Paper: arXiv 2403.01088

Authors: Hayden Brown

Abstract

Over the past 60 years, there has been a gradual increase in the volatility of daily returns for the S&P 500 Index. Hypothetically, suppose that market forces determine daily volatility such that a daily leveraged S&P 500 fund cannot outperform a standard S&P 500 fund in the long run. Then this hypothetical volatility happens to support the increase in volatility seen in the S&P 500 index. On this basis, it appears that the classic argument of the market portfolio being unbeatable in the long run is determining the volatility of S&P 500 daily returns. Moreover, it follows that the long-term volatility of the daily returns for the S&P 500 Index should continue to increase until passing a particular threshold. If, on the other hand, this hypothesis about market forces increasing volatility is invalid, then there is room for daily leveraged S&P 500 funds to outperform their unleveraged counterparts in the long run.

Complexity vs Empirical Score

  • Math Complexity: 3.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Philosophers — conceptual discussion, limited math and data

Why this score: The paper presents an intriguing philosophical and theoretical framing regarding leverage decay, volatility drag, and the unbeatable nature of the market portfolio. However, based on the provided text, it relies heavily on speculative hypotheses and lacks rigorous empirical backtesting or deep mathematical formulation.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain 60-Year Increase in S&P 500 Daily Volatility] --> B[Data Input: Historical S&P 500 Daily Returns]
    
    B --> C[Hypothesis Test: Market forces adjust volatility to ensure daily leveraged funds cannot beat standard funds long-term]
    
    C --> D{Is Hypothesis Valid?}
    
    D -- Yes --> E[Outcome 1: Validates S&P 500 volatility rise; predicts volatility will continue increasing to a specific threshold]
    
    D -- No --> F[Outcome 2: Invalidates hypothesis; leaves room for daily leveraged S&P 500 funds to outperform long-term]

Cited References (127)

  1. Numerical analysis: mathematics of scientific computing (2009)
  2. The discrete moment problem with nonconvex shape constraints (2021)
  3. On the relationship between the discrete and continuous bounding moment problems and their numerical solutions (2016)
  4. Mathematical foundations of robust and distributionally robust optimization (2021) — link
  5. Operations research: applications and algorithm (2004)
  6. Practical guidelines for solving difficult linear programs (2013)
  7. Linear semi-infinite programming theory: An updated survey (2002)
  8. Semi-infinite programming (2007)
and 119 more
  1. From infinite to finite programs: Explicit error bounds with applications to approximate dynamic programming (2018)
  2. Models and algorithms for distributionally robust least squares problems (2014)
  3. Forecasting UK stock market volatility (2000)
  4. On the economic sources of stock market volatility (2008)
  5. The impact of trades on daily volatility (2006)
  6. Forecasting daily volatility of stock price index using daily returns and realized volatility (2021)
  7. The increasing volatility of the stock market? (2016)
  8. Do ETFs increase volatility? (2018)
  9. Anticipating long-term stock market volatility (2015)
  10. Long-memory and level shifts in the volatility of stock market return indices (2010)
  11. Long-term returns estimation of leveraged indexes and ETFs — → 2301.03186
  12. The index of general nonlinear D A E S (1995)
  13. Clinical implications of dysregulated cytokine production (2000) — link
  14. Quasimonotonicity, regularity and duality for nonlinear systems of partial differential equations (1995)
  15. Algorithms for C omputer A lgebra (1992)
  16. Software engineering—from auxiliary to key technologies (1992)
  17. Conductive P olymers (1981)
  18. Neuromuscular blocking drugs in man (1976)
  19. Isolation and characterization of plasmid deoxyribonucleic acid from Streptomyces fradiae (1978)
  20. Global integrated drought monitoring and prediction system (GIDMaPS) data sets (2014)
  21. Quantum scissors: teleportation of single-mode optical states by means of a nonlocal single photon (2002)
  22. Mixing induced CP asymmetries in inclusive B decays (1997) — link
  23. deep SIP : deep learning of S upernova I a P arameters (2020) — link
  24. Optimal consumption and portfolio choice for pooled annuity funds (2008)
  25. Quantifying the trade-off between income stability and the number of members in a pooled annuity fund (2021)
  26. Wealth heterogeneity in a closed pooled annuity fund (2023)
  27. Practical analysis of a pooled annuity fund with integrated bequest (2022)
  28. Actuarial fairness and solidarity in pooled annuity funds (2015)
  29. The simple analytics of a pooled annuity fund (2005)
  30. Demand and adverse selection in a pooled annuity fund (2006)
  31. Self-annuitization and ruin in retirement (2000)
  32. A mutual fund to yield annuity-like benefits (2007)
  33. “A Mutual Fund to Yield Annuity-Like Benefits”: A Comment (2007)
  34. The tontine puzzle (2023)
  35. A short history of tontines (2009)
  36. Managing a Competitive Tontine Business (2022)
  37. Assessing default investment strategies in defined contribution pension plans (2010)
  38. The effect of objective formulation on retirement decision making (2015)
  39. A dynamic-programming approach to multiperiod asset allocation (1999)
  40. The accumulation of risky capital: A sequential utility analysis (1962)
  41. Optimal investment and consumption strategies under risk for a class of utility functions (1975)
  42. Safety first and the holding of assets (1952)
  43. Portfolio optimization under safety first expected utility with nonlinear probability distortion (2021)
  44. Portfolio choice with endogenous utility: A large deviations approach (2003)
  45. The safety first expected utility model: Experimental evidence and economic implications (2009)
  46. A reliable data-based bandwidth selection method for kernel density estimation (1991)
  47. Portfolio Selection: Efficient Diversification of Investments (1971)
  48. Dynamic programming and inventory control (2011)
  49. Dynamic programming : foundations and principles (2010)
  50. Dynamic programming and stochastic control (1976)
  51. Dynamic Programming: Determinist. and Stochast. Models (1987)
  52. General proof that diversification pays (1967)
  53. Lifetime portfolio selection by dynamic stochastic programming (1975)
  54. Alternative procedures for revising investment portfolios (1968)
  55. The optimal portfolio revision policy (1971)
  56. Optimal multiperiod portfolio policies (1968)
  57. Optimal consumption and portfolio policies when asset prices follow a diffusion process (1989)
  58. Stochastic optimal control: the discrete-time case (1996)
  59. Optimal portfolio and consumption decisions for a “small investor” on a finite horizon (1987)
  60. Value-at-risk-based risk management: optimal policies and asset prices (2001)
  61. Average cost optimal policies for Markov control processes with Borel state space and unbounded costs (1990)
  62. Positive dynamic programming (1967)
  63. A dynamic programming approach to constrained portfolios (2013)
  64. Martingales and Financial Mathematics in Discrete Time (2021)
  65. Probability with martingales (1991)
  66. Foundations of Modern Probability (2019)
  67. Dollar Cost Averaging Returns Estimation (2023)
  68. Dollar Cost Averaging Returns Estimation (2021) — link
  69. The behavior of stock-market prices (1965)
  70. Futures trading and investor returns: An investigation of commodity market risk premiums (1973)
  71. Stable distributions, futures prices, and the measurement of trading performance (1984)
  72. Estimation of stable law parameters: stock price behavior application (1975)
  73. Regression-type estimation of the parameters of stable laws (1980)
  74. An iterative procedure for the estimation of the parameters of stable laws: An iterative procedure for the estimation (1981)
  75. Studies on the Application of the Alpha-stable Distribution in Economics (2009)
  76. Univariate stable distributions (2020)
  77. Financial valuation of guaranteed minimum withdrawal benefits (2006)
  78. Retirement savings: Choosing a withdrawal rate that is sustainable (1998)
  79. Does international diversification increase the sustainable withdrawal rates from retirement portfolios? (2003)
  80. Asset valuations and safe portfolio withdrawal rates (2013)
  81. Guaranteed minimum withdrawal benefit in variable annuities (2008)
  82. Modeling financial data with stable distributions (2003)
  83. Modeling Chinese stock returns with stable distribution (2011)
  84. Analysing Financial Returns by Using Regression Models Based on Non-Symmetric Stable Distributions (1999)
  85. Asymmetric stable distributed security returns (1980)
  86. Simple consistent estimators of stable distribution parameters (1986)
  87. Portfolio returns and the random walk theory (1971)
  88. Testing the random walk hypothesis for real exchange rates (1999)
  89. Random walk hypothesis on Bucharest stock exchange (2018)
  90. Stock market prices and the random walk hypothesis: Further evidence from Nigeria (2010)
  91. A variance-ratio test of random walk in international stock markets (2012)
  92. Utility Theory for Decision Making (1970)
  93. The erroneous approximation of expected utility by means of a Taylor’s series expansion: analytic and computational results (1976)
  94. Techniques for the reconstruction of a distribution from a finite number of its moments (2007)
  95. On diversification given asymmetry in returns (1981)
  96. An analysis of dollar cost averaging and market timing investment strategies (2020)
  97. On the direction of preference for moments of higher order than the variance (1980)
  98. A continuous-time reexamination of dollar-cost averaging (2003)
  99. Within-horizon exposure to loss for dollar cost averaging and lump sum investing (2005)
  100. On the integral of geometric Brownian motion (2003)
  101. The integral of geometric Brownian motion (2001)
  102. Nobody gains from dollar cost averaging analytical, numerical and empirical results (1992)
  103. The random character of stock market prices (1964)
  104. On the validity of the geometric Brownian motion assumption (2005)
  105. Online data Robert Shiller (cited October 2020)
  106. Investing (cited October 2020)
  107. S&P 500 (cited October 2020)
  108. An Analysis of the S&P 500 Index and Cowles’s Extensions: Price Indexes and Stock Returns, 1870–1999 (2002)
  109. Lump-sum investing versus dollar-averaging (1994)
  110. An empirical examination of the effectiveness of dollar-cost averaging using downside risk performance measures (2003)
  111. Lump sum beats dollar-cost averaging. (1993)
  112. Dollar-Cost Averaging Versus Lump-Sum-Investing: Evidence from Sweden (2021)
  113. The concept of comonotonicity in actuarial science and finance: applications (2002)
  114. The concept of comonotonicity in actuarial science and finance: theory (2002)
  115. Approximating a sum of random variables with a lognormal (2007)
  116. The sum of log-normal probability distributions in scatter transmission systems (1960)
  117. On the distribution function and moments of power sums with log-normal components (1982)
  118. An optimal lognormal approximation to lognormal sum distributions (2004)
  119. Comparison of methods of computing lognormal sum distributions and outages for digital wireless applications (1994)

1 of 127 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.