Traditional financial metrics like skewness provide insights into the distribution of returns around their average. Positive skewness signals frequent large positive moves, while negative skewness indicates prevalent large downward shifts. But what if we could measure how sequential returns relate to each other, capturing market reversals and volatility transitions more effectively?
Enter Sequential Skew—a novel measure that explicitly analyzes the asymmetry between pairs of consecutive returns. Unlike standard skewness, Sequential Skew directly captures whether large moves tend to reverse or continue strongly into subsequent periods.1
How Sequential Skew Works:
Consider three price points at distinct times labeled by indices . Sequential Skew calculates the cubic differences of sequential log returns across these intervals, normalizing by the squared differences and applying cubic and square roots:
where:
By incorporating cubic and square roots, Sequential Skew effectively normalizes large directional shifts, clearly highlighting abrupt reversals or volatility jumps.
Bounds and Interpretation:
Sequential Skew typically produces values centered around zero. It can theoretically range from negative infinity to positive infinity, but in practical scenarios, values usually stay within a moderate range. The interpretation of Sequential Skew values is as follows:
Values close to zero: Indicate stability, meaning sequential returns are relatively symmetrical and consistent, without notable volatility jumps or reversals.
High positive values: Suggest frequent abrupt reversals or volatility spikes following upward price movements, indicating market uncertainty or instability in bullish conditions.
High negative values: Indicate frequent abrupt reversals or volatility spikes following downward price movements, highlighting uncertainty or instability in bearish conditions.
Moderate absolute values (slightly away from zero): Reflect mild asymmetry in sequential returns, suggesting moderate stability but potential for minor volatility shifts.
Low absolute values (near zero): Often signal reduced volatility and potential reversal points, making these moments particularly useful for identifying local tops and bottoms in market movements.
Practical Significance:
Sequential Skew provides traders and analysts with a sensitive tool for market analysis:
Enhanced Volatility Detection: Accurately detects changes in market stability.
Improved Trend Stability Analysis: Clearly identifies if market movements will likely continue or reverse.
Advanced Risk Management: Better understanding of sequential risk dynamics and volatility changes.
Local Tops and Bottoms Detection: Low Sequential Skew values can help identify potential local tops and bottoms in price movements.
Conclusion:
Sequential Skew significantly advances traditional financial analysis by explicitly measuring sequential return behaviors. Traders and researchers gain a powerful new tool to assess market dynamics, volatility shifts, and trend stability with heightened accuracy and relevance.
Head-to-Head Comparison: Regular Skew vs. Sequential Skew
Regular Skew
Average of the product of three sequential points.
What it captures: Overall distribution asymmetry.
Limitation: Ignores the specific sequence or order of returns.
Sequential Skew
Average of the cubed differences between two sequential intervals.
What it captures: Temporal asymmetry and directional shifts in returns.
Benefit: Highlights the importance of the order in which returns occur.
This concise side-by-side layout clearly differentiates the two concepts, visually emphasizing their distinct calculations and analytical insights.