AlphaTrAI_White paper_Tail Risk
P. 1

 Portfolio Construction Based on Management of Tail Risk
November 2020
 Crucial to the construction of a successful portfolio is having a proper measure and model of risk. Here, we provide a critical review of commonly used risk measures and their deficiencies in characterizing the so-called tail risk. We then describe our approach at AlphaTrAI to modeling and managing the tail risk within a portfolio. These concepts are illustrated through case studies, including unprecedented events in 2020 triggered by the pandemic.
1. Introduction
The most important part of solving any problem is coming up with a proper, well-defined problem definition. The saying goes, "If I had only one hour to save the world, I would spend fifty-five minutes defining the problem, and only five minutes finding the solution.” Solving the market is no exception. The underperformance of many funds can be partially attributed to the lack of proper problem definition. Note that a fund’s stated objective (e.g., outperforming S&P500) is not a complete problem definition.
Defining the problem of investing in financial markets starts with recognizing that reward does not come without risk: the two must be taken together. Harry Markowitz’s 1952 paper, “Portfolio Selection," was among the first to recognize that expected reward can be gained by taking on risk and, conversely, that risk can be reduced by giving up expected
reward. Furthermore, this relationship is nonlinear. One should not seek to maximize their expected reward in a vacuum: portfolio construction should follow from exposure to risk as efficiently as possible. “Modern portfolio theory," as Markowitz’s framework would later be
called, seeks to maximize the expected reward at a fixed risk-tolerance level. The set of optimal portfolios across different levels of risk are referred to as the “efficient frontier." Constructing this efficient frontier and selecting from it the portfolio that matches an investor’s personal risk-tolerance level is an early portfolio construction technique that has been widely adopted and is still used to this day due to its simplicity and conceptual appeal.
However, there are several major issues with Markowitz’s original framework, due in large part to its use of variance as a measure of risk. In section 2, we describe the traditional measures of risk, including variance, and their limitations, and outline our preferred tail-risk-centric alternative. Section 3 discusses a family of probabilistic models that can effectively model tail risk, and we include two case studies that highlight the utility of this approach. Section 4 describes a general class of portfolio construction and evaluation approaches beyond Markowitz’s model. Finally, section 5 provides a summary of the topics covered.
By: Hudson Cooper, Director of Algo-Statistical Wizardry, Jason Wilkes, Director of Machine Learning, Yury Kiselev, Director of Research, and Homa Karimabadi, Chief Science Officer
   
























































































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