. This applies to both winning and losing trades.
“Costs” in Forex trading are often in the form of “bid/ask” spreads, Forex brokerage fees or commissions are often small or non-existent. There are still real costs listed in the expectation of the system.
Slippage is defined as the difference between the price a trader expected to pay when placing a trade and the actual price paid. The Forex market is always in motion 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 also has an average known slippage value in the system.
To make this easier to understand, let’s put some numbers on it. These are simplified examples to illustrate the concept and the numbers may or may not match actual forex trading strategies.
If my automatic Forex trading system follows a set of rules that allows a $10 exit loss before it stops, and my costs are $10 and my “slippage” averages $5, then my average loss will be: $10 loss exit + $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 profit.
Now all we need to figure out our expectation 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 average payout over time as flipping a coin.
The expectation equation
Pp = Probability of Profit
Ap = average profit
Pl = Probability of loss
Al = Average loss
Expectation = (Pp x Ap) – (Pl x Al)
In our first case:
Pp = 0.5
app = $35
pl = 0.5
Everything = $25
Expectation = (0.5 X $35) – (0.5 X $25)
= ($17.5) – ($12.5) = $5
So this system trading at $1000 per trade has a positive expectation of $5 per trade when trading 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 behaviors can affect our profits. Let’s first assume that we have experienced a losing streak and we are low on money because we are not adequately capitalized. What happens if we reduce the amount of money at risk and only trade $500 per trade? This cuts our profits in half, but doesn’t affect costs or slippage. An average winning trade is now $25, after costs and slippage we have $25 – $10 – $5 = $10 of profit. This is a big hit to earnings, but it’s still a win… right?
If we examine our expectation, our numbers look like this:
Pp = 0.5
Ap = $10
pl = 0.5
Everything = $25
Expectation = (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 at an average of $7.50 per trade.
NEGATIVE EXPECTATION! 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 looking at the effect of costs and slippage. Trading many small trades can drive a good Forex trading system into negative expectation with costs and slippage.
Now let’s make a different assumption, double our trade size and start trading at $2000 per trade (assuming our account is adequately capitalized to do this). An average winning trade is now $100, after costs and slippage we have $100 – $10 – $5 = $85 of profit.
Pp = 0.5
A = $85
pl = 0.5
Everything = $25
Expectation = (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 average net profit per trade by SIX TIMES! The profit percentage is also increased to 1.5%, a THREE TIMES increase in profit per dollar risked. This is a very good result.
Let’s examine one more case and double our trade amount back to $4000 per trade (again assuming our account is adequately capitalized to do this). An average winning trade is now $200, we assume the costs for this remain the same as one lot, after costs and slippage we have $200 – $10 – $5 = $185 of profit.
Pp = 0.5
Ap = $185
pl = 0.5
Everything = $25
Expectation = (0.5 X $185) – (0.5 X $25)
= ($92.5) – ($12.5) = $80
Another good average profit per trade. We doubled the amount of venture capital again, but this time it has only increased our average net earnings by 2.67 times. The profit percentage is also increased to 2.0%, an increase in profit per dollar risked of only 1/3 of the previous increase. From this point on, increasing our trade size, assuming fees and slippage stay the same, has only a small, gradually diminishing effect on our trading efficiency as it gets bigger and bigger. Gross and net earnings will increase, but the average percentage return on our risk capital will remain roughly the same.
The above examples are simplified to facilitate arithmetic and illustrate concepts. Lot size, leverage, and many other factors complicate the equations in real world trading, but the basics remain the same. Without a positive expectation, the trader is sure to lose his money.
This goes to show 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 Forex training “on the job” while making timid small trades with an “too small” account is not a way to “increase or protect your money”, in fact, it can be the sure path to bankruptcy. businessman.
The joy of automated Forex trading systems and mechanical trading software is that it enforces a trading discipline that keeps losses small and allows winning positions to be executed with built-in positive expectation. It’s Forex made easy. There are websites that do online reviews of various automated systems that have the ability to do simulated Forex trading online, on a Forex demo account, so that the average trader can try them out for 60 days risk-free and each has a 100% money back. guarantee. Many offer suggestions for the best Forex broker compatible with your online Forex trading platform and offer full support in setting up your Forex demo account.
The beginning trader, who is just learning how to trade Forex, can learn a great deal just by running the demo accounts and can learn the best Forex system trading software for their goals. Instead of spending money on Forex training, a forex trading seminar, or trying to create their own FX trading strategies and implement them, the astute trader can let the experts do that and simply test their work for profitable results. Then sit back and watch Forex auto trading robots make money while you sit back and accumulate profits.
