VIX and liquidity premium*

Previous studies find as the VIX goes up, the return and the Sharpe ratio on liquidity provision increase. We argue these two phenomena are correlated because they depend on the same fundamentals: investors' risk aversion, asset variances and asset correlations. Our theoretical model shows (1) when investors are more risk-averse, they expect a higher return for providing liquidity, (2) when assets are volatile, liquidity shocks create stronger trading demands and thus liquidity demanders pay a higher premium, and (3) when assets are highly correlated, the higher risk of spillover of liquidity shocks across assets raises the price of liquidity. An increase in any of these three factors, besides increasing the expected return and the Sharpe ratio of liquidity providers, leads to a higher value for the VIX index. Our empirical analyses show that one standard-deviation increase in each of these three factors raise liquidity providers' expected daily return (annualized Sharpe ratio) by 0.16%, 0.38% and 0.40% (0.82, 1.27 and 2.10 units), respectively.