Portfolio Optimization Using Financial Chaos Index and Time-Homogeneous Top-K Ranking

We develop a new stock market index that captures the chaos existing in the market by measuring the mutual changes of asset prices. This new index relies on a tensor-based embedding of the stock market information, which in turn frees it from the restrictive value- or capitalization-weighting assumptions that commonly underlie other various popular indexes. We show that our index is a robust estimator of the market volatility which enables us to characterize the market by performing its regime analysis and the task of segmentation with a high degree of reliability. In addition, we analyze the dynamics and kinematics of the actual market volatility as compared to the implied volatility by introducing a time-dependent dynamical system model. In turn, we will be able to address several long-standing questions on the nature of a relation between equity and option markets. Apart from this, we establish causal relations which exist between our proposed index and an important category of news-based indexes which measure uncertainty in a wide spectrum of economic and financial policies. Another new feature of this work is to define a time-dependent index to capture the overall behavior of the stock market fundamentals. We then design a set of statistical tests which enable us to assess different types of the efficient market hypothesis, revealing weak and semi-strong efficiency of the U.S. stock market for the time frame January 1990-December 2019 using monthly and quarterly time frequencies. In contrast, the stock market during this time frame turned out to be weakly and semi-strongly inefficient as per daily time frequency. Besides, using the introduced tensor-based embedding of the stock market information, enables us to tackle the problem of time-dependent top-K ranking. More specifically, given N items, all having positive latent strengths, top-K ranking problem aims to identify the K items receiving the highest ranks based on partially revealed comparisons among the items. This problem has been widely studied in the case for which comparisons are performed independently. However, identifying the top-K rankings becomes a more intricate task when comparisons per se are performed along some temporal dimension. In this work, we further investigate potential impacts of temporality on sequences of top-K items and propose a time-homogeneous ranking scheme. Our framework relies mainly on tensor decompositions, rank centrality, and an innovative continuous extension of the Bradley-Terry-Luce (BTL) model. The proposed continuous BTL model extends the win/loss nature of the logistic model to a continuous setting, further reflecting preference degrees that may exist among the compared items. Our computations, which pertain to the analysis of S&P500 data during the same time period January 2007-December 2019, confirm that the our developed top-K ranking scheme is an effective approach to optimize cardinality-constrained portfolios which involve large volumes of noisy and incomplete data.

Author dc:creator

• Ataei, Masoud

Advisors dc:contributor.advisor

• Chen, Michael
• Yang, Zijiang

• Finance

Statement dc:rights

• Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.

Language dc:language

en

Handle dc:identifier.uri

http://hdl.handle.net/10315/37949

OAI identifier oai:identifier

oai:yorkspace.library.yorku.ca:10315/37949