Portfolio Allocation under Heterogeneous Scales and Multifractality

Battle Count: 87

Highly relevant to quantitative trading and portfolio management. The paper provides a concrete, implementable portfolio optimization framework that demonstrably reduces tail risk (VaR, ES, drawdown) relative to mean-variance benchmarks in both synthetic and empirical settings. The MFCCA-based risk criterion captures scale-dependent and amplitude-dependent cross-correlation structures that conventional covariance matrices miss. The empirical application to Nikkei, S&P 500, WTI crude oil, and gold demonstrates practical applicability. However, the framework is primarily a risk management tool rather than a return-generating alpha signal, and the no-short-sale constraint limits its direct applicability to some trading strategies.

Implementation requires: (1) MFCCA algorithm with polynomial detrending and signed fluctuation function computation across multiple scales and fluctuation orders; (2) Construction of the MFCCA fluctuation matrix for all asset pairs; (3) PSD regularization when needed; (4) Quadratic programming for portfolio optimization with return and budget constraints; (5) Aggregation of weights across scales and fluctuation orders. The MFCCA algorithm itself is well-documented but requires careful implementation of detrending, segment handling, and sign preservation. The multi-scale, multi-order aggregation adds computational overhead. Rolling-window backtesting further increases complexity.

The paper provides fixed random seeds for simulations, specifies all parameter settings (ARFIMA parameters d1=0.4, d2=0.2, W=0.7; MSM parameters mx=1.2, my=1.5, k=10, b=2, gamma_k=0.5), defines scale subsets S and fluctuation order subsets Q explicitly, and states that processed datasets and analysis code are available from the corresponding author upon reasonable request. The raw data source (histdata.com) is publicly available. However, code is not directly hosted in a public repository.