earnings or dividend announcements) that can be readily evaluated by investors using generally-accepted structural models. Consider, however, the informational event of publication in a scientific journal of the empirical discovery of an anomalous profit opportunity (e.g, smaller-capitalized firms earn excessive risk-ad justed average returns). The expected duration between the creation of this investment opportunity and its elimination by rational investor actions in the market place can be considerable Before results are published, an anomaly must in fact exist for a long enough period of time to permit sufficient statistical documentation. 7 After publication, the diffusion rate of this type of information from this source is likely to be significantly slower than for an earnings announcement. If the anomaly applies to a large collection of securities (e.g, all small stocks), then its correction"will require the actions of many investors. If an investor does not know about the anomaly, he will not, of course. act to correct it Once an investor becomes aware of a study, he must decide whether the reported historical relations will apply in the future. On the expected duration of this decision, I need only mention that six years have passed since publication of the first study on the small-firm effect and we in academic finance have yet to agree on whether it even exists. Resolving this issue is presumably no easier a task for investors. Beyond this decision, the investor must also determine whether the potential gains to him are sufficient to warrant the cost of implementing the strategy. Included in the cost are the time and expense required to build the model and create the data base necessary to support the strategy. Moreover, professional money managers may have to expend further time and resources to market the strategy to clients
-5- earnings or dividend announcements) that can be readily evaluated by investors using generally-accepted structural models. Consider, however, the informational event of publication in a scientific journal of the empirical discovery of an anomalous profit opportunity (e.g., smaller-capitalized firms earn excessive risk-adjusted average returns). The expected duration between the creation of this investment opportunity and its elimination by rational investor actions in the market place can be considerable. Before results are published, an anomaly must in fact exist for a long enough period of time to permit sufficient statistical documentation. After publication, the diffusion rate of this type of information from this source is likely to be significantly slower than for an earnings announcement. If the anomaly applies to a large collection of securities (e.g., all small stocks), then its "correction" will require the actions of many investors. If an investor does not know about the anomaly, he will not, of course, act to correct it. Once an investor becomes aware of a study, he must decide whether the reported historical relations will apply in the future. On the expected duration of this decision, I need only mention that six years have passed since publication of the first study on the "small-firm effect" and we in academic finance have yet to agree on whether it even exists. Resolving this issue is presumably no easier a task for investors. Beyond this decision, the investor must also determine whether the potential gains to him are sufficient to warrant the cost of implementing the strategy. Included in the cost are the time and expense required to build the model and create the data base necessary to support the strategy. Moreover, professional money managers may have to expend further time and resources to market the strategy to clients
and to satisfy prudence requirements before implementation. If profitable implementation requires regulatory and business practice changes or the creation of either new markets or new channels of intermediation, then the delay between announcement of an anomaly and its elimination by corrective action in the market place can, indeed, be a long one. Much the same story applies in varying degrees to the adoption in practice of new structural models of evaluation (e. g, option pricing models)and to the diffusion of innovations in financial products (cf. Rogers, 1972 for a general discussion of the diffusion of innovations). Recognition of the different speeds of information diffusion is particularly important in empirical research where the growth in sophisticated and sensitive technique s to test evermore-refined financial-behavioral patterns severely strains the simple information structure of our asset pricing models. To avoid inadvertent positing of a Connecticut Yankee in King Arthur's Court, empirical studies that use long historical time series to test financial- market hypotheses should take care to account for the evolution of institutions and information technologies during the sample period. It is, for example, common in tests of the weak form of the Efficient Market Hypothesis to assume that real-world investors at the time of their portfolio decisions had access to the complete prior history of all stock returns When, however, investors'decisions were made, the price data may not have been in reasonably-accessible form and the computational technology necessary to analyze all these data may not even have been invented. In such cases, the classification of all prior price data as part of the publicly-available information set may introduce an important bias against the null hypothesis All of this is not to say that the perfect-market model has not been and
III -6- and to satisfy prudence requirements before implementation. If profitable implementation requires regulatory and business practice changes or the creation of either new markets or new channels of intermediation, then the delay between announcement of an anomaly and its elimination by corrective action in the market place can, indeed, be a long one. Much the same story applies in varying degrees to the adoption in practice of new structural models of evaluation (e.g., option pricing models) and to the diffusion of innovations in financial products (cf. Rogers, 1972 for a general discussion of the diffusion of innovations). Recognition of the different speeds of information diffusion is particularly important in empirical research where the growth in sophisticated and sensitive techniques to test evermore-refined financial-behavioral patterns severely strains the simple information structure of our asset pricing models. To avoid inadvertent positing of a "Connecticut Yankee in King Arthur's Court," empirical studies that use long historical time series to test financialmarket hypotheses should take care to account for the evolution of institutions and information technologies during the sample period. It is, for example, common in tests of the weak form of the Efficient Market Hypothesis to assume that real-world investors at the time of their portfolio decisions had access to the complete prior history of all stock returns. When, however, investors' decisions were made, the price data may not have been in reasonably-accessible form and the computational technology necessary to analyze all these data may not even have been invented. In such cases, the classification of all prior price data as part of the publicly-available information set may introduce an important bias against the null hypothesis. All of this is not to say that the perfect-market model has not been and
will not continue to be a useful abstraction for financial analysis. The model may indeed provide the best description of the financial system in the long run. It does, however, suggest that researchers be cognizant of the insensitivity of this model to institutional complexities and explicitly assess the limits of precision that can be reasonably expected from its predictions about the nature and timing of financial behavior. Moreover, I believe that even modest recognition of institutional structures and information costs can go a long way toward explaining financial behavior that is otherwise seen as anomalous to the standard frictionless-market model. To illustrate this thesis, I now turn to the development of a simple model of capital market equilibrium with incomplete information
-7- will not continue to be a useful abstraction for financial analysis. The model may indeed provide the best description of the financial system in the long run.8 It does, however, suggest that researchers be cognizant of the insensitivity of this model to institutional complexities and explicitly assess the limits of precision that can be reasonably expected from its predictions about the nature and timing of financial behavior. Moreover, I believe that even modest recognition of institutional structures and information costs can go a long way toward explaining financial behavior that is otherwise seen as anomalous to the standard frictionless-market model. To illustrate this thesis, I now turn to the development of a simple model of capital market equilibrium with incomplete information
8 II. Capital Market Equilibrium With Incomplete Information In this section, we develop a two-period model of capital market equilibrium in an environment where each investor knows only about a subset of the available securities. In subsequent sections, we explore the impact on the structure of equilibrium asset prices caused by this particular type of incomplete information There are n firms in the economy whose end-of-period cash flows are technologically specified by where denotes a random variable common factor with E(Y)=0 E(Y)-1andE()-E(1,2…;-1,+1……,,Y)=0,k=1,…n I denotes the amount of physical investment in firm k and and s, represent parameters of firm k's production technology, Let v, denote the equilibrium value of firm k at the beginning of the period. If is the equilibrium return per dollar from investing in the firm over the period, then 段瓦1++k, (2) where from(1),x-e(r )=Ikk/k,"T and "%Kkk k - l,..., n. By inspection of (2), the structure of returns is like that of the Sharpe (1964)"diagonal"model or the" one-factor version of the Ross (1976) Arbitrage Pricing Theory(APT) model In addition to shares in the firms, there are two other traded
-8- II. Capital Market Equilibrium With Incomplete Information In this section, we develop a two-period model of capital market equilibrium in an environment where each investor knows only about a subset of the available securities. In subsequent sections, we explore the impact on the structure of equilibrium asset prices caused by this particular type of incomplete information. There are n firms in the economy whose end-of-period cash flows are technologically specified by: ik -LIk Elk y +k (1) where Y denotes a random variable common factor with E(Y) = 0 and E(r) = 1 and E(Ek) = E(Ek l 1 C ,... 2 ,+ , l ,.. , n Y) = O , k =n. Ik denotes the amount of physical investment in firm k and 1 k' ak and sk represent parameters of firm k's production technology. Let Vk denote the equilibrium value of firm k at the beginning of the period. If Rk is the equilibrium return per dollar from investing in the firm over the period, then Rk = Ck/Vk, and % - % % R = + bkY + ki (2) R 2=R~+b~a , (2) where from (1), R = E(Rk) = Ikpk/Vk; bk = akk/Vk and = SkIk/Vk k = l,...,n. By inspection of (2), the structure of returns is like that of the Sharpe (1964) "diagonal" model or the "one-factor" version of the Ross (1976) Arbitrage Pricing Theory (APT) model. In addition to shares in the firms, there are two other traded
securities: a riskless security with sure return per dollar R and a security that combines the riskless security and a forward contract with cash settlement on the observed factor index Y. without loss of generality, it is assumed that the forward price of the contract is such that the standard deviation of the equilibrium return on the security is unity. Thus, the return on the security can be written as R+Y (3) It is assumed that both this and the riskless security are"inside"securities and therefore, investors' aggregate demand for each of them must be zero in equilibrium. The model assumes the standard frictionless-market conditions of no taxes, no transactions costs, and borrowing and shortselling without restriction There are n investors where n is sufficiently large and the distribution of wealth sufficiently disperse that each acts as a price taker Each investor is risk averse and selects an optimal portfolio according to the Markowitz-Tobin mean-variance criterion applied to end-of-period wealth The preference of investor is represented as U,=E(RW> Var(R-N> (4) where denotes the value of his initial endowment of shares in the firms evaluated at equilibrium prices; Ry R denotes the return per dollar on his portfolio; and 5,>0,1=1,., N. In addition to an initial endowment of shares, each investor is endowed with an information set described as follows: Common knowledge in all
-9- securities: a riskless security with sure return per dollar R and a security that combines the riskless security and a forward contract with cash settlement on the observed factor index Y. Without loss of generality, it is assumed that the forward price of the contract is such that the standard deviation of the equilibrium return on the security is unity. Thus, the return on the security can be written as: R + '(3 RR Rn + Y *(3) n+l n+l It is assumed that both this and the riskless security are "inside" securities and therefore, investors' aggregate demand for each of them must be zero in equilibrium. The model assumes the standard frictionless-market conditions of no taxes, no transactions costs, and borrowing and shortselling without restriction. There are N investors where N is sufficiently large and the distribution of wealth sufficiently disperse that each acts as a price taker. Each investor is risk averse and selects an optimal portfolio according to the Markowitz-Tobin mean-variance criterion applied to end-of-period wealth. The preference of investor j is represented as: Uj = E(R W) Wj Var(RWA) ,(4) 2WJ where W denotes the value of his initial endowment of shares in the firms evaluated at equilibrium prices; R denotes the return per dollar on his portfolio; and 6> , j = .. .N. In addition to an initial endowment of shares, each investor is endowed with an information set described as follows: Common knowledge in all