Paper: arXiv 2411.07949
Abstract
We consider a simplified model for optimizing a single-asset portfolio in the presence of transaction costs given a signal with a certain autocorrelation and cross-correlation structure. In our setup, the portfolio manager is given two one-parameter controls to influence the construction of the portfolio. The first is a linear filtering parameter that may increase or decrease the level of autocorrelation in the signal. The second is a numerical threshold that determines a symmetric “no-trade” zone. Portfolio positions are constrained to a single unit long or a single unit short. These constraints allow us to focus on the interplay between the signal filtering mechanism and the hysteresis introduced by the “no-trade” zone. We then formulate an optimization problem where we aim to minimize the frequency of trades subject to a fixed return level of the portfolio. We show that maintaining a no-trade zone while removing autocorrelation entirely from the signal yields a locally optimal solution. For any given “no-trade” zone threshold, this locally optimal solution also achieves the maximum attainable return level, and we derive a quantitative lower bound for the amount of improvement in terms of the given threshold and the amount of autocorrelation removed.
Complexity vs Empirical Score
- Math Complexity: 7.5/10
- Empirical Rigor: 2.5/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper employs advanced stochastic calculus, AR(1) process modeling, and optimization theorems, indicating high mathematical complexity. However, the empirical evidence is purely theoretical, lacking backtests, real data, or implementation details, placing it in the Lab Rats quadrant.
Research Flowchart
flowchart TD
A["Research Goal: Minimize trades for fixed portfolio return<br>in single-asset strategy with transaction costs"] --> B["Model Inputs: Signal w/ Autocorrelation & Cross-Correlation"]
B --> C["Methodology: Optimize 2-parameter controls"]
C --> D{"Strategy Controls"}
D --> E["Linear Filter: Adjusts Autocorrelation"]
D --> F["Symmetric No-Trade Zone: Hysteresis"]
E --> G["Optimization Objective: Minimize Trades"]
F --> G
G --> H["Findings: Remove Autocorrelation + Maintain No-Trade Zone = Locally Optimal Solution"]
H --> I["Outcome: Maximizes Return & Quantifies Improvement Bound"]
Cited References (22)
- Stochastic optimal control: the discrete-time case (1996)
- The O rnstein– U hlenbeck process as a model of a low pass filtered white noise (2008)
- Trades, quotes and prices: financial markets under the microscope (2018)
- Time series analysis: forecasting and control (2015)
- Multi-period trading via convex optimization (2017)
- Multiperiod consumption and investment behavior with convex transactions costs (1979)
- Portfolio selection with transaction costs (1990)
- Multiperiod portfolio optimization with multiple risky assets and general transaction costs (2016)
and 14 more
- Dynamic trading with predictable returns and transaction costs (2013)
- Forecasting, structural time series models and the K alman filter (1990)
- Portfolio selection with transactions costs (1976)
- Optimal properties of exponentially weighted forecasts (1960)
- Time series: modeling, computation, and inference (2010)
- Moving averages for financial data smoothing (2013)
- Lifetime portfolio selection under uncertainty: The continuous-time case (1969)
- Optimum consumption and portfolio rules in a continuous-time model (1975)
- Operators on inhomogeneous time series (2001)
- An introduction to high-frequency finance (2001)
- Forecasting economic time series (2014)
- Non-linear and non-stationary time series analysis (1988)
- Time series analysis (2020)
- Multiperiod portfolio optimization with multiple risky assets and general transaction costs (2016)
0 of 22 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.