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Open AccessArticle

Forecasting Efficient Risk/Return Frontier for Equity Risk with a KTAP Approach—A Case Study in Milan Stock Exchange

1,2,*,†, 2,† and 2,†
Department of Engineering, University of Messina, 98166 Messina ME, Italy
Business School, King’s College London, London WC2B 4BG, UK
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(8), 1055;
Received: 1 August 2019 / Revised: 13 August 2019 / Accepted: 14 August 2019 / Published: 16 August 2019
PDF [331 KB, uploaded 16 August 2019]


We introduce and discuss a dynamics of interaction of risky assets in a portfolio by resorting to methods of statistical mechanics developed to model the evolution of systems whose microscopic state may be augmented by variables which are not mechanical. Statistical methods are applied in the present paper in order to forecast the dynamics of risk/return efficient frontier for equity risk. Specifically, we adopt the methodologies of the kinetic theory for active particles (KTAP) with stochastic game-type interactions and apply the proposed model to a case study analyzing a subset of stocks traded in Milan Stock Exchange. In particular, we evaluate the efficient risk/return frontier within the mean/variance portfolio optimization theory for 13 principal components of the Milan Stock Exchange and apply the proposed kinetic model to forecast its short-term evolution (within one year). The model has the aim to pave the way to many different research perspectives and applications discussed eventually in the paper. In particular, the case of efficient frontier obtained by minimizing the Conditional Value-at-Risk (CVaR) is introduced and a preliminary result is proposed. View Full-Text
Keywords: Efficient frontier; kinetic theory; CVaR Efficient frontier; kinetic theory; CVaR

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Dolfin, M.; Leonida, L.; Muzzupappa, E. Forecasting Efficient Risk/Return Frontier for Equity Risk with a KTAP Approach—A Case Study in Milan Stock Exchange. Symmetry 2019, 11, 1055.

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