Liquidity and Volatility

Abstract

Liquidity provision is a bet against private information: if private information turns out to be higher than expected, liquidity providers lose. Since information generates volatility, and volatility co-moves across assets, liquidity providers have a negative exposure to aggregate volatility shocks. Aggregate volatility shocks carry a large premium, hence this negative exposure explains why liquidity provision earns high average returns. We show this by incorporating uncertainty about the amount of private information into an otherwise standard model of liquidity provision. We test the model in the cross section of short-term reversals, which mimic the portfolios of liquidity providers. As predicted by the model, reversals have large negative betas to aggregate volatility shocks. These betas explain reversals' average returns with the same price of volatility risk that prevails in option markets. Volatility risk thus explains the liquidity premium among stocks, and why it increases in volatile times. Our results provide a novel view of the risks and returns to liquidity provision.

Keywords: liquidity, volatility, reversals, VIX, variance premium