| Abstract: | The Arbitrage Pricing Theory (APT) was proposed by Ross (1976) as an alternative to the Capital Asset Pricing Model (CAPM) for computing the theoretical price of freely traded securities. The APT is based on the premise of linear return generating factors, rather than on the frequently criticized CAPM assumption of investor expected utility maximization. The APT expresses an asset's return as a linear combination of priced systematic factors multiplied by the sensitivity of the asset's return to the change in the particular factor. This study uses the Chen, Roll, and Ross (1986) parameterization of the APT to analyze the time series properties of the pricing factors over the seventy-two year period from March, 1927 through December, 1989. Ten variables are examined: the five pricing factors hypothesized as important by Chen, Roll, and Ross, and the underlying indexes from which they were constructed. Each variable is graphed, tested for autocorrelation and stationarity, and screened for Autoregressive Conditional Heteroskedasticity (ARCH) processes. Then a cointegrating regression is used to identify stochastic trends that affect two or more factors. First, the Engle-Granger two-step cointegration test methodology is used as proposed. This test is then extended to incorporate an ARCH process, and finally restated as a Generalized ARCH (GARCH) model. A Johansen test for cointegration is also performed. The residuals from the three models are analyzed and compared, and the implications of non-normal data are considered. The results indicate that the macroeconomic indexes are nonstationary in levels, but are stationary in the difference variables constructed by Chen, Roll, and Ross. They also exhibit conditional heteroskedasticity. A cointegrating relationship exists among the indexes, and the Chen, Roll and Ross APT may also be considered as a cointegrating model. The results suggest that there are three cointegrating vectors, indicating two underlying trends that drive all of the pricing factors. |
|---|