Understanding time-of-day expectancy allows traders to allocate capital and effort efficiently. Not all trading hours offer equal opportunity. Market dynamics shift throughout the trading day. These shifts impact volatility, liquidity, and the efficacy of specific trading strategies. Quantifying these changes provides an objective basis for optimizing trading schedules.
Expectancy Review
Expectancy (E) quantifies the average profit or loss per trade. The formula is:
E = (P * A) - (L * B)
Where:
- P = Probability of a winning trade
- A = Average win amount
- L = Probability of a losing trade (1 - P)
- B = Average loss amount
Positive expectancy is necessary for long-term profitability. Maximizing expectancy involves increasing P, increasing A, decreasing L, or decreasing B. Time-of-day analysis focuses on how these variables change during different market hours.
Market Phases and Their Impact on Expectancy
The trading day typically divides into distinct phases:
- Opening Hour (e.g., 9:30 AM - 10:30 AM EST): High volatility, high volume. Price discovery is rapid. Gaps often fill or extend. Strategies requiring quick execution and capitalizing on large moves may perform well. Slippage can be higher.
- Mid-Morning (e.g., 10:30 AM - 12:00 PM EST): Volatility often subsides from the open. Trends may establish or reverse. Volume typically remains robust.
- Lunch Hour (e.g., 12:00 PM - 1:30 PM EST): Lower volume, reduced volatility. Price action can be choppy or range-bound. Many institutional traders are away.
- Mid-Afternoon (e.g., 1:30 PM - 3:00 PM EST): Volume and volatility may increase as European markets close and US traders return. News events can trigger moves.
- Closing Hour (e.g., 3:00 PM - 4:00 PM EST): High volatility and volume return. Positions are closed or adjusted. End-of-day rebalancing occurs.
Each phase presents different conditions. A strategy profitable in one phase may be unprofitable in another.
Calculating Time-of-Day Expectancy
To calculate time-of-day expectancy, segment historical trade data by specific time intervals. Common intervals include 30-minute or 60-minute blocks. For each interval, calculate P, A, L, and B.
Example Data Collection:
A trader executes 500 trades over three months using a specific strategy. The trader logs entry time, exit time, profit/loss, and position size for each trade.
Step 1: Define Time Intervals
Divide the trading day into hourly blocks:
- 9:30 AM - 10:30 AM
- 10:30 AM - 11:30 AM
- 11:30 AM - 12:30 PM
- 12:30 PM - 1:30 PM
- 1:30 PM - 2:30 PM
- 2:30 PM - 3:30 PM
- 3:30 PM - 4:00 PM (or 3:30 PM - 4:30 PM for futures/options)
Step 2: Aggregate Trade Data by Interval
For each interval, count wins and losses, and sum win amounts and loss amounts.
Hypothetical Data for a Futures Strategy (ES Mini):
Assume a trader trades ES Mini futures contracts. Each contract has a point value of $50.
Interval: 9:30 AM - 10:30 AM (Opening Hour)
- Total Trades: 150
- Winning Trades: 75
- Losing Trades: 75
- Total Win Amount: $15,000 (average 4 points per contract, 5 contracts per trade)
- Total Loss Amount: $12,000 (average 3.2 points per contract, 5 contracts per trade)
Interval: 10:30 AM - 11:30 AM (Mid-Morning)
- Total Trades: 120
- Winning Trades: 66
- Losing Trades: 54
- Total Win Amount: $11,880 (average 3.6 points per contract, 5 contracts per trade)
- Total Loss Amount: $8,100 (average 3 points per contract, 5 contracts per trade)
Interval: 11:30 AM - 12:30 PM (Late Morning)
- Total Trades: 80
- Winning Trades: 36
- Losing Trades: 44
- Total Win Amount: $5,400 (average 3 points per contract, 5 contracts per trade)
- Total Loss Amount: $6,600 (average 3 points per contract, 5 contracts per trade)
Interval: 12:30 PM - 1:30 PM (Lunch Hour)
- Total Trades: 50
- Winning Trades: 20
- Losing Trades: 30
- Total Win Amount: $2,000 (average 2 points per contract, 5 contracts per trade)
- Total Loss Amount: $3,750 (average 2.5 points per contract, 5 contracts per trade)
Interval: 1:30 PM - 2:30 PM (Early Afternoon)
- Total Trades: 60
- Winning Trades: 33
- Losing Trades: 27
- Total Win Amount: $6,600 (average 4 points per contract, 5 contracts per trade)
- Total Loss Amount: $4,050 (average 3 points per contract, 5 contracts per trade)
Interval: 2:30 PM - 3:30 PM (Late Afternoon)
- Total Trades: 30
- Winning Trades: 18
- Losing Trades: 12
- Total Win Amount: $3,600 (average 4 points per contract, 5 contracts per trade)
- Total Loss Amount: $1,800 (average 3 points per contract, 5 contracts per trade)
Interval: 3:30 PM - 4:00 PM (Closing Half-Hour)
- Total Trades: 10
- Winning Trades: 4
- Losing Trades: 6
- Total Win Amount: $600 (average 3 points per contract, 5 contracts per trade)
- Total Loss Amount: $900 (average 3 points per contract, 5 contracts per trade)
Step 3: Calculate Expectancy for Each Interval
Interval: 9:30 AM - 10:30 AM
- P = 75 / 150 = 0.50
- A = $15,000 / 75 = $200
- L = 75 / 150 = 0.50
- B = $12,000 / 75 = $160
- E = (0.50 * $200) - (0.50 * $160) = $100 - $80 = $20 per trade
Interval: 10:30 AM - 11:30 AM
- P = 66 / 120 = 0.55
- A = $11,880 / 66 = $180
- L = 54 / 120 = 0.45
- B = $8,100 / 54 = $150
- E = (0.55 * $180) - (0.45 * $150) = $99 - $67.50 = $31.50 per trade
Interval: 11:30 AM - 12:30 PM
- P = 36 / 80 = 0.45
- A = $5,400 / 36 = $150
- L = 44 / 80 = 0.55
- B = $6,600 / 44 = $150
- E = (0.45 * $150) - (0.55 * $150) = $67.50 - $82.50 = -$15 per trade
Interval: 12:30 PM - 1:30 PM
- P = 20 / 50 = 0.40 **
