SmartDCA superiority

ArXiv ID: 2308.05200 “View on arXiv”

Authors: Unknown

Abstract

Dollar-Cost Averaging (DCA) is a widely used technique to mitigate volatility in long-term investments of appreciating assets. However, the inefficiency of DCA arises from fixing the investment amount regardless of market conditions. In this paper, we present a more efficient approach that we name SmartDCA, which consists in adjusting asset purchases based on price levels. The simplicity of SmartDCA allows for rigorous mathematical analysis, enabling us to establish its superiority through the application of Cauchy-Schwartz inequality and Lehmer means. We further extend our analysis to what we refer to as $ρ$-SmartDCA, where the invested amount is raised to the power of $ρ$. We demonstrate that higher values of $ρ$ lead to enhanced performance. However, this approach may result in unbounded investments. To address this concern, we introduce a bounded version of SmartDCA, taking advantage of two novel mean definitions that we name quasi-Lehmer means. The bounded SmartDCA is specifically designed to retain its superiority to DCA. To support our claims, we provide rigorous mathematical proofs and conduct numerical analyses across various scenarios. The performance gain of different SmartDCA alternatives is compared against DCA using data from S&P500 and Bitcoin. The results consistently demonstrate that all SmartDCA variations yield higher long-term investment returns compared to DCA.

Keywords: Dollar-Cost Averaging (DCA), Lehmer Means, Cauchy-Schwartz Inequality, Investment Optimization, Volatility Mitigation, Equities & Cryptocurrencies

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper heavily employs advanced mathematical concepts like Cauchy-Schwarz inequalities, Lehmer means, and introduces novel quasi-Lehmer means, requiring significant derivation. However, the empirical validation is limited to numerical analyses on two asset classes without providing backtest-ready code, datasets, or rigorous statistical metrics.

  flowchart TD
    A["Research Goal:<br>Enhance DCA efficiency"] --> B["Key Methodology:<br>SmartDCA & ρ-SmartDCA<br>using Lehmer Means"]
    B --> C["Mathematical Analysis:<br>Cauchy-Schwartz Inequality<br>& Proofs"]
    B --> D["Numerical Analysis:<br>Testing bounded/unbounded<br>quasi-Lehmer versions"]
    C --> E["Key Findings:<br>1. SmartDCA superior to DCA<br>2. Higher ρ = Higher returns<br>3. Bounded version maintains gains"]
    D --> E
    E --> F["Outcome:<br>Validated on S&P500 &<br>Bitcoin (Equities & Crypto)"]