An Asset‐Pricing Theory Unifying the CAPM and APT

  • Author(s): K. C. JOHN WEI
  • Published: Apr 30, 2012
  • Pages: 881-892
  • DOI: 10.1111/j.1540-6261.1988.tb02610.x

ABSTRACT

This study shows that the competitive‐equilibrium version of the APT may be extended to develop an exact model if idiosyncratic risks obey the Ross separating distribution. The results indicate that one only need add the market portfolio as an extra factor to the factor model in order to obtain an exact asset‐pricing relation. Thus, this study presents an extension and integration of the CAPM and APT. The “empirical” APT is also generalized to allow for some factors to be omitted from the econometric model employed to test the theory. The developed model is extremely robust and may be reduced to the CAPM or expanded to approximate Ross's APT depending upon the number of omitted factors. Further, the importance of the market portfolio is shown to be a monotonic increasing function of the number of omitted factors. Finally, the study demonstrates that, in a finite economy, the pricing‐error bound of the Ross APT in a correlated‐residuals factor structure is an increasing function of the absolute value of market‐residual beta, rather than the weight of the asset in the market portfolio as is the case of uncorrelated factor residuals. However, under the normality assumption, the pricing error becomes an extra component related to the market‐portfolio factor, and the exact asset‐pricing relation is once again obtained.

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