This paper examines the impact of the joints tails of the portfolio return and its empirical volatility on the optimal portfolio choices. We assume that the portfolio return and its volatility dynamic is approximated by a bivariate Markov chain constructed on its historical distribution. This allows the introduction of a non parametric stochastic volatility portfolio model without the explicit use of a GARCH type or other parametric stochastic volatility models. We describe the bi-dimensional tree structure of the Markov chain and discuss alternative portfolio strategies based on the maximization of the Sharpe ratio and of a modified Sharpe ratio that takes into account the behaviour of a market benchmark. Finally, we empirically evaluate the impact of the portfolio and its stochastic volatility joint tails on optimal portfolio choices. In particular, we examine and compare the out of sample wealth obtained optimizing the portfolio performances conditioned on the joint tails of the proposed stochastic volatility model.
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We used the Matlab R2018b function ’pattersearch’. At each iteration, the 2n directions given by the canonical basis and its opposite are explored. Finally the closest point to the current solution which satisfies working set constraints and provide the best improvement of the objective function is selected as new current solution.
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The authors thank for grants ex-MURST 60% 2019, 2018. Rosella Giacometti acknowledges the support of the Czech Science Foundation (GACR) under Project 19-11965S.
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Bonomelli, M., Giacometti, R. & Ortobelli Lozza, S. Joint tails impact in stochastic volatility portfolio selection models. Ann Oper Res (2020). https://doi.org/10.1007/s10479-020-03531-w
- Markov chain
- Sharpe ratio
- Stochastic dominance
- Stochastic volatility