Reliability in Portfolio Optimization using Uncertain Estimates

Raghu Nandan Sengupta (), Rachit Seth () and Peter Winker
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Raghu Nandan Sengupta: IIT Kanpur
Rachit Seth: IIT Kanpur

Sankhya B: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 7, 199-233

Abstract: Abstract Portfolio optimization problems are rather easy to solve if one assumes normality of the (joint) distribution of returns with given parameters and a linear objective function, subject to some risk constraints. Higher degrees of complexities arise when taking into account (i) non- linear asset classes, (ii) non-normal distributions, (iii) constraints on lot size, portfolio shares etc., and (iv) uncertainty of parameter estimates. In this paper a Reliability-Based Design Optimization (RBDO) framework is developed to tackle the last two issues, namely, to solve portfolio optimization problems, taking into account the constraints on lot sizes, portfolio shares, etc., and the uncertainty of parameter estimates (i.e., return and risk). Thereby, standard methods and heuristics, available in the literature for handling reliability-based constraints, are adopted. The Block-Bootstrap method is used to obtain estimates of the uncertainty of parameter estimates. For an application to stocks which are components of the DAX, efficient portfolios are obtained taking into account the trade-off between optimal values of the objective function and the reliability of results.

Keywords: Financial Optimization; Uncertainty; Reliability Analysis; Risk Analysis; Value at Risk; Block Bootstrap; C44; C61; C63 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13571-022-00285-2

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