Risk, Reward, and Expectancy

The concepts of Risk, Reward, and Expectancy are crucial for effective trading. Many traders neglect these steps, which often results in significant losses. Properly defining these metrics can help optimize money management for any chosen trading method.

1. Defining Risk to Reward Ratio (R:R)

The risk to reward ratio (R:R) demonstrates the potential profit on a trade versus the amount of money being risked. To calculate the R:R, both the risk and potential profit must be clearly defined.

  • Risk Definition: Determined by using a Stop Loss order, which is designed to limit an investor's loss on a position.
  • Reward Definition: Determined by using a Take Profit order (or profit target), which establishes an exit point should the trade move favorably.

Risk to Reward Examples

The R:R is expressed as a ratio (Risk : Reward).

  1. Example 1 (Positive R:R):
    • Risk: $200
    • Reward: $400
    • Calculation: $200 / $400 = 1/2
    • R:R Ratio: 1 to 2 (Risking one unit to gain two units)
  2. Example 2 (High Reward):
    • Risk: $500
    • Reward: $1,500
    • Calculation: $500 / $1,500 = 1/3
    • R:R Ratio: 1 to 3
  3. Example 3 (Negative R:R):
    • Risk: $1,000
    • Reward: $500
    • Calculation: $1,000 / $500 = 2/1
    • R:R Ratio: 2 to 1 (Risking two units to gain one unit)

Foreign Exchange (Forex) Example

Assume a trade to buy the Euro with the following defined levels:

  • Entry Level: 1.15
  • Stop Loss Level (Risk): 1.14 (Risking 100 pips)
  • Take Profit Level (Reward): 1.1650 (Potential profit of 150 pips)

In this scenario, the trader is risking 100 pips to make 150 pips. The R:R ratio is 1 to 1.5. This means the trader is risking one unit in search of a potential reward 1.5 times the risk involved.

2. Understanding Trading Expectancy

Expectancy is the average amount a trader can expect to win or lose per dollar at risk. It links the R:R ratio with the system's accuracy (win rate).

Expectancy Formula

Expectancy = (Probability of Win × Average Win) – (Probability of Loss × Average Loss)

Positive Expectancy Example

A trader has a system with low accuracy but high reward:

  • Winning Trades: 30% of the time (Probability of Win = 0.3)
  • Losing Trades: 70% of the time (Probability of Loss = 0.7)
  • Average Winning Trade Profit: $1,000
  • Average Losing Trade Loss: $200

Calculation:

(0.3 × $1,000) – (0.7 × $200) = $300 – $140 = $160

Conclusion: The expectancy is positive ($160). Even though this system loses 70% of the time, the trader is expected to make a profit of $160 per trade on average over time.

Negative Expectancy Example

A trader has a system with high accuracy but poor reward/risk management:

  • Winning Trades: 80% of the time (Probability of Win = 0.8)
  • Losing Trades: 20% of the time (Probability of Loss = 0.2)
  • Average Winning Trade Profit: $200
  • Average Losing Trade Loss: $1,000

Calculation:

(0.8 × $200) – (0.2 × $1,000) = $160 – $200 = -$40

Conclusion: The expectancy is negative (-$40). Even though the system wins 80% of the time, the large average loss compared to the average win means the trader will lose money over time.

3. Expectancy and Required Accuracy

Any method with a positive expectancy will make money in the long run. If expectancy is zero, the trader is at breakeven. Expectancy demonstrates the minimum accuracy needed for a given R:R to reach the breakeven point:

  • R:R of 1 to 0.25 requires 80% accuracy to breakeven.
  • R:R of 1 to 1.5 requires 40% accuracy to breakeven.
  • R:R of 1 to 4 requires only 20% accuracy to breakeven.

The percentage of winning trades (accuracy) is not the sole, nor most important, factor in building a robust trading system. While accuracy is important, it must always be discussed alongside the concept of Expectancy.

Detailed Summary

The text emphasizes the critical importance of integrating Risk, Reward, and Expectancy into effective trading practices, noting that neglecting these concepts often leads to significant losses. The Risk to Reward Ratio (R:R) defines potential profit versus risk, determined by setting a Stop Loss (risk) and a Take Profit (reward). Examples illustrate how R:R is calculated and expressed, highlighting that a positive R:R means risking less than the potential gain (e.g., 1 to 2). Finally, Expectancy links the R:R ratio with the trading system's accuracy (win rate), calculating the average expected profit or loss per dollar risked. A system must have a positive expectancy to be profitable long-term, demonstrating that high accuracy alone does not guarantee success if the average loss outweighs the average win.

Key Takeaways

  • Risk, Reward, and Expectancy are crucial concepts for optimizing money management in trading.
  • The Risk to Reward Ratio (R:R) measures the potential profit against the amount risked.
  • Risk is defined by the Stop Loss order, while reward is defined by the Take Profit order.
  • A positive R:R ratio means the potential reward is greater than the risk (e.g., 1 to 3).
  • Expectancy calculates the average amount a trader expects to win or lose per trade, linking R:R and win rate.
  • The Expectancy Formula is: (Probability of Win × Average Win) – (Probability of Loss × Average Loss).
  • A trading system must have a positive expectancy to be profitable in the long run, regardless of high accuracy.
  • Systems with very high reward relative to risk require lower win rates to break even (e.g., 1 to 4 R:R requires only 20% accuracy).
  • Accuracy (win rate) is important, but Expectancy is the ultimate metric for a robust trading system.