Markowitz’s celebrated mean–variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the estimates into the efficient frontier that assumes known parameters has led to portfolios that may perform poorly and have counter-intuitive asset allocation weights; this has been referred to as the “Markowitz optimization enigma.” After reviewing different approaches in the literature to address these difficulties, we explain the root cause of the enigma and propose a new approach to resolve it. Not only is the new approach shown to provide substantial improvements over previous methods, but it also allows flexible modeling to incorporate dynamic features and fundamental analysis of the training sample of historical data, as illustrated in simulation and empirical studies.
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We are the bridge between the academia and industry. We screen hundreds of highly refereed journal papers and pick the best trading ideas. We turn these ideas on paper into solid tools that you can actually use in trading. Our collection of quantitative models and algorithms are good building blocks for your strategies. By putting together these modules, you can construct quantitative trading strategies like assembling LEGO pieces. Moreover, these math models enable you to translate vague trading ideas in English into precise mathematics in Greek.
This course introduces students to quantitative trading. A “quant” portfolio manager or a trader usually starts with an intuition or a vague trading idea. Using mathematics, s/he turns the intuition into a mathematical trading model for analysis, back testing and refinement. When the quantitative investment model proves to be likely profitable after passing rigorous statistical tests, the portfolio manager implements the model on a computer system for automatic execution. In short, quantitative trading is the process where ideas are turned into mathematical models and then coded into computer programs for systematic trading. It is a science where mathematics and computer science meet. In this course, students study investment strategies from the popular academic literature and learn the fundamental mathematics and IT aspects of this emerging field.