Essays on arbitrage

“Optimal Hedging of Noise Trader Risk” derives the optimal hedge ratio for an arbitrageur who faces noise trader risk. A continuous-time model is derived in which price discrepancies are expected to disappear over time, but may get worse due to unexpected changes in sentiment. Rule-of-thumb strategies utilized by arbitrage practitioners are suboptimal in that they do not take advantage of the tradeoff between fundamental and sentiment risk, since investors care only about aggregate risk and not its source. These simple rules do not account for the noise trader risk that is borne by loading on the sentiment asset, even when its expected returns are extreme. The properties and performance of the optimal hedge ratio are compared with those of the simple rules using simulated data. Closed-end funds and dual-listed shares are used to calibrate and test the model.; “Massively Confused Investors Making Conspicuously Ignorant Choices (MCI-MCIC)” examines the co-movement of stocks with similar ticker symbols. For one such pair of firms, there is a significant correlation between returns, volume, and volatility at short frequencies. Deviations from “fundamental value” tend to be reversed within several days, although there is some evidence that the return co-movement persists for longer horizons. Arbitrageurs appear to be limited in their ability to eliminate these deviations from fundamentals. This anomaly allows the observation of noise traders and their effect on stock prices independent of changes in information and expectations.; “Stock Demand Curve Elasticity Differences Across Countries” studies additions to the Morgan Stanley Capital International (MSCI) World Index for evidence of the existence of downward sloping demand curves. The average cumulative abnormal return for index additions is approximately 2.5%, but there are large cross sectional and time series differences. Most of the addition effect occurs on the day of addition, as opposed to the day of announcement. Addition effects for United States firms in the MSCI Index are comparable to those for the S&P 500 Index even though the index demand for MSCI stocks is much smaller. Transaction costs, margin requirements, and the availability of options trading are found to explain cross-sectional differences in the price effects.