Using proprietary, trader-level data, we study the order submission and cancellation behavior of high-frequency market makers. Studying a multi-market setting enables us to provide novel evidence for the existence of the so-called quote-fade phenomenon (quotes disappear market-wide immediately after orders) and latency arbitrage by high frequency market makers, and we identify the intra-day determinants of the phenomena. Using an event that eliminated latency between two of the three main markets, we find that reductions in latency exacerbate quote-fade and latency arbitrage. As market makers accumulate inventories, they post on average more conservative prices, and at the same time, they post more orders that are aggressively priced, presumably to trade out of these inventories. As trading in the market becomes one-directional, market makers post fewer orders against the market. High frequency market makers thus temporarily improve posted bid- and ask prices, even though they generally do not lean against the order flow.