Class of topological portfolios: Are they better than classical portfolios?

Battle Count: 56

Highly relevant to quantitative trading and portfolio management. The paper introduces a parameter-free, estimation-error-free risk measure that consistently outperforms seven classical portfolio optimization models and two benchmarks across multiple evaluation settings. The TDA-based approach avoids reliance on mean/covariance estimation, addressing a fundamental weakness of Markowitz-type models. The convex quadratic formulation ensures computational tractability. The cardinality-constrained variant (TDA-IPO) is directly applicable to practical portfolio construction. Results are robust across varying holding periods (1-12 months) and training windows (1-2 years). The turnover analysis and transaction cost sensitivity study add practical implementation value.

Moderate complexity. The core optimization (TDA-PO) is a standard convex QP solvable with off-the-shelf solvers. However, the TDA pipeline requires: (1) Takens embedding of time series, (2) Vietoris-Rips filtration computation, (3) persistence diagram extraction, (4) persistence landscape construction, (5) Lp norm computation across sub-windows, and (6) mean landscape calculation. The cardinality-constrained variant (TDA-IPO) requires mixed-integer programming (Gurobi). Libraries exist in Python (giotto-tda, ripser, Dionysus) and R, but integrating them into a rolling-window backtesting framework requires careful engineering. The sub-windowing scheme (126-day windows, 21-day shifts) adds computational overhead.

The paper provides detailed algorithmic steps (Algorithm 1), specifies all parameters (τ=1, d=3, p=1, k=1, sub-window size 126 days, shift 21 days), lists all benchmark models with mathematical formulations, and identifies software (R with quadprog, ROI/GLPK, CVXR/Gurobi, PortfolioAnalytics packages). However, no code repository is provided, and the data source (Thomson Reuters Datastream) requires institutional access. The rolling window scheme and evaluation protocol are well-documented.