High frequency trading (HFT) depends on sophisticated algorithms to closely monitor price changes across securities. Theory predicts this technological advantage should translate into market-wide liquidity co-variation, by transmitting information-based liquidity shocks. Using a dataset of orders and trades from the French stock market, we investigate whether HFT algorithms constitute a source of systematic liquidity risk. We demonstrate that, across securities, the liquidity offered by high frequency traders is significantly less diverse than that of traditional traders; this finding is in line with the cross-asset learning hypothesis. The excessive co-movement in liquidity is also partly explained by common market making rules. In periods of increased market stress, we find HFT, designated market making, and order size to be important sources of liquidity commonality. Our results have policy implications for market regulators in Paris, suggesting the inclusion of maximum spread-limit rules in market making contracts will reduce the possibility of liquidity drying up when markets are in turmoil.