Knowledge that Transforms

The value of information to the investor is best described by Samuelson [15] in his prologue to the theory of speculation: “…Suppose my reactions are not better than those of other speculators, but rather one second quicker… in a world of uncertainty, I note the consequences of each changing event one second faster than anyone else. I make my fortune not once, but every day that important events happen…” Furthermore, the role of heterogeneous expectations was emphasized by Hirshleifer [7]: “…Speculation…emerges not from differences in individual risk aversion, but rather solely from differences in individual belief as to what the future will reveal.” Thus, information which is always partial and different to different investors, in imperfect markets, is perfectly consistent with the existence of heterogeneity in investors' expectations.

In this paper, we present a new version of the capital asset pricing model CAPM) that provides a linear pricing equation substantially different from that implied by the traditional CAPM of Sharpe [18], Lintner [12], and Mossin [14, 15] (hereafter SLM model). It is assumed that each of the investors has an initial endowment of real resources (say, corn) which can be either consumed invested in investment opportunities available to the investor. A set of simultaneous equations is derived from the model. The set of equations determines the equilibrium values of these interdependent endogenous variables: the amount to be consumed by the investor; the proportion of each investment project be owned by the investor; the amount to be invested in each of the available investment projects; the market value of each project; the market price of risk; and the return imputed by the capital market for a risky project which has a zero-beta risk. If a riskless project exists, the zero-beta rate is just a risk-free rate.

In a recent paper the net present value (NPV) accept-reject decision rule, invoking the conventional definition of expected net cash flows of a finite, uneven character along with a weighted average cost of capital, was derived from the condition of shareholder wealth maximization (Beranek [2]). Since the entire textbook-NPV expression was established–its logical form, the content of its variables, and the implied specification of its parameters–this has served as a partial rescue of textbook approaches to capital budgeting, approaches which had heretofore rested on an intuitive basis. But attempts to rescue textbook treatments of mutually exclusive (ME) choices and capital rationing must fail. Explaining why they must fail, and developing what we shall denote as the AB alternative solution, is the object of this paper.

Richard H. Bernhard, Carl J. Norstrom, A Further Note on Unrecovered Investment, Uniqueness of the Internal Rate, and the Question of Project Acceptability, The Journal of Financial and Quantitative Analysis, Vol. 15, No. 2 (Jun., 1980), pp. 421-423

Stephen M. Schaefer, Discussion: Analyzing Convertible Bonds, The Journal of Financial and Quantitative Analysis, Vol. 15, No. 4, Proceedings of 15th Annual Conference of the Western Finance Association, June 19-21, 1980, San Diego, California (Nov., 1980), pp. 931-932

Uri Dothan, Joseph Williams, Term-Risk Structures and the Valuation of Projects, The Journal of Financial and Quantitative Analysis, Vol. 15, No. 4, Proceedings of 15th Annual Conference of the Western Finance Association, June 19-21, 1980, San Diego, California (Nov., 1980), pp. 875-905

Based on the theory of the pricing of capital assets developed by Sharpe [12], Lintner [9] and Mossin [11], Professor Jensen formulated a return-generating model to measure portfolio performance [5]. In a subsequent paper, Professor Jensen [6] investigated the impact of the investment horizon on the functional form of the model. Lee [8] has proposed a generalized specification of the model to resolve this problem. Alternative estimation methods for testing the linearity of the model in terms of time-series data have also been suggested by Lee. Moreover, the stability of the beta coefficient over time and the impact of the market's condition on both the alpha (or, Jensen's measure of performance [5]) and beta of the model have come under scrutiny in financial research.

The mean-variance capital asset pricing model (CAPM) of Sharpe and Lintner was extended by Brennan [3] to incorporate divergent borrowing and lending rates. He found that in equilibrium the security market line (SML) has the same structure as the SML under the single-rate CAPM of Sharpe and Lintner. That is, the expected return of a security or a portfolio remains linear in its systematic risk, with the intercept replaced by an equivalent risk-free return, which is an average of the divergent borrowing and lending rates weighted by the investors' taste parameters. The equivalent risk-free return is larger than the riskless lending rate and, hence, does not represent an inconsistency with the empirical findings by Friend and Blume [4] and by Black, Jensen and Scholes [1[ that the intercept of empirical SML estimated for the single-rate CAPM is larger than the riskless rate. Moreover, Brennan attempted to show that his construct can be extended to the extreme case where there are no riskless opportunities. The case of no riskless opportunities was of course investigated by Black [2], who generalized the CAPM and SML by inventing the concept of zero-beta port-folio to account for the same empirical problem encountered in the traditional SML tests of CAPM. Since the Sharpe-Lintner single-riskless-rate CAPM implies a perfect loan market, we may view the attempts by Black and Brennan as generalizing the CAPM by incorporating financial restrictions and loan market imperfections. Their primary motive, however, is empirical, i.e., to reconcile the results from the traditional SML tests with their generalized CAPM.

Modern contingent pricing theory (CPT) dates its genesis from the pioneering work of Arrow [1] and Debreu [9] in the context of complete markets. Beja [2, 3] demonstrated the application of contingent pricing concepts to incomplete markets. The approach has been applied to the valuation of options (Cox and Ross [7]; Rubinstein [30]) and a variety of other financial instruments (e.g., Ross [28])- Tne fundamental insight of CPT is that in arbitrage-free markets complex securities may always be viewed as additive combinations of simple “state-claims” having positive value which, in effect, pay off one unit if and only if a given state is attained at a given date. Concurrently, the continuoustime viewpoint pioneered by Black and Scholes [4] and Merton [22] has grown in significance. The basic simplification of the continuous-time approach is that relevant valuation quantities may all be expressed in terms of the first two moments, i.e., mean and variance, of the state variable distributions employed. When CPT adopts a continuous-time format, it has been shown (Garman [13]) that a basic differential equation holds for all securities; that differential equation involves, of course, the state-claim values, the distributional parameters of state variable evolution, and the prices and dividends of securities. Alternatively, somewhat stronger assumptions which lead to the existence of a rational consensus investor allow thedifferential equation to be expressed in terms of marginal utilities (Cox, Ingersoll, and Ross [8]). This paper applies the techniques of continuous-time CPT to the foreign exchange market. Since we wish to substantively treat inflationary and productive sources of risk in two countries, four state variables are necessarily involved. In a sense, therefore, this is an ambitious attempt since the mostcomplex continuous-time models to date (e.g.. Brennan and Schwartz [5]), have substantively treated only two state variables. Such complexity is simplified through the use of some compact notation, but not by the use of ad hoc modeling. Indeed, it should be emphasized that the present treatment is a full-equilibrium approach, and that while the compact quality of the notation might be made to incorporate a significant amount of possible additional structure, nothing here is inconsistent with a complete equilibrium.

The existence of default risk is an important characteristic of most lending operations, and many of the studies dealing with lending behavior incorporate default risk considerations. Two basic approaches to the modeling of such behavior can be identified according to their treatment of default probabilities: the first approach assumes that the likelihood of default is independent of the actions of the lender under consideration, namely, the volume of the loan granted by the current lender has no impact on the default probability (e.g., the works by Yawitz [9], Feder and Just [3], and Bierman and Hass [2]). Such an assumption may be quite appropriate in situations where the volume of operations of a single lender is rather small relative to the size of borrower's assets (or previous debt), as is the case with most bond buyers or with banks who lend to sovereign borrowers.