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What is Positive Expectancy?

Positive expectancy is a term often associated with motivational speakers or psychiatrists, but in the world of Forex trading, statistics and math play a crucial role in defining it. An automatic Forex trading system offers a significant advantage by providing built-in discipline that maintains a high positive expectancy, leading to substantial profits. Simply put, positive expectancy means that, on average, there is a higher probability of making more money than losing it.

It is crucial for Forex traders to understand that positive expectancy is the most important aspect of any trading system, whether it’s automatic or not. Without positive expectancy, no money management procedures or trading techniques can prevent the risk of losing all of one’s money.

Many traders mistakenly confuse positive expectancy with the probability of winning. They boast about systems that “pick winners 97.3% of the time,” assuming that a high percentage of wins translates to high profits. Unfortunately, this is not true. Even if a system wins 97.3% of the time, if the remaining 2.7% of losing trades wipe out the account, there will be no profits. This confusion between win probability and positive expectancy ultimately leads to a phenomenon known as Trader’s Ruin.

Trader’s Ruin mathematically guarantees that if a trader lacks positive expectancy, he/she will lose all their money to the market over time. On the other hand, many successful traders and auto Forex trading systems have a win probability of only around 40%, but possess a high positive expectancy that results in substantial profits.

For instance, if an automatic currency trading program wins 9 out of 10 times (90% wins), with an average win of $10 but an average loss of $100, it has a negative expectancy and will lose money. Conversely, if an automatic Forex currency trading system wins only once every 20 trades (5% wins), losing an average $5 per losing trade but making an average $100 on each win, it has positive expectancy and will generate profits over the long run.

To determine whether a trading system has positive expectancy, one must assess its average profitability compared to its average loss over a significant number of trades, typically ranging from 30 to 100 or more. Moreover, the trader and the trading tool must be adequately capitalized, with trades sized to ensure the system can withstand inevitable periods of losses.

“Properly capitalized” refers to having enough money in the trading account to make appropriately sized trades and survive long enough for the average returns to grow the account. If the account is too small, a series of losses is likely to deplete the funds before any profits can be generated.

“Properly sized” trades imply that the average expected profit on any trade is large enough to cover expected average losses, trading costs, and still maintain positive expectancy.

In this article, “exit loss” refers to the predetermined point at which a trader will exit a losing trade using a stop loss order. This also applies to winning trades.

Forex trading costs typically include bid/ask spreads, while brokerage fees or commissions are usually small or non-existent. However, these costs still impact the overall expectancy of the system.

“Slippage” describes the price difference between what a trader expects to pay when placing a trade and the actual price paid. As the Forex market constantly fluctuates, if the market moves against the trade during the time between order placement and execution, the price may change. Good Forex automated trading systems consider the average known slippage value in their calculations.

To better understand these concepts, let’s illustrate them with simplified examples. Please note that these numbers might not accurately represent real FX trading strategies.

Suppose an automatic Forex trading system allows an exit loss of $10, incurs costs of $10, and experiences an average slippage of $5. In this scenario, the average loss per losing trade would be $10 (exit loss) + $10 (costs) + $5 (average slippage) = $25. These trades typically move against the trader.

If the trader executes each trade at $1000 per trade and the Forex trading system has an average winning trade of $50 (which includes the $10 exit loss), after costs and slippage, the profits would amount to $50 – $10 – $5 = $35.

To calculate expectancy, one needs to determine the probability of a winning trade using the following equation:

Pp = Probability of Profit
Ap = Average Profit
Pl = Probability of Loss
Al = Average Loss

Expectancy = (Pp x Ap) – (Pl x Al)

For example, considering a system with a 50% chance of winning:

Pp = 0.5
Ap = $35
Pl = 0.5
Al = $25

Expectancy = (0.5 x $35) – (0.5 x $25) = ($17.5) – ($12.5) = $5

Therefore, this system, traded at $1000 per trade, exhibits a positive expectancy of $5 per trade over multiple trades. This profit represents 0.5% of the $1000 at risk during each trade.

Now, let’s examine how our Forex trading techniques, rules, and behavior can impact profits. Suppose we have experienced a series of losses and have limited funds due to inadequate capitalization. What happens if we reduce the amount of money at risk and only trade $500 per trade? This action cuts our profits in half, but it does not affect costs and slippage. As a result, the average winning trade would be $25, resulting in $25 – $10 – $5 = $10 in profits. While a profit is still achieved, it significantly reduces profitability.

Assessing the expectancy in this scenario, the numbers are as follows:

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, traded at $500 per trade, is expected to lose an average of $7.50 per trade.

This negative expectancy demonstrates the importance of having a properly capitalized account and the need to monitor the impact of costs and slippage. Engaging in numerous small trades can push a promising Forex trading system into negative expectancy due to these factors.

Let’s now examine another case where we double the trade size and start trading at $2000 per trade (assuming proper capitalization). With this adjustment, the average winning trade would be $100, resulting in $100 – $10 – $5 = $85 in 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

By doubling the capital at risk, the net average profit per trade increases sixfold. The percentage gain also rises to 1.5%, representing a threefold increase in profit per dollar risked. This outcome is highly favorable.

Let’s examine one more situation where we double the trade amount again to $4000 per trade (assuming the account is properly capitalized for this). In this case, the average winning trade is $200, and after costs and slippage, the profits would amount to $200 – $10 – $5 = $185.

Pp = 0.5
Ap = $185
Pl = 0.5
Al = $25

Expectancy = (0.5 x $185) – (0.5 x $25) = ($92.5) – ($12.5) = $80

Exhibiting another favorable average profit per trade, the percentage gain remains high at $80.

These examples clearly illustrate the impact of trading techniques, rules, and behavior on profits. By considering the concepts of positive expectancy, proper capitalization, and monitoring costs and slippage, Forex traders can maximize their profitability and achieve long-term success.
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Ihab Salloum