Adoption of spectral analysis as a mainstream tool for portfolio management has languished despite the growing body of academic research. The highly theoretical nature of the recent publications have slowed the application of spectral analysis to specific use cases. In this paper, we show a step-by-step approach, advantages and results of spectral decomposition in portfolio reallocation. Specifically, we show how spectral decomposition solves two of the most pressing large-scale portfolio reallocation problems: extreme weights and transaction costs. We further show the empirical results of portfolio reallocation under different common portfolio composition scenarios, and how spectral decomposition helps speed up and outperform traditional portfolio allocation techniques.
New York University (NYU) – Courant Institute of Mathematical Sciences; Finance Concepts LLC
NYU Polytechnic School of Engineering – Department of Finance and Risk Engineering
We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a stationary stochastic process in which the most likely state is a contango with VIX ≈ 12% and a long-term futures price V∞ ≈ 20%. We analyze the behavior of ETFs and ETNs based on constant-maturity rolling futures strategies, such as VXX, XIV and VXZ, assuming stationarity and through a multi-factor model calibrated to historical data. We find that buy-and-hold strategies consisting of shorting ETNs that roll long futures, or buying ETNs that roll short futures, will produce theoretically-sure profits if it is assumed that CMFs are stationary and ergodic (see Proposition 3.1). To quantify further, we estimate a 2-factor lognormal model with mean-reverting factors to VIX and CMF historical data from 2011 to 2016. The results confirm the profitability of buy-and-hold strategies, but also indicate that the latter have modest Sharpe ratios, of the order of SR = 0.5 or less, and high variability over 1-year horizon simulations. This is due to the surges in VIX and CMF backwardations which are experienced sporadically, but also inevitably, in the volatility futures market.
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New research from Jian Di and Xinyue Gou forthcoming in the Journal of Computers.
Abstract: The initial clustering centers of traditional bisecting K-means algorithm are randomly selected and the k value of traditional bisecting K-means algorithm could not determine beforehand. This paper proposes a improve bisecting K-means algorithm based on automatically determining K value and the optimization of the cluster center. Firstly, the initial cluster centers are selected by using the point density and the distance function; Secondly, automatically determining K value is proposed by using Intra cluster similarity and inter cluster difference. the experiment results on UCI database show that the algorithm can effectively avoid the influence of noise points and outliers, and improve the accuracy and stability of clustering results.