measuring the pricing error of the arbitrage pricing theory this article provides an exact bayesian frame work for analyzing the arbitrage pricing the ory apt based on the gibbs sampler we show how to obtain the exact posterior distributions for functions of interest in the factor model in particular we propose a measure of the apt pricing deviations and obtain its exact posterior distribution using monthly portfolio returns grouped by industry and market capitalization we find that there is little improvement in reduc ing the pricing errors by including more factors beyond the first one as an important extension of the asset pricing model of sharpe 1964 and lintner 196 5 ross 1976 1977 derived the arbitrage pricing theory apt which addresses a fundamental problem in finance to char acterize the expected return on a security the apt implies that the expected return is approximately a

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

consumption time in household production implications for the goods time elasticity of substitution abstract under some reasonable assumptions we show analytically that the goods time elasticity of substitution will be greater if consumption time is not included as an input an empirical example with food production is consistent with this result

interpreting the factor risk premia in the arbitrage pricing theory abstract in the arbitrage pricing theory of ross assets expected returns are shown to be approximately linear in the factor loadings of the process generating returns this note provides a very simple and direct proof of the proposition that the coefficients in this approximate pricing relation can be interpreted as the excess returns on portfolios perfectly correlated with the factors whenever a riskless asset and such mimicking portfolios exist

treasury bill factors and common stock returns capital asset pricing theory gives a linear ex ante relationship between a security s return and one special portfolio return the return on all assets this linear equation is called the capital asset pricing model capital asset pricing theory alone provides no empirical hypotheses because it is derived and defined wholly with expectations tests of empirical hypotheses with historical data require an additional proposition that relates ex ante and ex post returns a model for this second proposition is called a return generating equation arbitrage pricing theory gives a more compact method for deriving a linear ex ante security return model in the arbitrage theory developed by ross 6 the return generating equation is the basis for the ex ante return relationship briefly an approximate linear expected return equation is derived directly from the return generating equation so two separate models are not required in addition the ex ante return equation is defined in terms of an arbitrary number of special factor portfolio returns rather than a single market portfolio return in this sense arbitrage pricing theory has richer implications and a simpler structure than capital asset pricing arbitrage pricing theory starts with a linear return generating equation for each security

on the diversification observability and measurement of estimation risk this paper reexamines how risk return relationships are affected by investor uncertainty about the exact parameters of the joint rate of return distribution we attempt to clarify results relating to three central issues first we address the issue of diversification focusing on an apt factor model framework second we discuss the observability of estimation risk and describe research experimental designs that should encompass the existence of estimation risk and reveal it in the data finally we suggest exploiting contemporaneous return observations on high and low information securities to aid in the measurement of return parameters for low information securities

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

exact arbitrage pricing and the minimum variance frontier the author examines the relationship between the arbitrage pricing theory of ross and mean variance analysis in particular conditions are derived on the vector of the factor risk premia that are equivalent to the existence of a strictly positively weighted portfolio on the minimum variance frontier also a sufficient condition is given under which the existence of a positive minimum variance portfolio of all the assets in the economy will imply the existence of a positive minimum variance portfolio on a subset this means that rejection of the hypothesis of the existence of a positive minimum variance portfolio on a subset satisfying this condition implies rejection for the whole set a growing body of literature explores the relationship between the arbitrage pricing theory apt of ross 13 14 and the mean variance model among the early work in this direction were the papers of chamberlain and rothschild 2 and chamberlain 1 these papers examine a sequence of economies and characterize the relationship in the limit between the mean and portfolio cost functionals and the minimum variance frontier chamberlain 1 also gives a condition under which exact arbitrage pricing will hold dybvig 4 and grinblatt and titman 7 examine equilibrium models in an apt context for a finite economy they derive sharp bounds on the deviation from exact arbitrage pricing recent papers by huberman kandel and stambaugh 9 and grinblatt and titman 8 explore the relationship between the apt and the mean variance model by studying portfolios that can be used as proxies for the factors and examining the relationship these portfolios bear to the minimum variance frontier these two papers also deal with equilibrium models in spite of the number and variety of equilibrium apt models the question of the pricing of factor risk in equilibrium remains largely unexplored this paper makes some progress in addressing that issue by looking at a given equilibrium restriction and studying the constraints it imposes on the vector of factor premia itself the most familiar equilibrium restriction we might study is the central implication of the capital asset pricing model capm that the market portfolio is efficient in particular no portfolio with the same expected return as the market portfolio has a smaller variance the restriction we actually study is weaker than

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

arbitrage and diversification in a general equilibrium asset economy this paper presents a theory of equilibrium asset pricing that generalizes the recent work of connor the model extends connor s results to more general sets of asset returns and consumer preferences introduces production and provides a framework for analyzing exact and approximate equilibrium asset pricing the other major contribution of the paper is the introduction of geometric arguments that exploit the properties of induced prefer ences over assets this method of analyzing asset pricing provides an intuitively appealing way of analyzing equilibrium asset pricing theories unifies several well known asset pricing models this paper extends connor s finite asset model in a number of directions these extensions are nontrivial because they allow the theory to encompass asset pricing models that were excluded by connor s assumptions the second major contribution of the paper is to introduce a method of argument that exploits the geometric properties of induced preferences over assets and characterizes asset prices using these proper ties this technique provides an intuitively appealing way of analyzing asset pricing theories for a simple geometric exposition of the main ideas in this paper see milne 1987 0 2 to place this paper in the context of the literature it is important to appreciate the development of asset pricing models over the last two decades the first and perhaps the most famous asset pricing model is the capital asset pricing model capm developed by sharpe 1964 and lintner 1965 the model demonstrated a striking result assuming i consumers characterize portfolios in terms of the means and variance of rates of return ii there exists a risk free asset and iii asset market equilibrium then any asset s expected rate of return could be written as a linear function of the riskless interest rate and the expected rate of return on the endowment of risky assets the so called market portfolio the original capm result was derived from a one period model but merton 1973 showed that in a continuous time model where returns could be char acterized by a diffusion process the same mean variance argument could be applied to obtain the capm formula it was well known that if consumers had von neumann morgenstern prefer ences then either quadratic utility and or multivariate normality of returns were

small sample tests of portfolio efficiency abstract this paper presents an eigenvalue test of the efficiency of a portfolio when there is no riskless asset complementing the test of gibbons ross and shanken 1989 besides optimal upper and lower bounds an easily implented numerical method is provided for computing the exact p value our approach makes it possible to draw statistical inferences on the efficiency of a given portfolio both in the context of the zero beta capm and with respect to other linear pricing models as an application using monthly data for every consecutive five year period from 1926 to 1986 we reject the efficiency of the crsp value weighted index for most periods

on testing the arbitrage pricing theory inter battery factor analysis this paper tests the arbitrage pricing theory apt by estimating the factor loadings that are consistent between two industry groups of securities one of the pitfalls in the study by roll and ross is that the factors estimated in one group may not be the same with the factors estimated in another group this raises some concerns on the acceptability of their conclusions for our study we employ inter battery factor analysis which enables us to estimate factor loadings by constraining the factors to be the same between two different groups our results show that there seem to be five or six inter group common factors that generate daily returns for two industry groups of securities and these inter group common factors do not seem to depend on the size of groups also based on our cross sectional tests on the risk premia we conclude that the apt should not be rejected the arbitrage pricing theory apt introduced by ross 35 36 provides another model for explaining the relationship between return and risk the apt may be conceived as an alternative to the well known capital asset pricing model capm introduced by sharpe 39 lintner 27 and mossin 29 and later modified by black 1 both models assert that every asset must be compensated only according to its systematic risk one of the major differences is that in the capm the systematic risk of an asset is defined to be the covariability of the asset with the market portfolio whereas in the apt the systematic risks are defined to be the covariability with not only one factor but also possibly with several economic factors another difference is that the capm requires the economy to be in equilibrium whereas the apt requires only that the economy has no arbitrage opportunities note that the absence of arbitrage condition is necessary but not sufficient for the economy to be in equilibrium thus the apt is a more fundamental relationship than the capm in the sense that a rejection of the apt implies the rejection of the capm but not vice versa despite numerous attempts the capm has not been satisfactorily tested and furthermore roll s critique 32 33 casts serious doubts on the testability of the capm itself roll argues that the linear relationship between return and risk will hold for any efficient portfolio thus unless the market portfolio is observed a test of the capm using ex post data is ambiguous it results only in testing the

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

an asset pricing theory unifying the capm and apt this study shows that the competitive equilibrium version of the arbitrage pricing theory may be extended to develop an exact mode l if idiosyncratic risks obey the ross separating distribution the r esults indicate that one only need add the market portfolio as an ext ra factor to the factor model in order to obtain an exact asset prici ng relation the empirical arbitrage pricing theory is also general ized to allow for some factors to be omitted from the econometric m odel employed to test the theory the importance of the market portfo lio is shown to be a monotonic increasing function of the number of o mitted factors copyright 1988 by american finance association

misspecification of capital asset pricing this study documents empirical anomalies which suggest that either the simple one period capital asset pricing model capm is misspecified or that capital markets are inefficient in particular portfolios based on firm size or earnings price e p ratios experience average returns systematically different from those predicted by the capm furthermore the abnormal returns persist for at least two years this persistence reduces the likelihood that these results are being generated by a market inefficiency rather the evidence seems to indicate that the equilibrium pricing model is misspecified however the data also reveals that an e p effect does not emerge after returns are controlled for the firm size effect the firm size effect largely subsumes the e p effect thus while the e p anomaly and value anomaly exist when each variable is considered separately the two anomalies seem to be related to the same set of missing factors and these factors appear to be more closely associated with firm size than e p ratios

consumption versus expenditure previous authors have documented a dramatic decline in food expenditures at the time of retirement we show that this is matched by an equally dramatic rise in time spent shopping for and preparing meals using a novel data set that collects detailed food diaries for a large cross section of u s households we show that neither the quality nor the quantity of food intake deteriorates with retirement status we also show that unemployed households experience a decline in food expenditure and food consumption commensurate with the impact of job displacement on permanent income these results highlight how direct measures of consumption distinguish between anticipated and unanticipated shocks to income whereas measures of expenditures obscure the distinction

coal policies and trade barriers abstract the purpose of this paper is to treat in some depth recent work performed by the iea secretariat in analysing barriers to coal trade in member countries the concept of the producer subsidy equivalent pse as a measure of financial transfers to the coal industry is described along with its advantages and limitations as illustration summary results for the years 1982 1988 are given the paper concludes with a discussion of the arguments for and against maintaining support for domestic coal production

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

portfolio performance evaluation old issues and new insights this article presents a model that provides insights about various measures of portfolio performance the model explores several criticisms of these measures these include the problem of identifying an appropriate benchmark portfolio the possibility of overestimating risk because of market timing ability and the failure of informed investors to earn positive risk adjusted returns because of increasing risk aversion the article argues that these need not be serious impediments to performance evaluation

estimates of returns to scale elasticity of substitution and the thrifty food plan meal poverty rate from a direct household meal production function abstract many nutritional policies are designed to make home food production more affordable and yet very little is actually known about the home food production process a better understanding of home food production can be used to help explain shortcomings in current nutrition policies and consequently help in designing better nutrition policies this paper provides results from several home meal production function specifications that are rather robust the median returns to scale and elasticity of substitution between money and time is in the 1 2 1 9 range and 33 56 range respectively indicating increasing returns to scale but difficulty in substituting money for time in home meal production a home meal poverty rate is estimated which is the percentage of the sample that produces fewer meals at home than consistent with dietary guidelines the estimated home meal poverty rate is about 85 which is consistent with recent research taking a less rigorous approach though the approach taken here is novel the overall message is consistent with the recent literature time is a more important factor in achieving nutritional targets than money

factor pricing in a finite economy abstract 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

a new approach to international arbitrage pricing this paper uses a nonlinear arbitrage pricing model a conditional linear model and an unconditional linear model to price international equities bonds and forward currency contracts unlike linear models the nonlinear arbitrage pricing model requires no restrictions on the payoff space allowing it to price payoffs of options forward contracts and other derivative securities only the nonlinear arbitragepricing model does an adequate job of explaining the time series behavior of a cross section of international returns the idea that a few relevant state variables explain expected returns is the main driving force of the seminal papers of merton 1973 and ross 1976 these seminal ideas have been extended to the pricing of international assets by ikeda 1991 ross and walsh 1983 solnik 1974 1983 and stulz 1981 among others the key implication of these arbitrage pricing models is that only risks related to these factors state variables are relevant in determining asset prices testable implications of these international asset pricing models have been derived either by placing restrictions on the payoff structure i e payoffs are linear in factors as in ikeda 1991 ross and walsh 1983 and solnik 1983 or on the joint distributions of the payoffs and state variables as in constantinides 1989 these restrictions lead to the testable implication that expected asset returns are linear in the conditional covariances with the factor payoffs in what follows we refer to these models as linear arbitrage models or linear models

shocks plausible shocks in world energy in the 1990s this paper contrasts the calm developments in world energy markets in the 1990s with three unlikely yet plausible shocks and their implications for energy consumers and producers a series of nuclear disasters followed by worldwide closure of nuclear power generation a collapse in the aging world tanker capacity and a set of ominous climatic events resulting in an international decision to cut co2 emissions are considered in turn

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

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

asset financing with credit risk abstract this paper develops a model for the unified valuation of all forms of real asset financing such as bank loans leases securitization vehicles and credit guarantees secured by assets that generate a stochastic service flow to the operator or a rental stream to the lessor and depreciate over a finite economic life to their scrap value examples include mobile equipment such as aircraft railroad equipment ships trucks and trailers as well as energy generation assets heavy factory equipment and construction equipment in the event of obligor default after a repossession delay and incurring costs of repossession maintenance re marketing and re deployment the lender repossesses the asset and sells it on the secondary market and is thus subject to the risk of decline in the market value of the asset the model we develop in this paper treats all forms of asset financing in a unified fashion as contingent claims on the collateral asset and the credit of the borrower as an application we estimate the collateral asset model on historical secondary market data for aircraft values and calibrate the financing model to the enhanced equipment trust certificates eetcs issued in 2007 by continental airlines and secured by a fleet of new aircraft we then apply the calibrated model to value private market financing including bank loans leases and credit guarantees consistently with the capital market financing and assess the impact of repossession delays on credit spreads this analysis leads to a policy insight suggesting that bankruptcy laws limiting asset repossession delays lead to lower costs of asset financing

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

tests of asset pricing with time varying expected risk premiums and market betas tests of asset pricing models are developed that allow expected risk premiums and market betas to vary over time these tests exploit the relation between expected excess returns and current market values using weekly data for 1963 through 1982 on ten common stock portfolios formed according to equity capitalization a single risk premium model is not rejected if the expected premium is time varying and is not constrained to correspond to a market factor conditional mean variance efficiency of a value weighted stock index is rejected and the rejection is insensitive to how much variability of expected risk premiums is assumed financial economists have studied valuation models in which securities expected returns are related to the covariances of unanticipated returns with the return on the market portfolio or with other risk factors empirical tests of such models typically have employed unconditional sample moments of returns recent studies provide mounting evidence that expected returns change over time with information such evidence presents an opportunity to develop new approaches for evaluating and implementing asset pricing models that exploit this time variation this paper presents new tests of financial valuation models in which expected returns are allowed to vary over time time series of relative

the pricing of interest rate risk evidence from the stock market this paper addresses the issue of whether firms are required to pay an ex ante premium to investors for bearing the risk of interest rate changes a two factor apt model with the market and changes in the yield on long term government bonds as factors is employed the paper shows that empirically most of the interest sensitive stocks are in the utility industries and that there is reasonable evidence that the interest factor is priced in the sense of the apt several sources for the interest sensitivity are considered and regulatory lags are focused on as a likely candidate some firms exhibit ex post sensitivity in their stock returns to unanticipated changes in interest rates are these firms required to pay investors ex ante for bearing this risk of interest rate changes the framework for examining pricing of unanticipated interest rate changes is a two factor apt model with the market and changes in the yield on long term government bonds as factors the issue is whether the interest rate change premium is significant to study this the paper uses full information maximum likelihood fiml estimation on groups of twenty five individual firms with both cross equation constraints and withinequation nonlinear constraints on the parameters as mandated by the apt model whether the risk of unanticipated changes in interest rates is priced in the market is of particular interest with regard to regulated firms regulated firms especially electric utilities turn out to comprise the big majority of firms that are sensitive to unanticipated interest rate changes after some preliminary investigation the analysis focuses on electric utilities much empirical work on the apt relies on factor analysis e g roll and ross 30 bower bower and logue 5 use factor analysis in comparing the apt and the capm to explain utilities returns the present paper however uses observable variables at the macro level chan chen and hsieh cch 7 and chen roll and ross crr 8 also examine apt models with specific macroeconomic factors cch and crr use a traditional fama macbeth type of cross sectional estimation approach in the premia calculations rather than a fiml approach gibbons and stambaugh have applied fiml techniques to models using only the market as an explanatory variable gibbons 20 used a noniterative algorithm on portfolios of firms equivalent to a two step cross sectional approach stam

taxes and time allocation evidence from single women and men the classic model of becker 1965 suggests that labor supply decisions should be analyzed within the broader context of time allocation and market good consumption choices but most empirical work on policy has focused exclusively on measuring impacts on market work this paper examines how income taxes affect time allocation during the entire day and how these time allocation decisions interact with expenditure patterns using the panel study of income dynamics from 1975 to 2004 we analyze the response of single women s housework labor supply and other time to variation in tax and transfer schedules across income levels number of children states and time we find that when the economic reward to participating in the labor force increases market work increases and housework decreases with the decrease in housework accounting for approximately two thirds of the increase in market work analysis of repeated cross sections of time diary data from 1975 to 2004 shows that home production decreases substantially when market hours of work increase in response to policy changes data on expenditures from the consumer expenditure survey from 1980 to 2003 show some evidence that expenditures on market goods likely to substitute for housework increase in response to a greater incentive to join the labor force the baseline estimates imply that the elasticity of substitution between consumption of home and market goods is 2 61 the results are consistent with the becker model meanwhile single men show little response to changes in tax policy and we are able to rule out an elasticity of substitution between home and market goods for this group of more than 1 52

exchange rate and foreign inflation risk premiums in global equity returns abstract we test for the pricing of exchange rate and foreign inflation risk in equities our tests are motivated by the empirical implications of the models of solnik 1974b solnik b 1974b the international pricing of risk an empirical investigation of the world capital market structure journal of finance 365 377 as revised by sercu 1980 sercu p 1980 a generalization of the international asset pricing model revue de l association francaise de finance 1 91 135 grauer et al 1976 grauer f litzenberger r stehle r 1976 sharing rules and equilibrium in an international capital market under uncertainty journal of financial economics 3 233 256 and adler and dumas 1983 adler m dumas b 1983 international portfolio choice and corporation finance a synthesis journal of finance 38 925 984 both exchange rate and foreign inflation risk factors can explain part of the within country cross sectional variation in returns our results have important implications for hedging exchange rate risk they also demonstrate that home bias at least in us equity portfolios cannot be the result of us investors efforts to hedge their domestic inflation

the sampling error in estimates of mean variance efficient portfolio weights this paper presents an exact finite sample statistical procedure for testing hypotheses about the weights of mean variance efficient portfolios the estimation and inference procedures on efficient portfolio weights are performed in the same way as for the coefficients in an ols regression ols t and f statistics can be used for tests on efficient weights and when returns are multivariate normal these statistics have exact t and f distributions in a finite sample using 20 years of data on 11 country stock indexes we find that the sampling error in estimates of the weights of a global efficient portfolio is large

on the impact of infrequent trading on the apt systematic risk components evidence from a thin security market abstract the purpose of this note is to analyze the effects of infrequent trading on the apt systematic risk components using finnish data infrequent trading is reported to influence especially the first systematic risk component produced by factor analysis on stock returns

portfolio selection and asset pricing three parameter framework idiosyncratic security risks are modelled as following a joint spherical distribution characterized by a mean vector and a generalized covariance matrix skewness is generated by a single factor for the whole economy but upon which different securities have different loadings this results in three fund separation two funds to span the spherical risk and one more fund to span the additional skewness risk a three parameter normative portfolio analysis that allows short sales restrictions is developed in addition a three parameter capital asset pricing model is provided

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

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

cost of capital to the hospital sector this paper provides estimates of the cost of equity and debt capital to for profit and non profit hospitals in the u s for the years 1972 83 the cost of equity is estimated using alternatively the capital asset pricing model and arbitrage pricing theory we find that the cost of equity capital using either model substantially exceeded anticipated inflation the cost of debt capital was much lower accounting for the corporate tax shield on debt and capital paybacks by cost based insurers lowered the net cost of capital to hospitals

posterior predictive and utility based approaches to testing the arbitrage pricing theory abstract to provide a framework for judging the economic significance of departures from the arbitrage pricing theory we adopt a utility based metric based on optimal portfolio choices this measure is examined using both predictive and posterior analysis our predictive analysis shows very large and economically significant departures from the model restrictions however the high level of parameter uncertainty suggests that we cannot conclusively either affirm or reject the apt our conclusions differ markedly from other studies which employ traditional significance testing procedures and in many instances fail to reject the apt restrictions

not enough money or not enough time to satisfy the thrifty food plan a cost difference approach for estimating a money time threshold abstract food production at home requires money and time food assistance programs focus exclusively on the money cost while ignoring the time cost this one dimensional focus could undermine the effectiveness of food assistance programs in the spirit of vickery 1977 this paper uses a cost difference approach to develop a money time threshold and several related metrics to determine whether money or time is the most limiting resource in reaching the thrifty food plan tfp target in our empirical analysis we find that when time is ignored single headed households spend on average 35 more than required to meet the tfp target however when time is included these households spend on average 40 less than required to meet the tfp target in addition we find that when time is ignored 62 of single headed households on average spend enough money to reach the tfp target but when time is included only 13 of single headed households spend enough on average to reach the tfp target our empirical results suggest that time is more constraining than money in reaching the tfp target these results imply that metrics solely focusing on money could severely underestimate the gap between actual expenditures and those required to reach the tfp target

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

an explicit bound on individual assets deviations from apt pricing in a finite economy abstract 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

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

general factor models and the structure of security returns based on markowitz s pioneering study 40 sharpe 56 and lintner 38 advanced the first positivist formulations of the capital asset pricing model capm their models were subsequently refined by mossin 45 fama 15 black 1 and others even though the capm has been studied extensively it has not been empirically validated according to roll 48 the capm cannot be tested in an unambiguous fashion because of a number of intractable measurement and computational difficulties and the joint nature of the hypotheses to be tested

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

equilibrium factor pricing with heterogeneous beliefs this paper develops an equilibrium factor pricing theory when investors have heterogene ous beliefs about asset payoffs generated by the ross linear factor model investors receive private information about the unknown parameters of the payoff process they use this private information and equilibrium prices to predict asset payoffs the paper de velops a closed form price function for a noisy rational expectations equilibrium and relates it to the general solution even though we allow for a large number of investors diversity of beliefs and parameter uncertainty both persist in equilibrium we show that investors beliefs about expected payoffs are approximately linear in the asset s betas thus establishing the apt as investors prefer to hold high information assets in equilib rium the relative weight of these assets in the apt pricing bound is higher the reverse is true for low information assets

excess returns of industrial stocks and the real estate factor 1 introduction for more than three decades numerous studies have been devoted to capital asset pricing issues identifying key factors influencing returns on capital assets remains the major focus of the studies according to the first important asset pricing theory the capital asset pricing model capm of sharpe 1964 and lintner 1965 there is a positive linear relationship between expected stock returns and market betas this single factor model is theoretically challenged by the arbitrage pricing theory apt developed by ross 1976 the apt provides a theoretical framework to identify more macro factors that have significant explanatory power for stock returns roll and ross 1980 chen 1983 bower bower and logue 1984 and chen roll and ross 1986 in order to be included in a multifactor model a factor must represent a source of nondiversifiable or systematic risk in addition to theoretical challenges the evidence of many empirical studies casts doubts on the adequacy of the long existing capm for example the findings of fama and french 1996 suggest that ps alone cannot explain expected returns on common stocks meantime other macro factors related to the bond market such as unanticipated changes in the term structure chen roll and ross 1986 are used to explain stock returns in recent years more risk factors have been suggested in the literature for example in their time series study about common risk factors in the returns on common stocks fama and french 1993 argue that there are three stock market factors an overall market factor a size factor stock price times number of shares and a book to market equity factor that have a significant impact on stock returns in addition two bond market factors the term structure and risk factors can capture common variation in stock and bond returns fama and french 1993 similar to fama and french s 1993 multifactor models the present study uses all three stock market factors an overall stock market factor a size factor and a book to market equity factor two bond market factors related to maturity and default risks and a real estate market factor the reason for introducing a new risk factor real estate market factor although not so obvious is engendered by the theoretical spirit of the apt real estate is a major asset class and as almost all firms have operating expenses under this category it does not matter if the properties are acquired or rented according to zeckhauser and silverman 1983 a significant portion of corporate assets on average as high as 25 is real estate related changes in real estate market value therefore potentially have a direct impact on the value of corporate assets and operating expenditures if this impact is significant as are other systematic risk factors the real estate market factor must play an important role in stock pricing in addition the real estate market risk is a macro factor therefore results about this factor do not have any interpretation problems that are associated with firm specific variables in order to identify significant factors in explaining returns for industrial stocks this study estimates various models based on the following six risk factors an overall stock market factor a size factor a book to market equity factor a term structure factor a default risk factor and an unsecuritized real estate market factor results of this study provide some empirical evidence about the significance of the six risk factors on excess returns for industrial stocks in addition this study also investigates how the inclusion of additional risk factors for example the inclusion of the bond market factors or the real estate market factor in the single market factor model increases the explanatory power of the model the remainder of this study is organized as follows section 2 describes the data and methodology section 3 presents the empirical results and section 4 contains the conclusions

limits to oil pricing scenario planning as a device to understand oil price developments abstract the bad record of oil price forecasting indicates that conventional oil market models should be critically reassesed scenario planning may be one alternative approach this approach does not contradict other theories of the market but it claims that no single discipline is able to tell the whole truth about the market the sp approach stresses and clarifies the role of uncertainty it argues that without a cross disciplinary approach with an adequate choice of parameters at the right level of in depth discussion the analysis may either lose essential imput or drown in detail as an example of the methodology an analysis of the oil market in the 1990s is presented this shows low upper and lower limits for the price can be constructed and which actual price development can be expected in a combination of economic and political reasoning

the impact of the return interval on common factors in stock returns evidence from a thin security market abstract the purpose of this paper is to analyze the effect of the return interval on common factors estimated in finnish stock returns firstly common factors are identified by factor analysis using daily weekly and monthly return intervals the similarity of these factors is then studied applying transformation analysis it is discovered that the factors produced by alternative return intervals significantly differ from each other an exception is the first factor representing the market index of securities

diversification and the optimal construction of basis portfolios nontrivial diversification possibilities arise when a factor model describes security returns this paper catalogs the merits of alternative strategies for constructing basis portfolios to mimic the common factors we show how to use the 2 statistic for the joint significance of mean basis portfolio returns to rank alternative procedures and the bootstrap to perform inferences on the disparity between 2 statistics across portfolio formation procedure estimation method cross section size and number of factors our main conclusion is that maximum likelihood factor analysis coupled with minimum idiosyncratic risk portfolio formation yields economically and statistically superior basis portfolios compared with those derived from asymptotic principal components

time to eat household production under increasing income inequality eating requires the raw food materials that make up meals and also the time devoted to buying food preparing meals and eating them and cleaning up afterwards using time diary and expenditure data for the u s for 1985 and 2003 i examine how income and time prices affect time and goods inputs into this household produced commodity focusing on these two years between which income and earnings inequality increased allows examining how household production is affected by changing economic opportunities the results demonstrate that both inputs into eating increase with income and that higher time prices at a given level of income reduce time inputs over this period the relative goods intensity of producing this commodity increased especially at the lower part of the income distribution and the average time input dropped substantially the results are consistent with goods time substitution being relatively difficult for eating and with substitution being more difficult as production expands

direct estimates of household production abstract using time diary and expenditure data for a set of american households in 2003 and 2004 i examine the relation between the inputs into eating time food purchasing preparation consumption and clean up and goods purchased foods goods and time expenditures are positively correlated and direct estimates of a ces household production function indicate the relative difficulty of goods time substitution in producing this commodity

multi beta capm or equilibrium apt a reply in their influential empirical paper roll and ross 11 state we think that in many discussions of the capm scholars were actually thinking of the apt and of process 1 the factor model with just a single factor in light of recent developments in the asset pricing literature i think it can now meaningfully be suggested that in many discussions of the apt scholars may have actually been thinking of a multi beta interpretation of the capm indeed much can be said in support of each of these perspectives for a single paradigm is emerging which integrates fundamental aspects of both the capm and the apt broadly speaking the equilibrium capm paradigm emphasizes the role of covariance between asset returns and an endogenous preference based aggregate while the arbitrage apt paradigm focuses on the covariance between asset returns and factors in the return generating process the emerging equilibrium factor paradigm encompasses each of these relations as well as a third covariance between the factors and the equilibrium aggregate my thesis in shanken 17 was that i the arbitrage paradigm has not produced a refutable hypothesis and that ii recognition of the role of the factor aggregate covariance relation appears to be essential if positive economic significance is to be attributed to asset pricing empirical work dybvig and ross d r attempt to resolve the empirical indeterminacy of the arbitrage paradigm by appealing to the condition that residual variance should not be too large i explain in section ii that this condition is inherently ambiguous from an empirical perspective and does not permit the formulation of a precise testable implication the equilibrium factor models which d r discuss do yield testable restrictions on parameters in the return generating process however consistent with my second point above these restrictions involve joint hypotheses that cannot be verified without observing the entire universe of assets thus contrary to their claim considerations similar to those in roll s 10 critique are indeed relevant to the testing of these models this and other similarities between the equilibrium apt and the capm are discussed in section iii i begin by clarifying some basic terminology

a super criterion for testing portfolio efficiency empirical evidence on finnish stock data abstract in this paper a markovian super criterion is formulated for testing the portfolio efficiency of competing capital market theories the portfolio efficiency of the arbitrage pricing theory apt and the capital asset pricing model capm is tested on finnish weekly price index data over the 1970 1983 time frame the efficiency test results imply that the apt dominates the capm a considerable deviation between the expected pareto frontier and the best expectational frontier according to the apt is observed

seasonal and size anomalies in the japanese stock market little attention has been paid by the academic community in the united states to the japanese stock market and its structure japan has the second largest economy in the western world and the tokyo stock exchange tse is second only to the new york stock exchange nyse in terms of aggregate market values and sales volume analysis of the japanese stock market is useful given its relative importance but in addition examination of the japanese market may offer insights into controversies surrounding u s markets this study focuses on two such current controversies the january and size anomalies