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Sparse and stable Markowitz portfolios | | Joshua Brodie
; Ingrid Daubechies
; Christine De Mol
; Domenico Giannone
; | | Date: |
1 Aug 2007 | | Abstract: | The Markowitz mean-variance optimizing framework has served as the basis for
modern portfolio theory for more than 50 years. However, efforts to translate
this theoretical foundation into a viable portfolio construction algorithm have
been plagued by technical difficulties stemming from the instability of the
original optimization problem with respect to the available data. In this paper
we address these issues of estimation error by regularizing the Markowitz
objective function through the addition of an $ell_1$ penalty. This penalty
stabilizes the optimization problem, encourages sparse portfolios, and
facilitates treatment of transaction costs in a transparent way. We implement
this methodology using the Fama and French 48 industry portfolios as our
securities. Using only a modest amount of training data, we construct
portfolios whose out-of-sample performance, as measured by Sharpe ratio, is
consistently and significantly better than that of the na"{i}ve portfolio
comprising equal investments in each available asset. In addition to their
excellent performance, these portfolios have only a small number of active
positions, a highly desirable attribute for real life applications. We conclude
by discussing a collection of portfolio construction problems which can be
naturally translated into optimizations involving $ell_1$ penalties and which
can thus be tackled by algorithms similar to those discussed here. | | Source: | arXiv, 0708.0046 | | Services: | Forum | Review | PDF | Favorites | |
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