Chapter 1: What Expectancy Really Means Lesson 4: Calculating Your Personal Expectancy from Trade History
Calculating personal expectancy from trade history quantifies a trading strategy's long-term profitability. This calculation moves beyond theoretical models. It uses actual performance data. This provides a direct measure of a strategy's edge.
Expectancy Defined
Expectancy is the average profit or loss a trader can expect per trade. It is expressed in dollars or as a percentage of risk. A positive expectancy indicates a profitable system over many trades. A negative expectancy suggests a losing system.
The fundamental formula for expectancy is:
$E = (P_w \times A_w) - (P_l \times A_l)$
Where:
- $E$ = Expectancy
- $P_w$ = Probability of a winning trade (Win Rate)
- $A_w$ = Average profit per winning trade
- $P_l$ = Probability of a losing trade (Loss Rate)
- $A_l$ = Average loss per losing trade
We know that $P_l = 1 - P_w$. Substituting this into the formula gives:
$E = (P_w \times A_w) - ((1 - P_w) \times A_l)$
This formula yields expectancy in monetary terms. To express expectancy as a percentage of the average loss (Risk-Adjusted Expectancy), divide the monetary expectancy by the average loss per trade. This provides a standardized metric for comparison across different strategies or instruments.
Data Collection for Expectancy Calculation
Accurate expectancy calculation requires detailed trade history. Each trade record must include:
- Date and time of entry and exit
- Instrument traded
- Position size
- Entry price
- Exit price
- Gross profit or loss
- Commissions and fees
Net profit or loss is essential for accurate calculation. Gross profit or loss minus commissions and fees equals net profit or loss.
Step-by-Step Calculation Example
Consider a futures day trader. The trader focuses on ES futures contracts. The trader has a history of 100 trades.
Step 1: Segregate Winning and Losing Trades
Review the 100 trades. Identify each as a win or a loss based on net profit.
Assume:
- 60 winning trades
- 40 losing trades
Step 2: Calculate Win Rate ($P_w$) and Loss Rate ($P_l$)
$P_w = \frac{\text{Number of winning trades}}{\text{Total number of trades}}$ $P_w = \frac{60}{100} = 0.60$ (or 60%)
$P_l = \frac{\text{Number of losing trades}}{\text{Total number of trades}}$ $P_l = \frac{40}{100} = 0.40$ (or 40%)
Verify: $P_w + P_l = 0.60 + 0.40 = 1.00$.
Step 3: Calculate Average Profit per Winning Trade ($A_w$)
Sum the net profits of all winning trades. Divide by the number of winning trades.
Assume the sum of net profits from 60 winning trades is $18,000.
$A_w = \frac{\text{Sum of net profits from winning trades}}{\text{Number of winning trades}}$ $A_w = \frac{$18,000}{60} = $300$
Step 4: Calculate Average Loss per Losing Trade ($A_l$)
Sum the net losses of all losing trades. Divide by the number of losing trades. Losses are positive values for this calculation.
Assume the sum of net losses from 40 losing trades is $10,000.
$A_l = \frac{\text{Sum of net losses from losing trades}}{\text{Number of losing trades}}$ $A_l = \frac{$10,000}{40} = $250$
Step 5: Calculate Expectancy ($E$)
Using the formula: $E = (P_w \times A_w) - (P_l \times A_l)$
$E = (0.60 \times $300) - (0.40 \times $250)$ $E = $180 - $100$ $E = $80$
This trader's expectancy is $80 per trade. This means, on average, for every trade executed, the system expects to generate $80 in profit.
Risk-Adjusted Expectancy
To express expectancy as a percentage of the average loss, divide the monetary expectancy by the average loss per trade ($A_l$).
Risk-Adjusted Expectancy $= \frac{E}{A_l}$ Risk-Adjusted Expectancy $= \frac{$80}{$250} = 0.32$ or 32%
This means for every $1 risked on average, the system expects to return $0.32.
Impact of Commissions and Fees
Commissions and fees significantly impact expectancy. They reduce net profits and increase net losses.
Consider the previous example. Assume commissions and fees average $5 per round trip (entry and exit) per contract.
Original $A_w = $300$. With $5 in commissions, adjusted $A_w = $295. Original $A_l = $250$. With $5 in commissions, adjusted $A_l = $255.
Recalculate Expectancy with commissions:
$E_{adjusted} = (0.60 \times $295) - (0.40 \times $255)$ $E_{adjusted} = $177 - $102$ $E_{adjusted} = $75$
The expectancy dropped from $80 to $75 due to commissions. This $5 difference per trade, over 100 trades, equates to $500. Over 1,000 trades, it's $5,000. This illustrates the importance of including all costs.
Statistical Significance and Sample Size
The accuracy of the calculated expectancy depends on the sample size of trades. A small sample size (e.g., 10-20 trades) may not accurately represent the true expectancy of the system. Market conditions, volatility, and strategy adjustments can skew results over short periods.
A minimum of 50-100 trades provides a more reliable estimate. For high-frequency strategies, thousands of trades are preferable. The Law of Large Numbers applies here. As the number of trades increases, the observed expectancy converges towards the true expectancy of the system.
Traders should periodically recalculate their expectancy. This accounts for market changes and strategy evolution. A rolling expectancy calculation, using the most recent 100-200 trades, offers a dynamic view of performance.
Practical Application: Options Trading Example
An options day trader focuses on selling out-of-the-money call spreads on SPY. Over 200 trades:
- 150 winning trades
- 50 losing trades
Win Rate ($P_w$) $= \frac{150}{200} = 0.75$ (75%) Loss Rate ($P_l$) $= \frac{50}{200} = 0.25$ (25%)
Average profit per winning trade ($A_w$): Assume total net profit from 150 winning trades is $22,500. $A_w = \frac{$22,500}{150} = $150$
Average loss per losing trade ($A_l$): Assume total net loss from 50 losing trades is $10,000. $A_l = \frac{$10,000}{50} = $200$
Calculate Expectancy ($E$): $E = (0.75 \times $150) - (0.25 \times $200)$ $E = $112.50 - $50$ $E = $62.50$
This options strategy has an expectancy of $62.50 per trade.
Risk-Adjusted Expectancy $= \frac{$62.50}{$200} = 0.3125$ or 31.25%.
This means for every $1 risked, the system expects to return $0.3125.
Using Expectancy for Position Sizing
Expectancy informs position sizing models. A higher positive expectancy supports larger position sizes within risk management constraints. A lower positive expectancy dictates smaller sizes.
If a system has an expectancy of $80 per trade and a trader aims for $1,600 profit per month, the trader needs to execute $1,600 / $80 = 20 trades per month. This assumes consistent expectancy.
Limitations of Expectancy
Expectancy is an average. It does not guarantee any single trade's outcome. It does not account for sequence risk or drawdowns.
