Some empirical tests on the arbitrage pricing theory: a portfolio approach

Abstract

This study proposes a portfolio approach to reduce the factor specification problem in tests of the Arbitrage Pricing Theory. In portfolios, a more stable, reliable, and representative factor structure estimate is expected than in individual securities mainly due to the diversification of nonpervasive factors and measurement errors.

Application of Confirmatory Factor Analysis to contemporaneous holdout samples across 5 different grouping schemes and 6 different portfolio sizes indicates two sets of main empirical evidence in favor of a portfolio approach. (1) Regardless of the portfolio size and the grouping scheme. Explanatory Factor Analysis (EFA) extracts only on(verifiable factor, suggesting that one-factor structure is the true underlying factor structure in EFA. (2) clearcut consistent pattern of an increasingly distinct one-factor structure across all grouping schemes is shown mainly due to the rapid degradation in the performance of the 0-factor model, as the portfolio size increases. The rapid degradation of the 0-factor model appears to be a clear evidence in favor of the main thrust of this study that, as the portfolio size increases, the noisy terms of measurement error and uniqueness become diversified away and, as a result, a more distinct one (true) factor structure is revealed.

Tests of a hybrid model indicate that the market factor is of equivalent explanatory value, and that market model residuals do not contain any information which can be extracted by factor-analytic techniques. Tests of GLS indicate that the portfolio size effect on the pricing tests appears to be significant only under the 'firm size' grouping scheme. The possibility of an alternative factor structure, or of factors which cannot be inferred from factor analysis, cannot be ruled out.