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We investigate Grossman and Laroque's (1990) conjecture that costs of adjusting consumption can account, in part, for the empirical failure of the consumptionbased capital asset pricing model (CCAPM). We incorporate small fixed costs of consumption adjustment into a CCAPM with heterogeneous agents. We find that undetectably small consumption adjustment costs can account for much of the discrepancy between the observed variance of nondurable aggregate consumption growth and the predictions of the CCAPM, and can partially reconcile nondurable consumption data with the observed equity premium. We conclude that the CCAPM's implications are nonrobust to extremely small adjustment costs. THE CONSUMPTION-BASED CAPITAL ASSET PRICING MODELS (CCAPMs)1 of Lucas (1978), Breeden (1979), and Grossman and Shiller (1982) have difficulty matching the high volatility of equity returns and the high mean equity premium found in U.S. data. First, the variance of the CCAPM asset pricing kernel is too low to generate plausible equity-return volatility. More precisely, Hansen and Jagannathan (1991) and Cochrane and Hansen (1992) show that, for any conjectured pricing kernel mean, the variance of the kernel is too low to satisfy the Hansen-Jagannathan bounds without implausibly high risk aversion or substantial habit formation.2 Second, the covariance between the CCAPM asset pricing kernel and excess equity returns is too low to generate a plausible equity premium. More precisely, let us define EP' as follows

There is now considerable evidence suggesting that estimated betas of unconditional capital asset pricing models (CAPMs) exhibit statistically significant time variation. Therefore, many have advocated the use of conditional CAPMs. If we succeed in capturing the dynamics of beta risk, we are sure to outperform constant beta models. However, if the beta risk is inherently misspecified, there is a real possibility that we commit serious pricing errors, potentially larger than with a constant traditional beta model. In this paper we show that this is indeed the case, namely that pricing errors with constant traditional beta models are smaller than with conditional CAPMs. LINEAR FACTOR MODELS such as the unconditional capital asset pricing model (CAPM) and the arbitrage pricing theory (APT) have been the cornerstone of theoretical and empirical finance for decades now. Supported by seminal papers, like those of Sharpe (1964), Lintner (1965), Merton (1973), and Ross (1976), they are the most widely used tools to value the return on risky assets. Although the theory maintains a linear and stable relationship between risk factors and returns, there is now considerable empirical evidence documenting time variation in market betas and other factor payoffs. This is perhaps not so surprising because the theoretical underpinnings of the unconditional arbitrage-pricing theory reveal that timeinvariant linear factor structures are only obtained when one imposes strong assumptions on the underlying probability distributions and investors’ attitudes toward risk. 1 In practice, many portfolio managers constantly update and reestimate factor returns, and indeed Harvey (1989), Ferson and Harvey (1991, 1993)

Prize Lecture to the memory of Alfred Nobel, December 7, 1990. (This abstract was borrowed from another version of this item.)

IT IS COMMON PRACTICE to attempt to assess the relative attractiveness of proposed investment projects by adjusting the capitalization rates applied to project cash flows, for the perceived riskiness of the flows; the greater the risk, the higher the discount rate. Alternatively, projects thought to contain substantial risks may be required to surmount more stringent "internal rate of return" hurdles-these being directly related to cash flow unpredictability. Such procedures, while by no means the only approaches to comprehending project risk, are also the most frequently taught in school of business. They are sanctioned, in principle, by the lessons of the Capital Asset Pricing Model-which establishes that, in a competitive securities market peopled by well-diversified investing entities, there will be a positive linear relationship between the yield required on an asset and that asset's contribution to portfolio risk [7] [9] [13]. Hence, the greater the (systematic) risk involved, the larger the market-required (expected) return. The associated capital budgeting prescription thereupon is a risk-adjusted discount rate. There are, of course, some troublesome aspects to this approach. The major one is the leap from the basically single-period format of the CAPM to the inherently multi-period nature of the great bulk of real-asset investment opportunities. It is not entirely clear that the CAPM scenario inevitably legitimizes the application of risk-adjusted project yield criteria in the multi-period case, although there is support for that position [21 [8]. A risk-adjusted discount rate also implies certain possibly bothersome assumptions about the inter-period pattern of risk resolution [10]. Nonetheless, risk-adjusted rates are widely used and widely recommended despite these caveats. Even if they are considered only as approximations to value measurement-as surrogates for the underlying securities market responses to projects-they appear to have gained acceptance as the most practical enbodiment

Tax based dividend models of capital asset pricing assume that dividends are known at the time prices are set. Dividends which are announced and paid in the same month, and dividends which were expected but cancelled in the month constitute surprises which interfere with many empirical tests of the effects of expected dividend yield on returns. This paper avoids these problems by relating returns to forecasts of dividend yield obtained from past data. THREE DISTINCT VIEWS OF the importance of dividends to investors have received support at one time or another. According to the two most important views, dividends have a neutral and a negative effect on security prices respectively. Miller and Modigliani [1] and Miller and Scholes [12, 13] favor complete substitutability of dividends and capital gain. Brennan [6] and Litzenberger and Ramaswamy [9] have developed models which incorporate differential taxation of income and capital gain. In these models, the tax disadvantage of income changes the investor's portfolio problem from one of optimization of mean and variance of portfolio before-tax return to optimization in after-tax terms. Stocks with relatively large dividend yields should provide high expected returns (and so sell for low prices) to compensate the investor for the tax. Much of the empirical evidence seems to favor the view that tax disadvantages of dividend income do not escape investors' attention and that returns are higher when they include dividend income to compensate the investor for the tax liability. However, interpretation of the available evidence is difficult and it is significant that most of these researchers remain unconvinced that their own findings can be satisfactorily explained by tax effects. Ball, Brown, Finn, and Officer [1] interpret their estimates as being far too strong to be explained in terms of differential taxation. Blume [3] reaches a similar conclusion, but Litzenberger and Ramaswamy attribute their results to the tax disadvantage of

IN CAPITAL ASSET pricing theory, investors are assumed to base their asset decisions on expected risks and returns. Although this theory has been widely accepted in the academic community, the behavioral assumption underlying the theory has not been directly tested by surveying actual investors regarding their decision processes. One method of empirically researching decision behavior could begin with quantifying investors' perceptions of the differences among assets. Logically, for an investor to choose assets in regard to expected risks and returns, he must first perceive differences among the assets in at least a risk-return space; only then could he render preference or evaluative judgments. But whether investors actually perceive the differences among assets with a two-dimensional, risk-return framework, remains relatively uninvestigated. In the only published study regarding stock perceptions, Green and Maheshwari [11] found that graduate business students' perceptions could be modeled well by two or three dimensions.They found that two of these dimensions correlated highly with the students' perceptions of risk and growth but not with ex post data, such as earnings per share. Unfortunately, Green and Maheshwari did not survey important equity investors nor did they use relevant data such as total returns to describe the perceptions estimated. This paper remedies these deficiencies and covers new ground. We show that while investor groups' average stock perceptions are highly related to relevant risk and return measures, significant differences may exist between portfolio managers' and nonprofessional investors' average multidimensional perceptions. These and additional empirical results, plus their implications and the behavioral design, are detailed in the following three sections.

Two FEATURES OF MANY capital asset pricing theories are a) that the relationship between risk and expected returns is linear and b) that risk is defined as the covariability of an asset's returns with the returns on a properly defined hedging portfolio. Among such theories, the Sharpe [9]-Lintner [7] Capital Asset Pricing Model (CAPM), the Black [1] CAPM, and the Ross [8] Arbitrage Pricing Theory (APT) have received the greatest attention. Despite earlier evidence in support of the CAPM,1 recent findings by Tinic and West [11] challenge both the completeness of beta as a measure of relevant risk and the linearity of the relationship between risk and expected returns. In a separate study, Tinic and West [10] also demonstrate that beta risk may not be priced by the market, except in January and (to a lesser extent) July. Gultekin and Gultekin [5] report that APT factors are also not priced in non-January months. The above tests involve cross-sectional regressions of realized security returns against various measures of risk that are estimated in time-series regressions in preceding periods. Portfolio grouping procedures are used to create dispersion in the risk estimates and (hopefully) also in the average realized returns. Portfolio formation also helps to eliminate estimation errors. However, since the actual hedging portfolios and the securities' risk exposures are unobservable, it is difficult to determine whether the above findings reflect a) the absence of a riskreturn relationship or b) inadequacies in (testing) these specific asset-pricing models. This study seeks to disentangle the above two interpretations by comparing the month-to-month holding-period return spreads between stock and T-bill returns. No need exists to calculate beta (or other risk estimators) because stocks are universally accepted as being more risky than government T-bills. If these relative risk rankings are correct and if a consistent risk-return relationship exists, then the average monthly holding-period return spread should be systematically positive. However, we find that, between 1927 and 1983, average spreads between (even small firms') stocks and T-bills are significantly greater than zero only in January and (to a lesser extent) July. Subperiod results are similar. Thus, we fail to find a pervasive risk-return relationship, and its absence cannot be attributed to misspecification of asset-pricing models or to nonstationary or inefficient estimates of beta.

THE PROBLEMS OF CAPITAL BUDGETING seem to be, figuratively speaking, everyone's concern. Industrial engineers, economists, operations research analysts and finance specialists claim the subject matter as their domain. Each has a unique perspective and point of view; each tends to concentrate attention on a different type of problem because of slightly different goals; each tends to use a different set of tools and techniques; and each tends to talk among themselves. The literature has grown rapidly in each field and has tended to diverge from, rather than to converge to, a unified whole. The analysis of uncertainty in capital budgeting is a good example. With some oversimplification, it is convenient to characterize the engineeringmanagement science approach as one concerned primarily with norinative. models for decision making and to be primarily concerned with computing solutions. Weingartner [17], Naslund [13], Hillier [7], Oakford [14] and Bernhard [2] are examples. These approaches place minimum emphasis on the development of criteria and maximum emphasis on solution technique. Mathematical programming holds sway in these approaches. The economics-finance approach tends to pay little attention to computing technique and a great deal of attention to the development of general criteria and rules. Here the theoretical ideas of capital asset pricing of Sharpe [15], Lintner [8], and Mossin [1 1] serve as background for capital budgeting analysis by Litzenburger and Budd [9], Hamada [6], Stapleton [16] and Bierman and Hass [3], to name a few. One could further classify the approaches as being concerned with the selection of sets of projects under inter-relationships in the engineering-management science approach and with single projects in the economics-finance approach. Mutually exclusive, contingent, competitive and complementary projects are significant in the writings of the former, while they play a lesser role in the latter. What is the appropriate discount rate or the hurdle rate that projects must clear is usually the goal of the economics-finance approach, while this rate is taken for granted in the engineering-management science approach. The classifications that have been made are not perfect, to be sure. Weingartner [17], Baumol and Quandt [1], Naslund [13] and Bernhard [2], represent programming approaches which tie in with the criterion problem. Hamada [6] on the opposite side makes reference to programming analysis in his development of general criterion and rules for capital budgeting. However, explicit recognition of the role of programming in the general criterion of market value maximization using the capital asset pricing model has not been detailed.

IN THE SEPTEMBER 1979 issue of this journal, Bierman-Oldfield [1] show that the Modigliani-Miller Proposition I with corporate taxation is unaltered by the existence of risky debt. Bierman-Oldfield state on page 954 that the analysis implies the expected returns on debt, unlevered equity, and levered equity are determined simultaneously and linked together by the capital asset pricing equilibrium. The purpose of this extension is to examine the exact linkage of the aforementioned expectations resulting from pure capital structure rearrangements. Hamada [5], by integrating Modigliani-Miller Proposition I with the standard capital asset pricing model, has shown the exact linkage between the return expectations of unlevered equity and levered equity. The Hamada result assumes returns on corporate debt are risk free. An interesting, and not widely recognized, result is that the correlation between the levered firm and the market portfolio, a primary input to the measurement of diversification relative to the market, can be directly influenced by the financing decision of the firm.' This conclusion will obtain specifically by allowing for risky corporate debt. When considering that individual investors typically hold undiversified portfolios, the result takes on an added dimension [e.g., 2]. In Section II the equilibrium relationship of the return expectations is developed, and extended in Section III to demonstrate the effect of the financing decision on firm diversification relative to the market. The extension is concluded and implications are summarized in Section IV. The Bierman-Oldfield results are assumed throughout.

IN A GENERAL CAPITAL MARKET the pattern of state contingent payoffs from existing securities determine the feasible allocations of uncertain future wealth attainable by individuals in the economy. Recapitalizations, which are additions and/or partitions of the vectors of state contingent payoffs from existing securities (e.g., capital structure changes, or non-synergistic mergers and/or divestitures), may render an equilibrium allocation of uncertain wealth unattainable or may induce individuals to trade from the previous allocation to a mutually preferable allocation. Under either of these conditions, the equilibrium allocation of uncertain future wealth would be altered and the total market values of firms in the economy may change. Even when firms' total market values are affected by a recapitalization, as long as the capital market is perfect, the Modigliani-Miller thesis that the relative market of values of firms in the same risk class are independent of recapitalizations would hold as an arbitrage condition. That is, with unrestricted short sales and the absence of transactions costs, portfolios of securities offering identical uncertain future payoffs would sell at the same price or else riskless arbitrage profits would exist. However, under existing institutional arrangements for short selling, where interest is not received on funds impounded from a short position, the relative market values of firms in the same risk class may differ from the relative sizes of their uncertain future returns implying that the relative market values of firms within the same risk class could be affected by capital structure and hence by recapitalizations. Divergences in the relative market values of firms in the same risk class from the relative sizes of their uncertain future payoffs is shown to imply that the allocation of securities is Pareto inefficient. The existence of an inefficient allocation of wealth is shown to be inconsistent with models (capital asset pricing, option

Several recent writings have raised questions concerning the effectiveness of commonly used analytical measures and techniques which have their basis in Modern Portfolio Theory. Questions have been raised about the use of beta in the interpretation of risk adjusted equity performance and about the usefulness of the capital asset pricing model (CAPM) as a tool for measuring and interpreting investment performance. This paper restricts itself to questions concerning beta and CAPM as they relate to performance measurement. In the process of this examination it discusses some basic principles of performance measurement as they relate to judgments of investment management skill and ability. It has been shown that simple applications of beta used in adjusting equity performance for risk can possibly produce misleading or incorrect interpretations of risk adjusted performance. Errors have been shown to be related to the market index used as a basis for the determination of beta. These findings are independent of the validity of CAPM, but the line of reasoning which leads to these conclusions is not totally antithetical to the derivation of CAPM. This paper has three major sections: 1. The capital asset pricing model is assumed to be valid, and a broader index of capital assets is constructed. This index is "better" in the sense that it includes many more assets than the S&P 500 and hence is more complete. 2. The better index is then used to "game" performance measurement using current investment technology and the Standard & Poor's 500. 3. Some conclusions are drawn as to the effectiveness of gaming and the ways in which performance measurement numbers should be interpreted in general. General issues are discussed in the text. A parallel, more detailed and more technical argument is presented in the appendix.

In a multiperiod pure exchange world with investors displaying HARA-preferences, conditions for period-by-period application of one-period asset pricing models are derived first. The future investment opportunity set may be uncertain, provided that in every period a specific market portfolio variable depending on preferences is known as of the preceding date. This variable need not be completely deterministic. Second, conditions for a serially independent market excess return are derived. These conditions render serial independence very unlikely. Hence estimation methods assuming serial independence are likely to yield biased results. WHILE MULTIPERIOD capital asset pricing models generally involve intertemporal interdependencies in the pricing of assets, there exist conditions under which the multiperiod model becomes indistinguishable from a sequence of one-period models. If these conditions are met, then the price of an asset with cash flows at various dates can be derived by applying the one-period pricing model recursively period by period. The valuation process then is called quasi-myopic at every date.

This paper examines how and how well do leading economists forecast stock market returns. This question is fundamental in finance, since the Capital Asset Pricing foundation rests upon assumptions about the properties of investors' expectations for stock market returns. The results reveal that economists' expectations of market returns as exemplified in Livingston's data do not meet the necessary conditions of efficiency. It should be noted however, that in later period some improvement in the quality of economists' forecasts was observed.

THE EFFECTS OF DIVERSIFICATION on portfolio efficiency have been examined extensively over the past decade since the pioneering works of Markowitz [10], and later Sharpe [12] and Lintner [7]. The great majority of the empirical work has been limited to common stocks in the U.S. capital market. Recently papers have begun to appear examining the merits of diversifying across international boundaries ([1], [2], [4], [5], [6], [11]). The purpose of this paper is to examine several theoretical implications of such international diversification, with particular attention to the effects of imperfections in international financial markets on risk premia for capital assets, the cost of capital to firms, and the efficiency with which capital is allocated.

THE RELATION between the characteristics of uncertain cash flows and their equilibrium prices in perfect capital markets is one of the main topics of analysis in the theory of finance. Within this context, the issue of the existence of "unsystematic" risks has aroused considerable interest and controversy. One way of defining the problem can be the following: is it possible to consider all financial prospects as sums of two components, so that one-the systematic component-is perfectly correlated among all securities, and the other-the residual or unsystematic component-is uncorrelated with the first and does not affect the price of the prospect? The origin of the controversy is the apparent disagreement between the results of Sharpe [10] and Lintner [7]. Sharpe was first to consider the idea and he also coined the term "systematic." Given certain assumptions about the market, Sharpe's answer to the question as posed above is in the affirmative. Furthermore, the systematic component is shown in Sharpe's analysis to be perfectly correlated with the market portfolio, which is composed of all outstanding securities. Lintner's conclusions on this issue are exactly the opposite, namely: "Other things being equal, stock values.... will always vary inversely with the residual variance (or "standard error of estimate") of their regression on either external index of business conditions or the composite market preformance of the entire group of stocks composing the market" [7, p. 588]. In a comparative analysis of the two studies, Fama [4] distinguishes two different models in Sharpe's article. He shows the first-the capital asset pricing model-to be in complete agreement with Lintner's model. Fama calls the second model the market model, and shows that the assumptions implicit in it are inconsistent. As for the issue of systematic and unsystematic risk, Fama seems to adopt Lintner's position that unsystematic risks (as defined above) cannot exist. The present note is an additional (and probably not the last) chapter in this altogether intriguing discussion. We shall show that the so called "market model" can best be interpreted as an alternative presentation rather than a set of assumptions comprising a "model." Under the suggested interpretation, Sharpe's original result holds. The issue of systematic risk is then analyzed in the light of results derived by this author elsewhere [2]. It is shown that systematic and unsystematic components can be identified whenever equilbrium prices exist, regardless of

SHARPE [12] AND LINTNER [7] have recently proposed models directed at the following questions: (a) What is the appropriate measure of the risk of a capital asset? (b) What is the equilibrium relationship between this measure of the asset's risk and its one-period expected return?' Lintner contends that the measure of risk derived from his model is different and more general than that proposed by Sharpe. In his reply to Lintner, Sharpe [13] agrees that their results are in some ways conflicting and that Lintner's paper supersedes his. This paper will show that in fact there is no conflict between the SharpeLintner models. Properly interpreted they lead to the same measure of the risk of an individual asset and to the same relationship between an asset's risk and its one-period expected return. The apparent conflicts discussed by Sharpe and Lintner are caused by Sharpe's concentration on a special stochastic process for describing returns that is not necessarily implied by his asset pricing model. When applied to the more general stochastic processes that Lintner treats, Sharpe's model leads directly to Lintner's conclusions.

A RECENT ARTICLE in this Journal' explored the conditions for equilibrium in the market for capital assets under the assumptions that investors are riskaverters, have similar (probabilistic) beliefs about the future performance of various assets, and can borrow or lend funds at a common (pure) interest rate. Briefly, the article showed that under such conditions market prices of capital assets will adjust so that the predicted risk of each efficient portfolio's rate of return is linearly related to its predicted expected rate of return. Letting vi stand for the standard deviation of the subjective probability distribution of the rate of return on an efficient portfolio, and E1 for the expected value of the distribution, the prices of capital assets will adjust until all efficient portfolios conform to the relationship

reproducible real capital assets to the replacement costs of these assets.3 Straightforward application of this concept parallels that of use of neoclassical theory, with investment being made a function of marginal "q." Such functions are a simplistic approximation to asset portfolio selection principles, balancing expected returns, variances and convariances, with the preferences of asset holders as developed by Markowitz (1952, 1959), Tobin (1958, 1961), Sharpe (1964, 1970), Lintner (1965), and others.4 Generally known as the capital asset pricing model, these principles have been utilized almost exclusively for valuing financial (intangible) rather than physical (tangible) capital. Moreover, use of this model has almost wholly been restricted to structuring portfolios of private investors and financial intermediaries in contrast to that for structuring capital demand by producing sectors. A traditional approach in the economic theory of investment has been that decisions first are made about outlays for tangible assets and then decisions are made about how to finance these expenditures. Such sequential separation of tangible and intangible capital decisionmaking was most elegantly justified by Modigliani and Miller in a series of articles starting in the late 1950s (1958, 1961, 1963, and 1966). However, as Stiglitz (1974), Scott (1976) and others have shown, the proposition depends not only on existence of perfect capital markets but also