Learning

Jan 22

# Importance of Dispersion

When backtesting a trading strategy, dispersion (variance) plays a significant role in assessing the robustness and reliability of the strategy’s performance. Variance, in the context of backtesting, refers to the degree of fluctuation or dispersion in the strategy’s returns over a specific period.

Here’s a closer look at the importance of variance in backtesting:

### 1. Measure of Volatility

Dispersion provides a measure of the volatility of a trading strategy’s returns. Higher dispersion indicates greater dispersion of returns, suggesting that the strategy’s performance can be more unpredictable.

### 2. Risk Assessment

Understanding the variance of a trading strategy’s returns is crucial for assessing its risk profile. A strategy with high variance may experience significant fluctuations in returns, posing greater risk to the investor.

### 3. Impact on Drawdowns

Variance directly influences the potential drawdowns of a trading strategy. Higher variance can lead to more pronounced drawdowns, which can impact the overall performance and stability of the strategy.

### 4. Evaluation of Consistency

By analyzing the variance of a trading strategy’s returns, traders can gauge the consistency of its performance. Lower variance may indicate more stable and predictable returns, whereas higher variance suggests a less consistent performance.

### 5. Impact on Confidence Intervals

Variance affects the confidence intervals of a trading strategy’s returns. Understanding the range of potential outcomes based on historical variance is essential for risk management and setting realistic performance expectations.

### 6. Adjusting for Risk Tolerance

Traders can use variance as a factor in adjusting their risk tolerance and position sizing. A strategy with higher variance may require a more conservative approach to risk management and capital allocation.

### 7. Sensitivity to Market Conditions

Variance provides insights into how sensitive a trading strategy is to different market conditions.

In summary, variance is the deviation from the mathematical expectation. How does it look in practice? Imagine you have a deposit of 20,000 USD and a trading strategy with a mathematical expectation (profit factor) of 1.66. As a result, you have a profitable system for the distance, but you start trading, and the account reaches a stop-out. You have not violated the rules of strategy and risk management, so what happened? This could be a variance.

How do you see it on the graph? Let’s imagine we have the same conditions. We have a deposit of 20,000 USD and set Take Profit at 5,000 USD and Stop Loss at 3,200 USD. Then we generate 100 positions several times and get the following results:

### Example 1

In this example, the account grew rapidly from the beginning, but note that from 73 to 82 positions, we had a drawdown of more than 20,000 USD. If this had happened at the beginning, the account would have reached a stop-out point.

### Example 2

Here, the drawdown is 15,000 USD in the beginning, which is 75% of the account amount. Had such a thing happened in the beginning, could the trader further psychologically remain confident in the strategy?

### Example 3

In this example, there is no stability in trading. Visually, it looks like the strategy is not profitable, but after 79 positions, the situation improves. And this is the same strategy with a profit factor of 1.66.

### Example 4

In this example, the trading account quickly grows to 100,000 USD, but then there is a drawdown to 77,000 USD, which can hit the trader’s ambition and confidence.

Examples show that even having a profitable strategy, dispersion can lead to losing a deposit at the initial stage or doubting the strategy at one of the trading intervals. To exclude such moments, especially at the very beginning of trading, it is necessary to reduce risks. This allows you to get some “airbag” with smaller drawdowns, and only after that can you increase the risk so that the variance does not kill your deposit.

Now you realize that understanding the variance of a trading strategy’s returns is essential for making informed decisions and managing risk effectively.