Griveau-Billion, Théophile and Richard, Jean-Charles and Roncalli, Thierry (2013): A Fast Algorithm for Computing High-dimensional Risk Parity Portfolios.
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Abstract
In this paper we propose a cyclical coordinate descent (CCD) algorithm for solving high dimensional risk parity problems. We show that this algorithm converges and is very fast even with large covariance matrices (n > 500). Comparison with existing algorithms also shows that it is one of the most efficient algorithms.
Item Type: | MPRA Paper |
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Original Title: | A Fast Algorithm for Computing High-dimensional Risk Parity Portfolios |
Language: | English |
Keywords: | Risk parity, risk budgeting, ERC portfolio, cyclical coordinate descent algorithm, lasso |
Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions |
Item ID: | 49822 |
Depositing User: | Thierry Roncalli |
Date Deposited: | 14 Sep 2013 14:12 |
Last Modified: | 27 Sep 2019 12:18 |
References: | Bruder B. and Roncalli T. (2012), Managing Risk Exposures using the Risk Budgeting Approach, SSRN, www.ssrn.com/abstract=2009778. Cazalet Z., Grison P. and Roncalli T. (2013), The Smart Beta Indexing Puzzle, SSRN, www.ssrn.com/abstract=2294395. Chaves D.B., Hsu J.C., Li F. and Shakernia O. (2012), Efficient Algorithms for Computing Risk Parity Portfolio Weights, Journal of Investing, 21(3), pp. 150-163. Davies P.I. and Higham N.J. (2000), Numerically Stable Generation of Correlation Matrices and Their Factors, BIT Numerical Mathematics, 7(2), pp. 163-182. Friedman J., Hastie T. and Tibshirani R. (2010), Regularization Paths for Generalized Linear Models via Coordinate Descent, Journal of Statistical Software, 33(1), pp. 1-22. Maillard S., Roncalli T. and Teïletche J. (2010), The Properties of Equally Weighted Risk Contribution Portfolios, Journal of Portfolio Management, 36(4), pp. 60-70. Nesterov Y. (2004), Introductory Lectures on Convex Optimization: A Basic Course, Applied Optimization, 87, Kluwer Academic Publishers. Roncalli T. (2013), Introduction to Risk Parity and Budgeting, Chapman & Hall/CRC Financial Mathematics Series. Roncalli T. (2013), Introducing Expected Returns in Risk Parity Portfolios: A New Framework for Tactical and Strategic Asset Allocation, SSRN, www.ssrn.com/abstract=2321309. Spinu F. (2013), An Algorithm for the Computation of Risk Parity Weights, SSRN, www.ssrn.com/abstract=2297383. Tseng P. (2001), Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization, Journal of Optimization Theory and Applications, 109(3), pp. 475-494. Yen Y.M. and Yen T-S. (2013), Solving Norm Constrained Portfolio Optimization via Coordinate-Wise Descent Algorithms, Computational Statistics and Data Analysis, forthcoming. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/49822 |
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