The Impact of Covariance Misspecification in Risk-Based Portfolios

Ardia, David; Bolliger, Guido; Boudt, Kris; Fleury, Jean-Philippe

doi:10.2139/ssrn.2650644

Cited by 7 publications

(16 citation statements)

References 18 publications

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“…Practitioners tend to trust history for input estimation, because it is objective, interpretable, and available, but the nonstationary nature of nancial returns limits the number of relevant observations obtainable. As a result, the benets of diversication often are more than oset by estimation errors (Jorion, 1985;Michaud, 1989;Black and Litterman, 1992;Broadie, 1993;Chopra and Ziemba, 1993;Garlappi et al, 2006;Kan and Zhou, 2007;Ardia et al, 2017). Including transaction and holding costs and constraining portfolio weights are ways to regularize the optimization problem and reduce the risk due to estimation errors.…”

Section: Forecast-error Riskmentioning

confidence: 99%

Multi-period portfolio selection with drawdown control

et al. 2018

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Section: Forecast-error Riskmentioning

confidence: 99%

Multi-period portfolio selection with drawdown control

et al. 2018

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“…where diag(Σ) is a × 1 vector which takes all the asset variances Σ , and ′ diag(Σ) is the weighted average volatility. By construction it is ( ) ≥ 1, since the portfolio volatility is subadditive (Ardia et al 2017). Hence, the optimal allocation is the one with the highest DR:…”

Section: Risk-based Portfoliosmentioning

confidence: 99%

“…Lastly, (Ardia et al 2017) is the only work to implement shrinkage in risk-based portoflios. They shrink the sample covariance matrix as in (Ledoit and Wolf 2003), finding that the Minimum Variance and the Maximum Diversification portfolios are the most affected from covariance misspecification, hence they benefit the most from the shrinkage technique.…”

Section: Target Matrix Literature Reviewmentioning

confidence: 99%

“…Dealing with financial data, the shrinkage literature proposes six different models for the target matrix: the Single-Index market model (Ledoit and Wolf 2003), (Briner and Connor 2008), (Candelon, Hurlin, and Tokpavi 2012) and (Ardia et al 2017); the Identity matrix (Ledoit and Wolf 2004a), (Candelon, Hurlin, and Tokpavi 2012); the Variance Identity matrix (Ledoit and Wolf 2004a); the Scaled Identity matrix (DeMiguel, Martin-Utrera, and Nogales 2013); the Constant Correlation model (Ledoit and Wolf 2004b) and (Pantaleo et al 2011); the Common Covariance (Pantaleo et al 2011). All these targets belong to the class of more structured covariance estimators than the sample one, thus implying the latter is the matrix to shrink.…”

mentioning

confidence: 99%

“…Despite its great improvements in portfolio weights estimation under the Markowitz portfolio building framework, the shrinkage technique has been applied only in one work involving risk-based portfolios, (Ardia et al 2017). With our work, we contribute to the existing literature filling this gap and offering a comprehensive overview about shrinkage in risk-based portfolios.…”

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Target Matrix Estimators in Risk-Based Portfolios

Neffelli¹

2018

Preprint

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Portfolio weights solely based on risk avoid estimation error from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index model, the Common Covariance, the Constant Correlation and the Exponential Weighted Moving Average target matrices. By an extensive Monte Carlo simulation, we offer a comparative study of these target estimators, testing their ability in reproducing the true portfolio weights. We control for the dataset dimensionality and the shrinkage intensity in the Minimum Variance, Inverse Volatility, Equal-risk-contribution and Maximum Diversification portfolios. We find out that the Identity and Variance Identity have very good statistical properties, being well-conditioned also in high-dimensional dataset. In addition, the these two models are the best target towards to shrink: they minimise the misspecification in risk-based portfolio weights, generating estimates very close to the population values. Overall, shrinking the sample covariance matrix helps reducing weights misspecification, especially in the Minimum Variance and the Maximum Diversification portfolios. The Inverse Volatility and the Equal-Risk-Contribution portfolios are less sensitive to covariance misspecification, hence they benefit less from shrinkage.

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Minimum Rényi entropy portfolios

Lassance

Vrins²

2019

Ann Oper Res

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Accounting for the non-normality of asset returns remains challenging in robust portfolio optimization. In this article, we tackle this problem by assessing the risk of the portfolio through the "amount of randomness" conveyed by its returns. We achieve this by using an objective function that relies on the exponential of Rényi entropy, an information-theoretic criterion that precisely quantifies the uncertainty embedded in a distribution, accounting for higher-order moments. Compared to Shannon entropy, Rényi entropy features a parameter that can be tuned to play around the notion of uncertainty. A Gram-Charlier expansion shows that it controls the relative contributions of the central (variance) and tail (kurtosis) parts of the distribution in the measure. We further rely on a nonparametric estimator of the exponential Rényi entropy that extends a robust sample-spacings estimator initially designed for Shannon entropy. A portfolio selection application illustrates that minimizing Rényi entropy yields portfolios that outperform state-of-the-art minimum variance portfolios in terms of risk-return-turnover trade-off.

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The Impact of Covariance Misspecification in Risk-Based Portfolios

Cited by 7 publications

References 18 publications

Multi-period portfolio selection with drawdown control

Multi-period portfolio selection with drawdown control

Target Matrix Estimators in Risk-Based Portfolios

Minimum Rényi entropy portfolios

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