Brodie Joshua, Daubechies Ingrid, De Mol Christine, Giannone Domenico, Loris Ignace
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544-1000, USA.
Proc Natl Acad Sci U S A. 2009 Jul 28;106(30):12267-72. doi: 10.1073/pnas.0904287106. Epub 2009 Jul 15.
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights. This penalty regularizes (stabilizes) the optimization problem, encourages sparse portfolios (i.e., portfolios with only few active positions), and allows accounting for transaction costs. Our approach recovers as special cases the no-short-positions portfolios, but does allow for short positions in limited number. We implement this methodology on two benchmark data sets constructed by Fama and French. 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 naïve evenly weighted portfolio.
我们考虑在经典的马科维茨均值 - 方差框架内进行投资组合选择的问题，将其重新表述为一个约束最小二乘回归问题。我们建议在目标函数中添加一个与投资组合权重绝对值之和成比例的惩罚项。这个惩罚项使优化问题正则化（稳定化），鼓励形成稀疏投资组合（即只有少数活跃头寸的投资组合），并允许考虑交易成本。我们的方法在特殊情况下可以得到无卖空的投资组合，但也允许有限数量的卖空。我们在由法玛和弗伦奇构建的两个基准数据集上实施了这种方法。仅使用少量的训练数据，我们构建的投资组合，以夏普比率衡量，其样本外表现始终显著优于简单的等权重投资组合。
