A Reduced Rank Regression Approach to Tests of Asset Pricing
证明套利定价理论和资本资产定价模型对资产收益的条件期望施加的约束是降秩回归模型的特例，通过典型相关分析进行最大似然估计，并利用似然比检验判断股票收益的因子数量及宏观指标的相关性，以意大利股市数据为例。
Both the Arbitrage Pricing Theory (APT) and the Capital Asset Pricing Model (CAPM) place restrictions of the cross‐sectional variation of conditional expectations of asset returns and of macro indicators. We show that these restrictions imposed on the reference statistical models lead to special cases of the reduced rank regression model. The maximum likelihood problem is solved by canonical correlation analysis. Likelihood ratio tests about the number of factors underlying stock returns are straightforward to calculate, thus allowing discrimination between competing financial theories. Moreover LR tests on the relevance of each macroeconomic indicator within a chosen model can be implemented. Some of the tests are illustrated by an application to Italian stock market data.