arXiv subjects

Max Menzies

Publications and source records attributed to Max Menzies.

At least 19 recordsLinked to original sources

arXiv2024

Detecting imbalanced financial markets through time-varying optimization and nonlinear functionals

This paper studies the time-varying structure of the equity market with respect to market capitalization. First, we analyze the distribution of the 100 largest companies' market capitalizations over time, in terms of inequality, concentration at the top, and overall discrepancies in the distribution between different times. In the next section, we introduce a mathematical framework of linear and nonlinear functionals of time-varying portfolios. We apply this to study the market capitalization exposure and spread of optimal portfolios chosen by a Sharpe optimization procedure. These methods could be more widely used to study various measures of optimal portfolios and measure different aspects of market exposure while holding portfolios selected by an optimization routine that changes over time.

q-fin.MF↗

arXiv2024

Nonlinear shifts and dislocations in financial market structure and composition

This paper develops new mathematical techniques to identify temporal shifts among a collection of US equities partitioned into a new and more detailed set of market sectors. Although conceptually related, our three analyses reveal distinct insights about financial markets, with meaningful implications for investment managers. First, we explore a variety of methods to identify nonlinear shifts in market sector structure and describe the mathematical connection between the measure used and the captured phenomena. Second, we study network structure with respect to our new market sectors and identify meaningfully connected sector-to-sector mappings. Finally, we conduct a series of sampling experiments over different sample spaces and contrast the distribution of Sharpe ratios produced by long-only, long-short and short-only investment portfolios. In addition, we examine the sector composition of the top-performing portfolios for each of these portfolio styles. In practice, the methods proposed in this paper could be used to identify regime shifts, optimally structured portfolios, and better communities of equities.

q-fin.ST↗

arXiv2023

Portfolio diversification with varying investor abilities

We introduce new mathematical methods to study the optimal portfolio size of investment portfolios over time, considering investors with varying skill levels. First, we explore the benefit of portfolio diversification on an annual basis for poor, average and strong investors defined by the 10th, 50th and 90th percentiles of risk-adjusted returns, respectively. Second, we conduct a thorough regression experiment examining quantiles of risk-adjusted returns as a function of portfolio size across investor ability, testing for trends and curvature within these functions. Finally, we study the optimal portfolio size for poor, average and strong investors in a continuously temporal manner using more than 20 years of data. We show that strong investors should hold concentrated portfolios, poor investors should hold diversified portfolios; average investors have a less obvious distribution with the optimal number varying materially over time.

q-fin.PM↗

arXiv2023

An exploration of the mathematical structure and behavioural biases of 21st century financial crises

In this paper we contrast the dynamics of the 2022 Ukraine invasion financial crisis with notable financial crises of the 21st century - the dot-com bubble, global financial crisis and COVID-19. We study the similarity in market dynamics and associated implications for equity investors between various financial market crises and we introduce new mathematical techniques to do so. First, we study the strength of collective dynamics during different market crises, and compare suitable portfolio diversification strategies with respect to the unique number of sectors and stocks for optimal systematic risk reduction. Next, we introduce a new linear operator method to quantify distributional distance between equity returns during various crises. Our method allows us to fairly compare underlying stock and sector performance during different time periods, normalising for those collective dynamics driven by the overall market. Finally, we introduce a new combinatorial portfolio optimisation framework driven by random sampling to investigate whether particular equities and equity sectors are more effective in maximising investor risk-adjusted returns during market crises.

q-fin.ST↗

arXiv2023

Collective dynamics, diversification and optimal portfolio construction for cryptocurrencies

Since its conception, the cryptocurrency market has been frequently described as an immature market, characterized by significant swings in volatility and occasionally described as lacking rhyme or reason. There has been great speculation as to what role it plays in a diversified portfolio. For instance, is cryptocurrency exposure an inflationary hedge or a speculative investment that follows broad market sentiment with amplified beta? We have recently explored similar questions with a clear focus on the equity market. There, our research revealed several noteworthy dynamics such as: an increase in the market's collective strength and uniformity during crises, greater diversification benefits across equity sectors (rather than within them), and the existence of a "best value" portfolio of equities. In essence, we can now contrast any potential signatures of maturity we identify in the cryptocurrency market and contrast these with the substantially larger, older and better established equity market. This paper aims to investigate whether the cryptocurrency market has recently exhibited similar mathematical properties as the equity market. Instead of relying on traditional portfolio theory, which is grounded in the financial dynamics of equity securities, we adjust our experimental focus to capture the presumed behavioral purchasing patterns of retail cryptocurrency investors. Our focus is on collective dynamics and portfolio diversification in the cryptocurrency market, and examining whether previously established results in the equity market hold in the cryptocurrency market, and to what extent. Results reveal nuanced signatures of maturity related to the equity market, including the fact that correlations collectively spike around exchange collapses, and identify an ideal portfolio size and spread across different groups of cryptocurrencies.

q-fin.ST↗

arXiv2023

Distributional trends in the generation and end-use sector of low-carbon hydrogen plants

This paper uses established and recently introduced methods from the applied mathematics and statistics literature to study trends in the end-use sector and capacity of low-carbon hydrogen projects in recent and upcoming decades. First, we examine distributions in plants over time for various end-use sectors and classify them according to metric discrepancy, observing clear similarity across all industry sectors. Next, we compare the distribution of usage sectors among different continents and examine the changes in sector distribution over time. Finally, we judiciously apply several regression models to analyse the association between various predictors and the capacity of global hydrogen projects. Across our experiments, we see a welcome exponential growth in the capacity of zero-carbon hydrogen plants and significant growth of new and planned hydrogen plants in the 2020's across every sector.

physics.soc-ph↗

arXiv2023

Geometric persistence and distributional trends in worldwide terrorism

This paper introduces new methods for studying the prevalence of terrorism around the world and over time. Our analysis treats spatial prevalence of terrorism, the changing profile of groups carrying out the acts of terrorism, and trends in how many attacks take place over time. First, we use a time-evolving cluster analysis to show that the geographic distribution of regions of high terrorist activity remains relatively consistent over time. Secondly, we use new metrics, inspired by geometry and probability, to track changes in the distributions of which groups are performing the terrorism. We identify times at which this distribution changes significantly and countries where the time-varying breakdown is most and least homogeneous. We observe startling geographic patterns, with the greatest heterogeneity from Africa. Finally, we use a new implementation of distances between distributions to group countries according to their incidence profiles over time. This analysis can aid in highlighting structural similarities in outbreaks of extreme behavior and the most and least significant public policies in minimizing a country's terrorism.

physics.soc-ph↗

arXiv2022

Dual-domain analysis of gun violence incidents in the United States

This paper applies new and recently introduced approaches to study trends in gun violence in the United States. We use techniques in both the time and frequency domain to provide a more complete understanding of gun violence dynamics. We analyze gun violence incidents on a state-by-state basis as recorded by the Gun Violence Archive. We have numerous specific phenomena of focus, including periodicity of incidents, locations in time where behavioral changes occur, and shifts in gun violence patterns since April 2020. First, we implement a recently introduced method of spectral density estimation for nonstationary time series to investigate periodicity on a state-by-state basis, including revealing where periodic behaviors change with time. We can also classify different patterns of behavioral changes among the states. We then aim to understand the most significant shifts in gun violence since numerous key events in 2020, including the COVID-19 pandemic, lockdowns, and periods of civil unrest. Our dual-domain analysis provides a more thorough understanding and challenges numerous widely held conceptions regarding the prevalence of gun violence incidents.

physics.soc-ph↗

arXiv2022

Collective infectivity of the pandemic over time and association with vaccine coverage and economic development

This paper uses new and existing methods to study collective trends across countries throughout the pandemic, with a focus on the multivariate time series of reproduction numbers and vaccine proliferation. We begin with a time-varying analysis of the collective nature of infectivity, where we evaluate the eigenspectrum and collective magnitude of reproduction number time series on a country-by-country basis. Next, we study the topology of this eigenspectrum, measuring the deviation between all points in time, and introduce a graph-theoretic methodology to reveal a clear partition in global infectivity dynamics. Then, we compare countries' vaccine rollouts with economic indicators such as their GDP and HDI in a collective fashion. We investigate time-varying consistency and determine points in time where there is the greatest discrepancy between these indicators as a whole. Our two primary findings are a considerable increase in collective infectivity in the latter half of the period, and a concave-up (``down then up'') pattern in the collective consistency between vaccine coverage and economic/development indicators across countries.

physics.soc-ph↗

arXiv2022

Economic state classification and portfolio optimisation with application to stagflationary environments

Motivated by the current fears of a potentially stagflationary global economic environment, this paper uses new and recently introduced mathematical techniques to study multivariate time series pertaining to country inflation (CPI), economic growth (GDP) and equity index behaviours. We begin by assessing the temporal evolution among various economic phenomena, and complement this analysis with `economic driver analysis,' where we decouple country economic trajectories and determine what is most important in their association. Next, we study the temporal self-similarity of global inflation, growth and equity index returns to identify the most anomalous historic periods, and windows in the past that are most similar to current market dynamics. We then introduce a new algorithm to construct economic state classifications and compute an economic state integral, where countries are determined to belong in one of four candidate states based on their inflation and growth behaviours. Finally, we implement a decade-by-decade portfolio optimisation to determine which equity indices and portfolio assets have been most beneficial in maximising portfolio risk-adjusted returns in various market conditions. This could be of great interest to those looking for asset allocation guidance in the current period of high economic uncertainty.

q-fin.ST↗

arXiv2022

On financial market correlation structures and diversification benefits across and within equity sectors

We study how to assess the potential benefit of diversifying an equity portfolio by investing within and across equity sectors. We analyse 20 years of US stock price data, which includes the global financial crisis (GFC) and the COVID-19 market crash, as well as periods of financial stability, to determine the `all weather' nature of equity portfolios. We establish that one may use the leading eigenvalue of the cross-correlation matrix of log returns as well as graph-theoretic diagnostics such as modularity to quantify the collective behaviour of the market or a subset of it. We confirm that financial crises are characterised by a high degree of collective behaviour of equities, whereas periods of financial stability exhibit less collective behaviour. We argue that during times of increased collective behaviour, risk reduction via sector-based portfolio diversification is ineffective. Using the degree of collectivity as a proxy for the benefit of diversification, we perform an extensive sampling of equity portfolios to confirm the old financial adage that 30-40 stocks provide sufficient diversification. Using hierarchical clustering, we discover a `best value' equity portfolio for diversification consisting of 36 equities sampled uniformly from 9 sectors. We further show that it is typically more beneficial to diversify across sectors rather than within. Our findings have implications for cost-conscious retail investors seeking broad diversification across equity markets.

q-fin.PM↗

arXiv2022

Global and regional changes in carbon dioxide emissions: 1970-2019

We introduce new frameworks to study spatio-temporal patterns in carbon dioxide emissions, demographic trends and economic patterns across 50 countries over the past 50 years. Our analysis is broken up into four sections. First, we introduce a new method to classify countries into one of three characteristic emissions classes based on a one, two or three-segment piecewise linear model. We reveal that most countries are best represented by a piecewise linear model with one change point. Next, we perform a decade-by-decade study of carbon dioxide trajectories. There, we demonstrate notable changes in cluster structures in each decade. We then study the spatial propagation of emissions over time, highlighting a peak in spatial dispersion in 2000, beyond which there has been a gradual decline in spatial emissions variance over space. Finally, we use carbon dioxide, GDP, and population data and apply dimensionality reduction and clustering to group countries based on similarity in their real and carbon economies.

physics.soc-ph↗

arXiv2022

Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil

This paper compares and contrasts the spread and impact of COVID-19 in the three countries most heavily impacted by the pandemic: the United States (US), India and Brazil. All three of these countries have a federal structure, in which the individual states have largely determined the response to the pandemic. Thus, we perform an extensive analysis of the individual states of these three countries to determine patterns of similarity within each. First, we analyse structural similarity and anomalies in the trajectories of cases and deaths as multivariate time series. Next, we study the lengths of the different waves of the virus outbreaks across the three countries and their states. Finally, we investigate suitable time offsets between cases and deaths as a function of the distinct outbreak waves. In all these analyses, we consistently reveal more characteristically distinct behaviour between US and Indian states, while Brazilian states exhibit less structure in their wave behaviour and changing progression between cases and deaths.

physics.soc-ph↗

arXiv2021

A new measure between sets of probability distributions with applications to erratic financial behavior

This paper introduces a new framework to quantify distance between finite sets with uncertainty present, where probability distributions determine the locations of individual elements. Combining this with a Bayesian change point detection algorithm, we produce a new measure of similarity between time series with respect to their structural breaks. First, we demonstrate the algorithm's effectiveness on a collection of piecewise autoregressive processes. Next, we apply this to financial data to study the erratic behavior profiles of 19 countries and 11 sectors over the past 20 years. Our measure provides quantitative evidence that there is greater collective similarity among sectors' erratic behavior profiles than those of countries, which we observe upon individual inspection of these time series. Our measure could be used as a new framework or complementary tool for investors seeking to make asset allocation decisions for financial portfolios.

q-fin.ST↗

arXiv2021

Understanding spatial propagation using metric geometry with application to the spread of COVID-19 in the United States

This paper introduces a novel approach to spatio-temporal data analysis using metric geometry to study the propagation of COVID-19 across the United States. Using a geodesic Wasserstein metric, we analyse discrepancies between the density functions of new case counts on any given day, incorporating the geographic spread of cases. First, we apply this to identify the periods during which the changes in the geographic distribution of COVID-19 were most profound. The greatest shift occurred between May and June of 2020, when COVID-19 shifted from mostly dominating the Northeastern states to a wider distribution across the country. We support our findings with a new measure of the extent of geodesic variance of a distribution, demonstrating that the geographic imprint of COVID-19 was most concentrated in May 2020. Next, we investigate whether the epidemic exhibited meaningful patterns of spatial reversion, where similar geographic distributions return later. We identify broad similarity between the spread of COVID-19 across the US between the second and third waves, and to a lesser extent, the reemergence of the first wave's Northeastern dominance closer to the present day. This methodology could provide new insights for analysts to monitor the dynamical spread of epidemics and enable regional policymakers to protect their localities. More broadly, the framework we introduce could be applied to a variety of problems evolving over space and time.

physics.soc-ph↗

arXiv2021

Estimating a continuously varying offset between multivariate time series with application to COVID-19 in the United States

This paper introduces new methods to track the offset between two multivariate time series on a continuous basis. We then apply this framework to COVID-19 counts on a state-by-state basis in the United States to determine the progression from cases to deaths as a function of time. Across multiple approaches, we reveal an "up-down-up" pattern in the estimated offset between reported cases and deaths as the pandemic progresses. This analysis could be used to predict imminent increased load on a healthcare system and aid the allocation of additional resources in advance.

physics.soc-ph↗

arXiv2021

Spatio-temporal trends in the propagation and capacity of low-carbon hydrogen projects

This paper uses established and recently introduced methods from the applied mathematics and statistics literature to study trends in the propagation and capacity of low-carbon hydrogen projects over the past two decades. First, we judiciously apply a regression model to estimate the association between various predictors and the capacity of global hydrogen projects. Next, we turn to the geographic propagation of low-carbon hydrogen projects, where we apply a recently introduced method to explore the geographic variance of hydrogen projects over time. Then, we demonstrate that most geographic regions display linear growth in cumulative plants and apply distance correlation to determine the nonlinear dependence between the two most prolific regions - North America and Europe. Finally, we study the time-varying regional consistency between the contribution of green vs fossil fuel plants to the total number and capacity of hydrogen plants.

physics.soc-ph↗

arXiv2021

In search of peak human athletic potential: A mathematical investigation

This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and findings. First, we perform a detailed regression study to reveal the existence of an "Olympic effect", where average performance improves during Olympic years. Next, we study the rate of change in athlete performance and fail to reject the notion that athlete scores are leveling off, at least among the top 100 annual scores. Third, we examine the relationship in performance trends among men and women's categories of the same event, revealing striking similarity, together with some anomalous events. Finally, we analyze the geographic composition of the world's top athletes, attempting to understand how the diversity by country and continent varies over time across events. We challenge a widely held conception of athletics, that certain events are more geographically dominated than others. Our methods and findings could be applied more generally to identify evolutionary dynamics in group performance and highlight spatio-temporal trends in group composition.

physics.soc-ph↗