Expectancy quantifies a trading strategy's average profit or loss per trade. It is not static. Market conditions directly influence a strategy's win rate, average win, and average loss. Therefore, expectancy changes. Understanding this variability is essential for adaptive strategy deployment.
Expectancy Formula Review
Expectancy is calculated as:
$E = (W \times AW) - (L \times AL)$
Where:
- $E$ = Expectancy
- $W$ = Win Rate (probability of a winning trade)
- $AW$ = Average Win (average profit of winning trades)
- $L$ = Loss Rate (probability of a losing trade, $L = 1 - W$)
- $AL$ = Average Loss (average loss of losing trades)
Alternatively, using the average profit per trade:
$E = (Total Profit - Total Loss) / Number of Trades$
This lesson focuses on how changes in $W$, $AW$, and $AL$ due to market conditions impact $E$.
Market Condition Variables
Market conditions impact trading outcomes. Key variables include:
- Volatility: Measured by ATR (Average True Range) or standard deviation. High volatility often means larger price swings, potentially increasing $AW$ and $AL$.
- Trend Strength: Measured by ADX (Average Directional Index) or moving average slopes. Strong trends can increase $W$ for trend-following strategies or decrease it for counter-trend strategies.
- Liquidity: Measured by bid-ask spread and volume. Low liquidity can increase slippage, impacting $AL$ and $AW$.
- Market Structure: Ranging, trending, or choppy. A strategy optimized for trending markets will perform differently in a range.
Impact of Volatility on Expectancy
Consider a futures day trading strategy on ES (E-mini S&P 500 futures).
Scenario 1: Low Volatility (ATR = 10 points) A strategy aims for a 4-point profit target and a 2-point stop loss.
- Average Win ($AW$) = 4 points
- Average Loss ($AL$) = 2 points
- Historical Win Rate ($W$) = 0.60 (60%)
Expectancy: $E = (0.60 \times 4 \text{ points}) - (0.40 \times 2 \text{ points})$ $E = 2.40 \text{ points} - 0.80 \text{ points}$ $E = 1.60 \text{ points per trade}$
If 1 contract ES = $50 per point, then $E = 1.60 \times $50 = $80 per trade.
Scenario 2: High Volatility (ATR = 20 points) The same strategy with fixed 4-point profit target and 2-point stop loss. In high volatility, price moves faster. This can lead to:
- Increased stop-outs (higher $AL$ frequency, lower $W$).
- But also faster target hits (maintaining $AW$).
Assume in high volatility:
- Win Rate ($W$) drops to 0.45 (45%)
- Average Win ($AW$) remains 4 points (target hit)
- Average Loss ($AL$) remains 2 points (stop hit)
Expectancy: $E = (0.45 \times 4 \text{ points}) - (0.55 \times 2 \text{ points})$ $E = 1.80 \text{ points} - 1.10 \text{ points}$ $E = 0.70 \text{ points per trade}$
$E = 0.70 \times $50 = $35 per trade.
The expectancy decreased from $80 to $35. This illustrates how a fixed-target strategy suffers when volatility increases without adjustment. An adaptive strategy might widen targets and stops in high volatility to maintain $W$ or increase $AW$.
Impact of Trend Strength on Expectancy
Consider a stock day trading strategy (e.g., AAPL) using a breakout entry.
Scenario 1: Strong Trend (ADX > 25) A trend-following breakout strategy.
- Average Win ($AW$) = $0.75 per share
- Average Loss ($AL$) = $0.30 per share
- Historical Win Rate ($W$) = 0.55 (55%)
Expectancy: $E = (0.55 \times $0.75) - (0.45 \times $0.30)$ $E = $0.4125 - $0.1350$ $E = $0.2775 per share
If trading 500 shares, $E = 500 \times $0.2775 = $138.75 per trade.
Scenario 2: Weak Trend / Ranging Market (ADX < 20) The same breakout strategy. Breakouts in ranging markets often fail.
- Win Rate ($W$) drops to 0.35 (35%)
- Average Win ($AW$) might decrease slightly due to lack of follow-through, say $0.60 per share
- Average Loss ($AL$) might remain $0.30 per share (stop hit)
Expectancy: $E = (0.35 \times $0.60) - (0.65 \times $0.30)$ $E = $0.2100 - $0.1950$ $E = $0.0150 per share
If trading 500 shares, $E = 500 \times $0.0150 = $7.50 per trade.
The expectancy decreased from $138.75 to $7.50. The strategy becomes marginally profitable, nearing breakeven. This highlights the need to identify and adapt to trend strength.
Impact of Liquidity and Slippage on Expectancy
Consider an options day trading strategy on SPY options. Assume a strategy with a $0.50 profit target and a $0.25 stop loss per contract.
Scenario 1: High Liquidity (Tight Spreads, High Volume)
- Average Win ($AW$) = $0.50 (target hit, minimal slippage)
- Average Loss ($AL$) = $0.25 (stop hit, minimal slippage)
- Win Rate ($W$) = 0.58 (58%)
Expectancy: $E = (0.58 \times $0.50) - (0.42 \times $0.25)$ $E = $0.290 - $0.105$ $E = $0.185 per contract
If trading 10 contracts, $E = 10 \times $0.185 = $1.85 per trade. (Note: Options contracts represent 100 shares, so $185 per trade).
Scenario 2: Low Liquidity (Wide Spreads, Low Volume) The same strategy. Low liquidity leads to increased slippage on entry and exit.
- Average Win ($AW$) decreases due to slippage on profit target. Instead of $0.50, it might be $0.40.
- Average Loss ($AL$) increases due to slippage on stop loss. Instead of $0.25, it might be $0.35.
- Win Rate ($W$) might slightly decrease if slippage causes more stop-outs before target. Assume $W = 0.55 (55%).
Expectancy: $E = (0.55 \times $0.40) - (0.45 \times $0.35)$ $E = $0.220 - $0.1575$ $E = $0.0625 per contract
If trading 10 contracts, $E = 10 \times $0.0625 = $0.625 per trade. (Note: Options contracts represent 100 shares, so $62.50 per trade).
The expectancy decreased from $185 to $62.50. Slippage, a direct consequence of liquidity, significantly erodes profitability.
Step-by-Step Example: Adapting to Market Structure
Consider a mean-reversion strategy on NQ (Nasdaq 100 E-mini futures).
Initial Strategy Parameters (Optimized for Ranging Market):
- Entry: Price touches lower Bollinger Band.
- Exit 1 (Profit Target): Price touches middle Bollinger Band.
- Exit 2 (Stop Loss): Fixed 15 points below entry.
- Position Size: 2 contracts.
Backtested Performance in Ranging Market (e.g., Q2 2023):
- Total Trades: 100
- Winning Trades: 65
- Losing Trades: 35
- Total Profit from Winners
