Antifragile Option Course - Expected Value

Key Takeaways

Expected Value (EV) is a statistical measure that calculates the average outcome of a trade if it were repeated multiple times.
In trading, EV helps determine whether a strategy is likely to be profitable over the long term by assessing the probabilities and outcomes of different scenarios.
The formula for EV is: EV = (Probability of Winning × Amount Won) – (Probability of Losing × Amount Lost).
Traders use EV to evaluate the potential profitability of trades, ensuring that their strategies have a positive expected value.

In the realm of trading, understanding and applying the concept of Expected Value (EV) is crucial for making informed decisions that lead to long-term profitability. EV provides a framework for evaluating the potential outcomes of trades by considering both the probabilities of various scenarios and their associated returns or losses.

What is Expected Value?

Expected Value is a statistical measure that calculates the average result of a random event if it were repeated many times. In trading, EV helps assess whether a particular strategy or trade is likely to be profitable over the long run by weighing all possible outcomes by their probabilities and magnitudes.

Importance of Expected Value in Trading

Incorporating EV into trading strategies allows traders to:

Assess Profitability: Determine if a trade will be profitable on average, ensuring that each trade contributes positively to the overall trading plan.
Manage Risk: Understand the potential losses associated with a trade and make informed decisions about risk management.
Develop Consistency: Focus on strategies with positive EV to build a consistent and profitable trading approach over time.

Calculating Expected Value

The formula for calculating Expected Value in trading is:

EV = (Probability of Winning × Amount Won) – (Probability of Losing × Amount Lost)

Where:

Probability of Winning: The likelihood of a successful trade.
Amount Won: The profit gained from a successful trade.
Probability of Losing: The likelihood of an unsuccessful trade.
Amount Lost: The loss incurred from an unsuccessful trade.

Example of Expected Value Calculation

Consider a trading strategy with the following characteristics:

Probability of Winning: 52% (0.52)
Amount Won per Trade: $10
Probability of Losing: 48% (0.48)
Amount Lost per Trade: $10

Applying these values to the EV formula:

EV = (0.52 × $10) – (0.48 × $10) = $5.20 – $4.80 = $0.40

This positive expected value of $0.40 indicates that, on average, the trader can expect to earn 40 cents per trade over a large number of trades. This concept is similar to how casinos operate, where each game is designed to have a slight statistical advantage, ensuring profitability over time.

Applying Expected Value in Trading Strategies

Traders can apply the concept of EV by:

Evaluating Trades: Before entering a trade, calculate its EV to ensure it aligns with profitability goals.
Optimizing Strategies: Focus on strategies with higher EV to maximize returns over time.
Risk Management: Use EV calculations to set appropriate stop-loss and take-profit levels, balancing potential gains against possible losses.

Conclusion

Understanding and utilizing Expected Value is fundamental for traders aiming for long-term success. By evaluating the probabilities and outcomes of trades, EV provides a clear framework for making decisions that are statistically sound and aligned with profitability objectives. Incorporating EV into your trading strategy ensures that each decision contributes positively to your overall trading performance.