Smart leverage? Rethinking the role of Leveraged Exchange Traded Funds in constructing portfolios to beat a benchmark

ArXiv ID: 2412.05431 “View on arXiv”

Authors: Unknown

Abstract

Leveraged Exchange Traded Funds (LETFs), while extremely controversial in the literature, remain stubbornly popular with both institutional and retail investors in practice. While the criticisms of LETFs are certainly valid, we argue that their potential has been underestimated in the literature due to the use of very simple investment strategies involving LETFs. In this paper, we systematically investigate the potential of including a broad stock market index LETF in long-term, dynamically-optimal investment strategies designed to maximize the outperformance over standard investment benchmarks in the sense of the information ratio (IR). Our results exploit the observation that positions in a LETF deliver call-like payoffs, so that the addition of a LETF to a portfolio can be a convenient way to add inexpensive leverage while providing downside protection. Under stylized assumptions, we present and analyze closed-form IR-optimal investment strategies using either a LETF or standard/vanilla ETF (VETF) on the same equity index, which provides the necessary intuition for the potential and benefits of LETFs. In more realistic settings, we use a neural network-based approach to determine the IR-optimal strategies, trained on bootstrapped historical data. We find that IR-optimal strategies with a broad stock market LETF are not only more likely to outperform the benchmark than IR-optimal strategies derived using the corresponding VETF, but are able to achieve partial stochastic dominance over the benchmark and VETF-based strategies in terms of terminal wealth.

Keywords: Leveraged Exchange Traded Funds (LETFs), Information Ratio (IR), Neural Network-based Optimization, Call-like Payoffs, Stochastic Dominance, Equities (ETFs)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics, including closed-form solutions under stylized jump-diffusion dynamics and neural network optimization for dynamic strategies, indicating high mathematical density. Empirical rigor is strong, utilizing bootstrapped historical data since 1926 and practical constraints like infrequent trading, making the research highly backtest-ready and data-intensive.

  flowchart TD
    A["Research Goal:<br>Optimize LETF allocation for IR > Benchmark"] --> B{"Methodology"}
    B --> C["Stylized Analytical Model"]
    B --> D["Data & Bootstrapping"]
    D --> E["NN-based IR Optimization"]
    C --> F["Closed-form Solutions"]
    E --> F
    F --> G["Key Findings:<br>Superior IR & Partial Stochastic Dominance"]