The first essay examines the events of May 6, 2010: the ``Flash Crash". The Flash Crash, a brief period of extreme market volatility on May 6, 2010 raised questions about the current structure of the U.S. financial markets. Audit-trail data from U.S. Commodity Futures Trading Commission (CFTC) is used to describe the structure of the E-mini S&P 500 stock index futures market on May 6. In this study, three questions are asked. How did High Frequency Traders (HFTs) trade on May 6? What may have triggered the Flash Crash? What role did HFTs play in the Flash Crash? There is evidence which supports that HFTs did not trigger the Flash Crash, but their responses to the unusually large selling pressure on that day exacerbated market volatility.

The second essay examines the relationship between mutual fund trading and liquidity consumption in financial markets. Using Thompson Mutual Funds holdings data and the Trade and Quotes (TAQ) data, we relate the mutual fund trading to liquidity consumption. Mutual fund trading is positively correlated with liquidity consumption. Mutual fund sensitivity to liquidity consumption differs based on mutual fund investment style. Large trades reveal the trading activity of actively managed mutual funds whereas the trading activity of index funds can be explained by small trades. This is consistent with a plausible explanation that index funds need to use small trades to rebalance their portfolios and information motivates the large trades of active mutual funds.

The third essay tests the predictions of trading game invariance using the sample of trades from TAQ dataset from 1993 to 2008. The theory of trading game invariance predicts that the distribution of trade sizes as a fraction of trading volume should vary across stocks proportionally to their trading activity in -2/3 power and that the number of trades should vary across stocks proportionally to their trading activity in 2/3 power. The data supports predictions of the invariance theory. For the number of trades, the estimated power coefficient of 0.69 (with standard errors of 0.001) is especially close to the predicted one of 2/3 on the subsample before 2001. These estimates increases to 0.79 (with standard errors of 0.004) after 2001 following a structural break related to a reduction in tick size and a consequent spread of algorithmic trading. Furthermore, the entire distribution of trade size shifts with the trading activity in a manner predicted by invariance theory. When trade sizes are adjusted for differences in trading activity, then their distribution is stable across stocks and similar to the distribution of a log-normal variable, truncated at the 100-share threshold.