Straightening skewed markets with an index tracking optimizationless portfolio

42 Pages Posted: 6 Apr 2022

See all articles by Daniele Bufalo

Daniele Bufalo

Università degli Studi di Bari “Aldo Moro” (UNIBA)

Michele Bufalo

Sapienza University of Rome

Francesco Cesarone

University of Rome III - Department of Business Studies

Giuseppe Orlando

Università degli Studi di Bari “Aldo Moro” (UNIBA) - Department of Economics and Mathematical Methods

Date Written: March 25, 2022

Abstract

Among professionals and academics alike, it is well known that active portfolio management is unable to provide additional risk-adjusted returns relative to their benchmarks. For this reason, passive wealth management has emerged in recent decades to offer returns close to benchmarks at a lower cost. In this article, we first refine the existing results on the theoretical properties of oblique Brownian motion. Then, assuming that the returns follow skew geometric Brownian motions and that they are correlated, we describe some statistical properties for the \emph{ex-post}, the \emph{ex-ante} tracking errors, and the forecasted tracking portfolio. To this end, we develop an innovative statistical methodology, based on a benchmark-asset principal component factorization, to determine a tracking portfolio that replicates the performance of a benchmark by investing in a subset of the investable universe. This strategy, named hybrid Principal Component Analysis (hPCA), is applied both on normal and skew distributions. In the case of skew-normal returns, we propose a framework for calibrating the model parameters, based on the maximum likelihood estimation method. For testing and validation, we compare four alternative models for index tracking. The first two are based on the hPCA when returns are assumed to be normal or skew-normal. The third model adopts a standard optimization-based approach and the last one is used in the financial sector by some practitioners. For validation and testing, we present a thorough comparison of these strategies on real-world data, both in terms of performance and computational efficiency. A noticeable result is that, not only, the suggested lean PCA-based portfolio selection approach compares well versus cumbersome algorithms for optimization-based portfolios, but, also, it could provide a better service to the asset management industry.

Keywords: Index tracking, Passive fund management, Portfolio optimization, Tracking error, Skewed distributions

JEL Classification: G11, C44, C61, C53

Suggested Citation

Bufalo, Daniele and Bufalo, Michele and Cesarone, Francesco and Orlando, Giuseppe, Straightening skewed markets with an index tracking optimizationless portfolio (March 25, 2022). Available at SSRN: https://ssrn.com/abstract=4066692 or http://dx.doi.org/10.2139/ssrn.4066692

Daniele Bufalo

Università degli Studi di Bari “Aldo Moro” (UNIBA) ( email )

Piazza Umberto I
Bari, 70121
Italy

Michele Bufalo

Sapienza University of Rome ( email )

Francesco Cesarone (Contact Author)

University of Rome III - Department of Business Studies ( email )

Via Silvio D'Amico 77
Rome, Rome 00145
Italy

HOME PAGE: http://www.francescocesarone.com/

Giuseppe Orlando

Università degli Studi di Bari “Aldo Moro” (UNIBA) - Department of Economics and Mathematical Methods ( email )

Via C. Rosalba 53
VI Floor, Room 12
Bari, 70124
Italy
+39 080 5049218 (Phone)

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