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Cross-Regime Performance Analysis of an Algorithmic Strategy for a Diversified Leverage Index Fund Portfolio

Author:Frankline Misango Oyolo
Date:July 2025
Institution:Arithmax Research
Portfolio Theory Leverage Risk Parity ETF Strategy

Summary

This report presents a diversified leverage strategy designed to capture enhanced returns through leveraged ETFs while managing downside risk through strategic asset allocation. The framework combines leveraged equity exposure, defensive bond positioning, and commodity diversification to create a robust portfolio amid evolving tariff policies and economic uncertainty.

Key Innovations

  • Dynamic rebalancing with momentum preservation
  • Multi-asset risk parity approach across leveraged instruments
  • Volatility-adaptive allocation methodology
  • Tariff-resilient sector diversification

Key Mathematical Framework

Portfolio Optimization:

$$\mathbf{w}_t = \arg\min_{\mathbf{w}} \left[ \mathbf{w}^T \boldsymbol{\Sigma}_t \mathbf{w} - \lambda \boldsymbol{\mu}_t^T \mathbf{w} \right]$$
Rebalancing Dynamics:

$$\begin{cases} \mathbf{w}_{\text{target}} = f(\boldsymbol{\mu}, \boldsymbol{\Sigma}, \boldsymbol{\beta}) & \text{(Target allocation)} \\ \tau_{\text{rebalance}} = 4 \text{ days} & \text{(Rebalancing frequency)} \\ \Delta \mathbf{w}_t = \mathbf{w}_{\text{target}} - \mathbf{w}_{\text{current}} & \text{(Portfolio adjustment)} \end{cases}$$
Risk Parity Allocation:

$$w_i \propto \frac{1}{\sigma_i \sqrt{\text{Leverage}_i}}$$
Equal risk contribution across leveraged assets

Algorithm

Diversified Leverage Strategy
  • Select leveraged ETFs across equity, bonds, and commodities
  • Calculate volatility-adjusted risk contributions
  • Optimize weights using risk parity principles
  • Rebalance every 4 days to maintain target allocation
  • Apply momentum preservation during rebalancing
  • Monitor drawdowns and adjust leverage dynamically
  • Incorporate transaction costs in rebalancing decisions

Full Paper

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