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The article by Conway and Reinganum demonstrates that cross-validation is a necessary part of any goodness-of-fit evaluation of multifactor asset-pricing models. The use of this procedure guards against overfitting, which is a common occurrence in large samples. It is illustrated here that if cross-validation cannot be used, two alternative goodness-of-fit measures that include a penalty based on parameters fitted can be used to assist in model selection. The two alternative…

Markowitz 有效投资组合的估计AI 解读

Given a set of N assets a portfolio is determined by a set of weights xi, i = 1, 2, …, N; Σ N i=1 xi = 1 indicating the proportion of the value of the portfolio devoted to each asset. A Markowitz efficient portfolio is the vector of weights X m that minimizes the variance σ m 2 of the total return from the portfolio, subject to the condition that the portfolio mean premium return μ m has a certain value. The estimators for the N × 1 vector X m , the return premium μ m , and…

协方差矩阵与参数向量存在函数关系时的最小二乘估计AI 解读

Estimation for the linear model y = Xβ + e with unknown diagonal covariance matrix G is considered. The diagonal elements of G are assumed to be known functions of the explanatory variables X and an unknown parameter vector Θ, where Θ is permitted to contain elements of β. A weighted joint least squares estimator is developed that is asymptotically equivalent to the maximum likelihood estimator. Asymptotic properties of the simple least squares estimator and of the weighted…