Introduction to Risk Parity and Budgeting

Roncalli, Thierry

doi:10.1201/b15151

Cited by 84 publications

(109 citation statements)

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“…This ratio is by construction always larger or equal to 1 and the investor typically prefers a higher value of the DR (Choueifaty and Coignard 2008). Finally, both the WDiv and RDiv measure the concentration of the portfolio in terms of weights and risk (Maillard et al 2010, Roncalli 2013. The WDiv ranges from 1 k for a perfectly concentrated portfolio to 1 for the equally weighted portfolio and can be computed as:…”

Section: Correlation -Sp500mentioning

confidence: 99%

“…But even in the GMV set-up, the sample covariance matrix might exhibit estimation error that can easily accumulate, especially when dealing with a large number of assets (Michaud 1989, Ledoit and Wolff 2003, DeMiguel and Nogales 2009, Fan et al 2012). Furthermore, as a result of multicollinearity and extreme observations, the Markowitz's set-up often leads to undesirable and unrealistic extreme long and short positions, which can hardly be implemented in practice due to regulatory and short selling constraints (Shefrin and Statman 2000, DeMiguel et al 2009b, Boyle et al 2012, Roncalli 2013). An ideal portfolio then has conservative asset weights, which are stable in time, to avoid high turnover and transaction costs, while still promoting the right amount of diversification and being able to control the total amount of shorting.…”

Section: Introductionmentioning

confidence: 99%

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Sparse portfolio selection via the sorted ℓ1-Norm

Kremer

Lee

Bogdan

et al. 2020

Journal of Banking & Finance

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We introduce a financial portfolio optimization framework that allows us to automatically select the relevant assets and estimate their weights by relying on a sorted 1 -Norm penalization, henceforth SLOPE. Our approach is able to group constituents with similar correlation properties, and with the same underlying risk factor exposures. We show that by varying the intensity of the penalty, SLOPE can span the entire set of optimal portfolios on the risk-diversification frontier, from minimum variance to the equally weighted. To solve the optimization problem, we develop a new efficient algorithm, based on the Alternating Direction Method of Multipliers. Our empirical analysis shows that SLOPE yields optimal portfolios with good out-of-sample risk and return performance properties, by reducing the overall turnover through more stable asset weight estimates. Moreover, using the automatic grouping property of SLOPE, new portfolio strategies, such as SLOPE-MV, can be developed to exploit the data-driven detected similarities across assets.

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Section: Correlation -Sp500mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sparse portfolio selection via the sorted ℓ1-Norm

Kremer

Lee

Bogdan

et al. 2020

Journal of Banking & Finance

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“…We conclude the section by presenting our major empirical findings. For further details about portfolio optimization procedures, we refer to the recent books of Jondeau et al (2007), Roncalli (2014), andEmbrechts (2015).…”

Section: Application To Portfolio Optimizationmentioning

confidence: 99%

The sparse method of simulated quantiles: An application to portfolio optimization

Stolfi

Bernardi

Petrella

2018

Statistica Neerlandica

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The sparse multivariate method of simulated quantiles (S-MMSQ) is applied to solve a portfolio optimization problem under value-at-risk constraints where the joint returns follow a multivariate skew-elliptical stable distribution. The S-MMSQ is a simulation-based method that is particularly useful for making parametric inference in some pathological situations where the maximum likelihood estimator is difficult to compute. The method estimates parameters by minimizing the distance between quantile-based statistics evaluated on true and synthetic data, simulated from the postulated model, penalized by adding the smoothly clipped absolute deviation 1 -penalty in order to achieve sparsity. The S-MMSQ aims to efficiently handle the problem of estimating large-dimensional distributions with intractable likelihood, such as the stable distributions that have been widely applied in finance to model financial returns. KEYWORDSportfolio optimization, SCAD, skew-elliptical stable distribution, sparse method of simulated quantiles, sparse regularization

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“…These indicators fluctuate in time and are also characterized by some covariance matrix Q ij = E[p i p j ]. 4 This matrix is in general non trivial, as one may systematically predict similar returns for two different assets i and j, leading to Q ij > 0. In any case, one can as above build N uncorrelated linear combinations of indicators, given by:…”

Section: Symmetriesmentioning

confidence: 99%

“…Unfortunately, the practical implementation of Markowitz' ideas is fraught with difficulties and yields very disappointing results. This has been known for long, with many papers attempting to identify its flaws and suggesting remedies [1,2,3,4,5,6]. The most important problems are well understood: the optimally diversified Markowitz portfolio often ends up -somewhat paradoxically -being very concentrated on a few assets only, which inevitably leads to disastrous out-of-sample risks.…”

Section: Introductionmentioning

confidence: 99%

Agnostic Risk Parity: Taming Known and Unknown-Unknowns

et al. 2016

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Markowitz' celebrated optimal portfolio theory generally fails to deliver out-of-sample diversification. In this note, we propose a new portfolio construction strategy based on symmetry arguments only, leading to "Eigenrisk Parity" portfolios that achieve equal realized risk on all the principal components of the covariance matrix. This holds true for any other definition of uncorrelated factors. We then specialize our general formula to the most agnostic case where the indicators of future returns are assumed to be uncorrelated and of equal variance. This "Agnostic Risk Parity" (AGP) portfolio minimizes unknown-unknown risks generated by over-optimistic hedging of the different bets. AGP is shown to fare quite well when applied to standard technical strategies such as trend following.

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Introduction to Risk Parity and Budgeting

Cited by 84 publications

References 0 publications

Sparse portfolio selection via the sorted ℓ1-Norm

Sparse portfolio selection via the sorted ℓ1-Norm

The sparse method of simulated quantiles: An application to portfolio optimization

Agnostic Risk Parity: Taming Known and Unknown-Unknowns

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