The residual market factor,the APT,and mean-variance efficiency

The rapidly increasing volume of both published and unpublished work on the arbitrage pricing theory (APT) of Ross (1976) has given rise to a number of misunderstandings at the interface of theoretical and econometric work. In this article we extend the theoretical structure of our previous work (McElroy and Burmeister, 1985, 1988; Burmeister and McElroy, 1987, 1988) to provide a broad yet rigorous framework both for econometric estimation and for better economic interpretation of new empirical results. We begin with the case where allK factors are observed, and then present the second case ofK−1≡J observed APT factors and one unobserved factor, theresidual market factor introduced in McElroy and Burmeister (1985). The economic interpretations for equivalent specifications of this model are discussed, and we enumerate several immediate payoffs to these specifications. The main new results are concerned with the sometimes intricate relationships among APT models withK factors and APT models withK factors that are constrained to satisfy mean-variance efficiency restrictions. These results are not only of theoretical interest, but more importantly they provide the basis for econometric estimation and testing of nested hypotheses. These econometric issues are discussed in detail.     

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.     

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.     

Share Prices and Macroeconomic Factors

The APT with macroeconomic factors put forward by Chen, Roll and Ross (1986) was tested using monthly Australian sectoral share-price indexes for 1980–1994. The inflation rate was found to be consistently priced. The significance of other factors was found to depend on the choice of sample period and estimation method. The model was compared to both an APT with artificial factors and the CAPM. Both versions of the APT were found to clearly out-perform the CAPM but neither version of the APT was clearly superior to the other in terms of both within- and out-of-sample explanatory power.     

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.     

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.     

Estimating the Model for Seasoned Equity Offering Underpricing: Application to the Chinese Financial Market

We estimate the binomial probit model to examine the significance of important explanatory variables documented in seasoned equity offering (SEO) underpricing literature using two statistical approaches: maximum likelihood estimation and Bayesian estimation. In particular, our estimation relies on SEO-related data in the Chinese financial market, where the pricing mechanism is less transparent compared to that in the U.S. market. We find that the signs of coefficients for the explanatory variables in each model are not different, but their magnitudes appear to be different. Our finding also shows that estimation results are generally consistent with the results observed in the U.S. market.     

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.     

An intertemporal equilibrium beta pricing model

This article develops an intertemporal, discrete-time, competitiveequilibrium version of the arbitrage pricing theory, (APT) andexplores the econometric implications of this model under variousrestrictions on investor preferences and on the dynamic behaviourof dividends. We describe conditions under which the econometrictechnique typically used for estimating and testing the APTcan be shown to be consistent with our economic model. We relateour intertemporal version of the APT to the static APT and toMerton's intertemporal capital asset pricing model.     

Semiparametric estimation of a characteristic-based factor model of common stock returns

We introduce an alternative version of the Fama–French three-factor model of stock returns together with a new estimation methodology. We assume that the factor betas in the model are smooth nonlinear functions of observed security characteristics. We develop an estimation procedure that combines nonparametric kernel methods for constructing mimicking portfolios with parametric nonlinear regression to estimate factor returns and factor betas simultaneously. The methodology is applied to US common stocks and the empirical findings compared to those of Fama and French.     

Arbitrage Asset Pricing under Exchange Risk

This paper extends the APT to an international setting. Specifying a linear factor return-generating model in local currency terms, we show that the usual risk-diversification rule in the APT does not yield a riskless portfolio unless currency fluctuations obey the same factor model as asset returns. We then consider an arbitrage portfolio whose exchange risk is hedged by foreign riskless bonds. Under the resulting no-arbitrage conditions, the expected returns are not on the same hyperplane, unlike the closed-economy APT, unless they are adjusted by the cost of exchange risk hedging.     

Notes on dynamic factor pricing models

These notes discuss three aspects of dynamic factor pricing (i.e., APT) models. First, the diversifiable component of returns is unpredictable in a no-arbitrage world. Second, conditional factor loadings or betas have an unconditional factor structure when returns follow an unconditional factor structure, which provides a link between conditional and unconditional factor pricing models. Third, the estimation of dynamic factor pricing models is easily simplified in large cross sections when returns follow an unconditional factor structure. These results aid in the interpretation of existing applications and identify some of the issues in the formulation and estimation of dynamic factor pricing models.     

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 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.     

New Tests of the APT and Their Implications

This paper provides new tests of the arbitrage pricing theory (APT). Test results appear to be extremely sensitive to the number of securities used in the two stages of the tests of the APT model. New tests also indicate that unique risk is fully as important as common risk. While these tests have serious limitations, they are inconsistent with the APT.     

The Estimation of Systematic Risk under Differentiated Risk Aversion: A Mean-Extended Gini Approach

This paper examines a mean-Gini model of systematic risk estimation that resolves some econometric problems with mean-variance beta estimation and allows for heterogeneous risk aversion across investors. Using the mean-extended Gini (MEG) model, we estimate systematic risks for different degrees of risk aversion. MEG betas are shown to be instrumental variable estimators that provide econometric solutions to biases generated by the estimation of mean-variance (MV) betas. When security returns are not normally distributed, MEG betas are proved to differ from MV betas. We design an econometric test that assesses whether these differences are significant. As an application using daily returns, we estimate MEG and MV betas for U.S. securities.     

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.     

Some comments on the APT

Abstract

The paper reviews some aspects of arbitrage pricing theory (APT). It derives an improved version of the model and examines it in view of the APT debate, adding some new observations in favour of the model. The topics examined include: (a) model testability; (b) implications of approximate APT pricing to Fama-Macbeth testing methodology; and (c) a comparison between APT pricing and approximate exact pricing.     

THE ARBITRAGE PRICING THEORY AND COST-OF-CAPITAL ESTIMATION: THE CASE OF ELECTRIC UTILITIES

Capital asset pricing model (CAPM) and alternative arbitrage pricing theory (APT) methodologies are used to estimate the cost of capital for a sample of electric utilities. The statistical factors APT method is found to produce significantly different estimates depending on the number of factors specified and the set of firms factor analyzed. The use of macroeconomic factors is explored, and it is shown that this methodology has advantages over the statistical factors APT and the market model.     

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.