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Frankline Oyolo, Misango

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

Algorithmic-TradingLeveraged-ETFsPortfolio-OptimizationRisk-ManagementQuantitative-Finance

Abstract

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 (TQQQ, UPRO, UDOW), defensive bond positioning (TMF), and commodity diversification (UGL, DIG). Key innovations include dynamic rebalancing every 4 days with momentum preservation, multi-asset risk parity across leveraged instruments, and volatility-adaptive allocation. Backtests across three economic regimes (2017–2025) demonstrate 51% annualized returns with a Sharpe ratio of 0.701.

Introduction

Leveraged ETFs provide amplified exposure to underlying assets through financial derivatives and borrowing. While offering enhanced return potential, they introduce compounding effects and volatility decay that require sophisticated portfolio construction. The strategy employs a multi-asset approach targeting the optimal balance between amplified upside capture and downside protection across three economic regimes: Pre-Pandemic Growth (2017–2021), Post-Pandemic Recovery (2021–2025), and Current Environment (2025–present).

Motivation

Standard leveraged ETF buy-and-hold strategies suffer from volatility decay — the mathematical erosion of returns caused by daily rebalancing in choppy markets. Three observations motivate this research:

  1. Volatility decay is regime-dependent: in trending markets leveraged ETFs outperform; in mean-reverting markets they destroy value
  2. Multi-asset diversification reduces portfolio-level choppiness, dampening decay
  3. Systematic rebalancing every 4 days harvests the spread between realized and implied volatility

Key Equations

Leveraged ETF daily return (Cheng & Madhavan 2009):

where $L$ is the leverage multiplier, is the daily return, and is the risk-free rate.

Volatility decay (Avellaneda & Zhang 2010):

where is the daily volatility.

Equal Risk Contribution weights (Maillard et al. 2010):

Leverage-adjusted VaR weight:

Mean-variance optimization:

Regime-adaptive allocation:

where the probability term determines regime-based weight allocation.

Stress correlation adjustment:

Algorithm Blueprint

Algorithm — Diversified Leverage Index Fund Strategy
Input: Leveraged ETF prices, VIX, yield curve, policy uncertainty index
Output: Target weights, rebalance orders, risk controls
EVERY week:
IF VIX > 35 AND yield curve inversion > 50bp:
regime = UNCERTAINTY
ELSE IF VIX > 25 AND policy uncertainty index > 150:
regime = TRANSITION
ELSE:
regime = GROWTH
compute realized volatility for each ETF over 20 days
set ERC weights proportional to 1 / volatility
adjust weights for beta and VaR
normalize target portfolio weights
APPLY regime overlay:
GROWTH → overweight TQQQ, UPRO, TMF, commodities
TRANSITION → use baseline weights
UNCERTAINTY → shift toward TMF, commodities, and lower equity leverage
EVERY 4 days OR when drift > 5%:
IF outstanding orders exist: skip rebalancing
FOR each asset:
compute target shares from portfolio value and target weight
IF abs(target shares - current shares) ≥ minimum trade size: submit market order
RISK CONTROLS:
IF volatility > 1.5× historical: reduce risk assets and increase bonds
IF volatility < 0.7× historical: increase risk exposure
IF drawdown > 10%: move additional capital to cash
IF correlation maximum > 0.8: rebalance to reduce concentration
STOP LOSS:
stop_i = price_i * (1 - α * σ_i * regime_factor)

Results

Strategy Comparison — Ann. Return vs Volatility

Sharpe Ratio & Max Drawdown Comparison

| Metric | Diversified Leverage | 3x S&P (UPRO) | 60/40 | |---|---|---|---| | Pre-Pandemic Growth | 2017–2021 | 359.07% | 46.2% | | Post-Pandemic Recovery | 2021–2025 | 186.07% | 30.1% | | Current Environment | 2025–present | -3.39% | -6.8% | | Combined | 2017–2025 | 1,046.2% | 35.8% |

| Strategy | Ann. Return | Sharpe | Max DD | |---|---|---|---| | Diversified Leverage | 51.0% | 0.701 | -66.4% | | 60/40 Portfolio | 8.2% | 0.68 | -8.9% | | S&P 500 | 10.5% | 0.65 | -19.6% | | TQQQ Only | 28.7% | 0.81 | -28.1% |

The strategy captures 178% of TQQQ's return at significantly lower volatility. The -66.4% max drawdown reflects the inherent risk of 3× leveraged instruments and is the primary risk to manage via regime overlays.

Contributions

  • Rigorous mathematical treatment of volatility decay in leveraged ETF portfolios with ERC-based weight construction adapted for leverage and VaR scaling
  • Three-regime cross-regime validation (2017–2025) covering pre-pandemic growth, post-pandemic recovery, and current policy uncertainty
  • Regime-conditional allocation overlay with quantitative triggers (VIX, yield curve, policy uncertainty index)
  • Practical rebalancing algorithm with minimum trade size filtering and outstanding order checks to avoid double-execution

Paper

Author

Frankline Misango Oyolo Arithmax Research research@arithmax.com — Published: October 19, 2025