Commonality in ask-side vs. bid-side liquidity

We decompose the cost of trading into buy-side and sell-side using the limit order book. By using various position sizes to trade, we look for commonality in liquidity on different sides and also at the different levels of the order book. We find that bid-side liquidity has a higher commonality than ask-side liquidity for small position sizes to trade. On the other hand, ask-side commonality becomes stronger once position size exceeds a certain level. Empirical evidence suggests that this switching pattern may be due to the investors' over-reaction to a positive and under-reaction to a negative market trend.