Paper: arXiv 2311.06519

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced statistical methods, quantile regression, and concepts from statistical mechanics to analyze optimal portfolio size, indicating high mathematical complexity. It demonstrates strong empirical rigor by using over 20 years of daily equity data, conducting thorough regression experiments, and providing specific, backtest-ready insights on portfolio optimization across varying investor skill levels.

Research Flowchart

  flowchart TD
  A["Research Question:<br>What is the optimal portfolio size<br>for investors with varying skill?"] --> B["Data Input:<br>20+ years of equity returns"]
  B --> C["Methodology Step 1:<br>Annual Diversification Analysis<br>(Poor/Average/Strong Investors)"]
  B --> D["Methodology Step 2:<br>Quantile Regression on Risk-Adjusted Returns<br>(vs. Portfolio Size)"]
  B --> E["Methodology Step 3:<br>Continuous Temporal Optimization"]
  C --> F["Computational Process:<br>Define investor ability by percentiles<br>(10th/50th/90th risk-adjusted returns)"]
  D --> F
  E --> F
  F --> G["Key Findings/Outcomes:<br>• Strong Investors: Concentrated Portfolios<br>• Poor Investors: Highly Diversified Portfolios<br>• Average Investors: Optimal size varies over time"]

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  410. Cryptocurrencies Are Becoming Part of the World Global Financial Market — → 2303.00495
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  456. Infected Markets: Novel Coronavirus, Government Interventions, and Stock Return Volatility around the Globe (2020) — link
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  459. Is Gold a Hedge or Safe Haven Asset during COVID \textendash 19 Crisis? (2020) — link
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  475. Why Homicide Rates in US Spiked 30% During COVID Pandemic (2022)
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  477. How George Floyd Died, and What Happened Next (2022)
  478. Chaotic M inneapolis protests spread amid emotional calls for justice, peace (2020)
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  482. Intensified Scrutiny and Bureaucratic Effort: Evidence from policing and Crime After High-Profile, Officer-Involved Fatalities (2020) — link
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  497. Wall S treet Mines A pple and G oogle Mobility Data to Spot Revival (2020)
  498. New Z ealand, A ustralia tighten lockdown to combat coronavirus (2020)
  499. Sweden adds further restrictions on outdoor gatherings as coronavirus cases hit record highs (2020)
  500. Coronavirus: Is it time to move on and get back to normal life?
  501. Why the second wave of C ovid-19 appears to be less lethal
  502. Coronavirus: US and A ustralia close borders to C hinese arrivals
  503. Test, trace, contain: how S outh K orea flattened its coronavirus curve
  504. China becomes first major economy to recover from C ovid-19 pandemic
  505. How coronavirus almost brought down the global financial system (2020)
  506. Italy’s Virus Shutdown Came Too Late. What Happens Now?
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  508. How G reece is rethinking its once bustling tourism industry
  509. New Z ealand has 69 active C ovid cases after 13 more diagnosed
  510. A Devastating New Stage of the Pandemic
  511. First and Second Waves of Coronavirus
  512. UPDATED: Timeline of the C oronavirus
  513. This is where each state is during its phased reopening
  514. All 50 U.S. states have taken steps toward reopening in time for Memorial Day weekend
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  516. Georgia business owners are conflicted as the state reopens hair salons, gyms and bowling alleys (2020)
  517. Georgia’s Governor Issues Order Rescinding Local Mask Mandates (2020)
  518. Florida shatters single-day infection record with 15,300 new cases (2020)
  519. U.S. COVID-19 Deaths Near 130,000; F lorida And T exas Report Record Case Numbers (2020)
  520. Gov. Greg Abbott orders T exans in most counties to wear masks in public (2020)
  521. California tells six additional counties to close indoor businesses, all bars (2020)
  522. New Y ork Orders Residents to Wear Masks in Public (2020)
  523. Countries turn to rapid antigen tests to contain second wave of COVID -19 (2020)
  524. Analysis: Could COVID knock out flu in E urope this winter?
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  526. IMPATTO DELL’EPIDEMIA COVID -19 SULLA Mortalit `a TOTALE DELLA POPOLAZIONE RESIDENTE PRIMO QUADRIMESTRE 2020
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  528. India’s policy response to COVID -19 (2020)
  529. Britain Drops Its Go-It-Alone Approach to Coronavirus (2020)
  530. Italy coronavirus death toll to 107, 3089 cases: Live updates (2020)
  531. Brazil has record new coronavirus cases, surpasses F rance in deaths (2020)
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  533. Global coronavirus cases hit 20 million as pandemic accelerates (2020)
  534. Dow plunges 10% amid coronavirus fears for its worst day since the 1987 market crash (2020)
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  536. CO$_2$ and Greenhouse Gas Emissions (2022)
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  543. Painel C oronav 'i rus (2021)
  544. Details on cases (2021)
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  551. An exploration of the mathematical structure and behavioural biases of 21st century financial crises — → 2307.15402
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  553. Geometric persistence and distributional trends in worldwide terrorism (2023) — link
  554. On financial market correlation structures and diversification benefits across and within equity sectors (2022) — link
  555. Estimating a continuously varying offset between multivariate time series with application to COVID -19 in the U nited S tates (2022) — link
  556. Distributional trends in the generation and end-use sector of low-carbon hydrogen plants (2023) — link
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  562. Efficiency of communities and financial markets during the 2020 pandemic (2021) — link
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  564. Equivalence relations and $L^p$ distances between time series with application to the B lack S ummer A ustralian bushfires (2023) — link
  565. Dual-domain analysis of gun violence incidents in the U nited S tates (2022) — link
  566. Economic state classification and portfolio optimisation with application to stagflationary environments (2022) — link
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  568. Structural Clustering of Volatility Regimes for Dynamic Trading Strategies (2021) — link
  569. Optimally adaptive B ayesian spectral density estimation for stationary and nonstationary processes (2022) — link
  570. A new measure between sets of probability distributions with applications to erratic financial behavior (2021) — link
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  573. Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID -19 (2021) — link
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  575. Cluster-based dual evolution for multivariate time series: Analyzing COVID -19 (2020) — link
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  582. Threshold Similarity Queries in Large Time Series Databases (2006) — link
  583. Time Series Analysis Using the Concept of Adaptable Threshold Similarity (2006) — link
  584. Knowledge Discovery from Heterogeneous Dynamic Systems using Change-Point Correlations (2005) — link
  585. CID : an efficient complexity-invariant distance for time series (2013) — link
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  588. Sparse DTW : A Novel Approach to Speed up Dynamic Time Warping (2009)
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  590. A Unified Framework for Gesture Recognition and Spatiotemporal Gesture Segmentation (2009) — link
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  619. Game story space of professional sports: Australian rules football (2016) — link
  620. Athlete Atypicity on the Edge of Human Achievement: Performances Stagnate after the Last Peak, in 1988 (2010) — link
  621. As O lympic athletics begins, the data suggests we are at the peak of human ability
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  625. Scoring dynamics across professional team sports: tempo, balance and predictability (2014) — link
  626. Deaths and Hospitalizations Averted by Rapid U.S. Vaccination Rollout (2021) — link
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  630. Spatiotemporal Characteristics of the COVID -19 Epidemic in the U nited S tates (2020) — link
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  632. Spatio-temporal propagation of COVID -19 pandemics (2020) — link
  633. A Spatiotemporal Epidemiological Prediction Model to Inform County-Level COVID -19 Risk in the U nited S tates (2020) — link
  634. Progression of COVID -19 From Urban to Rural Areas in the U nited S tates: A Spatiotemporal Analysis of Prevalence Rates (2020) — link
  635. Growth of respiratory droplets in cold and humid air (2021) — link
  636. Aerosol agitation: Quantifying the hydrodynamic stressors on particulates encapsulated in small droplets (2021) — link
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  833. ZIF -L-derived porous C-doped ZnO / CdS graded nanorods with Z-scheme heterojunctions for enhanced photocatalytic hydrogen evolution (2022) — link
  834. Photoelectrocatalytic hydrolysis of ammonia borane by electrochemical deposited cuprous oxide on titanium dioxide nanotube arrays (2022) — link
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  906. Hot Summers: Effect of Extreme Temperatures on Ozone in S ydney, A ustralia (2018) — link
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3 of 921 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.