Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidence
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912478628151296 |
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| author | Karimi, Nader Salavati, Erfan |
| author_facet | Karimi, Nader Salavati, Erfan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidence Karimi, Nader Salavati, Erfan Portfolio Management 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. |
| title | Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidence |
| topic | Portfolio Management |
| url | https://arxiv.org/abs/2507.09196 |