Liquidity-adjusted Return and Volatility, and Autoregressive Models

ArXiv ID: 2503.08693 “View on arXiv”

Authors: Unknown

Abstract

We construct liquidity-adjusted return and volatility using purposely designed liquidity metrics (liquidity jump and liquidity diffusion) that incorporate additional liquidity information. Based on these measures, we introduce a liquidity-adjusted ARMA-GARCH framework to address the limitations of traditional ARMA-GARCH models, which are not effectively in modeling illiquid assets with high liquidity variability, such as cryptocurrencies. We demonstrate that the liquidity-adjusted model improves model fit for cryptocurrencies, with greater volatility sensitivity to past shocks and reduced volatility persistence of erratic past volatility. Our model is validated by the empirical evidence that the liquidity-adjusted mean-variance (LAMV) portfolios outperform the traditional mean-variance (TMV) portfolios.

Keywords: Liquidity Adjustment, ARMA-GARCH, Cryptocurrency, Volatility Modeling, Portfolio Optimization

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced econometric models (ARMA-GARCH with liquidity adjustments) and constructs new liquidity metrics (jump and diffusion), indicating high mathematical density. It validates the model using minute-level trading data, applies it to out-of-sample portfolio optimization, and compares performance across asset classes, demonstrating strong empirical rigor and implementation readiness.
  flowchart TD
    A["Research Goal: Model volatility & optimize portfolios for illiquid assets (e.g., cryptocurrencies)"] --> B["Data: Cryptocurrency OHLCV data<br>with specific liquidity metrics"]
    B --> C["Method: Construct Liquidity-Adjusted<br>Return & Volatility (Jump & Diffusion)"]
    C --> D["Computation: Integrate metrics into<br>Liquidity-Adjusted ARMA-GARCH Framework"]
    D --> E["Outcome: Improved Model Fit<br>Higher sensitivity to shocks<br>Lower persistence of erratic volatility"]
    E --> F["Validation: Liquidity-Adjusted Mean-Variance<br>Portfolios outperform Traditional Portfolios"]