an empirical examination of the implications of arbitrage pricing theory abstract 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

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

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 arbitrage pricing theory apt as originally developed by ross 22 23 is built on the twin assumptions of no arbitrage opportunities in the capital market and a linear relationship between actual returns and k common factors the principal hypothesis of the model is that expected returns should be linearly related to the weights of the common factors in the assumed linear process in every test of the model the focus has been to use factor analysis to extract k factors from sample covariance matrices and then to test the hypothesis by regressing returns or average returns against the factor loadings of the common factors most previous tests have either assumed that the number of factors is equal to some predetermined number or have estimated k simultaneously with estimation of the factor loadings thus existing tests of the apt are joint tests of the apt pricing result and an assumed or estimated number of factors the question of how many factors are important has not been addressed separately from the pricing tests because the apt pricing result is the significant prediction of a theory which has little to say about the value of k nevertheless crosssection linear models have been a central part of financial economics and it is clearly important to know at least the approximate number of factors which will be significant in such regressions particularly given the computational difficulties of large scale factor analysis furthermore dhrymes friend and gultekin 6 report that the number of factors needed for standard chi squared tests increases university at buffalo suny i am in debt to donald bosshardt gary chamberlain thomas ho richard roll lemma senbet mark zmijewski and the participants in finance workshops at the universities of michigan wisconsin and buffalo for their extensive comments nevertheless i am solely responsible for what remains this paper would not have been started without the unselfish cooperation of jay leavitt director of academic computing university at buffalo suny who designed the eigenvalue algorithm which i used i am also grateful for partial financial support and lavish computer funds from the school of management and for the expert programming assistance provided by ravi shukla

a note on factor analysis and arbitrage pricing theory abstract 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

arbitrage pricing with estimation risk this paper considers the arbitrage pricing theory when investors have incomplete infor mation on the parameters generating asset returns each asset in the economy may have a different amount of information available on it bayesian investors use their prior beliefs in conjunction with the total available information to assign an expected return and a set of factor betas to each asset the assigned expected returns are shown to be linear in their associated factor betas however the factor betas and prices of assets differ from those under complete information specifically risky assets with high low information are priced relatively higher lower on the other hand factor betas of high low information assets are relatively lower higher the analysis has econometric implications for testing the apt in this paper s framework maximum likelihood estimates of factor betas which are based on normality assumptions are too high low for high low information assets in addition sequentially increasing the sample size by adding new securities to a factor analysis procedure can result in the detection of apparent additional priced factors when they do not really exist

assessing the financial performance of forestry related investment vehicles capital asset pricing model vs arbitrage pricing theory capital asset pricing model capm and arbitrage pricing theory apt are used to assess the financial performance of eight forestry related investment vehicles although results from apt support previous findings from capm about timberland investments three bodies of evidence show that apt findings are more robust the major conclusions are a institutional timberland investments and timberland limited partnerships have a low risk level and excess returns b forestry industry companies have not earned risk adjusted returns and the performance of medium forest industry firms is worse than that of large firms c stumpage price does not resemble the return generation process of timberland investments and d lumber futures have little excess return copyright 2001 oxford university press

the collapse of purchasing power parities during the 1970 s one of the striking facts concerning the relationship beiveen prices and exchange rates during the 1970 s has been the dismal performance of the predictions of the simple versions of the purchasing power parity doctrine ppp that doctrine in its absolute version states that the equilibrium exchange rate between domestic and foreign currencies equals the ratio of domestic to foreign price levels the relative version of the doctrine relates equilibrium changes in exchange rates to changes in the ratio of domestic to foreign prices during the 1970 s short run changes in exchange rates bore little relationship to short run differentials in national inflation rates and frequently divergences from purchasing power parities have been cumulative this paper reviews and analyzes the empirical record of exchange rates and prices during the 1970 s and the analysis is based on the experience of the dollar pound the dollar frecch franc and the dollar dm exchange rates section 2 presents the evidence on ppp during the 1970 s and contrasts it with the evidence from the 1920 s a period during which the doctrine held up reasonably well this analysis is relevant for assessing whether the flexible exchange rate system was successful in providing national economies with an added degree of insulation from foreign shocks and whether it provided policymakers with an added instrument for the conduct of macroeconomic policy the evidence regarding devia tions from purchasing power parities is also relevant for determining whether there is a case for managed float section 3 attempts to explain what went wrong with

some results in the theory of arbitrage pricing this paper derives a stronger version of huberman s recent preference free pricing theorem this pricing result relates the expected return on an asset to its factor responses and the covariance structure of the residuals from a linear factor model it must characterize any infinite asset economy in which no arbitrage opportunities are present whether or not the factor model has uncorrelated residuals this result provides the intuition for the role of residual risk in the pricing model and eliminates some classes of arbitrage opportunities still present under huberman s bound some applications to empirical tests and performance measurement are also discussed the arbitrage pricing theory is one of several financial pricing models which attempts to explain the cross sectional variation in expected returns on assets in certain respects it is similar to the capital asset pricing model but there are both substantive and subtle differences one of the key advantages of the apt is that it derives a simple linear pricing relation approximating that in the capm without some of the latter s objectionable assumptions perhaps the key disadvantage of the apt is that it provides no clues as to what might be important factors nor as to how to interpret the factor premiums which appear in the pricing equation this paper serves several purposes after reviewing the linear factor model formulation in section i it derives in section ii a stronger version of huberman s 9 recent preference free pricing theorem this pricing result relates the expected return on an asset to its factor responses and the covariance structure of the residuals this relation must characterize any infinite asset economy in which no arbitrage opportunities are present whether or not a linear factor model with uncorrelated residuals is the appropriate returns generating mechanism section iii specializes this result by eliminating the effects of residual covariances and compares the results here to those of previous apt models when applied to the standard linear factor model with uncorrelated residuals this new pricing bound eliminates arbitrage opportunities which remain under huberman s bound this result also provides for the first time the intuition for the role of residual risk in the approximate pricing relation section v provides an interpretation of the factor premiums and gives a valid asset pricing model interpretation to the apt which is consistent with merton s

treasury yield curves and cointegration previous studies find that there is only one common stochastic trend in a set of interest rate series the result is interpreted as the evidence for supporting the expectations hypothesis cf hall et al 1992 this study finds that there are three common stochastic trends when whole spectrum stucture is analysed the three common stochastic trends can be interpreted as the shift the slope and the curvature of the term structure

stable factors in security returns identification using cross validation recent papers in financial research focus on identifying a stable factor structure for security returns the likelihood ratio test typically is used to determine the number of factors from exploratory factor analysis models in this article we consider the use of cross validation to identify a stable factor structure in security returns when applied to actual stock return data cross validation identifies a smaller number of stable factors than the likelihood ratio test in groups of 30 60 randomly selected securities cross validation suggests one dominant factor whereas the likelihood ratio test identifies from four to six factors furthermore when groups are designed to highlight industry or size effects the discovery of more than one dominant factor is problematic even if there are multiple economic factors generating stock returns they may be difficult to disentangle if the underlying factors tend to be correlated

the relation between mean variance efficiency and arbitrage pricing the mean standard deviation diagram has proven to be a valuable tool for understanding equilibrium asset pricing theory first introduced by markowitz 1952 1959 and tobin 1958 the diagram helps students and researchers alike to develop intuition about the capital asset pricing model capm its properties are useful for analyzing the conditions under which the market portfolio is mean variance efficient and for linking the location of the market portfolio in the diagram with the validity of the capm in addition its simple geometry seems to be the critical inspiration for roll s 1977 argument that the capm cannot feasibly be tested because the market portfolio is unobservable and because of a mathematical equivalence between the individual return beta linearity relation and the market portfolio s mean variance efficiency p 129 recent research on equilibrium asset pricing both theoretical and empirical has tended to focus on multibeta pricing models especially the arbitrage pricing theory apt this paper will show that the simple intuition derived from the

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 in roll and ross rr 10 an empirical investigation of the ross 11 arbitrage theory of pricing apt was carried out the central core of the apt as outlined in rr is that the return generating process for a population of n assets is a linear function of only a few say k k n systematic factors or components and as a consequence many portfolios are close substitutes the central conclusion of the apt is that the mean premium return vector lies in a k dimensional subspace spanned by the factor loadings the purpose of the empirical investigation as claimed by rr was to investigate the existence of the factors and their association with the risk premia as stressed by rr their methodology does not determine k but is designed to test the hypothesis that there exist several factors whose factor loadings together explain a significant portion of the variation in the mean premium returns the empirical results in rr however indicate the presence of three to four priced factors the first empirical test outlined by rr involves two steps using time series data the mean return premium vector is estimated and a factor analysis procedure is used to estimate the k factors and their loadings a complex weighted least squares procedure is then used to estimate the linear model relating the mean return premium vector to the factor loadings the weighted least squares procedure requires estimation of the matrix of weights and is carried out for t 1 2 t cross sections in this paper the central conclusion of the apt is shown to be equivalent to a statement about the intercept term in the multivariate regression function of a

an empirical investigation of international asset pricing we investigate several asset pricing models in an international setting we use data on a large number of assets traded in the united states japan the united kingdom and france the models together with the hypothesis of capital market integration imply testable restrictions on multivariate regressions relating asset returns to various benchmark portfolios we find that multifactor models tend to outperform single index models in both domestic and international forms especially in their ability to explain seasonality in asset returns we also find that the behavior of the models is affected by changes in the regulatory environment in international markets

an international comparison of prices and exchange rates a new test of purchasing power parity abstract this paper introduces a new approach based on divisia index numbers to test ppp with both short run and long run data for all major currencies simultaneously the short run results indicate that the predictions of ppp do not hold up at all well on the other hand however the long run data are quite consistent with the ppp hypothesis the results also identify five years as a broad measure of the length of the long run insolar as ppp is concerned

some empirical tests in the arbitrage pricing theory macro variables vs derived factors abstract this study investigates the ability of two models based on the arbitrage pricing theory apt to predict portfolio returns over the period 1971 1986 the difference between the two models lies in the factors used in the factor loading model flm the factors are produced by factor analysis and are thus unspecified in the macroeconomic variable model mvm the factors are defined as innovations in a set of macrovariables the two approaches are compared in several different ways observed differences in test results between the two models are generally relatively small given some attractive features of the mvm such as economically interpretable factors this finding is encouraging and suggests that factor analysis may be unnecessary in implementing the apt

system identification in noisy data environments an application to six asian stock markets abstract this paper analyzes the systematic relationship between the stock market valuations the nominal gdps and the interest rates of six asian countries using not single equation regression but an alternative methodology based on complete multidirectional least squares projections in the tradition of frisch 1934 we compare the results with the spectral analysis of the information matrices and determine the noise levels the objective is to extract the multidimensional economic system structures from the noisy empirical observations this complete methodology sharply contrasts with the incomplete methodology of fama fama e f 1990 stock returns expected returns and real activity journal of finance 45 1089 1108 and schwert schwert g w 1990 stock returns and real activity a century of evidence journal of finance 45 1237 1257 etc who presume planal relations fit them to the multidimensional data by only one prejudiced unidirectional projection thereby ignoring between 75 and 92 of the available covariance information and not publishing all possible model projections the results in this paper show that the analyzed countries are better analyzed using such complete multidirectional ls projections even though the analysis is combinatorially much more complex all six asian financial economic systems are high data noise environments in which it is very difficult to separate the systematic signals from the noise because of these high noise levels spectral analysis is very unreliable we identify taiwan s stock market economy and financial market to be rationally coherent in contrast malaysia singapore philippines and indonesia show only partially coherent systems while no coherent system can be identified among japan s data

price regulation in property liability insurance a contingent claims approach a discrete time option pricing model is used to derive the fair rate of return for the property liability insurance firm the rationale for the use of this model is that the financial claims of shareholders policyholders and tax authorities can be modeled as european options written on the income generated by the insurer s asset portfolio this portfolio consists mostly of traded financial assets and is therefore relatively easy to value by setting the value of the shareholders option equal to the initial surplus an implicit solution for the fair insurance price may be derived unlike previous insurance regulatory models this approach addresses the ruin probability of the insurer as well as nonlinear tax effects

a new approach to testing asset pricing models the bilinear paradigm we propose a new approach to estimating and testing asset pricing models in the context of a bilinear paradigm introduced by kruskal 18 this approach is both simple and at the same time quite general as an illustration we apply it to the special case of the arbitrage pricing model where the number of factors is pre specified the data appear to be generally in conflict with a five or seven factor representation of the model used by roll and ross 30 when we consider the number of replications of our test and the large number of observations on which it is performed the frequency with which we reject the three factor apm does not lead us to conclude that this model is unrepresentative of security returns further the rejection of the five and seven factor versions is to be expected if the three factor version is correct the paradigm gives insight into the appropriate specification of the model and suggests that there may be a small number of economy wide factors that affect security returns tests of asset pricing models on the basis of observed stock market data have represented a staple of the financial economics literature of the past twenty years the early work is reviewed in the famous paper by jensen 12 and papers by fama and macbeth 6 rosenberg and marathe 31 and roll and ross 30 there has been a great deal of confusion regarding what testable propositions are implied by these models see discussion in roll 29 in this paper we show that at a minimum all asset pricing models yet proposed imply a simple easily testable hypothesis which we refer to as the bilinear hypothesis while specific models may imply further testable propositions if the bilinear hypothesis is rejected the model is inconsistent with the data and should be rejected our test exploits the fact that the economic content of any equilibrium asset pricing model can be expressed in the form of a potentially refutable constraint on the set of parameters of the process generating security returns this constraint specifies that given a set of security specific characteristics there exists a linear relationship common across securities relating expected returns to these

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 the apt model as exposited by ross 17 18 and extended by huberman 9 has provided the basis of an extensive literature as for example brown and weinstein 1 chen 3 hughes 10 ingersoll 11 jobson 12 reinganum 15 roll and ross rr 16 and shanken 17 to mention but a few it has also been treated in a more general context by chamberlain and rothschild 2 our purpose here is not to comment on this collection of papers many of which are unpublished but to reexamine the evidence presented by rr and point out major pitfalls involved in the empirical methodology employed by them and others who have followed their lead rr claim that on theoretical and more importantly on empirical grounds arbitrage pricing theory apt is an attractive alternative to the capital asset pricing model capm the apt it is argued requires less stringent and presumably more plausible assumptions is more readily testable since it does not require the measurement of the market portfolio and may be better able to explain the anomalies found in the application of the capm to asset returns the acceptability of the apt like that of the capm or any other theory ultimately depends on its ability to explain the relevant empirical evidence our subsequent discussion will show that many of the prqblems associated with the capm are also present in the apt context and that its ability to explain the relevant empirical evidence is not markedly superior moreover it raises questions not only about the rr and related empirical investigations of the apt but also about the testability of that theory in the present state of the art a major part of the problem results from the necessity to break down the universe being analyzed through the apt model this is forced upon the investigator by the fact

the empirical foundations of the arbitrage pricing theory abstract this paper uses maximum likelihood factor analysis of large cross sections to examine the validity of the arbitrage pricing theory apt we are unable to explain the expected returns on firm size portfolios although we do explain the expected returns on portfolios formed on the basis of dividend yield and own variance where risk adjustment using the usual capm market proxies fails we also compare alternate versions of the apt and sharply reject the hypothesis that basis portfolios formed to mimic the factors span the mean variance frontier of the individual assets

top management s attention to discontinuous technological change corporate venture capital as an alert mechanism technological discontinuities pose serious challenges to top managers attention these discontinuities which often occur at the fringes of an industry are usually driven by innovative and often venture capital backed start ups creating new products and transforming existing industries in ways that are difficult for incumbent managers to understand against the backdrop of their existing cognitive schemata however failing to appreciate and embrace successful technological discontinuities might endanger incumbents very existence extending the attention based view we explore whether and how interorganizational relationships guide top managers attention either to or away from technological discontinuities we propose that homophilous relationships e g alliances with industry peers should exhibit a negative relationship with incumbents timely attention to technological discontinuities whereas heterophilous relationships e g with venture capitalists as a result of coinvestments should exhibit a positive relationship furthermore we hypothesize that the status of the partners strengthens the effect of homophilous and heterophilous relationships with the timely attention of top managers to technological discontinuities based on a longitudinal study of the incumbents in four information and communications technology industry sectors we find that heterophilous ties through corporate venture capital cvc coinvesting with high status venture capital firms exhibit a strong positive relationship with timely attention cvc when it connects senior management to high status venture capitalists through coinvestments has a special role in directing top managers attention to technological discontinuities and ensuing business opportunities implications for the understanding of the role of interorganizational ties as structural determinants of top managers attention are discussed

incorporating contemporaneous residual relationships for security prices abstract using a recent procedure developed by jalilvand and kryzanowski 1985 to capture the contemporaneous residual dependencies in a system of regression equations this paper tests the impact of such residual based relationships in explaining security prices utilizing a multi industry sample of securities over two non overlapping periods the empirical findings show that not only are these contemporaneous residual relationships statistically significant but their inclusion significantly improves the explanatory power of the underlying return generating model

multivariate proxies and asset pricing relations abstract a framework is developed in which inferences can be made about the validity of an equilibrium asset pricing relation even though the central aggregate in this relation is unobservable a multivariate proxy for the true market portfolio consisting of an equal weighted stock index and a long term government bond index is employed in an investigation of the sharpe lintner capm the empirical evidence suggests that we can reject the joint hypothesis that a capm is valid and b multiple correlation between the true market portfolio and proxy assets exceeds 0 7 connections to the equilibrium factor pricing literature are also explored

purchasing power parity in the 1920s and the 1970s a note abstract in a recent article of the european economic review frenkel 1981 claims that purchasing power parity ppp held farily well in the 1920s but collapsed in the 1970s frenkel s study does not include the swiss case the present paper aims to answer three questions 1 to what extend does the evidence of the 1920s and the 1970s support ppp for switzerland 2 is there a significant difference of price level and exchange rate behavior between the 1920s and the 1930s as claimed by frenkel and 3 is the swiss experience significantly different from that of the countries

the number of factors in security returns both factor analysis of security returns and the analysis of eigenvalues seem to indicate that a market factor explains the major part of security returns we find that such evidence is consistent with an economy where there are in fact k equally important priced factors eigenvalue analysis in the context of such an economy will lead an investigator to the false inference that the one important factor is the return on an equally weighted market index this paper examines a particular exact k factor economy where each of the k factors is priced and contributes equally on average to the variance of returns we show analytically that for such an economy the approximate factor solution identifies the first factor as the return on an equally weighted market index and would lead to the inference that the remaining h 1 factors are not priced using a cross section regression technology our particular model is consistent with existing empirical work that has studied the number of factors in security markets these results suggest an important caveat to the interpretation of approximate factor solutions in an apt or multibeta pricing context one might also infer a capm bias in tests of the apt using the factor analysis technology on a more positive note the results suggest a simple rotation of the factor analysis solution that will lead to more powerful tests of the asset pricing relations to motivate this study consider the fact that the single factor market model suggested by markowitz 1959 and developed by sharpe 1963 remains one of the most popular empirical models of the return generating process the widespread acceptance of this model owes much to the work of king 1966 through a seven factor analysis of return data he concludes that one factor explains a large percentage of the variance of stock prices a factor on which each security tends to weight positively he interpreted this result to mean that there exists a basic market factor in operation which has a major effect on all securities this work supported the development of empirical research into the capital asset pricing model the model has been extensively applied in the event study context

diversification of macroeconomic risk and international integration of capital markets the case of mexico this article tests the arbitrage pricing theory in the context of the unstable macroeconomic years in mexico 1977 87 using information on returns on assets available to domestic investors primarily stocks traded at the local stock exchange an attempt is made to ascertain the extent to which these assets have offered premia for a set of proposed sources of risk the pervasive factors that play an important role in asset pricing in mexico are unexpected inflation unexpected money growth innovations in the standard poor s 500 price series and innovations in the dollar oil price a residual market factor is obtained using the mcelroy and burmeister model given that these risks get premia over and above the riskless rate expected rates of return in mexico have been higher during the years of erratic macroeconomic conditions mexico is not considered to be well integrated with the international capital markets because local sources of risk such as inflation are not priced in the united states whereas international sources of uncertainty such as oil price shocks are priced locally but not in the united states capital markets are becoming increasingly important in developing countries because of the international debt problem it seems unlikely that semi industrial nations will be able to raise substantial amounts of funds in the international financial markets the development and growth of modern domestic capital markets will allow these economies to tap additional savings and to improve the allocation of scarce funds organized and liquid capital markets are a vital factor in promoting overall development they provide a means of allocating capital to alternative private and public projects and they furnish essential information for evaluating investment undertakings ross 1978 black 1988

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

risk and return abstract this paper examines the seasonality in the basic relationship between expected return and risk during 1935 82 the results reveal that the positive relationship between return and risk is unique to january the risk premiums during the remaining eleven months are not significantly different from zero

a simple approach to arbitrage pricing theory the following sections are included introductionarbitrage pricingdiscussionreferencesdiscussion notes on the arbitrage pricing theorypure arbitrage pricing theoryapproximate arbitrage and the aptapproximate factor modelsthe competitive equilibrium version of the aptconclusionnotereferences this abstract was borrowed from another version of this item

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

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 it is now a very well known phenomenon that stock returns exhibit a peculiar seasonal pattern while such a seasonal pattern in stock returns is an interesting phenomenon in itself and has yet to be fully explained there is a serious implication of the observed seasonality in stock returns on the tests of the assetpricing models 1 tinic and west 17 for example report that the risk return relation described by the capital asset pricing model capm also exhibits a similar seasonality in january a result rozeff and kinney 16 report as well more importantly however they show that only one month january shows a consistently positive and reliable relation between expected return and risk once the data for january are excluded from the analysis of the risk return tradeoff the estimates of risk premia are no longer reliably different from zero although tinic and west do not offer an explanation for their findings their results raise serious questions about the empirical tests of the capm and ultimately its validity as a viable model to explain the pricing of risky assets the purpose of this paper is to investigate the impact of stock return seasonality on the empirical tests of the arbitrage pricing theory apt a number of researchers argue on both theoretical and empirical grounds that the apt is a good alternative to the capm although there is a growing body of empirical literature on the apt the empirical tests of the apt thus far have produced inconclusive results and a good deal of controversy it now seems appropriate to

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 nume raire currency chosen numerous authors notably solnik 21 grauer litzenberger and stehle 11 and stulz 24 have derived various versions of the international asset pricing model iapm under alternative views of the structure of international capital markets however only a few serious attempts have been made to test various versions of the iapm these tests are largely inconclusive see solnik 20 and stehle 23 apart from the problem stressed by roll 16 of identifying the world market portfolio previous tests of the iapms suffer from the technical problem of aggregating assets of national investors using different numeraire currencies differences in the numeraire arise from differences in consumption baskets in an environment characterized by exchange rate uncertainty in a fruitful attempt to extend the arbitrage pricing theory apt of ross 18 to an international setting solnik 22 derives an international arbitrage pricing theory which is largely devoid of the aforementioned difficulties and thus more amenable to empirical testing 1 as shown by solnik testability of the apt in an

arbitrage pricing theory as a restricted nonlinear multivariate regression model iterated nonlinear seemingly unrelated regression estimates by replacing the unknown random factors of factor analysis with observed macroeconomic variables the arbitrage pricing theory apt is recast as a multivariate nonlinear regression model with across equation restrictions an explicit theoretical justification for the inclusion of an arbitrary well diversified market index is given using monthly returns on 70 stocks iterated nonlinear seemingly unrelated regression techniques are employed to obtain joint estimates of asset sensitivities and their associated apt risk prices without the assumption of normally distributed errors these estimators are strongly consistent and asymptotically normal with the additional assumption of normal errors they are also full information maximum likelihood estimators classical asymptotic nonlinear nested hypothesis tests are supportive of the apt with measured macroeconomic factors

data frequency and the number of factors in stock returns abstract determining the number of factors that explain stock returns plays an important role in empirical tests of the arbitrage pricing theory this paper examines the sensitivity of the number of factors to different data frequencies using daily weekly and monthly returns the empirical results are consistent with the null hypothesis that the number of factors is the same for different data frequencies once daily returns are adjusted for nonsynchronous trading the evidence also identifies only one or two factors

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 seasonality of common stock returns has received considerable attention in financial economics research studies by officer 23 rozeff and kinney 29 gultekin and gultekin 11 and others have investigated the stock returns of the u s and other countries on a monthly basis they generally have found that on average january returns are significantly higher than the returns for other months banz 1 and reinganum 25 26 have found abnormally high returns in small market value firms and keim 17 has related this to the first few trading days of january schwert 30 points out the current difficulty of explaining these empirical regularities and the need for further investigations several studies have examined seasonality in risk premiums rozeff and kinney 29 found that seasonality appeared in the risk premiums obtained from a twoparameter capm and that january displayed a relatively large risk premium compared with the other months keim 16 also found seasonality in the risk premiums more recently tinic and west 32 examined the risk premiums of the two parameter capm and observed the previously reported seasonality and high january premium they also found that january is the only month in which there is a consistently positive statistically significant relationship between expected return and risk very recently using the two stage procedure with the

capital controls and international capital market segmentation the evidence from the japanese and american stock markets the paper focuses on two countries japan and the u s to test the integration of capital markets in japan the enactment of the foreign exchange and foreign trade control law in december of 1980 amounted to a true regime switch that virtually eliminated capital controls using multifactor asset pricing models we show that the price of risk in the u s and japanese stock markets was different before but not after the liberalization this evidence supports the view that governments are the source of international capital market segmentation the notion that world capital markets are perfectly integrated is central to most theoretical developments in both international finance and macroeconomics indeed it also lies behind much of the recent international policy discussion capital markets are integrated if assets with perfectly correlated rates of return have the same price regardless of the location in which they are traded 1 segmentation may arise either because of government impediments to capital movements or because of individuals attitudes or irrationality if the hypothesis that the international capital markets are integrated is rejected there is still an important empirical question left unanswered which is related to the source of segmentation while there is a rich body of theoretical research on international market integration only a few studies have tried to investigate this important question empirically a first group of empirical studies on market integration has generally adopted

yes the apt is testable the arbitrage pricing theory apt has been proposed as an alternative to the meanvariance 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 arbitrage pricing theory apt has been the subject of extensive research efforts since it was introduced by ross 36 37 the research has included theoretical papers and a growing empirical literature 2 nonetheless there seems to be some confusion in the literature about the relation between the theoretical underpinnings of the apt and its empirical tests this paper is an attempt to alleviate the confusion to illustrate the issues and to provide a focus section i of this paper is devoted to examining and refuting some points raised in shanken 40 which considers the testability of the apt the underlying premise of the apt is that asset returns ri are generated by a factor model of the form

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 notwithstanding initial skepticism and recent challenges the capital asset pricing model capm has been used to develop project screening rates value companies measure the impact of policy change on risk and construct portfolios recently the federal energy regulatory commission ferc proposed it as the principal measure of risk for the electric utilities it regulates it would be ironic for acceptance of capm by policymakers to occur just as arbitrage pricing theory apt threatens to replace it as an explanation of the relationship between return and risk and it would be a pity if ferc were to adopt the single risk factor approach of capm when it could be demonstrated that the multiple factors of apt provide a better indication of asset risk and a better estimate of expected return this paper presents some new evidence that apt may lead to different and better estimates of expected return than capm and that it may be more helpful to policymakers as a result we describe capm and apt note work done by others show how estimates of required returns for utilities developed by applying each model may differ and finally report the evidence that convinces us that if one model is to be relied upon for policy purposes apt would be the better choice

a critical reexamination of the empirical evidence on the arbitrage pricing theory a reply the paper by dhrymes friend and gultekin dfg in this issue criticizes empirical work on the arbitrage pricing theory apt conducted by ourselves rr 3 and by a number of others we are honored that such eminent professors as dfg have taken an interest in our work unfortunately the dfg paper contains analysis which might foster misconceptions in the casual reader our purpose here is to present a brief nontechnical comment we are confident that those who are inclined to study the dfg paper in detail will be able to discern its merit for themselves the introductory section and the concluding section viii of dfg stress three points first that the method of rr has major pitfalls and is seriously flawed second that individual factors should not be tested for their pricing influence and third that more than three to five factors can be found by increasing the size of the group analyzed we will comment on the reasonableness of the second and third point in some detail the first is a value judgment and as such cannot be disputed on logical grounds we would be the last to object to a reasoned opinion judiciously drawn by dispassionate and unbiased scholars but of course we do not agree with the particular opinion expressed by dfg in sections i and ii dfg repeat the standard development of the apt and make much of the argument that the apt as a null hypothesis in a statistical test is independent of any rotation of the factors they stress their view that the only meaningful tests are those of whether any factors are priced rather than those which test whether some of them are priced and others are not rr raise and analyze precisely this same point 1 and in fact our awareness of this issue led us to conduct f tests of the joint significance of all factor prices see our tables iv and vi despite the rotation problem tests of individual factor pricing have meaning since the factors are extracted in the order of their importance in explaining the covariance matrix of returns it is not only perfectly valid it is also interesting to ascertain if they each have an influence upon pricing the number of statistically significant estimated priced factors can be different than the number of true factors because of chance rotation in the

the relative importance of common factors across the european equity markets abstract in this paper we try to shed additional light on the question of integration or segmentation of european equity markets by studying the statistical relevance of some intuitively appealing international factors of return the relevance of these factors is also investigated through time in order to evaluate a possible increase in market integration over the recent past

calculating the equity cost of capital using the apt the impact of the erm abstract one of the expected benefits of membership of the exchange rate mechanism erm was a reduction in risk which should lead to a lower cost of capital and foster investment and growth using the apt we investigate the behavior of the equity market risk premium for the london stock exchange prior to and during sterling s membership of the erm we find that prior to and during the first year of membership the equity market risk premium fell quite dramatically however when conflict between domestic and erm policy requirements arose at the turn of 1991 the equity risk premium increased and continued to do so until sterling s exit partially wiping out the benefits of membership of the erm

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 monthahead forecasts of excess returns using factor generating models are compared with corresponding naive predictions or predictions using the market model with various