This dissertation includes three essays. The first essay studies the effects of margin requirements. The second essay studies how asymmetric information and imperfect competition affect equilibrium illiquidity. The third essay derives new comparative statics results for the distribution of portfolio payoffs.;Margin requirements have long been implemented in almost all financial markets and are often used as an important regulatory tool for improving market conditions. However, their economic impact beyond affecting default risk is still largely unknown. The first essay proposes a tractable and flexible equilibrium model with and without information asymmetry to examine how margin requirements on both long and short stock positions affect asset prices, market volatility, market illiquidity and the welfare of market participants. Most of my main results are obtained in closed-form. Contrary to one of the main regulatory goals, I find that margin requirements can significantly increase market volatility. In addition, margin requirements always increase market illiquidity (as measured by price impact) and can lead to a greater return reversal exactly when they amplify market volatility. I also find that information asymmetry may reverse or dampen the impact of margin requirements. Moreover, margin requirements always make unconstrained investors worse off and can make constrained investors better off. The model provides new testable implications.;The second essay proposes a novel and tractable equilibrium model to study how information asymmetry, competition among market makers, and investors' risk aversion affect asset pricing, market illiquidity and welfare. The main innovation is that market makers compete through choosing simultaneously quantities to buy at the bid and to sell at the ask and accordingly market clears separately at the bid and at the ask. Equilibrium bid and ask prices, bid and ask depths, trading volume and market makers' inventory levels are all derived in closed-form. Our model can help explain some of the puzzling empirical findings, such as bid-ask spreads can be lower with asymmetric information and can be positively correlated with trading volume. In addition, we find that information asymmetry may make informed investors worse off, may reduce the welfare loss due to market power and may increase the competition among market makers in equilibrium.;Hart(1975) proved the difficulty of deriving general comparative statics in portfolio weights. Instead, in the third essay, we derive new comparative statics for the distribution of payoffs: A is less risk averse than B iff A's payoff is always distributed as B's payoff plus a non-negative random variable plus conditional-mean-zero noise. If either agent has nonincreasing absolute risk aversion, the non-negative part can be chosen to be constant. The main result also holds in some incomplete markets with two assets or two-fund separation, and in multiple periods for a mixture of payoff distributions over time (but not at every point in time).
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