Statistical Properties and Tests of Efficient Frontier Portfolios

Adcock, Chris

doi:10.1002/9781119080305.ch9

Cited by 4 publications

(5 citation statements)

References 26 publications

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“…It is shown that this changes the shape of the efficient frontier and leads to different insights into the maximum Sharpe ratio or market portfolio. The results in this paper substantially extend those reported in Adcock [7,24,25].…”

Section: Introductionsupporting

confidence: 80%

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Ex Post Efficient Set Mathematics

Adcock¹

2013

JMF

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This paper considers efficient set mathematics for the case where the covariance matrix of asset returns is assumed known but ex ante the vector of expected returns is replaced by an estimated or forecast value. It is shown that the ex post mean and variance differ from the standard results. Consequently the maximum Sharpe ratio portfolio also differs from the standard result. However, even with uncertainty about the vector of expected returns, subject to the assumptions made about the joint distribution of actual returns and estimated mean returns, ex post Sharpe ratio maximisers hold the ex post market portfolio. The properties of the zero beta portfolio are similar to the standard results leading to a capital market line. The ex post Capital Asset Pricing Model incorporates an intercept and the betas are not the same as those computed ex ante. The results are illustrated with an example.

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Section: Introductionsupporting

confidence: 80%

“…example was first reported in conference proceedings in Adcock [24]. In this case   Ρ I , where I is the n n  unit matrix, in which case…”

Section: Equal Correlations and Unbiased Estimatementioning

confidence: 99%

Ex Post Efficient Set Mathematics

Adcock¹

2013

JMF

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“…Frahm and Memmel [37], Bodnar et al [23], Adcock [1], Woodgate and Siegel [64], Bodnar et al [19], Bodnar et al [13], Simaan et al [61], Bodnar et al [18], Bodnar et al [11]). On the other hand, the quantities (1.1) cannot be directly used to compute the weights and the characteristics of these portfolios, since both µ and Σ are unobservable parameters in practice.…”

Section: Introductionmentioning

confidence: 99%

Sampling distributions of optimal portfolio weights and characteristics in small and large dimensions

Bodnar

Dette

Parolya

et al. 2023

Random Matrices: Theory Appl.

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Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realise the position suggested by the optimal portfolios, he/she needs to estimate the unknown parameters and to account for the parameter uncertainty in the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset return distribution. In this paper, we characterise the exact sampling distribution of the estimated optimal portfolio weights and their characteristics. This is done by deriving their sampling distribution by its stochastic representation. This approach possesses several advantages, e.g. (i) it determines the sampling distribution of the estimated optimal portfolio weights by expressions, which could be used to draw samples from this distribution efficiently; (ii) the application of the derived stochastic representation provides an easy way to obtain the asymptotic approximation of the sampling distribution. The later property is used to show that the high-dimensional asymptotic distribution of optimal portfolio weights is a multivariate normal and to determine its parameters. Moreover, a consistent estimator of optimal portfolio weights and their characteristics is derived under the high-dimensional settings. Via an extensive simulation study, we investigate the finite-sample performance of the derived asymptotic approximation and study its robustness to the violation of the model assumptions used in the derivation of the theoretical results.

show abstract

Section: Introductionmentioning

confidence: 99%

Sampling distributions of optimal portfolio weights and characteristics in small and large dimensions

Bodnar

Dette

Parolya

et al. 2021

Random Matrices: Theory Appl.

View full text Add to dashboard Cite

Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realize the position suggested by the optimal portfolios, he/she needs to estimate the unknown parameters and to account for the parameter uncertainty in the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset return distribution. In this paper, we characterize the exact sampling distribution of the estimated optimal portfolio weights and their characteristics. This is done by deriving their sampling distribution by its stochastic representation. This approach possesses several advantages, e.g. (i) it determines the sampling distribution of the estimated optimal portfolio weights by expressions, which could be used to draw samples from this distribution efficiently; (ii) the application of the derived stochastic representation provides an easy way to obtain the asymptotic approximation of the sampling distribution. The later property is used to show that the high-dimensional asymptotic distribution of optimal portfolio weights is a multivariate normal and to determine its parameters. Moreover, a consistent estimator of optimal portfolio weights and their characteristics is derived under the high-dimensional settings. Via an extensive simulation study, we investigate the finite-sample performance of the derived asymptotic approximation and study its robustness to the violation of the model assumptions used in the derivation of the theoretical results.

show abstract

Statistical Properties and Tests of Efficient Frontier Portfolios

Cited by 4 publications

References 26 publications

Ex Post Efficient Set Mathematics

Ex Post Efficient Set Mathematics

Sampling distributions of optimal portfolio weights and characteristics in small and large dimensions

Sampling distributions of optimal portfolio weights and characteristics in small and large dimensions

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