A Reduced Rank Regression Approach to Tests of Asset Pricing.

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. The authors 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 to discriminate 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. Copyright 1997 by Blackwell Publishing Ltd