The course will develop a general quantitative approach to modern portfolio theory, optimization, and trading. Topics to include: factor models and Arbitrage Pricing Theory (APT); modeling risk including VaR, expected shortfall, variance decompositions, contributions to risk, dynamic volatilities and correlations, etc. We then discuss valuation including fundamental analysis and dividend discount models; forecasting; event studies and cross-sectional studies; the information ratio and information horizons; Fundamental Law of Active Management, Information Coefficient, Transfer Coefficient and related issues. We go on to give a mathematical background in optimization including Lagrange multipliers and the dual, primal-dual and interior point methods, the Barrier method, and second-order cone methods. We then apply this to portfolio optimization in particular, including multi-period optimization with transaction costs and constraints. As special cases, we will discuss mean-variance, Black-Litterman and bayesian generalizations, and optimal dynamic hedging of derivatives via the offsetting replicating portfolio. We then move on to study market microstructure theory and optimal execution, including standard broker execution algos and models of the limit order book dynamics. Time permitting we may discuss various advanced topics such as the Ross Recovery Theorem and inferring information about the underlying instrument from the derivatives markets. In each case, the focus will be on using advanced statistics to achieve a deeper understanding of the model and the data. Where appropriate, we will apply the relevant statistical models to real financial data, and in the part of the course dealing with intraday data, we will discuss efficient implementations of statistical estimation procedures on large data sets.