In this article part of our Clustering series, [1] [2] [3] [4] which began by identifying clusters in relative percentile ranking vs. S&P 500 component returns. We discovered that market capitalization (MCAP) was a poor variable for clustering and highlighted a growth bias. We then extended the periodicities to observe the evolution of this growth bias. Today, we conclude by compiling all these periodicities of growth bias into a single chart. This "composite of a composite" (COC) reveals a moving picture of market dynamics, reminiscent of the seminal work on curvatures by Nobel Prize winner William Sharpe.
William Sharpe’s 1988 paper with Perold on dynamic strategies and the concepts of convexity and concavity in portfolio management [5] is a masterpiece. Their work focused on understanding how different rebalancing strategies affect portfolio performance and serves as a foundational reference for convexity and concavity in portfolio design. Convexity refers to a situation where the portfolio's value increases more when the market rises than it decreases when the market falls. Conversely, concavity indicates that the portfolio's value decreases more when the market falls than it increases when the market rises.
Our COC chart illustrates similar principles, showing convexity and concavity in the same data when viewed across different time frames. We used polynomial regression to analyze stock market data over various periodicities—weekly, monthly, quarterly, yearly, and rolling periods of 2 and 5 years. This method captured the non-linear relationships between stock returns and their relative percentile rankings, revealing more complex market dynamics. By fitting polynomial curves to the data, we observed how stock returns behave over different periods. For example, short-term data (weekly, monthly) exhibited high variability with frequent fluctuations, while long-term data (yearly, rolling periods) showed smoother, more stable trends.
The distinct curvatures we observed highlight how short-term volatility aggregates into long-term trends. Rising curves indicate that winners continue to amplify as herding behavior occurs, suggesting that winner’s create herding (high relative percentile ranking are winners). Falling curves, on the other hand, indicate how previous winners destroy wealth as herding is unsustainable after a point and loses steam and growth crashes. Sinusoidal waves, or oscillating patterns, make markets hard to predict because they reflect the cyclical nature of market fluctuations. These patterns suggest that while markets may have periods of growth, they also experience inevitable downturns, making precise predictions challenging.
This deeper understanding of market dynamics allows for the development of more adaptive investment strategies. Our research helps lay down a new paradigm for investing based on context (relative ranked state matters) agnostic to content (component does not matter). Using Discrete decile states, investors can create better strategies by understanding the complex, changing nature of the market. The COC images shows how simple clustering vs. relative percentile ranking can enhance returns while reducing risk.
Our findings also confirm and extend Sharpe’s and Perold’s thinking by using a different approach. The commonality of non-linear behavior in market elements and the dynamic nature of markets reveal how stability and variability coexist, providing deeper insights into market operations. Moreover, the methods we employed, such as polynomial regression and relative ranking, lend themselves easily to machine learning techniques. These techniques can further refine predictive models and enhance the robustness of investment strategies by learning from vast amounts of data and identifying patterns that may not be immediately apparent.
[5] Sharpe, William F., and André F. Perold. "Dynamic Strategies for Asset Allocation." Financial Analysts Journal, vol. 51, no. 1, 1995, pp. 149-160.
Oliviu Cigan and Mukul Pal