Expectancy defines your trading system's long-term profitability. A positive expectancy indicates a profitable system. A negative expectancy indicates a losing system. Traders often focus on increasing win rate or average winner size. However, reducing average loser size frequently offers the most direct path to positive expectancy.
Expectancy is calculated as:
$E = (W \times AW) - (L \times AL)$
Where: $E$ = Expectancy $W$ = Win Rate (as a decimal) $AW$ = Average Winner $L$ = Loss Rate (as a decimal, $1 - W$) $AL$ = Average Loser
Impact of Average Loser on Expectancy
Consider a trading system with the following parameters: Win Rate ($W$) = 0.50 (50%) Average Winner ($AW$) = $200 Loss Rate ($L$) = 0.50 (50%) Average Loser ($AL$) = $250
Calculate the expectancy: $E = (0.50 \times $200) - (0.50 \times $250)$ $E = $100 - $125$ $E = -$25$
This system has a negative expectancy. Each trade, on average, loses $25.
Now, reduce the average loser by 20% while keeping other parameters constant. New Average Loser ($AL_{new}$) = $250 $\times$ (1 - 0.20) = $200
Calculate the new expectancy: $E_{new} = (0.50 \times $200) - (0.50 \times $200)$ $E_{new} = $100 - $100$ $E_{new} = $0$
The system is now breakeven. A 20% reduction in average loser moved the system from losing $25 per trade to breaking even.
Next, reduce the average loser by 30% from the original $250. New Average Loser ($AL_{new}$) = $250 $\times$ (1 - 0.30) = $175
Calculate the new expectancy: $E_{new} = (0.50 \times $200) - (0.50 \times $175)$ $E_{new} = $100 - $87.50$ $E_{new} = $12.50$
A 30% reduction in average loser transformed the system from losing $25 per trade to gaining $12.50 per trade. This demonstrates the sensitivity of expectancy to average loser size.
Strategies for Reducing Average Losers
Reducing average losers requires disciplined trade management. Specific actions include:
- Strict Stop-Loss Placement: Define your maximum acceptable loss before entering a trade. Adhere to this stop-loss without exception.
- Dynamic Stop-Loss Adjustments: As a trade moves in your favor, adjust your stop-loss to reduce risk or lock in profits.
- Position Sizing: Proper position sizing ensures that even a full stop-loss hit does not disproportionately impact your capital.
Example: Futures Trading
Consider a day trader specializing in E-mini S&P 500 futures (ES). Each point in ES is $50. The trader typically uses a 4-point stop-loss. Initial Average Loser ($AL$) = 4 points $\times$ $50/point = $200.
The trader identifies a pattern of letting losing trades run an extra 2 points before exiting. This increases the average loser to 6 points. New Average Loser ($AL_{actual}$) = 6 points $\times$ $50/point = $300.
Assume the trader's system has: Win Rate ($W$) = 0.45 (45%) Average Winner ($AW$) = 8 points $\times$ $50/point = $400 Loss Rate ($L$) = 0.55 (55%) Average Loser ($AL_{actual}$) = $300
Calculate current expectancy: $E = (0.45 \times $400) - (0.55 \times $300)$ $E = $180 - $165$ $E = $15$
The system is profitable, but the trader is leaving money on the table by not adhering to the 4-point stop.
If the trader strictly adheres to the 4-point stop: New Average Loser ($AL_{target}$) = 4 points $\times$ $50/point = $200
Calculate expectancy with disciplined stop-loss: $E_{target} = (0.45 \times $400) - (0.55 \times $200)$ $E_{target} = $180 - $110$ $E_{target} = $70$
By simply cutting the average loser from $300 to $200 (a 33.33% reduction), the expectancy per trade increases from $15 to $70. This is a 366.67% increase in profitability without changing win rate or average winner.
Step-by-Step Numerical Example: Stock Trading
A day trader trades XYZ stock. Entry Price: $50.00 Initial Stop-Loss: $49.50 (0.50 risk per share) Target Price: $51.50 (1.50 reward per share) Position Size: 1,000 shares
Trader's historical performance data: Win Rate ($W$) = 0.40 (40%) Average Winner ($AW$) = $1.50 per share Average Loser ($AL$) = $0.75 per share (due to sometimes letting losers run to $49.25)
Step 1: Calculate Current Expectancy First, calculate the average winner and average loser for the 1,000-share position. Average Winner (position) = $1.50/share $\times$ 1,000 shares = $1,500 Average Loser (position) = $0.75/share $\times$ 1,000 shares = $750
Now, calculate the expectancy: $E = (0.40 \times $1,500) - (0.60 \times $750)$ $E = $600 - $450$ $E = $150$
The system is profitable, earning $150 per trade on average.
Step 2: Identify the Discrepancy The trader's initial stop-loss plan was $0.50 per share. However, the actual average loser is $0.75 per share. This means the trader is letting losers run an additional $0.25 per share, or 50% beyond the planned stop.
Step 3: Calculate Potential Average Loser If the trader strictly adheres to the $0.50 per share stop-loss: Potential Average Loser (position) = $0.50/share $\times$ 1,000 shares = $500
Step 4: Calculate New Expectancy with Reduced Average Loser Assume win rate and average winner remain constant. New Average Loser (position) = $500
$E_{new} = (0.40 \times $1,500) - (0.60 \times $500)$ $E_{new} = $600 - $300$ $E_{new} = $300$
By reducing the average loser from $750 to $500 (a 33.33% reduction), the expectancy per trade increases from $150 to $300. This is a 100% increase in profitability.
Options Trading Application
Consider an options day trader buying calls on a stock. Stock price: $100.00 Call option strike: $100, expiration in 10 days. Option premium: $2.50 per contract (100 shares per contract). Initial Stop-Loss: 20% of premium, or $0.50 per contract. Target Profit: 40% of premium, or $1.00 per contract. Position Size: 10 contracts.
Trader's historical performance data: Win Rate ($W$) = 0.55 (55%) Average Winner ($AW$) = $0.90 per contract (due to sometimes taking profits early) Average Loser ($AL$) = $0.60 per contract (due to sometimes letting losers run)
Step 1: Calculate Current Expectancy Average Winner (position) = $0.90/contract $\times$
