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.     

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.     

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.     

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.     

Measuring the pricing error of the arbitrage pricing theory

This article provides an exact Bayesian framework for analyzingthe arbitrage pricing theory (APT). Based on the Gibbs sampler,we show how to obtain the exact posterior distributions forfunctions of interest in the factor model. In particular, wepropose a measure of the APT pricing deviations and obtain itsexact posterior distribution. Using monthly portfolio returnsgrouped by industry and market capitalization, we find thatthere is little improvement in reducing the pricing errors byincluding more factors beyond the first one.     

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 Seasonal Stability of the Factor Structure of Stock Returns

This paper investigates the month-by-month stability of (a) daily returns and correlation coefficients of stock returns, (b) correlation and covariance matrices, (c) number of return-generating factors, and (d) the APT pricing relationship. The results show that there is a January effect and a small-firm effect in stock returns. Correlation matrices are more stable than covariance matrices, but both types of matrices are not stable across months and across the sample groups. The number of return-generating factors is rather stable most of the time and for most of the sample groups, but there is some significant instability that is related to the average correlation coefficients among stocks. The APT pricing relationship does not seem to be supported by the two-stage process using the maximum-likelihood factor analysis.     

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.     

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.     

AN INVESTIGATION INTO THE ROLE OF THE MARKET PORTFOLIO IN THE ARBITRAGE PRICING THEORY

This paper investigates the role of the market portfolio in the arbitrage pricing theory (APT). We show that if the multifactor return-generating process put forth in the APT is valid, then unexpected deviations in the return on the market portfolio must be completely explained by unexpected deviations in the underlying return-generating factors. As well, market betas are developed as a combination of return-generating factor sensitivity coefficients. These results lead us to conclude that an empirically significant “market factor’ is evidence of omitted return-generating factors, rather than evidence that the market is a factor. Finally, results obtained when market betas are regressed against factor sensitivity coefficients are consistent with these insights. The results suggest that there are at least three return-generating factors. This evidence does not rely on ex post pricing of estimated factors.     

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.     

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.     

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.     

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.     

Equity prices and fundamentals: a DDM–APT mixed approach

This paper focuses on the linkage between equity prices and fundamentals for 27 individual shares belonging to the French stock price index (CAC40). To assess fundamental value, the traditional dividend discount model (DDM) is coupled with the arbitrage pricing theory (APT), which assumes that investors hold efficient portfolios. This yields a simple equity valuation relationship for which the APT determines the long-term risk premium included in the DDM. Accordingly, equity risk premia are determined by common factors reflecting the non diversifiable risk. These factors are not a priori identified by the theory, and therefore must be exhibited through an empirical analysis. Four domestic and three international common factors are found, all being among those identified by empirical analyses of the APT in the literature. While studies related to stock price indices showed that DDM fundamental values are very smooth compared to stock indices, our DDM–APT model reproduces both trends and major fluctuations of share prices. Further, as for studies based on stock indices, a mean-reverting process of equity prices towards fundamentals is highlighted, but the linear error correction model that was considered contains shortcomings suggesting a more complex adjustment process.     

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.     

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.     

Fundamental Economic Variables,Expected Returns,and Bond Fund Performance

In this article, we develop relative pricing (APT) models that are successful in explaining expected returns in the bond market. We utilize indexes as well as unanticipated changes in economic variables as factors driving security returns. An innovation in this article is the measurement of the economic factors as changes in forecasts. The return indexes are the most important variables in explaining the time series of returns. However, the addition of the economic variables leads to a large improvement in the explanation of the cross-section of expected returns. We utilize our relative pricing models to examine the performance of bond funds.     

Deriving the arbitrage pricing theory when the number of factors is unknown

This paper examines the use of proxies (or reference variables) for the true factors in the arbitrage pricing theory (APT). It generalizes other authors' existing work and shows that, when there are more reference variables than the true factors, the APT still holds. The possibility of fewer reference variables than the true factors is also considered, but the APT is not shown to hold, in the same sense, for this case. This work builds on an earlier paper by Ingersoll (Ingersoll J 1984 J. Finance 39 1021-39), and our propositions can be thought of as specializations of his theorems. Similar to Nawalkha (Nawalkha S 1997 J. Financial Economics 46 357-81), our work does not use the mathematics of Hilbert and Banach spaces and, thus, is open to a much wider audience. The practical implication of our results is that model builders should be generous with the number of factors they use, as excessively parsimonious models suffer from inaccuracy.     

Government Bond Returns,Measurement of Interest Rate Risk,and the Arbitrage Pricing Theory

Empirical tests are reported for Ross' arbitrage pricing theory using monthly data for U.S. Treasury securities during the 1960–1979 period. We find that mean returns on bond portfolios are linearly related to at least two factor loadings. Multivariate test results, however, are not consistent with the APT. Our sample data in the U.S. Treasury securities market are also not consistent with either version of the CAPM. One-month-ahead forecasts of excess returns using factor-generating models are compared with corresponding naive predictions or predictions using the “market model” with various market portfolios.