Liquidity, Liquidity Commonality and its Impact on Portfolio Theory

We measure liquidity as a functional of supply and demand schedules, and measure commonality in liquidity as functional covariance. We show that liquidity commonality is due to supply and demand co-movements, through which order types play an important role; order types include market and limit orders. Contrarily, return commonality is mainly caused by order-flow co-movement; order flows include order directions and sizes. Since return commonality and liquidity commonality are caused by different forces, it is possible for stocks to have negative or little correlations in returns but strong positive correlations in liquidity. Both simulation results and empirical evidence from the Australian Stock Exchange support the above statement. Therefore, liquidity commonality poses a problem to diversification strategies based solely on picking stocks that do not correlate in returns. It is in this sense that not only the first moment of liquidity matters to asset pricing, its second moment matters as well.