SIAM Journal on Financial Mathematics, Volume 12, Issue 1, Page 410-445, January 2021.
This paper proposes a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, and investigates its application to finance to provide an innovative construction of a relative-volatility-managed portfolio. The proposed iterative algorithm, called DECODE, jointly estimates a performance measure of the market and the effective parameter vector in the optimal portfolio solution, where the relative-volatility timing is introduced into the risk exposure of an efficient portfolio via the control of its sparsity. The portfolio's risk exposure level, which is linked to its sparsity in the proposed framework, is automatically tuned with the latest market condition without using cross validation. The algorithm is efficient as it costs only a few computations of quadratic programming. We prove that the iterative algorithm converges and show the oracle inequalities of the DECODE, which provide sufficient conditions for a consistent estimate of an optimal portfolio. The algorithm can also handle the curse of dimensionality in that the number of training samples is less than the number of assets. Our empirical studies of over-12-year backtest illustrate the relative-volatility timing feature of the DECODE and the superior out-of-sample performance of the DECODE portfolio, which beats the equally weighted portfolio and improves over the shrinkage portfolio.

中文翻译：

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相对波动率管理的投资组合选择的稀疏学习方法

SIAM 金融数学杂志，第 12 卷，第 1 期，第 410-445 页，2021 年 1 月。
本文提出了一种用于估计稀疏目标向量的自校准稀疏学习方法，它是一个精度矩阵和一个向量的乘积，并研究了它在金融中的应用，以提供一种相对波动率管理投资组合的创新构造。所提出的迭代算法称为 DECODE，联合估计市场的性能度量和最优投资组合解决方案中的有效参数向量，其中相对波动时间通过对其稀疏性的控制引入到有效投资组合的风险敞口中。投资组合的风险敞口水平与其在提议框架中的稀疏性相关联，会根据最新的市场状况自动调整，无需使用交叉验证。该算法是有效的，因为它只需要进行几次二次规划计算。我们证明了迭代算法收敛并显示了 DECODE 的预言不等式，这为最优投资组合的一致估计提供了充分条件。该算法还可以处理维数灾难，因为训练样本的数量少于资产的数量。我们对超过 12 年回测的实证研究说明了 DECODE 的相对波动时间特征和 DECODE 投资组合的卓越样本外表现，它击败了同等权重的投资组合并优于收缩投资组合。该算法还可以处理维数灾难，因为训练样本的数量少于资产的数量。我们对超过 12 年回测的实证研究说明了 DECODE 的相对波动时间特征和 DECODE 投资组合的卓越样本外表现，它击败了同等权重的投资组合并优于收缩投资组合。该算法还可以处理维数灾难，因为训练样本的数量少于资产的数量。我们对超过 12 年回测的实证研究说明了 DECODE 的相对波动时间特征和 DECODE 投资组合的卓越样本外表现，它击败了同等权重的投资组合并优于收缩投资组合。