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 MAGNITUDE OF PRICING ERRORS IN THE ARBITRAGE PRICING THEORY

In this paper the arbitrage pricing theory (APT) pricing errors for individual securities are estimated employing maximum likelihood factor analysis and Fama-MacBeth style aggregation. Results show that the pricing errors are large and statistically significant and that there is a high degree of variability in pricing errors across securities. This evidence contradicts the prevailing APT intuition that the pricing errors can be ignored as negligible. Pricing errors are also found to be related to residual variance and firm size.     

A note on factor analysis and arbitrage pricing theory

This paper examines some theoretical and empirical properties of factor analysis and spells out their implications for Arbitrage Pricing Theory (APT). Doubts on the appropriateness of conventional factor analytic procedures for testing APT are raised on theoretical as well as empirical grounds.     

Do Assumptions About Factor Structure Matter in Empirical Tests of the APT?

The effect of assumptions about factor structure on empirical tests of multifactor models such as the Arbitrage Pricing Policy Theory has received little attention in the literature. Using data on securities traded on the London Stock Exchange, we examine whether returns are best described by an approximate factor structure and whether assumptions about correlations across idiosyncratic returns have a significant impact on estimated prices of risk and their significance. Our findings suggest that returns are best described by an approximate factor structure and, if this is taken into account when empirically testing the APT, six factors carry significant prices of risk. However, if a strict factor structure is imposed, no factors carry significant prices of risk. These findings suggest that assumptions about factor structure matter in empirically testing the APT.     

Yes,The APT Is Testable

The Arbitrage Pricing Theory (APT) has been proposed as an alternative to the mean-variance Capital Asset Pricing Model (CAPM). This paper considers the testability of the APT and points out the irrelevance for testing of the approximation error. We refute Shanken's objections, including his assertion that Roll's critique of the CAPM is applicable to the APT. We also explain the testability of the APT on subsets, and we explore the relationship between the APT and the CAPM.     

The attributes,behavior, and performance of U.S. mutual funds

This article examines the risk and return characteristics of U.S. mutual funds. We employ an equilibrium version of the Arbitrage Pricing Theory (APT) and a principal-components-based statistical technique to identify performance benchmarks. We also consider the Capital Asset Pricing Model (CAPM) as an alternative. We implement a procedure for overcoming the rotational indeterminacy of factor models. This procedure is a hybrid of statistical factor estimation and prespecification of factors. We estimate measures of timing ability for the CAPM and extend it to the APT. We find that this timing test is misspecified due to noninformation-based changes in mutual fund betas. We develop a modification of the timing measure that, under certain conditions, distinguishes true timing ability from noninformation-based beta changes.     

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.     

Reference Variables,Factor Structure,and the Approximate Multibeta Representation

The Arbitrage Pricing Theory (APT) implies that if asset returns have a factor structure, then an approximate multibeta representation holds with respect to the factors as reference variables. This paper assumes that asset returns satisfy a factor structure and derives a condition under which the approximate multibeta representation holds with respect to a set of reference variables which may not be the factors. This condition is that the regression matrix of the reference variables on the factors is nonsingular. Implications for the testability of the APT are also discussed.     

An Empirical Test of the Arbitrage Pricing Theory on Australian Stock Returns 1974-85

This paper examines empirically, issues concerning the Arbitrage Pricing Theory (APT). Firstly, in the spirit of Chamberlain and Rothschild [1983], the existence of an approximate factor structure is explored. Secondly, following Beggs [1986] and employing a principal components approach, a test of arbitrage pricing and the importance of the error of approximation, is conducted. Finally, using a non nested framework, the APT and CAPM are tested against each other. The results show mixed support for the APT having up to 3 priced factors.     

Alternative Models for Estimating the Cost of Equity Capital for Property/Casualty Insurers

This paper estimates the cost of equity capital for Property/Casualty insurers by applying three alternative asset pricing models: the Capital Asset Pricing Model (CAPM), the Arbitrage Pricing Theory (APT), and a unified CAPM/APT model (Wei (1988). The in-sample forecast ability of the models is evaluated by applying the mean squared error method, the Theil U2 (1966) statistic, and the Granger and Newbold (1978) conditional efficiency evaluation. Based on forecast evaluation procedures, the APT and Wei's unified CAPM/APT models perform better than the CAPM in estimating the cost of equity capital for the PC insurers and a combined forecast may outperform the individual forecasts.     

An explicit bound on individual assets' deviations from APT pricing in a finite economy

Ross's Arbitrage Pricing Theory (APT) is a tractible and reasonable alternative to the mean-variance model. Nonetheless, understanding of the theory has been obscured by the complexity of the sequence economy models used for motivation. By contrast, we give a simple and direct derivation of the APT in a finite economy. Using an explicit bound on the deviations from APT prices across assets, a coarse calculation shows that theoretical deviations from APT pricing are negligible in our economy.     

Stock Return Anomalies and the Tests of the APT

This paper shows that the empirical tests of the Arbitrage Pricing Theory (APT) model are very sensitive to the anomalies observed in January in the stock returns data. There is a strong seasonal pattern in the estimates of the risk premia from the APT model. The most important implication of the findings in this paper is that the APT model can explain the risk-return relation mostly for January. Once the January returns are excluded from the data, there is no significant relation between the expected stock returns and the risk measures predicted by the APT model.     

An empirical examination of the implications of arbitrage pricing theory

This paper presents a comprehensive set of tests of the implications of the Arbitrage Pricing Theory. We find, unlike previously reported results, a very limited relationship between the expected returns and the covariance (factor loadings) measures of risk. Furthermore, unique variance measures of risk, while generally making only small contributions to the explanation of asset returns, turn out to be significant about as frequently as the coveriance measures of risk — which is inconsistent with the Arbitrage Pricing Theory model. The intercept tests are more mixed but provide only limited support to the model.     

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.     

Temperature shocks and the cost of equity capital: Implications for climate change perceptions

Financial market information can provide an objective assessment of losses anticipated from temperature changes. In an APT model in which temperature shocks are a systematic risk factor, the risk premium is significantly negative, loadings for most assets are negative, and asset portfolios in more vulnerable industries have stronger negative loadings on a temperature shock factor. Weighted average increases in the cost of equity capital attributed to uncertainty about temperature changes are 0.22 percent, implying a present value loss of 7.92 percent of wealth. These costs represent a new channel that may contribute to cost of climate change assessment.     

Sequential Tests of the Arbitrage Pricing Theory: A Comparison of Principal Components and Maximum Likelihood Factors

We examine the cross-sectional pricing equation of the APT using the elements of eigenvectors and the maximum likelihood factor loadings of the covariance matrix of returns as measures of risk. The results indicate that, for data assumed stationary over twenty years, the first vector is a surprisingly good measure of risk when compared with either a one- or a five-factor model or a five-vector model. We conclude that in some circumstances principal components analysis may be preferred to factor analysis.     

Multifactor Asset Pricing Models

Since the early 1960s, the mean-variance Capital Asset Pricing Model (CAPM) has been a dominant paradigm in modern finance. Recently, the accumulation of anomalous evidence, and a realisation that empirical tests of the model are tautologically related to the efficiency of the market index, have pushed that paradigm to a point of crisis. This paper reviews alternative asset pricing models which coexisted with the CAPM and may provide plausible substitutes. The major distinguishing feature of these models is that they predict multiple risk factors and, with the exception of the Arbitrage Pricing Theory (APT), are extensions of the CAPM.     

Estimation of the underlying structure of systematic risk with the use of principal component analysis and factor analysis

We present an improved methodology to estimate the underlying structure of systematic risk in the Mexican Stock Exchange with the use of Principal Component Analysis and Factor Analysis. We consider the estimation of risk factors in an Arbitrage Pricing Theory (APT) framework under a statistical approach, where the systematic risk factors are extracted directly from the observed returns on equities, and there are two differentiated stages, namely, the risk extraction and the risk attribution processes. Our empirical study focuses only on the former; it includes the testing of our models in two versions: returns and returns in excess of the riskless interest rate for weekly and daily databases, and a two-stage methodology for the econometric contrast. First, we extract the underlying systematic risk factors by way of both, the standard linear version of the Principal Component Analysis and the Maximum Likelihood Factor Analysis estimation. Then, we estimate simultaneously, for all the system of equations, the sensitivities to the systematic risk factors (betas) by weighted least squares. Finally, we test the pricing model with the use of an average cross-section methodology via ordinary least squares, corrected by heteroskedasticity and autocorrelation consistent covariances estimation. Our results show that although APT is very sensitive to the extraction technique utilized and to the number of components or factors retained, the evidence found partially supports the APT according to the methodology presented and the sample studied.     

Factor pricing in a finite economy

Prior theoretical derivations of the Arbitrage Pricing Theory (APT) bound an aggregate measure of the deviation of mean asset returns from that predicted by a linear pricing equation. It is conceivable, given this bound, that some assets might be badly mispriced by the model. In this paper, a more intuitive derivation of the factor pricing equation is presented which describes the deviation on an asset by asset basis. The deviation is shown to be small for assets in a realistic finite economy and is arbitrarily close to zero for those assets with arbitrarily small size relative to aggregate wealth. It follows that the linear pricing equation provides a good approximation for the mean returns of all traded assets.     

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.