Risk Reduction and Efficiency Increase in Large Portfolios: Leverage and Shrinkage

Zhao, Zhao; Ledoit, Olivier; Jiang, Hui

doi:10.2139/ssrn.3421538

Cited by 7 publications

(11 citation statements)

References 48 publications

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“…In particular, we work with the set of fully-invested portfolios, i.e., portfolios whose weights sum up to 1, which is the default choice for the bulk of the asset management industry. However, we let the weights be negative and we use the norm-constraint in Zhao et al (2020) to set a lower bound on the weights' values. Then, we introduce a transformation to represent the set of all possible fully-invested portfolios by a convex polytope; i.e., each point in the interior of the polytope corresponds to a single asset allocation.…”

Section: Contributionsmentioning

confidence: 99%

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Modeling asset allocations and a new portfolio performance score

et al. 2021

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We discuss and extend a powerful, geometric framework to represent the set of portfolios, which identifies the space of asset allocations with the points lying in a convex polytope. Based on this viewpoint, we survey certain state-of-the-art tools from geometric and statistical computing to handle important and difficult problems in digital finance. Although our tools are quite general, in this paper, we focus on two specific questions. The first concerns crisis detection, which is of prime interest for the public in general and for policy makers in particular because of the significant impact that crises have on the economy. Certain features in stock markets lead to this type of anomaly detection: Given the assets' returns, we describe the relationship between portfolios' return and volatility by means of a copula, without making any assumption on investors' strategies. We examine a recent method relying on copulae to construct an appropriate indicator that allows us to automate crisis detection. On real data the indicator detects all past crashes in the cryptocurrency market and from the DJ600-Europe index, from 1990 to 2008, the indicator identifies correctly 4 crises and issues one false positive for which we offer an explanation. Our second contribution is to introduce an original computational framework to model asset allocation strategies, which is of independent interest for digital finance and its applications. Our approach addresses the crucial question of evaluating portfolio management, and is relevant the individual managers as well as financial institutions. To evaluate portfolio performance, we provide a new portfolio score, based on the aforementioned framework and concepts. In particular, it relies on statistical properties of portfolios, and we show how they can be computed efficiently.

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Section: Contributionsmentioning

confidence: 99%

“…First, we compute the minimum and the maximum value of portfolio volatility. The first one is also called Global Minimum Variance portfolio (Zhao et al 2020). In particular, we solve the following optimization problems, (…”

Section: Set the Levels Of Riskmentioning

confidence: 99%

Modeling asset allocations and a new portfolio performance score

et al. 2021

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“…While this parameter can only be calculated afterward in the Standard model, it is directly linked to the most influential tuning parameter in the LASSO model: the λ Lagrange parameter. δ also provides information on the short-sale budget as well as practitioners' investment rules, as shown by Zhao et al (2019). Naturally, as represented by the black line of Standard models' δ, this parameter is stable over a few months but can have high fluctuations over years.…”

Section: Resultsmentioning

confidence: 99%

“…Hence, we do not set the value of δ so that it meets specific well-known constraints such as the shortsale constraint (see DeMiguel et al (2009a)). In contrast to other authors such as Zhao et al (2019), we do not want to achieve any practitioner's rule for investment and therefore do not keep δ as a constant, independent of the present market situation. By contrast, we allow the δ value to change in every period, as we always want to achieve the optimization goal, that is, finding the portfolio with the lowest variance.…”

Section: Empirical Studymentioning

confidence: 90%

Sparsity and Stability for Minimum-Variance Portfolios

Husmann¹,

Shivarova²,

Steinert³

2019

Preprint

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The popularity of modern portfolio theory has decreased among practitioners because of its unfavorable out-of-sample performance. Estimation errors tend to affect the optimal weight calculation noticeably, especially when a large number of assets is considered. To overcome these issues, many methods have been proposed in recent years, although most only address a small set of practically relevant questions related to portfolio allocation. This study therefore sheds light on different covariance estimation techniques, combines them with sparse model approaches, and includes a turnover constraint that induces stability. We use two datasets -comprising 319 and 100 companies of the S&P 500, respectively -to create a realistic and reproducible data foundation for our empirical study. To the best of our knowledge, this study is the first to show that it is possible to maintain the low-risk profile of efficient estimation methods while automatically selecting only a subset of assets and further inducing low portfolio turnover. Moreover, we provide evidence that using the LASSO as the sparsity-generating model is insufficient to lower turnover when the involved tuning parameter can change over time.

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“…total short position of at most 50% and thus a gross leverage of at most 2.0; for example, such portfolios are also considered by Zhao et al (2022). Table 5 presents the corresponding results for N = 1, 000.…”

Section: Global Minimum Variance Portfoliomentioning

confidence: 99%

Large dynamic covariance matrices: Enhancements based on intraday data

Nard

Engle

Ledoit

et al. 2022

Journal of Banking & Finance

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Multivariate GARCH models do not perform well in large dimensions due to the so-called curse of dimensionality. The recent DCC-NL model of Engle et al. (2019) is able to overcome this curse via nonlinear shrinkage estimation of the unconditional correlation matrix. In this paper, we show how performance can be increased further by using open/high/low/close (OHLC) price data instead of simply using daily returns. A key innovation, for the improved modeling of not only dynamic variances but also of dynamic correlations, is the concept of a regularized return, obtained from a volatility proxy in conjunction with a smoothed sign of the observed return.

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Risk Reduction and Efficiency Increase in Large Portfolios: Leverage and Shrinkage

Cited by 7 publications

References 48 publications

Modeling asset allocations and a new portfolio performance score

Modeling asset allocations and a new portfolio performance score

Sparsity and Stability for Minimum-Variance Portfolios

Large dynamic covariance matrices: Enhancements based on intraday data

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