🎲Expected Value and Edge as the Core of Profitable Strategies

Introduction

Expected Value (EV) is a key concept in investment strategies. It reveals potential profit or loss from an investment over the long term. In this article, we will look at the formula for expected value, risk-reward asymmetry, and how to effectively use this information with the QMA tool.

The Expected Value Formula

The formula for expected value is the following:

EV = (Win Rate × Average Profit) - (Loss Rate × Average Loss)

* Win Rate is the percentage of successful trades.
* Average Profit reflects the average amount the investor makes when a trade is successful.
* Loss Rate is the percentage of unsuccessful trades, calculated as: 1 - Win Rate.
* Average Loss is the average loss in unsuccessful trades.

How Can a Strategy with WR Below 50% Be Profitable?

Many investors believe that profitability requires a win rate above 50%. However, this is not true. Even when the win rate drops below this threshold, a strategy can remain profitable due to risk-reward asymmetry.

For example, if a strategy has a win rate of 40%, average profit per trade is 1000 CZK and average loss is 500 CZK, the expected value would be:

EV = (0.40 × 1000 CZK) - (0.60 × 500 CZK) = 400 CZK - 300 CZK = 100 CZK

This strategy is profitable despite having a win rate below 50%. The key is to have sufficiently high average profits compared to average losses.

Measuring Edge on Your Own Data

Edge in an investment strategy represents the advantage that an investor has over the market or other investors. To measure edge, historical data can be used to analyze the performance of a strategy.

Statistical Honesty

When testing a strategy, it is important to have a sufficiently large sample size. Too small samples can lead to misleading conclusions. It is also important to pay attention to overfitting, which is the situation where a model is too closely tailored to historical data and does not reflect actual performance.

T-Statistics and Their Importance in Analysis

T-statistics are used to determine the statistical significance of results. They allow investors to assess whether the performance achieved is the result of trial testing or the actual performance of the strategy.

* If the t-statistic is greater than 2, it usually indicates that the result is statistically significant.
* A minimum sample size for a statistically relevant result should typically exceed 30 trades.

How to Do This in QMA

In QMA, investors can easily analyze their historical performance and strategy metrics and obtain important statistics of verified strategies.

* /strategy: This section displays individual strategies and their metrics, including win rate, alpha (returns above benchmark), and t-statistics.
* /journal: Here, you can record and analyze your trading decisions and their results.
* /screener: Allows you to filter stocks by various criteria, which is useful for searching for potentially profitable trading opportunities.

All this data can help you better understand your edge and expected value of the strategies you employ. Monitor verified strategies (✅) versus experimental ones (⚠️) for better decision-making based on historical returns.

Disclaimer

QMA is an analytical and educational tool, not investment advice. Past performance is not a guarantee of future results. All investment decisions are your own responsibility.