Quantitative Analysis · Data Science · Machine Learning

# Skewness in Trading Strategy PnL Distributions

In trading, analyzing the distribution of profit and loss (PnL) can offer valuable insights into the performance characteristics and risk profile of different strategies. Two key types of skewness in these distributions are positive skewness and negative skewness. Understanding these concepts is crucial for optimizing trading strategies and managing risk effectively.

## What is Skewness?

Skewness is a measure of the asymmetry of a probability distribution. In the context of trading strategies, skewness helps describe how the distribution of returns deviates from a normal (Gaussian) distribution. Skewness can be quantitatively calculated using statistical formulas. The skewness coefficient is derived from the third standardized moment of the distribution. A skewness value close to zero indicates a relatively symmetrical distribution, while positive or negative values show the degree of skewness.

##### Chart: Positive vs negative negative skewness in PnL distributions (Generated with QF Alphawolf software)

Positive Skewness: The distribution has a longer or fatter tail on the right side. This means there are more frequent small losses and fewer but more significant gains. Positive skewness indicates that while losses are more common, there are occasional large gains that can offset these losses.

Negative Skewness: The distribution has a longer or fatter tail on the left side. This implies more frequent small gains and fewer but larger losses. Negative skewness indicates that while small gains are common, occasional large losses can significantly impact overall performance.

## Positively Skewed Trading Strategies (Trend Following)

Trend following strategies typically exhibit positive skewness. These strategies aim to capitalize on long-term trends by entering positions that benefit from sustained market movements. Key characteristics include:

##### Chart: Example of positively skewed trading strategy (Generated with QF Alphawolf software)

• Skewness: Positively skewed. Trend following strategies often exhibit a distribution of returns where losses are frequent but small, while occasional large gains lead to a positive skewness.
• Win Rate: Typically lower, around 30-40%. Trend following strategies may have a lower win rate because they only capitalize on significant trends. Many trades could end in losses if the market does not trend strongly.
• Reward-to-Risk Ratio: Generally higher, for example 2:1 or 3:1. The reward-to-risk ratio tends to be favorable due to the potential for large gains from extended trends. The aim is to capture a significant portion of a major trend, which can lead to substantial profits.
• Typical Returns: Trend followers often achieve substantial returns when they catch a major trend, although the profits might come less frequently. The strategy thrives in trending markets and can struggle during sideways or choppy market conditions.
• Risk Management: Trend following strategies often use trailing stops or other techniques to lock in profits as trends develop. Risk management focuses on cutting losses quickly and allowing profits to run.
• Market Conditions: Performs well in trending markets where price movements are sustained in one direction. Less effective in range-bound or highly volatile markets without clear trends.

## Negatively Skewed Trading Strategies (Mean Reversion)

Mean reversion strategies tend to display negative skewness. These strategies assume that prices will revert to a mean or average level, taking advantage of short-term deviations. Key characteristics include:

##### Chart: Example of negatively skewed trading strategy (Generated with QF Alphawolf software)

• Skewness: Negatively skewed. Mean reversion strategies typically exhibit a distribution where small gains are frequent but occasional large losses lead to negative skewness.
• Win Rate: Typically higher, around 50-65%. Mean reversion strategies often have a higher win rate because they take advantage of price movements returning to a mean or average level, resulting in more frequent smaller wins.
• Reward-to-Risk Ratio: Generally lower, often a reward-to-risk ratio of 1:1 or less is achieved. The reward-to-risk ratio can be less favorable because gains are usually smaller compared to the occasional large losses. The strategy aims to capture short-term reversals rather than long-term trends.
• Typical Returns: Mean reversion strategies can achieve consistent returns by capturing small price deviations. However, they might experience larger losses when trends persist longer than expected, leading to substantial negative impacts.
• Risk Management: Effective risk management is crucial, as the strategy might encounter significant drawdowns when the market trends strongly against the mean. Techniques such as setting stop-loss orders or using volatility-based position sizing are commonly used.
• Market Conditions: Performs well in range-bound or sideways markets where prices frequently revert to a mean. Less effective in trending markets where prices may not revert as expected.

## Benefits of Combining Positively with Negatively Skewed Strategies

Both trend following and mean reversion strategies offer unique advantages and challenges. Understanding the skewness of trading strategy PnL distributions provides valuable insights into their performance characteristics.

Characteristic Trend Following Mean Reversion
Skewness Positively skewed Negatively skewed
Typical Win Rate Lower (30-40%) Higher (50-65%)
Reward-to-Risk Ratio Higher (2:1 or 3:1) Lower (1:1 or less)
Typical Returns Substantial during trends, less frequent Consistent smaller returns, occasional large losses
Risk Management Focuses on cutting losses and letting profits run Emphasizes protecting against large losses with stops
Market Conditions Effective in trending markets Effective in range-bound or sideways markets
##### Table: Quick summary of strategy distribution characteristics

Trend following strategies can provide substantial gains during strong market trends, albeit with a lower win rate and higher reward-to-risk ratios. On the other hand, mean reversion strategies can achieve frequent small gains with a higher win rate, but they carry the risk of occasional large losses, leading to negative skewness in returns.

By combining positively skewed trend following strategies with negatively skewed mean reversion strategies, traders can create a more balanced and consistent approach to trading. This blend can help diversify risk, meaning that the large losses from one strategy can be offset by the gains from another resulting in more stable returns, smoother equity curves and enhance overall performance stability.