Browse > Article
http://dx.doi.org/10.5351/KJAS.2022.35.2.229

Linear programming models using a Dantzig type risk for portfolio optimization  

Ahn, Dayoung (Department of Statistics, Sungkyunkwan University)
Park, Seyoung (Department of Statistics, Sungkyunkwan University)
Publication Information
The Korean Journal of Applied Statistics / v.35, no.2, 2022 , pp. 229-250 More about this Journal
Abstract
Since the publication of Markowitz's (1952) mean-variance portfolio model, research on portfolio optimization has been conducted in many fields. The existing mean-variance portfolio model forms a nonlinear convex problem. Applying Dantzig's linear programming method, it was converted to a linear form, which can effectively reduce the algorithm computation time. In this paper, we proposed a Dantzig perturbation portfolio model that can reduce management costs and transaction costs by constructing a portfolio with stable and small (sparse) assets. The average return and risk were adjusted according to the purpose by applying a perturbation method in which a certain part is invested in the existing benchmark and the rest is invested in the assets proposed as a portfolio optimization model. For a covariance estimation, we proposed a Gaussian kernel weight covariance that considers time-dependent weights by reflecting time-series data characteristics. The performance of the proposed model was evaluated by comparing it with the benchmark portfolio with 5 real data sets. Empirical results show that the proposed portfolios provide higher expected returns or lower risks than the benchmark. Further, sparse and stable asset selection was obtained in the proposed portfolios.
Keywords
portfolio optimization; linear programming; Dantzig; perturbation; weighted covariance;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Ross SA (1976). The arbitrage theory of capital asset pricing, Handbook of the Fundamentals of Financial Decision Making: Part I, 11-30.
2 Candes E and Tao T (2007). The Dantzig selector: Statistical estimation when p is much larger than n, The annals of Statistics, 35, 2313-2351.   DOI
3 DeMiguel V, Garlappi L, and Uppal R (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?, The Review of Financial Studies, 22, 1915-1953.   DOI
4 Dantzig GB and Infanger G (1993). Multi-stage stochastic linear programs for portfolio optimization, Annals of Operations Research, 45, 59-76.   DOI
5 Fastrich B, Paterlini S, and Winker P (2015). Constructing optimal sparse portfolios using regularization methods, Computational Management Science, 12, 417-434.   DOI
6 Ledoit O and Wolf M (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection, Journal of Empirical Finance, 10, 603-621.   DOI
7 Li J (2015). Sparse and stable portfolio selection with parameter uncertainty, Journal of Business & Economic Statistics, 33, 381-392.   DOI
8 Lintner J (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, In Stochastic Optimization Models in Finance, 131-155.
9 Markowitz H (1952). Portfolio Selection, The Journal of Finance, 7, 77-91.   DOI
10 Konno H and Wijayanayake A (1999). Mean-absolute deviation portfolio optimization model under transaction costs, Journal of the Operations Research Society of Japan, 42, 422-435.   DOI
11 Zhou S, Lafferty J, and Wasserman L (2010). Time varying undirected graphs, Machine Learning, 80, 295-319.   DOI
12 Brodie J, Daubechies I, De Mol C, Giannone D, and Loris I (2009). Sparse and stable Markowitz portfolios. In Proceedings of the National Academy of Sciences, 106, 12267-12272.   DOI
13 Cai T, Liu W, and Luo X (2011). A constrained ℓ 1 minimization approach to sparse precision matrix estimation, Journal of the American Statistical Association, 106, 594-607.   DOI
14 Mansini R, Ogryczak W, and Speranza MG (2014). Twenty years of linear programming based portfolio optimization, European Journal of Operational Research, 234, 518-535.   DOI
15 Millington T and Niranjan M (2017). Robust portfolio risk minimization using the graphical lasso. In International Conference on Neural Information Processing, 863-872, Springer.
16 Koberstein A (2005). The dual simplex method, techniques for a fast and stable implementation, Unpublished doctoral thesis, Universitat Paderborn, Paderborn, Germany.
17 Cesarone F, Scozzari A, and Tardella F (2011). Portfolio Selection Problems in Practice: A Comparison between Linear and Quadratic Optimization Models, arXiv preprint arXiv:1105.3594
18 Fan J, Liao Y, and Mincheva M (2013). Large covariance estimation by thresholding principal orthogonal complements, Journal of the Royal Statistical Society. Series B, Statistical methodology, 75.
19 Lee TH and Seregina E (2020). Optimal Portfolio Using Factor Graphical Lasso, arXiv preprint arXiv:2011.00435
20 Andersen ED, Gondzio J, Meszaros C, and Xu X (1996). Implementation of interior point methods for large scale linear programming, HEC/Universite de Geneve.
21 Best MJ and Grauer RR (1991). On the sensitivity of mean-variance-efficient portfolios to changes in asset means: some analytical and computational results, The review of financial studies, 4, 315-342.   DOI
22 Bixby RE (2002). Solving real-world linear programs: A decade and more of progress, Operations research, 50, 3-15.   DOI
23 Rockafellar RT and Uryasev S (2000). Optimization of conditional value-at-risk, Journal of risk, 2, 21-42.   DOI
24 Chen C, Li X, Tolman C, Wang S, and Ye Y (2013). Sparse Portfolio Selection via Quasi-Norm Regularization, arXiv preprint arXiv:1312.6350
25 Murillo JML and Rodr'iguez AA (2008). Algorithms for Gaussian bandwidth selection in kernel density estimators. Advances in Neural Information Processing Systems.
26 Park S, Song H, and Lee S (2019b). Linear programing models for portfolio optimization using a benchmark, The European Journal of Finance, 25, 435-457.   DOI
27 Konno H and Yamazaki H (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management science, 37, 519-531.   DOI
28 Pantaleo E, Tumminello M, Lillo F, and Mantegna RN (2011). When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators, Quantitative Finance, 11, 1067-1080.   DOI
29 Park S, Lee ER, Lee S, and Kim G (2019a). Dantzig type optimization method with applications to portfolio selection, Sustainability, 11, 3216.   DOI
30 Pun CS and Wong HY (2015). High-dimensional static and dynamic portfolio selection problems via l1 minimization, Working paper of the Chinese University of Hong Kong.
31 Sharpe WF (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, The Journal of Finance, 19, 425-442.   DOI
32 Shen W, Wang J, and Ma S (2014). Doubly regularized portfolio with risk minimization, Twenty-Eighth AAAI Conference on Artificial Intelligence, 28, 1286-1292.