L2-Relaxation：预测组合与投资组合分析
L2-Relaxation: With Applications to Forecast Combination and Portfolio Analysis
摘要：
本文研究了多个预测的预测组合问题或多个资产的最小方差投资组合问题。提出了一种新的凸问题L2-松弛。与标准公式相比，L2松弛最小化了受一组松弛线性不等式约束的权重向量的平方欧几里德范数。由调整参数控制的弛豫幅度平衡了偏差和方差。当个体预测误差或金融资产的方差-协方差（VC）矩阵表现出潜在的组结构--块等相关矩阵加上特质噪声的VC时，L2-松弛的解决方案提供了大致相等的组内权重。当横截面单元数$N$的增长速度远快于时间维度$T$时，在渐近框架下建立了新方法的最优性.蒙特卡罗模拟结果表明，该方法具有良好的有限样本性能。它的广泛适用性突出了三个真实的数据的例子，关于微观经济学，宏观经济学和金融的经验应用。
英文摘要：
This paper tackles forecast combination with many forecasts or minimum variance portfolio selection with many assets. A novel convex problem called L2-relaxation is proposed. In contrast to standard formulations, L2-relaxation minimizes the squared Euclidean norm of the weight vector subject to a set of relaxed linear inequality constraints. The magnitude of relaxation, controlled by a tuning parameter, balances the bias and variance. When the variance-covariance (VC) matrix of the individual forecast errors or financial assets exhibits latent group structures -- a block equicorrelation matrix plus a VC for idiosyncratic noises, the solution to L2-relaxation delivers roughly equal within-group weights. Optimality of the new method is established under the asymptotic framework when the number of the cross-sectional units $N$ potentially grows much faster than the time dimension $T$. Excellent finite sample performance of our method is demonstrated in Monte Carlo simulations. Its wide applicability is highlighted in three real data examples concerning empirical applications of microeconomics, macroeconomics, and finance.
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