Algorithmic Portfolio Tilting to Harvest Higher Moment Gains

Boudt, Kris; Cornilly, Dries; Holle, Frederiek Van; Willems, Joeri

doi:10.2139/ssrn.3378491

Cited by 2 publications

(9 citation statements)

References 19 publications

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“…By this development, the mean-variance-skewness-kurtosis case is also covered. This case is also covered in the related analysis of Boudt et al (2020a) who also apply shrinkage methods for the estimation of higher moments as we do subsequently.…”

Section: Introductionmentioning

confidence: 94%

“…Given independence the co-skewness and co-kurtosis matrices in particular would have many zeros and the estimator is shrunk towards this target. Shrinkage methods for covariance matrix estimation are outlined by Wolf (2003, 2004) as well as by Boudt et al (2020a) and Martellini and Ziemann (2010) for higher moment matrices (co-skewness and co-kurtosis). Computations are performed using the R-package 'PerformanceAnalytics' (Peterson and Carl 2020).…”

Section: Portfolio Momentsmentioning

confidence: 99%

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Nonparametric portfolio efficiency measurement with higher moments

Krüger

2020

Empir Econ

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The paper considers a nonparametric approach to determine portfolio efficiency using specific directions toward the portfolio frontier function. This approach allows for a straightforward incorporation of higher moments of the returns distribution beyond mean and variance. The nonparametric approach is extended by the computation of optimal directions endogenously by maximizing the distance toward the portfolio frontier as a novel methodological feature. An empirical application to Fama-French portfolios demonstrates the applicability of the nonparametric approach. The results show that the optimal directions to the frontier depend on the portfolio considered as well as on the period for which the moments are estimated. Skewness in particular plays a role in determining the optimal direction, whereas kurtosis seems to be less crucial.

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Section: Introductionmentioning

confidence: 94%

Section: Portfolio Momentsmentioning

confidence: 99%

Nonparametric portfolio efficiency measurement with higher moments

Krüger

2020

Empir Econ

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“…However, the investors might want to modify another existing portfolio w 0 toward a MVSK efficient portfolio. This can be done by tilting these portfolios in a direction that increases their first moment and third central moment and decreases their second and fourth central moments [12], i.e., maximize…”

Section: B Mvsk Tilting Portfoliomentioning

confidence: 99%

“…where f (x) and g i (x) are nonconvex functions and K is a convex set. In order to solve the problem (12), which is directly intractable, we may turn to successively solving a sequence of strongly convex approximating problems. Denote by x k the current iterate at k-th iteration, then the SCA algorithm constructs a strongly convex approximating problem for (12) as [19]:…”

Section: The Successive Convex Approximation Algorithmmentioning

confidence: 99%

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Solving High-Order Portfolios via Successive Convex Approximation Algorithms

Zhou

Palomar

2020

Preprint

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The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing the portfolios. The two moments can well describe the distribution of the portfolio return when it follows the Gaussian distribution. However, the real world distribution of assets return is usually asymmetric and heavy-tailed, which is far from being a Gaussian distribution. The asymmetry and the heavy-tailedness are characterized by the third and fourth central moments, i.e., skewness and kurtosis, respectively. Higher skewness and lower kurtosis are preferred to reduce the probability of extreme losses. However, incorporating high-order moments in the portfolio design is very difficult due to their non-convexity and rapidly increasing computational cost with the dimension. In this paper, we propose a very efficient and convergence-provable algorithm framework based on the successive convex approximation (SCA) algorithm to solve high-order portfolios. The efficiency of the proposed algorithm framework is demonstrated by the numerical experiments.

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Algorithmic Portfolio Tilting to Harvest Higher Moment Gains

Cited by 2 publications

References 19 publications

Nonparametric portfolio efficiency measurement with higher moments

Nonparametric portfolio efficiency measurement with higher moments

Solving High-Order Portfolios via Successive Convex Approximation Algorithms

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