Application of the moving Lyapunov exponent to the S&amp;P 500 index to predict major declines

Tsakonas, Stefanos; Hanias, M. P.; Magafas, L.; Zachilas, Loukas

doi:10.21314/jor.2022.033

JOR

2022

DOI: 10.21314/jor.2022.033

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Application of the moving Lyapunov exponent to the S&P 500 index to predict major declines

Stefanos Tsakonas¹,

M. P. Hanias²,

L. Magafas³

et al.

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2024

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Hedging downside risk before substantial price corrections is vital for risk management and long-only active equity manager performance. This study proposes a novel methodology for crafting timing signals to hedge sectors’ downside risk. These signals can be integrated into existing strategies simply by purchasing sector index put options. Our methodology generates successful signals for price corrections in 2000 (dot-com bubble) and 2008 (global financial crisis). A key innovation involves utilizing sector correlations. Major price swings within six months are signaled when a sector exhibits high valuation alongside abnormal correlations with others. Utilizing the price-to-earnings ratio for identifying sectors’ high valuations is more beneficial than the bond–stock earnings yield differential. Our signals are also more efficient than those of standard technical analyses.

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When to Hedge Downside Risk?

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et al. 2024

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Predicting Tipping Points in a Family of PWL Systems: Detecting Multistability via Linear Operators Properties

Echenausía-monroy,

Cuesta-garcía,

Gilardi-velázquez

et al. 2024

Chaos Theory and Applications

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The study of dynamical systems is based on the solution of differential equations that may exhibit various behaviors, such as fixed points, limit cycles, periodic, quasi-periodic attractors, chaotic behavior, and coexistence of attractors, to name a few. In this paper, we present a simple and novel method for predicting the occurrence of tipping points in a family of Piece-Wise Linear systems (PWL) that exhibit a transition from monostability to multistability with the variation of a single parameter, without the need to compute time series, i.e., without solving the differential equations of the system. The linearized system of the model is analyzed, the stable and unstable manifolds are taken to be real vectors in space, and the changes suffered by these vectors as a result of the modification of the parameter are examined using such simple metrics as the magnitude of a vector or the angle between two vectors in space. The results obtained with the linear analysis of the system agree well with those obtained with the numerical resolution of the dynamical system itself. The work presented here is an extension of previous results on this topic and contributes to the understanding of the mechanisms by which a system changes its stability by fragmenting its basin of attraction. This, in turn, enriches the field by providing an alternative to numerical resolution to identify quantitative changes in the dynamics of complex systems without having to solve the differential equation system.

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Application of the moving Lyapunov exponent to the S&P 500 index to predict major declines

Cited by 2 publications

References 0 publications

When to Hedge Downside Risk?

When to Hedge Downside Risk?

Predicting Tipping Points in a Family of PWL Systems: Detecting Multistability via Linear Operators Properties

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