Liquidity Premium, Liquidity-Adjusted Return and Volatility, and a Unified Modern Portfolio Theory: illustrated with Crypto Assets

Abstract

We establish innovative measures of liquidity premium Beta on both asset and portfolio levels, and corresponding liquidity-adjusted return and volatility, for selected crypto assets. We develop a liquidity-adjusted ARMA-GARCH/EGARCH representation to model the liquidity-adjusted return for individual assets, and a liquidity-adjusted VECM/VAR-DCC/ADCC structure to model the liquidity-adjusted variance for portfolios. Both models exhibit improved predictability at high liquidity, which enables a liquidity-adjusted mean-variance (LAMV) framework a clear advantage over its traditional mean variance (TMV) counterpart in portfolio performance. Collectively, they extend the return/volatility-based Modern Portfolio Theory (MPT) to a Unified Modern Portfolio Theory (UMPT) with built-in treatments on liquidity risk.

Keywords: liquidity, liquidity premium Beta, liquidity-adjusted return and volatility, liquidity-adjusted ARMA-GARCH/EGARCH and VECM/VAR-DCC/ADCC, liquidity-adjusted mean variance (LAMV)

JEL Classification: C32, C53, C58, G11, G12, G17