Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles

This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines on a cubic threefold and an ample hypersurface of an Abelian variety. For the desingularized elliptic self fiber product, we use an isotypic decomposition of the motive to deduce the Murre conjectures. We also prove a result about the intersection product. For the Fano surface of lines, we prove the finite-dimensionality of the Chow motive. Finally, we prove that an ample hypersurface on an Abelian variety possesses a Chow-Kunneth decomposition for which a motivic version of the Lefschetz hyperplane theorem holds.

Efficient Prices at Any Cost: Does Algorithmic Trading Deter Information Acquisition?

I demonstrate a powerful tension between acquiring information and incorporating it into asset prices, the two core elements of price discovery. As a salient case, I focus on the transformative rise of algorithmic trading (AT) typically associated with improved price efficiency. Using a measure of the relative information content of prices and a comprehensive panel of 37,325 stock-quarters of SEC market data, I establish instead that algorithmic trading strongly decreases the net amount of information in prices. The increase in price distortions associated with the AT “information gap” is roughly $42.6 billion/year for U.S. common stocks around earnings announcement events alone. Information losses are concentrated among stocks with high shares of algorithmic liquidity takers relative to algorithmic liquidity makers, suggesting that aggressive AT powerfully deters fundamental information acquisition despite its importance for translating available information into prices.