Expectancy Really Means, Lesson 8
How Commissions and Slippage Destroy Marginal Expectancy
Expectancy is the average profit or loss per trade. It is a core metric for evaluating a trading strategy. Many traders calculate gross expectancy, ignoring the real costs of trading. Commissions and slippage are direct costs that reduce net expectancy. For strategies with marginal gross expectancy, these costs can render a system unprofitable.
Gross Expectancy vs. Net Expectancy
Gross expectancy is calculated before accounting for commissions and slippage. Net expectancy includes these costs.
Gross Expectancy Formula: $E_g = (P_w \times A_w) - (P_l \times A_l)$
Where: $E_g$ = Gross Expectancy $P_w$ = Probability of a winning trade $A_w$ = Average win amount $P_l$ = Probability of a losing trade $A_l$ = Average loss amount
Net Expectancy Formula: $E_n = E_g - C - S$
Where: $E_n$ = Net Expectancy $C$ = Average commission cost per trade $S$ = Average slippage cost per trade
A strategy with a positive gross expectancy is not necessarily profitable. A strategy must have a positive net expectancy to generate profits.
Understanding Commission Costs
Commissions are fees paid to a broker for executing trades. These can be fixed per share, per contract, or a flat fee per trade. Day traders often execute many trades, making commission costs significant.
Example: Stock Trading Commissions A trader buys 1,000 shares of XYZ at $50.00 and sells them at $50.10. Broker charges $0.005 per share commission.
Buy commission: $1,000 \text{ shares} \times $0.005/\text{share} = $5.00$ Sell commission: $1,000 \text{ shares} \times $0.005/\text{share} = $5.00$ Total commission for the round trip: $$5.00 + $5.00 = $10.00$
Example: Futures Trading Commissions A trader buys 5 E-mini S&P 500 futures contracts and sells them. Broker charges $2.50 per contract per side.
Buy commission: $5 \text{ contracts} \times $2.50/\text{contract} = $12.50$ Sell commission: $5 \text{ contracts} \times $2.50/\text{contract} = $12.50$ Total commission for the round trip: $$12.50 + $12.50 = $25.00$
These costs directly subtract from the trade's profit or add to its loss.
Understanding Slippage Costs
Slippage is the difference between the expected price of a trade and the price at which the trade is actually executed. This occurs in fast-moving markets or when trading large sizes. Slippage can be positive (favorable) or negative (unfavorable). For most day trading strategies, especially those involving market orders or aggressive limit orders, slippage is a negative cost.
Slippage Cost Formula: $S = |P_{exec} - P_{expected}| \times N$
Where: $S$ = Slippage cost $P_{exec}$ = Actual execution price $P_{expected}$ = Expected execution price (e.g., bid/ask at order entry) $N$ = Number of shares or contracts
Example: Stock Trading Slippage A trader places a market order to buy 500 shares of ABC, expecting to fill at $100.00. The order fills at $100.05. Slippage per share: $100.05 - 100.00 = $0.05$ Total slippage cost: $500 \text{ shares} \times $0.05/\text{share} = $25.00$
This $25.00 is a direct cost reducing the trade's profit.
Example: Futures Trading Slippage A trader places a market order to sell 2 E-mini S&P 500 futures contracts, expecting to fill at 4500.00. The order fills at 4499.75. Slippage per contract: $4500.00 - 4499.75 = 0.25 \text{ points}$ Value per point for E-mini S&P 500: $50.00 Slippage per contract in dollars: $0.25 \text{ points} \times $50.00/\text{point} = $12.50$ Total slippage cost: $2 \text{ contracts} \times $12.50/\text{contract} = $25.00$
This $25.00 is a direct cost reducing the trade's profit.
Impact on Marginal Expectancy: A Worked Example
Consider a day trading strategy with the following characteristics: Probability of winning ($P_w$): 55% Probability of losing ($P_l$): 45% Average win amount ($A_w$): $100.00 Average loss amount ($A_l$): $110.00
Calculate Gross Expectancy: $E_g = (0.55 \times $100.00) - (0.45 \times $110.00)$ $E_g = $55.00 - $49.50$ $E_g = $5.50$
This strategy has a positive gross expectancy of $5.50 per trade.
Now, incorporate commissions and slippage. Assume: Average commission cost per trade ($C$): $15.00 Average slippage cost per trade ($S$): $10.00
Calculate Net Expectancy: $E_n = E_g - C - S$ $E_n = $5.50 - $15.00 - $10.00$ $E_n = $5.50 - $25.00$ $E_n = -$19.50$
The strategy, which appeared profitable with a gross expectancy of $5.50, becomes unprofitable with a net expectancy of -$19.50 after accounting for commissions and slippage.
This example illustrates how costs can destroy marginal expectancy. A strategy with a small positive gross edge can quickly turn negative.
The Importance of Tracking Real Costs
Traders must accurately track their commission and slippage costs.
- Commissions: Most brokers provide detailed commission reports. Average commission per trade can be calculated by dividing total commissions by total trades over a period.
- Slippage: This requires meticulous record-keeping. Compare the order entry price (e.g., bid/ask at the time of order submission for market orders, or limit price for limit orders) with the actual execution price. Sum these differences for all trades and divide by the number of trades to get an average slippage cost.
Strategies to Mitigate Cost Impact
- Reduce Trade Frequency: Fewer trades mean lower total commission costs.
- Increase Average Win Size: A larger average win can absorb fixed costs more effectively.
- Decrease Position Size: Smaller positions may reduce slippage, especially in illiquid markets. However, this also reduces potential profit.
- Use Limit Orders Strategically: Limit orders can eliminate negative slippage on entry/exit, but risk non-fill.
- Negotiate Commissions: High-volume traders may negotiate lower commission rates with their brokers.
- Trade More Liquid Instruments: Higher liquidity generally leads to less slippage.
- Optimize Entry/Exit Points: Precise entries and exits can minimize slippage by targeting specific price levels.
Conclusion
Commissions and slippage are not abstract concepts. They are direct, quantifiable costs that erode trading profits. For strategies with marginal gross expectancy, these costs are often the difference between profitability and consistent losses. Traders must calculate net expectancy using actual commission and slippage data. Ignoring these costs leads to an inaccurate assessment of strategy performance and ultimately, capital depletion. A positive gross expectancy is a necessary but insufficient condition for a profitable trading system. A positive net expectancy is the true measure of profitability.
