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Detecting low volatility anomaly in stock markets

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Smriti Tiwari edited this page Apr 11, 2021 · 9 revisions

Overview

The low volatility anomaly refers to the finding that stocks exhibiting lower volatility achieve higher returns. This is an example of a stock market anomaly since it contradicts the central prediction of many financial theories that taking higher risk must be compensated with higher returns. The student will exploit a geometrical representation of the set of feasible portfolios and will implement a computational framework to detect low volatility anomaly in a given stock market. In particular, the framework will be based on MCMC uniform sampling from the set of portfolios to capture the dependency between portfolios' return and volatility.

Related work

The low volatility anomaly has been extensively studied, e.g. [1], [2]. The evidence of the anomaly has been mounting due to numerous studies by both academics and practitioners which confirm the presence of the anomaly throughout the forty years since its initial discovery in the early 1970s. Besides evidence for the US stock market, there is also evidence for international stock markets.

Details of your coding project

The student will use the geometrical representation where the set portfolios is given as the intersection of the n-dimensional simplex with an n-dimensional polytope. The simplex condition ensures that portfolio weights are all positive (no short-selling constraint) and that the portfolio is fully invested (i.e., weights sum to one). This is a typical regulatory requirement for mutual funds. The polytope contains a set of linear constraint like upper or lower bounds on individual assets or group of assets (like countries or sectors). Then we cut this feasible reagion with ellipsoidal constraints which ensure that eligible portfolios are bounded in variance. The student will (a) implement an isometric transformation to compute a full dimensional body, (b) be based on volesti's C++ code to implement uniform sampling from the transformed body intersected by an ellipsoid, (c) develop a method to sample from a sequence of such bodies, (d) develop statistical methods to describe the dependency between portfolios' return and volatility (variance) and (e) implement visualization tools.

Expected impact

The projects will provide GeomScale with efficient methods to detect low volatility anomaly in a given stock market and thus make an important contribution for practitioners and researchers on computational finance.

[1] van der Grient, Bart; Blitz, David; van Vliet, Pim. "Is the Relation between Volatility and Expected Stock Returns Positive, Flat or Negative?"
[2] Ang, Andrew; Hodrick, Robert J.; Xing, Yuhang; Zhang, Xiaoyan (2006). "The Cross-Section of Volatility and Expected Returns"

Mentors

  • Apostolos Chalkis <tolis.chal at gmail.com> is a PhD student in Computer Science. His research focuses on mathematical computing, optimization and computational finance. He has previous experience in GSoC 2018 and 2019 as a student under Org. R-project, implementing state-of-the-art algorithms for sampling from high dimensional multivariate distributions. He was GSOC mentor in three projects with Geomscale (2020). He is one of the authors of volesti.

  • Bachelard Cyril <Cyril.Bachelard at olz.ch> He is a Senior Quantitative Research Analyst in OLZ AG since 2011. His is an expert on Quantitative Research, risk forecasting and optimization models. He is also a PhD student on Algorithmic Sampling and Portfolio Optimization at the University of Lausanne. He holds a master's degree in economics and has further completed studies in mathematics, statistics and computer science.

  • Vissarion Fisikopoulos <vissarion.fisikopoulos at gmail.com> is an expert in mathematical software, computational geometry and optimization, and has previous GSOC mentoring experience with Boost C++ libraries (2016-2020) and the R-project (2017-2019) and GeomScale (2020).

  • Elias Tsigaridas <elias.tsigaridas at inria.fr> is an expert in computational nonlinear algebra and geometry with experience in mathematical software. He has contributed to the implementation, in C and C++, of several solving algorithms for various open source computer algebra libraries and has previous GSOC mentoring experience with the R-project (2019) and GeomScale (2020).

Students, please contact the first and the third mentor after completing at least one of the tests below.

Tests

Students, please do one or more of the following tests before contacting the mentors above.

  • Easy: compile and run VolEsti. Use the R extension to visualize sampling in a polytope.
  • Medium: Sample approximate uniformly points from a random generated polytope using the implmented in volesti random walks, for various walk lengths. For each sample compute the PSRF and report on the results.
  • Hard: Implement Gibbs sampler for uniform sampling from a polytope in C++ following the code structure of volesti.

Solutions of tests

Students, please post a link to your test results here.

  • EXAMPLE STUDENT 1 NAME, LINK TO GITHUB PROFILE, LINK TO TEST RESULTS.
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