Visualizing Shifting Correlations in Financial Markets

The notions of diversification and correlation have always been essential for investors to consider when allocating capital within their portfolios. Diversification is a mainstay for mitigating risk and allowing returns that accurately represent the market or specific subsets of it. Understanding correlation among equities and the market allows for a greater understanding of market impacts on a portfolio and can enhance portfolio construction and risk management.

Despite its fundamental importance, the construction and management of well-diversified portfolios is highly challenging due to the great number of relations to analyze, which increases semi-quadratically with the number of securities held — an average-size investment portfolio (144 holdings) contains over 10,000 pairwise relations — and further complicated by the sheer volume of financial assets available for selection. Take, for example, the correlation matrix shown below, which displays pairwise correlations between the constituents of the S&P 500.

Figure 1: S&P 500 correlation heat map

In the past, investors have compared individual equities to indices through line graphs and correlation matrices in order to garner information about the correlations between individual stocks and indices. However, these methods offer only static information and do not accurately reflect the dynamic nature and changing characteristics of markets. Investors have long attempted to create a portfolio that mirrors market behavior or is market-neutral, but have not been able to utilize a tool that illustrates a network of equities and relations to benchmarks. 2020 in particular has shown an interesting set of market conditions, and investors without an understanding of interconnectedness of their portfolios were put in a position where they could incur greater portfolio volatility.

Commonly-used analytical approaches suffer from several deficiencies. Issues include the instability of financial correlations over time and in different market environments and the difficulty of identifying assets with low and/or stable correlations. Popular techniques appear particularly ill-equipped to deal with periods of high stress in markets, when the ability to track correlations is arguably most important. There is also no accepted ‘standard’ way of visualizing financial correlations beyond the tabular correlation matrix for point- in-time views, sometimes represented as a heat map.

Past comparisons of indices and simple line graphs have evolved to pairwise and hierarchical correlation to complex networks that can accurately account for the volatile and dynamic nature of markets.The network cluster approach to correlation visualization offers a new horizon in a relatively static field. There are novel ways to gauge data among all the individual equities in their portfolio and their dynamic relationships over various market conditions, allowing investors to look at their portfolios from a more intuitive angle.

Figure 2: A common method for understanding correlation between two instruments; here, XLE (energy ETF) and WTIC (Crude Oil)

A Novel Approach: The Network Cluster

Network clusters were originally developed in the mid-20th century, where they were used to analyze information in fields ranging from data science to archaeology to literature. Their nature allows for an enhanced degree of visualization not seen in other data analysis tools and can present an informative medium to review rendering of information. However, the majority of employment of network clusters has been under static conditions, even though valuable information can be gleaned from the dynamic motion of clusters.

Network clusters can be created on many frameworks, but for depicting high-dimensional data, there are two main techniques. Force directed graphs are one method to visualize correlation between data points. This structure portrays nodes as forces away from a center and boasts strong degrees of flexibility and interactivity, especially, as data changes(1). While force directed graphs offer a horizon for understanding forces and interactivity among data, we believe multidimensional scaling (MDS) allows for a better dynamic representation of financial data.

Figure 3: This basic force-directed graph relates to the interaction between companies in terms of mobile patents suits. The arrows point toward companies that have patent suits placed against them and illustrate the . This graph illustrates the assigned forces from central data points, such as Apple and Microsoft.

MDS plots data by degree of similarity around a central benchmark by projecting high dimensional data into 2 or 3 dimensions which preserves pairwise distances. This allows for an enhanced visualization of correlations, thus offering users unique insight. Force-directed graphs better represent movement and its velocity of nodes on the graph, which is important in seeing the time frame of changes. However, MDS paints a more detailed picture of the evolution of interactivity, which is much more valuable within the context of equity correlation (2).

Figure 4: This graph illustrates an example of multidimensional scaling, as higher dimensional data is transformed and plotted on a two-dimensional graph. This allows for a better visualization of the level of similarity among individual data points and the swarm of data. The above graphs also exhibit triple encoding, as data correlations are portrayed through color, lines, and highlighted areas, giving the viewer multiple visual differentiation methods that add to their understanding.

This is a novel approach and enables investors to view changing correlation dynamics, which allows for a greater degree of risk mitigation. In the past, it has been difficult to understand how the degree of correlation between portfolios and the market change over time. Cyclical portfolios are designed to capitalize on market trends while defensive portfolios tend to have more distant ties to greater market variability. Using a network cluster approach, Isogai finds that “the degree of correlation between the Cyclical and Defensive group portfolios can change significantly” during evolving market conditions, presenting phenomena that would go unnoticed in traditional methods for interpreting equities (3). The identification of these correlations only increases the ability to manage investment risk, especially when these correlations can be seen at both a market-wide and portfolio level.

From the lens of a market maker, this correlation visualization approach enables increased accuracy of options pricing, as intra-market forces can be better understood. For other market participants such as portfolio and fund managers, this framework allows for a better understanding of risk and market-wide behavior, which can improve asset selection during portfolio construction and upkeep.

Manifold: A Network Visualization Paradigm

We present an interactive tool that allows individuals unprecedented insight into correlation visualization, resulting in improved asset selection and risk management. Our asset correlation visualization tool pulls live data from financial markets in order to dynamically represent the evolving correlations between equities, indices, and the market as a whole.

Manifold allows users to visualize large subsets of assets in the form of a swarm, with distance between assets representing the degree of similarity among factors including data on prices and price movement. Assets near the center of the swarm have behavior that much more closely mirrors the greater market than those on the periphery. The time feature can be used to better visualize how these correlations vary under changing market conditions. Users can also select groupings of assets and compare their selections to various benchmarks on top of the wider market. Manifold offers a correlation frequency distribution model that gives an in-depth view of r-values between assets included in a portfolio , those that are not, and the broader market along with features that display cumulative returns against a number of possible benchmarks. These tools become especially valuable in portfolio construction, investment due diligence, and reporting/ insight among other uses.

Minimum variance portfolios are constructed in a manner that mitigates the level of risk and fluctuation that occurs within the market (4). In the past, these portfolios were formed via algorithms that weighted various stocks in a manner that limited their volatility, requiring that the equities are already selected. With Manifold, users can select assets on the outer edges of the swarm, as this will lead to a large number of unrelated equities, that as a whole will maintain a high degree of stability through various market conditions. Because of the inherent differences among correlation of equities, individual market events are likely to be less correlated to the portfolio, maintaining the higher degree of market resilience investors may desire.

Figure 5: This image shows a selection of peripheral assets from the body of assets included in the swarm, thus creating a portfolio that has a large degree of correlation dispersion as seen on the right hand side. This means that this portfolio will be less responsive to general market behavior.

Maximum return portfolios can utilize the past return data in order to select groupings that exhibit characteristics for the same degree of alpha in the future. Manifold allows users to effectively create and analyze portfolios that have outperformed the market. The tool allows users to understand the correlation between these assets, and in turn better understand the risk they are on-boarding on top of simply analyzing historical gains.

Figure 6: This portfolio was created by selecting assets that significantly outperformed the greater market. With Manifold, users have the ability to not only create maximum-return portfolios but to explore the evolving correlations between the assets that compose them.

Tangency portfolios can be created to mirror the market, specific industries, or the broader market. These are usually difficult to create without owning a large number of equities within the given sector. Utilizing Manifold, investors can implement a benchmark of their desired index and then select equities near the center of the swarm, as these points have the most correlation with the benchmark.

These are just a few of the ways this interface can be effectively used. As risk analysis continues to evolve, market participants must analyze a larger set of metrics that go beyond the commonly used Sharpe ratio. Manifold provides a new lens on top of traditional metrics that empowers users with a more detailed understanding of risk. The network cluster framework allows users to better understand correlation, and in turn, risk in a more effective manner. The dynamic nature of the tool allows users to see the real-time changes in the correlation among portfolio equities, enabling them with a competitive edge.

The Future of Manifold

The network cluster framework can be applied to additional financial data beyond price, such as liquidity and volume among other measures used as a base for an interactive tool that boasts even greater capabilities. Future updates will not only include financial data but also include data ranging from recent news and development data. The end goal for this product is to create a dynamic and all-encompassing multidimensional network analysis tool. We are also working on adding further infrastructure to analyze risk and parameterize portfolios powered by machine learning techniques. As Manifold continues to improve, we invite you to be a part of the development and share your insight. To learn more about Manifold and our work at Pareto Technologies, do not hesitate to reach out to us.

Works Cited

(1): Belmonte, Nicolas. Force Directed Layouts. philogb.github.io/blog/2009/09/30/force-directed-layouts/.

(2): De Leeuw, Jan; Michailidis, George. Graph layout techniques and multidimensional data analysis. Game theory, optimal stopping, probability and statistics, 219–248, Institute of Mathematical Statistics, Beachwood, OH, 2000. doi:10.1214/lnms/1215089755. https://projecteuclid.org/euclid.lnms/1215089755.

(3): Isogai, T. Dynamic correlation network analysis of financial asset returns with network clustering. Appl Netw Sci 2, 8 (2017). https://doi.org/10.1007/s41109-017-0031-6

(4): Zhifeng Dai, “A Closer Look at the Minimum-Variance Portfolio Optimization Model,” Mathematical Problems in Engineering, vol. 2019, Article ID 1452762, 8 pages, 2019.https://doi.org/10.1155/2019/1452762