Paper: arXiv 2507.09196

Authors: Nader Karimi, Erfan Salavati

Abstract

Assuming frictionless trading, classical stochastic portfolio theory (SPT) provides relative arbitrage strategies. However, the costs associated with real-world execution are state-dependent, volatile, and under increasing stress during liquidity shocks. Using an Ito diffusion that may be connected with asset prices, we extend SPT to a continuous-time equity market with proportional, stochastic transaction costs. We derive closed-form lower bounds on cost-adjusted relative wealth for a large class of functionally generated portfolios; these bounds provide sufficient conditions for relative arbitrage to survive random costs. A limit-order-book cost proxy in conjunction with a Milstein scheme validates the theoretical order-of-magnitude estimates. Finally, we use intraday bid-ask spreads as a stand-in for cost volatility in a back-test of CRSP small-cap data (1994–2024). Despite experiencing larger declines during the 2008 and 2020 liquidity crises, diversity- and entropy-weighted portfolios continue to beat the value-weighted benchmark by 3.6 and 2.9 percentage points annually, respectively, after cost deduction.

Complexity vs Empirical Score

  • Math Complexity: 9.2/10
  • Empirical Rigor: 6.0/10 (capped from 6.8: no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper relies heavily on advanced stochastic calculus (Itô diffusions, Milstein scheme, Fernholz theory) and presents a non-trivial extension of stochastic portfolio theory to stochastic costs with formal proofs and inequalities. Empirically, it includes a 30-year backtest using CRSP data, an intraday cost proxy (bid-ask spreads), and quantitative performance metrics (2.9-3.6% annual alpha after costs), demonstrating substantial data and implementation effort.

Research Flowchart

  flowchart TD
  A["Research Goal: Does SPT relative arbitrage survive stochastic transaction costs?"] --> B["Methodology: Ito diffusion & Stochastic Costs"]
  B --> C["Data: CRSP Small-Cap 1994-2024 & Intraday Spreads"]
  C --> D["Computation: Limit-Order-Book Proxy & Milstein Scheme"]
  D --> E["Key Finding: 3.6% & 2.9% annual alpha after costs"]

Cited References (20)

  1. Stochastic portfolio theory: an overview (2009)
  2. Trading Strategies Generated by Lyapunov Functions (2017)
  3. Adaptive universal portfolios (2015)
  4. How efficiency shapes market impact (2013)
  5. Model-Free Hedging of Impermanent Loss in Geometric Mean Market Makers with Proportional Transaction Fees (2024)
  6. The impact of proportional transaction costs on systematically generated portfolios (2020)
  7. Optimal execution of portfolio transactions (2001)
  8. Optimal trading strategy and supply/demand dynamics (2013)
and 12 more
  1. A stochastic optimal stopping model for storable commodity prices (2024)
  2. Optimal order placement in limit order markets (2017)
  3. Stochastic portfolio theory (2002)
  4. The problem of regulatory arbitrage: A transaction cost economics perspective (2021)
  5. Empirical performance of an ESG assets portfolio from US market (2024)
  6. Key features of the financial sectors in EU accession countries (2002)
  7. Diversification in financial and crypto markets (2023)
  8. Liquidity uncertainty and Bitcoin’s market microstructure (2018)
  9. Why do equally weighted portfolios beat value-weighted ones? (2023)
  10. Dynamic Trading with Predictable Returns and Transaction Costs (2013)
  11. Limit Order Book as a Market for Liquidity (2005)
  12. Exchange‐Traded Funds, Market Structure, and the Flash Crash (2012)

0 of 20 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.