Trading Expectancy

Definition:

Trading expectancy is a mathematical calculation that tells you, on average, how much profit or loss you can expect to make per trade if you execute your trading strategy many times. It's like calculating the expected return on an investment. If the expectancy is positive, your strategy is likely profitable over time. If it's negative, you're likely to lose money.

Key Takeaway: Expectancy is a critical metric that quantifies the long-term profitability of a trading strategy.

Mechanics

The expectancy formula is straightforward. It considers your win rate, average win size, loss rate, and average loss size. Here's the formula:

Expectancy = (Win Rate × Average Win) - (Loss Rate × Average Loss)

Let's break down each component:

Win Rate: This is the percentage of trades that result in a profit. If you take 100 trades and 60 are profitable, your win rate is 60%. This is often expressed as a decimal (0.60 in this case).
Average Win: This is the average amount of money you make when you win a trade. Calculate it by adding up all your winning trades and dividing by the number of winning trades.
Loss Rate: This is the percentage of trades that result in a loss. It's simply 100% minus your win rate. If your win rate is 60%, your loss rate is 40% (or 0.40 as a decimal).
Average Loss: This is the average amount of money you lose when you lose a trade. Calculate it by adding up all your losing trades and dividing by the number of losing trades.

Example:

Suppose you have a trading strategy with the following characteristics:

Win Rate: 50% (0.50)
Average Win: $100
Loss Rate: 50% (0.50)
Average Loss: $80

Plugging these numbers into the formula:

Expectancy = (0.50 × $100) - (0.50 × $80) = $50 - $40 = $10

This means that, on average, you can expect to make $10 per trade using this strategy. Over a large number of trades, this strategy should be profitable.

Interpreting Expectancy:

Positive Expectancy: Your strategy is likely to be profitable over the long term. The higher the positive expectancy, the more profitable the strategy is expected to be.
Negative Expectancy: Your strategy is likely to lose money over the long term. You should either adjust your strategy or abandon it.
Zero Expectancy: The strategy is expected to break even over the long term. This doesn't necessarily mean it's a bad strategy, but it requires careful risk management and potentially a high win rate to be worthwhile.

Trading Relevance

Expectancy is crucial for traders because it provides a quantitative measure of a strategy's effectiveness. It helps traders:

Evaluate Strategies: Before risking real capital, you can backtest a strategy (using historical data) to determine its expectancy. This helps you identify strategies that have a higher probability of success.
Manage Risk: Understanding your expectancy allows you to size your positions appropriately. A higher expectancy allows you to risk a larger percentage of your capital per trade, while a lower expectancy (or negative expectancy) requires more conservative position sizing.
Improve Trading: By tracking your expectancy over time, you can monitor the performance of your strategy and identify areas for improvement. If your expectancy declines, it signals that you need to adjust your approach.
Build Confidence: Knowing that your strategy has a positive expectancy can boost your confidence and help you stick to your trading plan, even during losing streaks.

How Price Moves:

Expectancy doesn't directly dictate how price moves. However, it helps you understand the probability of price movement in your favor. A strategy with a positive expectancy relies on the market moving in a way that allows you to profit. For example, a trend-following strategy will have a positive expectancy if the market trends more often than it consolidates. A mean-reversion strategy will have a positive expectancy if the market reverts to the mean more often than it continues trending.

Risks

Past Performance is Not Indicative of Future Results: Expectancy is calculated based on historical data. Market conditions change, and a strategy that worked well in the past may not work as well in the future. Regularly re-evaluate your expectancy.
Sample Size Matters: Expectancy calculations are more reliable with a larger sample size of trades. Don't base your decisions on a small number of trades, as the results can be skewed by random events.
No Guarantee of Profit: A positive expectancy doesn't guarantee that you'll make money on every trade or even in the short term. You can still experience losing streaks. It only predicts profitability over the long run.
Overfitting: Over-optimizing a strategy to a specific historical dataset can lead to a falsely inflated expectancy. The strategy may not perform as well on future, unseen data. Be wary of strategies that seem too good to be true.
Ignoring Risk Management: Even with a positive expectancy, poor risk management can wipe out your profits. Always use stop-loss orders and size your positions appropriately to protect your capital. Your expectancy is only one piece of the puzzle.

History/Examples

The concept of expectancy has been around for as long as people have been making bets and investing. However, it's particularly relevant in trading because of the availability of historical data and the ease with which strategies can be backtested. While not explicitly called "expectancy", the core principles have been used for centuries, from casino games to the stock market.

Early Applications:

Casino Games: Casino games are designed with a negative expectancy for the player. The house edge ensures that the casino profits over the long run. Understanding this concept is crucial for anyone who gambles.
Insurance: Insurance companies use expectancy to calculate premiums. They estimate the probability of various events (e.g., car accidents, house fires) and charge premiums that are designed to be profitable over time.

Trading Examples:

Trend Following: A trader using a trend-following strategy might have a relatively low win rate (e.g., 40%) but a high average win because they let their profits run. Their expectancy could be positive if the average win is significantly larger than the average loss.
Mean Reversion: A trader using a mean-reversion strategy might have a high win rate (e.g., 70%) but a smaller average win because they take profits quickly. Their expectancy could be positive if their average win is large enough to offset their losses.

Real-World Application:

Imagine a swing trader who tests a strategy on Bitcoin (BTC) from 2020-2023. They find the following:

Win Rate: 55%
Average Win: $500 (per trade)
Average Loss: $300 (per trade)

Their expectancy would be: (0.55 × $500) - (0.45 × $300) = $275 - $135 = $140

This trader can expect to make $140 per trade, on average, using this strategy. This gives them a mathematical edge. However, they still need to manage their risk and stick to their plan to realize this potential profit.

Trading Expectancy