Mispecification bootstrap tests of the capital asset pricing model

The development of the Capital Asset Pricing Model (CAPM) marks the birth of asset pricing framework in finance. The CAPM is a simple and powerful tool to describe the linear relationship between risk and expected return. According to the CAPM, all pricing errors should be jointly equal to zero. Many empirical studies were conducted to test the validity of the model in various stock markets. Traditional methods such as Black, Jensen, and Scholes (1972), Fama and MacBeth (1973) and cross-sectional regression have some limitations and encounter difficulties because they often involve estimation of the covariance matrix between all estimated price errors. It becomes even more difficult when the number of assets becomes larger. Our research is motivated by the objective to overcome the limitations of the traditional methods. In this study, we propose to use bootstrap methods which can capture the characteristics of the original data without any covariance estimation.

The principle philosophy of bootstrap procedures is to treat the data sample as the population to draw bootstrap re-samples. The bootstrap methods comprise two general steps. First, we use historical monthly returns to estimate the parameters using both ordinary least square and the Cochrane-Orcutt method. Next, we implement model-based procedures to generate bootstrap samples. Following the idea of the block bootstrap, we consider all assets at a point in time as one block under different bootstrap schemes to capture the dependence structure between different assets. With the assumption of no serial correlation in the CAPM, we conduct the independent bootstrap over time scale. Furthermore, we introduce the block bootstrap with blocks over time to capture the temporal dependence. The bootstrap tests were applied to the CAPM in the US and Vietnam (VN) stock markets, providing some interesting results.