on the exclusion of assets from tests of the mean variance efficiency of the market portfolio this paper presents an analysis of the testability of the mean variance efficiency of a market index when the returns on some components of the index itself are not perfectly observable the results are basically not supportive of the notion that mean variance efficiency is testable on a subset of the assets bounding the market share of the missing asset and its expected return is not sufficient to produce a valid test when the variance of the missing asset is bounded and the amount of wealth that might be missing is small it is possible in principle to reject correctly the mean variance efficiency of a market index in his famous critique of the asset pricing theory tests roll 7 concludes that the only testable hypothesis associated with the generalized two parameter asset pricing model of black 1 is that the market portfolio is mean variance efficient it has been emphasized by ross 10 and roll 7 that the mean variance efficiency of the market portfolio is mathematically equivalent to a positive linear relation between expected returns and the betas calculated against such a portfolio roll 7 deduces that the theory capm is not testable unless the exact composition of the market portfolio is known and used in the tests this implies that the theory is not testable unless all individual assets are included in the sample errors of type one or two might occur when a market proxy is used instead of the true market portfolio even if the ex ante true expected returns and the covariance variance matrix of the returns on all the assets are used these errors are the result of the choice of the portfolio and as roll puts it even a small misspecification of the proxy s composition can lead to the wrong conclusion the market proxy might be mean variance efficient while the true market portfolio is not and vice versa in principle however there are cases in which the above two conditions are not both necessary to reject the theory one such exception presented by roll 7 is the case in which no totally positive portfolio is efficient if any totally positive market proxy is used a large sample would reject the null hypothesis unambiguously while the market portfolio identification problem constitutes a severe limitation to the testability of the theory the question of the mean variance efficiency of a particular market index with respect to a subset of assets is a typical problem of statistical inference the mean variance efficiency can be tested directly or by

the pricing of currency risk in japan abstract previous work on the pricing of exchange rate risk has primarily focused on us firms and surprisingly found stock returns were not significantly affected by exchange rate fluctuations in this paper we conduct an in depth investigation that examines whether exchange rate risk is priced in the equity market of japan using an intertemporal asset pricing testing procedure that allows risk premia to change through time in response to changes in macroeconomic conditions our multiperiod asset pricing tests show that the foreign exchange rate risk premium is a significant component of japanese stock returns specifically the results suggest that currency risk exposure commands a significant risk premium for multinationals and high exporting japanese firms the currency risk factor is found to be less influential in explaining the behavior of average returns for low exporting and domestic firms however it is shown to exhibit large return volatility that is likely to be perceived by investors who wish to control portfolio risk as an important underlying source of risk furthermore japanese stock returns are found to be related to the relative distress and size factors above and beyond the covariation explained by the currency risk factor

using generalized method of moments to test mean variance efficiency this paper develops tests of unconditional mean variance efflciency under weak distributional assumptions using a generalized method of moments framework these tests are potentially more robust than commonly employed tests which rely on the assumption that asset returns are normally distributed and temporarily i i d using returns for size based portfolios from 1926 to 1988 we show that the conclusion concerning the mean variance effilciency of market indexes can be sensitive to the test considered the application of multivariate statistical techniques in financial economics has become common practice in recent years much of the development has been in the area of testing asset pricing models the assumption that asset returns follow a time invariant multivariate normal distribution permits tests of restrictions on model parameters in a pooled time series cross section framework these tests can be interpreted as tests of the mean variance efficiency of a portfolio or combination of portfolios gibbons 1982 jobson and korkie 1982 stambaugh 1982 shanken 1985 1987 kandel and stambaugh 1987 mackinlay 1987 and gibbons ross and shanken 1989 are examples of work presenting multivariate tests of the capital asset pricing model connor and korajczyk 1988 and lehmann and modest 1988 present multivariate tests of the arbitrage pricing model breeden gibbons and litzenberger 1989 present multivariate tests of the consumption based capm although these papers assume the normality of asset returns little analysis has been conducted to understand the sensitivity of the inferences to violations of this assumption 2 3

the mean variance efficiency of benchmark portfolios uk evidence abstract this paper examines the ex ante mean variance efficiency of four alternative benchmark portfolios within a uk context each of the benchmark portfolios is shown to be mean variance inefficient over the period january 1980 to december 1989 additionally the gibbons et al test statistic of efficiency appears to be fairly robust to violations in the distributional assumptions gibbons m r s a ross and j shanken 1989 test of the efficiency of a given portfolio econometrica 57 1121 1152

time series distributional properties of financial ratios empirical evidence from finnish listed firms abstract the distributional properties of time series accounting numbers are studied first the distributional characteristics of raw financial ratio distributions are investigated second the normality of the accounting index model residuals is researched by doing this one aims to consider the firm specific and economy wide effects on the observed nonnormalities in financial ratio distributions empirical evidence indicates that a substantial part of the nonnormalities in financial ratio distributions is caused by economy wide effects

multivariate tests of the zero beta capm abstract a cross sectional regression test csrt of the capm is developed and its connection to the hotelling t2 test of multivariate statistical analysis is explored algebraic relations between the csrt the likehood ratio test and the langrange multiplier test are derived and a useful small sample bound on the distribution function of the csrt is obtained an application of the csrt suggests that the crsp equally weighted index is inefficient but that the inefficiency is not explained by a firm size effect from february to december

asset pricing tests under alternative distributions given the normality assumption we reject the mean variance efficiency of the center for research in security prices value weighted stock index for three of the six consecutive ten year subperiods from 1926 to 1986 however the normality assumption is strongly rejected by the data under plausible alternative distributional assumptions of the elliptical class the efficiency can no longer be rejected when the normality assumption is violated but the ellipticity assumption is maintained many tests tend to be biased toward overrejection and both the accuracy of estimated beta and r2 are usually overstated many asset pricing models predict a linear relationship between the expected return on an asset and the covariance between the asset s return and one or more factors it is this mean variance framework that plays a central role in modern theories of asset pricing however chamberlain 1983 showed that the mean variance analysis is consistent with investor s portfolio decision making if and only if the returns are elliptically distributed moreover in the case of elliptical returns the capital asset pricing model capm of sharpe 1964 and lintner 1965 and multibeta models will remain valid theoretically 1 therefore it is important to test asset pricing models for the case where the returns are elliptically distributed and yet gibbons ross and shanken 1989 among others provide tests that are valid only under the normality assumption a special case of the elliptical distributions affleck graves and mcdonald 1989 and mackinlay and richardson 1991 examine tests without the normality assumption but their approaches are difficult to apply to obtain exact tests in the elliptical case complementing the existing studies we propose exact tests for both the case where the returns are elliptically distributed and the case where the residuals are elliptically distributed when the normality assumption is violated but the ellipticity assumption is maintained our results show that the usual tests can be biased and the widely used beta and r2 estimated

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

on multivariate tests of the capm abstract this paper evaluates the power of multivariate tests of the capital asset pricing model the results indicate that when employing an unspecified alternative hypothesis the ability of the tests to distinguish between the capm and other pricing models is poor an upper bound is derived for the distance the alternative distribution of the test statistic can be from the null distribution when the deviations from the capm are due to missing factors this upper bound explains the low power of the tests

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

nonnormalities and tests of asset pricing theories the robustness of the multivariate test of gibbons ross and shanken 1986 to nonnormalities in the residual covariance matrix is examined after considering the relative performance of various tests of normality simulation techniques are used to determine the effects of nonnormalities on the multivariate test it is found that where the sample nonnormalities are severe the size and or power of the test can be seriously misstated however it is also shown that these extreme sample values may overestimate the population parameters hence we conclude that the multivariate test is reasonably robust with respect to typical levels of nonnormality in traditional hypothesis testing a nonrandom test maps the values of a random variable into a sample space dichotomized into regions where a hypothesis is either accepted or rejected there are three possible outcomes from this process 1 a correct decision 2 a false rejection type i error or 3 failure to reject the hypothesis when it is false type ii error of the latter two types of error an error of the first kind is usually considered less desirable so typically a level of significance is selected with low probability of type i error e g 0 05 or 0 01 and a test is chosen so as to maximize power minimize probability of type ii error for the specified level of type i error knowledge of the relative level of these two errors is critical in assimilating the results of an experiment for example if the power of a test is equal to its significance level i e a weak test rejection of the null contains zero information 2 additionally in constructing parametric tests of hypotheses it is necessary to assume some distribution for the underlying data consequently when using parametric tests rejection of the null is only equivalent to rejection of at least one of the underlying hypotheses i e the null hypothesis or the distributional assumption interestingly the size significance level and power of procedures used to test

nonlinear dynamics in cee stock markets indices abstract we investigate the existence of nonlinearities in the dynamics of the returns of stock markets indices from cee economies we use several types of nonlinear tests we discuss the implications of the results with respect to the efficient market hypothesis

transforming european regional policy a results driven agenda and smart specialization the paper examines the nature rationale and logic of the reforms to eu cohesion policy a particular focus of the paper is on the concept of smart specialization and the use of this concept to help facilitate a results oriented policy agenda on the one hand the arguments underpinning the reforms in part relate to modern thinking regarding the role of industrial policy on the other hand they also partly relate to advances in our understanding of the relationships between economic geography technology and institutions at the same time the specific features of the eu context also heavily influence the nature and logic of the changes whereby legal and institutional matters linking cohesion policy to other eu policies all play an important role

subperiod aggregation and the power of multivariate tests of portfolio efficiency abstract when testing portfolio efficiency empiricists usually perform tests using subperiods and aggregate the results in some manner although the power of individual subperiod tests has been studied previously little is known about the power of the aggregate test power is evaluated here through simulations using two different aggregation techniques aggregate power is substantially higher than that for a single subperiod for example in one scenario the aggregate power is 0 77 over a sixty year period but only 0 17 for each five year subperiod in addition the level of power depends on the method of aggregation

on the exclusion of assets from tests of the mean variance efficiency of the market portfolio an extension this paper extends kandel s 3 analysis of the testability of the mean variance efficiency of a market index when the return on some component of the index is not perfectly observable in addition to information about the mean and variance of the missing asset considered by kandel we explore the usefulness of information about the beta of the missing asset on the observed sub portfolio in an economy with a riskless asset the results are somewhat more supportive of the notion that mean variance efficiency is testable on a subset of the assets in his important critique of tests of the capital asset pricing model roll 4 emphasizes that empirical results obtained with market proxies need not be indicative of the results that would be obtained in testing the efficiency of the true market portfolio were it observable more recently kandel 3 has analyzed the testability of the mean variance efficiency of a market portfolio when the return on some component of the portfolio is not perfectly observable but partial information about its characteristics is available he finds that knowledge of the market share and expected return of the missing asset is not sufficient to permit a test however bounding the variance of return on the missing asset does make it possible in principle to correctly reject the efficiency of the portfolio provided that the market share of the missing asset is not too large building on the analytical framework established by kandel we explore the value of information about the riskless rate of return and the covariance betwen the return on the missing asset and the observed sub portfolio given a riskless asset the question we address is whether the unobservable market portfolio of risky assets is equal to the tangency portfolio of the efficient frontier we find that knowledge of the market share and expected return of the missing asset is still not sufficient to permit a test of this more restrictive efficiency condition as in the no riskless asset case given a bound on the variance of the missing asset it is sometimes possible to correctly infer that the unobserved portfolio is inefficient this occurs when the market share of the missing asset or the variance of its return is small and the sub portfolio is sufficiently far from the linear

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

potential performance and tests of portfolio efficiency abstract the potential performance of an asset set may be obtained by choosing the portfolio proportions to maximize the sharpe 1966 performance measure if a portfolio has a sharpe measure equivalent to the potential performance of the underlying set of assets then it is efficient multivariate statistical procedures for comparing potential performance and testing portfolio efficiency are developed and then evaluated using simulations two likelihood ratio statistics are then used to compare stock and bond indices against sets of 20 and 40 portfolios the procedures are also compared to the gibbons 1982 methodology for testing financial models

on endogenous competitive business cycles the belief that the long run equilibrium of a competitive monetary economy that does not experience any exogeneous shocks whether originating from the external environment or from policy should be modelled as a state that is stationary or perhaps growing at a constant rate seems to be deeply rooted in the mind of some economists

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

when ideas trump interests preferences world views and policy innovations the contemporary approach to political economy is built around vested interests elites lobbies and rent seeking groups which get their way at the expense of the general public the role of ideas in shaping those interests is typically ignored or downplayed yet each of the three components of the standard optimization problem in political economy preferences constraints and choice variables rely on an implicit set of ideas once the manner in which ideas enter these frameworks is made explicit a much richer and more convincing set of results can be obtained in particular new ideas about policy or policy entrepreneurship can exert an independent effect on equilibrium outcomes even in the absence of changes in the configuration of political power

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

tail estimates of east european exchange rates in the literature a consensus exists that distributions of exchange rate returns are fat tailed we use a nonparametric tail index estimator based on extreme value theory to shed light on some of the characteristics of the empirical distribution of black market exchange rate returns for seven east european currencies between 1955 and 1990 focusing on the information in the tails of the distribution we modify an existing tail index estimator to take into account information in both tails the results support the existence of finite second moments in exchange rate returns implicitly the sum stable distribution is rejected

economic development as self discovery in the presence of uncertainty about what a country can be good at producing there can be great social value to discovering costs of domestic activities because such discoveries can be easily imitated we develop a general equilibrium framework for a small open economy to clarify the analytical and normative issues we highlight two failures of the laissez faire outcome there is too little investment and entrepreneurship ex ante and too much production diversification ex post optimal policy consists of counteracting these distortions to encourage investments in the modern sector ex ante but to rationalize production ex post we provide some informal evidence on the building blocks of our model

currency hedging for international portfolios this paper examines the benefits from currency hedging both for speculative and risk minimization motives in international bond and equity portfolios the riskreturn performances of globally diversified portfolios are compared with and without forward contracts over the period 1974 to 1990 inclusion of forward contracts results in statistically significant improvements in the performance of unconditional portfolios containing bonds conditional strategies are also implemented both in sample and out of sample and are shown to both significantly improve the risk return tradeoff of global portfolios and to outperform unconditional hedging strategies whether international portfolios should be hedged against currency risks is the subject of an active debate the theoretical side of the debate has been closely associated with two strands in the academic literature international asset pricing and optimal hedging in the futures markets in the international asset pricing model iapm of solnik 1974 optimal portfolios contain positions in forward contracts or equivalently foreign currency denominated bills these positions which can differ from the positions in foreign stocks have since been termed hedges black 1990 shows that under additional assumptions the hedge ratios should be identical for all investors regardless of their nationality universality and that investors should never fully hedge their foreign currency exposures similarly theoretical models from the futures literature produce demands for hedging instruments that contain both speculative and hedging components the empirical issue unanswered so far is whether adding forward contracts to international portfolios significantly improves the risk return profile of global investments empirical research has barely begun to respond to the challenges of theoretical models there exists little empirical evidence on either the relevance of black s universal hedge ratios or the optimality of hedge ratios less than one instead researchers have concentrated on the benefits of fully hedging exchange risk for example eun and resnick 1988 indicate that stock portfolios perform better when fully hedged but offer no statistical tests

an empirical comparison of alternative models of capital asset pricing in germany abstract in an empirical investigation this research finds that the capm is a better explanatory model of risk return relationships in the german stock market than the ccapm

a unified beta pricing theory abstract this paper derives ross s mutual fund separation theory and a new equilibrium version of ross s arbitrage pricing theory as special cases of a general theory the paper also reveals that the two theories are identical in their predictions of asset prices and portfolio returns the capital asset pricing model a restricted case of the mutual fund separation theory receives special treatment

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

a general distribution for describing security price returns this paper introduces a generalized distribution called the gb2 distribution for describing security returns the distribution is extremely flexible containing a large number of well known distributions such as the lognormal log t and log cauchy distribu tions as special or limiting cases and allowing large even infinite higher moments this flexibility allows a direct representation of different degrees of fat tails in the distribution the properties of the gb2 make it useful in empirical estimation of security returns and in facilitating the development of option pricing models and other models that depend on the specification and mathematical manipulation of distributions copyright 1987 by the university of chicago

the current state of the arbitrage pricing theory this paper provides a simple proof of a recent theorem presented by reisman 1992 concerning the use of proxies for the factors in the return generating process of the arbitrage pricing theory apt in the single factor case the theorem asserts that any variable correlated with the factor can serve as the benchmark in an approximate apt expected return relation the significance of this result is considered and a new direction for empirical work on arbitrage pricing is outlined given a factor model for an infinite sequence of asset returns ross 1976 showed that the absence of arbitrage implies an approximate linear relation between expected returns and the factor betas ross assumed that returns conform to a strict factor structure i e a factor model with uncorrelated disturbances but noted that this condition could be weakened in deriving the arbitrage pricing theory apt nonetheless statistical methods based on the strict factor model assumption dominated the early empirical work on the apt at first glance the requirement of a strict factor structure appeared to impose a strong restriction on the sets of factors that could be used as a benchmark for measuring systematic risk shanken 1982 demonstrated though that virtually any variables could serve as the factors in a welldefined strict factor model one need only repackage an initial finite set of assets into an equivalent set of portfolios in order to fundamentally alter the associated factor space 2 thus the statistical assumptions underlying the apt cannot by themselves characterize the economically relevant components of returns chamberlain and rothschild 1983 shifted attention away from strict factor structures by proving that the apt holds more generally if returns conform to an approximate factor model 3 in this case the disturbances need

on correlations and inferences about mean variance efficiency a framework is presented for investigating the mean variance efficiency of an unobservable portfolio based on its correlation with a proxy portfolio a sensitivity analysis derives the highest correlation between the proxy and a portfolio that reverses the inference of a test of sharpe lintner tangency for example the maximum correlation between the value weighted nyse amex portfolio and a portfolio inferred tangent ranges from 0 76 to 0 48 we also test whether the correlation between the proxy and the tangent portfolio exceeds a given level this hypothesis is often rejected for the nyse amex proxy at a correlation of 0 7

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

smart specialisation entrepreneurship and smes issues and challenges for a results oriented eu regional policy this paper discusses the ways that european regional policy has been re shaped in order to build on the role played by entrepreneurship in driving regional innovation the various lines of re thinking which have helped to reform the policy draw heavily on modern theories of entrepreneurship and innovation and these insights have contributed significantly to many of the elements of new policy logic and framework yet these ideas also derive both from worldwide rather than eu specific insights and also from a wide range of academic fields setting the eu agenda within the broader global context is therefore also important in order to help identify both the commonalities and differences between policy approaches in different types of places

multivariate tests of asset pricing the comparative power of alternative statistics this paper examines estimation issues associated with multivariate tests of asset pricing two issues are considered 1 the constraint that the sample size n must be less than the time series t and 2 the relative effect on power of using the multivariate statistic versus a univariate counterpart we find that an alternative statistic that allows for large n does not dominate the usual portfolio tests more notably we find that the power of a simple diagonal statistic usually dominates the multivariate statistic for cases considered inthis study

is there chaos in economic time series in recent years interest in deterministic chaos has increased tremendously and the literature is still growing besides its obvious intellectual appeal there are at least two reasons why chaos is so interesting first chaos is able to generate complex behaviour which appears random thereby representing a change of perspective in the explanation of fluctuations in economic time series second although chaos is unpredictable the fact that it is deterministic makes it exploitable and therefore usable chaos is a nonlinear deterministic process which looks random in fact chaotic processes have first and second moment properties that are the same as for white noise processes this is why they are also called white chaos the distinguishing feature of chaotic systems however is that they exhibit sensitive dependence on initial conditions to be more specific sensitivity to initial conditions implies that nearby identical chaotic systems in slightly different states will rapidly evolve toward very different states

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