Some Empirical Tests of the Theory of Arbitrage Pricing

We estimate the parameters of Ross's Arbitrage Pricing Theory (APT). Using daily return data during the 1963–78 period, we compare the evidence on the APT and the Capital Asset Pricing Model (CAPM) as implemented by market indices and find that the APT performs well. The theory is further supported in that estimated expected returns depend on estimated factor loadings, and variables such as own variance and firm size do not contribute additional explanatory power to that of the factor loadings.     

The Arbitrage Pricing Theory and Supershares

In a single-period model with options on the market portfolio, linear factor pricing holds if and only if the variance of the market conditional on the factors is zero. There is no need for factors other than nonlinear functions of the market. For accurate linear pricing of all payoff patterns the factors must be rotationally equivalent to Hakansson's “supershares.” In a multiperiod model, a similar set of results holds, but with consumption replacing the market payoff. The methodology of the empirical Arbitrage Pricing Theory literature is not consistent with either the single-period model or the multiperiod model.     

The Current State of the Arbitrage Pricing Theory

This paper provides a simple proof of a recent theorem presented by Reisman (1992) , concerning the use of proxies for the factors in the return-generating process of the arbitrage pricing theory (APT). In the single-factor case, the theorem asserts that any variable correlated with the factor can serve as the benchmark in an approximate APT expected return relation. The significance of this result is considered and a new direction for empirical work on “arbitrage pricing” is outlined.     

An Empirical Investigation of the Arbitrage Pricing Theory

Empirical tests are reported for Ross' [48] arbitrage theory of asset pricing. Using data for individual equities during the 1962–72 period, at least three and probably four priced factors are found in the generating process of returns. The theory is supported in that estimated expected returns depend on estimated factor loadings, and variables such as the own standard deviation, though highly correlated (simply) with estimated expected returns, do not add any further explanatory power to that of the factor loadings.     

A Semiautoregression Approach to the Arbitrage Pricing Theory

This paper developes a semiautoregression (SAR) approach to estimate factors of the arbitrage pricing theory (APT) that has the advantage of providing a simple asymptotic variance-covariance matrix for the factor estimates, which makes it easy to adjust for measurement errors. Using the extracted factors, I confirm the finding that the APT describes asset returns slightly better than the CAPM, although there is still some mispricing in the APT model. I find that not only are the factors “priced” by the market, but the factor premiums move over time in relation to business cycle variables.     

Arbitrage Pricing Theory and Utility Stock Returns

This paper presents some new evidence that Arbitrage Pricing Theory may lead to different and better estimates of expected return than the Capital Asset Pricing Model, particularly in the case of utility stock returns. Results for monthly portfolio returns for 1971–1979 lead to the conclusion that regulators should not adopt the single-factor risk approach of the CAPM as the principal measure of risk, but give greater weight to APT, whose multiple factors provide a better indication of asset risk and a better estimate of expected return.     

International Arbitrage Pricing Theory: An Empirical Investigation

In this paper, we test the arbitrage pricing theory (APT) in an international setting. Inter-battery factor analysis is used to estimate the international common factors and the Chow test is used in testing the validity of the APT. Our inter-battery factor analysis results show that the number of common factors between a pair of countries ranges from one to five, and our cross-sectional test results lead us to reject the joint hypothesis that the international capital market is integrated and that the APT is internationally valid. Our results, however, do not rule out the possibility that the APT holds locally or regionally in segmented capital markets. Finally, the basic results of both the inter-battery factor analysis and the cross-sectional tests are largely invariant to the numeraire currency chosen.     

A Multivariate Linear Regression Test for the Arbitrage Pricing Theory

A test for the arbitrage pricing theory which employs a multivariate linear regression model is developed. Given a sample of return premiums for a set of N assets which includes a subset of k linearly independent portfolios, the k factor APT hypothesis is accepted if the intercept term is zero in the multivariate regression of the $(N?k)$ returns on the k portfolios. The test may be carried out simply, by using univariate multiple regression software. The relation of this test to the concept of performance potential and Sharpe's measure of performance is also discussed. If the performance potential of the k portfolios is not significantly less than the performance potential of the complete set of N assets, then the k factor APT hypothesis is accepted.     

On Testing the Arbitrage Pricing Theory: Inter-Battery Factor Analysis

This paper tests the Arbitrage Pricing Theory (APT) by estimating the factor loadings that are consistent between two industry groups of securities. One of the pitfalls in the study by Roll and Ross is that the factors estimated in one group may not be the same with the factors estimated in another group. This raises some concerns on the acceptability of their conclusions. For our study, we employ inter-battery factor analysis which enables us to estimate factor loadings by constraining the factors to be the same between two different groups. Our results show that there seem to be five or six inter-group common factors that generate daily returns for two industry groups of securities, and these inter-group common factors do not seem to depend on the size of groups. Also, based on our cross-sectional tests on the risk premia, we conclude that the APT should not be rejected.     

The Arbitrage Pricing Theory: Is it Testable?

This paper challenges the view that the Arbitrage Pricing Theory (APT) is inherently more susceptible to empirical verification than the Capital Asset Pricing Model (CAPM). The usual formulation of the testable implications of the APT is shown to be inadequate, as it precludes the very expected return differentials which the theory attempts to explain. A recent competitive-equilibrium extension of the APT may be testable in principle. In order to implement such a test, however, observation of the return on the true market portfolio appears to be necessary.     

A Critical Reexamination of the Empirical Evidence on the Arbitrage Pricing Theory

This paper demonstrates that the Roll and Ross (RR) and other previously published tests of the APT are subject to several basic limitations. There is a general nonequivalence of factor analyzing small groups of securities and factor analyzing a group of securities sufficiently large for the APT model to hold. It is found that as one increases the number of securities, the number of “factors” determined increases. This increase in the number of “factors” with larger groups of securities cannot readily be explained by a distinction between “priced” and “nonpriced” risk factors as it is impermissible to carry out tests on whether a given “risk factor is priced” using factor analytic procedures.     

Joint Estimation of Factor Sensitivities and Risk Premia for the Arbitrage Pricing Theory

The APT is represented as a multivariate regression model with across-equations restrictions. Both observed and unobserved (latent) macroeconomic factors are included, thus generalizing and unifying two previous strands of literature. Large portfolios representing unobserved factors are treated as endogenous, and nonlinear 3SLS estimates are shown to differ sharply from estimates that ignore this endogeneity. Using monthly stock returns and six factors, we cannot reject January effects. The following results are invariant with respect to the inclusion of January effects: we reject the CAPM in favor of the APT; however, we cannot reject the APT restrictions on the linear factor model.     

An Examination of UK Unit Trust Performance within the Arbitrage Pricing Theory Framework

This paper examines the performance of a sample of 101 United Kingdom unit trusts within an Arbitrage Pricing Theory framework and considers the relationship between performance and the investment objective, size and expenses of the trusts. Also, portfolio strategies using past trust performances to rank the trusts fails to generate significant abnormal returns relative to two different benchmark portfolios.     

No Arbitrage and Arbitrage Pricing: A New Approach

We argue that arbitrage-pricing theories (APT) imply the existence of a low-dimensional nonnegative nonlinear pricing kernel. In contrast to standard constructs of the APT, we do not assume a linear factor structure on the payoffs. This allows us to price both primitive and derivative securities. Semi-nonparametric techniques are used to estimate the pricing kernel and test the theory. Empirical results using size-based portfolio returns and yields on bonds reject the nested capital asset-pricing model and linear APT and support the nonlinear APT. Diagnostics show that the nonlinear model is more capable of explaining variations in small firm returns.     

Simulating and Forecasting Utility Stock Returns: Arbitrage Pricing Theory vs. Capital Asset Pricing Model

Just when the capital asset pricing model (CAPM) has become accepted by public utility regulators as a method for estimating a utility's screening rate, academic criticism of the model's theoretical and empirical shortcomings has led to empirical testing of the alternative arbitrage pricing theory (APT). This paper expands on recent APT-CAPM performance comparisons by simulating returns of public utility stocks using versions of both models, as was done by Bower, Bower, and Logue in a 1984 paper. In addition, the models are used for ex-post forecasting of returns in a subsequent time period. The Litzenberger-Ramaswamy method is used to correct for errors-in-variables in the CAPM cross-sectional equation. This allows for estimating the security market line using firm betas. The same methodology is used in the APT stages. Three different criteria—the Theil inequality, the sources of mean square error, and Chen's estimated weights of expected return-are used to compare CAPM and APT simulation and forecasting of the equity screening rates. Tested on a sample of 128 public utility companies, results show that neither model is clearly dominant. There is a tendency for reversal of performance. The model that is superior for simulating returns tends to be inferior for forecasting them, and vice-versa.     

Exact Arbitrage Pricing and the Minimum-Variance Frontier

The author examines the relationship between the Arbitrage Pricing Theory of Ross and mean-variance analysis. In particular, conditions are derived on the vector of the factor risk premia that are equivalent to the existence of a strictly positively weighted portfolio on the minimum-variance frontier. Also, a sufficient condition is given under which the existence of a positive minimum-variance portfolio of all the assets in the economy will imply the existence of a positive minimum-variance portfolio on a subset. This means that rejection of the hypothesis of the existence of a positive minimum-variance portfolio on a subset satisfying this condition implies rejection for the whole set.     

On the Number of Factors in the Arbitrage Pricing Model

Recent theory has demonstrated that the Arbitrage Pricing Model with K factors critically depends on whether K eigenvalues dominate the covariance matrix of returns as the number of securities grows large. The purpose of this paper is to test whether sample covariance matrices can be characterized as having K large eigenvalues. Using all available data on the 1983 CRSP tapes, we compute sample covariance matrices of returns in sequentially larger portfolios of securities. Analyzing their eigenvalues, we find evidence that one eigenvalue dominates the covariance matrix indicating that a one-factor model may describe security pricing. We also find that, for values of K larger than one, there is no obvious way to choose the number of factors. Nevertheless, we find that while only the first eigenvalue dominates the matrix, the first five eigenvalues are growing more distinct.