French Regression Model

Mothodology

The testing assets applied in this report would be the 50 portfolios as the target returns (25 size and book to market portfolios and 25 size and momentum portfolios) for countries including Asia, Japan, North America and Europe.

As mentioned by Liew and Vassalou (2000), the size, book to market and momentum are good risk factors to predict future growth. And HML and SMB have significant information about future GDP growth, but not the case of WML. Also, Rouwenhorst (1998) found an international evidence for a momentum effect to state that the momentum in return is not restricted to any particular market. Hawawini and Keim (1995) studied that there is a size effect in European markets and in Japan.

Thus, the testing assets selected could be more accurate for the international assets pricing with these significant factors. Meanwhile, it hopes that the larger sample of the dataset could increase the accuracy as well. Finally, the application of international data in the same test is with an expectation to avoid the sample or region specific, since the correlation of factors in different countries are low, and exits a certain degree of independence. However, since the correlation between the factors is low, it still exits a bias from this correlation. And the dataset from the developed countries could not explain the global market well since it ignore some significant market in developing countries that also contribute a lot to the global markets.

Models

This report apply Fama-Macbeth regression model to compare the pricing ability of three different models including the MVE portfolio model, CAPM model, the 2-factor and Carhart four-factor model. There is a 2 stage regression model. The first stage is to perform time-series rolling regressions to the 4 different models between December 1995 to December 2000, and obtain the beta.

MVE model and CAPM model: The dependent variable is excess of individual portfolio return minus the risk-free rate and the independent variable is the excess of MVE portfolio return over the risk free rate.

2 factor model: the dependent variable is the excess of individual portfolio return over the risk free rate and all the four factors as independent variables comprise the SMB and HML.

Carhart four-factor model: the dependent variable is the excess of individual portfolio return over the risk free rate and all the four factors as independent variables including the excess of market return over the risk free rate, SMB, HML and WML.

The second regression apply here is a cross-sectional regression based on the betas that calculated from the first regression. The excess of individual portfolio return minus the risk free rate would be the dependent variable again and all the betas as independent variables.

This report applies the same factor models to test different regions.