| Both of the arbitrage pricing theory (APT) and intertemporal CAPM were generalized to include personal taxes and dividends. At the same time, the effect of inflation was also considered. Surprisingly, the modified APT, in which the market portfolio is included, is an exact pricing model without any approximation or the assumption of some agent holding a well-diversified portfolio. This modified APT is equivalent to the intertemporal CAPM with factors equivalent to state variables. Meanwhile, fund separation theorems were proved in different versions of the APT and the intertemporal CAPM. When simulation analysis was utilized to investigate the efficiency of previous studies used to test the APT, the evidence shows that: (1) The "scree" test is the most powerful method to determine the number of significant factors, but the bilinear paradigm is unable to. And, (2) the two-stage factor analysis is an efficient method in estimating true factors. When NYSE stocks were employed to test the linear asset pricing models with the most efficient approach determined by the simulation, with the linear combination approach and with the multiple factors and multiple indicators approach, the results indicate that: (1) While there is a single factor model (or a zero-beta CAPM) during 1963-1972, there is a two-factor APT (or one-state variable CAPM) during 1973-1982. The market portfolio and its transaction volume play a major role in the pricing relation in both periods. And the APT outperforms the CAPM, especially during 1973-1982. (2) The APT or the intertemporal CAPM is insignificantly different from the multi-index model. And, (3) the "own" residual variance, the dividend yield and the firm "size" all add the explanatory power on expected returns after adjusting risks. In the future, several directions can be extended from this study. First, the assumption of the linear factor model, of the normality, or of the quadratic utility may be indifferent in deriving multi-factor asset pricing models. Secondly, the APT, the CAPM, or the intertemporal CAPM under inflation might have the same pricing relation. Finally, both of the international APT and intertemporal CAPM may be extended to include inflation and/or tax differentials between domestic and foreign countries. |
