Robert C. Merton

Optimum Consumption and Portfolio Rules in a Continuous-time Model

A floatable apparatus provided with a lifting element for displacing it between the surface and bottom of a water basin has at least two jaws or grippers which are suitable for use as a clam-shell bucket or the like. The jaws are suspended from the lifting element and are articulated with respect to one another. The lifting element is constituted by a principal floatable buoyant caisson which permits the apparatus to be placed in a state of immersion or of floatation. At least one floatation chamber is associated with each of the jaws to achieve selectably a net density thereof equal to, less than or greater than that of water. The jaws are carried by the principal caisson.

Option pricing when underlying stock returns are discontinuous

Abstract The validity of the classic Black-Scholes option pricing formula depends on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying stock return dynamics can be described by a stochastic process with a continuous sample path. In this paper, an option pricing formula is derived for the more-general case when the underlying stock returns are generated by a mixture of both continuous and jump processes. The derived formula has most of the attractive features of the original Black-Scholes formula in that it does not depend on investor preferences or knowledge of the expected return on the underlying stock. Moreover, the same analysis applied to the options can be extended to the pricing of corporate liabilities.

On Estimating the Expected Return on the Market: An Exploratory Investigation

The expected market return is a number frequently required for the solution of many investment and corporate finance problems, but by comparison with other financial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market return adds the historical average realized excess market returns to the Current observed interest rate. While this model explicitly reflects the dependence of the market return on the interest rate, it fails to account for the effect of changes in the level of market risk. Three models of equilibrium expected market returns which reflect this dependence are analyzed in this paper. Estimation procedures which incorporate the prior restriction that equilibrium expected excess returns on the market must be positive arc derived and applied to return data for the period 1926- 1978. The principal conclusions from this exploratory investigation are: (1) in estimating models of the expected market return. the non-negativity restriction of the expected excess return should be explicitly included as part of the specification; (2) estimators which use realized returns should be adjusted for heteroscedasticity.

An analytic derivation of the cost of deposit insurance and loan guarantees An application of modern option pricing theory

Abstract It is not uncommon in the arrangement of a loan to include as part of the financial package a guarantee of the loan by a third party. Examples are guarantees by a parent company of loans made to its subsidiaries or government guarantees of loans made to private corporations. Also included would be guarantees of bank deposits by the Federal Deposit Insurance Corporation. As with other forms of insurance, the issuing of a guarantee imposes a liability or cost on the guarantor. In this paper, a formula is derived to evaluate this cost. The method used is to demonstrate an isomorphic correspondence between loan guarantees and common stock put options, and then to use the well developed theory of option pricing to derive the formula.

AN ANALYTIC DERIVATION OF THE EFFICIENT PORTFOLIO FRONTIER

The characteristics of the mean-variance, efficient portfolio frontier have been discussed at length in the literature. However, for more than three assets, the general approach has been to display qualitative results in terms of graphs. In this paper, the efficient portfolio frontiers are derived explicitly, and the characteristics claimed for these frontiers are verified. The most important implication derived from these characteristics, the separation theorem, is stated and proved in the context of a mutual fund theorem. It is shown that under certain conditions, the classic graphical technique for deriving the efficient portfolio frontier is incorrect.

On Market Timing and Investment Performance. I. An Equilibrium Theory of Value for Market Forecasts

The evaluation of the performance of investment managers is a much-studied problem in finance. The extensive study of this problem could be justified solely on the basis of the manifest function of these evaluations, which is to aid in the efficient allocation of investment funds among managers. However, an equally important latent function of these evaluations is to provide a method of testing the Efficient Markets Hypothesis.1 If market participants are rational, a necessary condition for superior performance is superior forecasting skills on the part of the performer. Hence, these evaluations can help resolve whether or not the existence of different information among market participants plays an empirically significant role in the formation of equilibrium security prices. One of the principal applications of modem capital market theory has been to provide a structural specification within which to measure investment performance and thereby to identify

An Asymptotic Theory of Growth Under Uncertainty

The neoclassical theory of capital accumulation and growth under certainty for both positive and optimal savings functions has received extensive study in the literature for almost two decades. However, the study of capital accumulation under uncertainty began much later and these analyses for the most part confined themselves to linear technologies. In his pioneering work, Phelps [19] and, later, Levhari and Srinivisan [10] ,Hahn [5] and Leland [23], examine the optimal consumption-saving decision under uncertainty with a given linear production technology. Hakansson [6], Leland [9] and Samuelson [21] in discrete time and Merton [12, 13] in continuous time, along with a host of other authors, have studied the combined consumption-saving-portfolio problem where the production functions are linear, but where there is a choice among alternative technologies. There have been a few notable exceptions to this concentration on linear technologies. In a seminal paper, Mirrlees [17] tackled the stochastic Ramsey problem in a continuoustime neoclassical one-sector model subject to uncertainty about technical progress. Later, in [18], he expanded his analysis to other types of technologies. Mirman [16] for positive savings functions and Brock and Mirman [1] for optimal savings functions, using a discrete-time, neoclassical one-sector model, proved the existence, uniqueness and stability of a steady-state (or asymptotic) distribution for the capital-labour ratio. These steadystate distributions are the natural generalizations under uncertainty to the golden-age/ golden-rule levels of the capital-labour ratio as deduced in the certainty case. While these papers are important contributions with respect to existence and uniqueness, they have little to say about the specific structure of these asymptotic distributions or about the biases (in an expected-value sense) induced by assuming a certainty model when, in fact, outcomes are uncertain. The basic model used in this paper is a one-sector neoclassical growth model of the Solow-type where the dynamics of the capital-labour ratio can be described by a diffusiontype stochastic process. The particular source of uncertainty chosen is the population size although the analysis would be equally applicable to technological or other sources of uncertainties. The first part of the paper analyses the stochastic processes and asymptotic distributions for various economic variables, for an exogeneously given savings function, and deduces a number of first-moment relationships which will obtain in the steady-state. In addition, the special case of a Cobb-Douglas production function with a constant savings function is examined in detail and the steady-state distributions for

ON THE PRICING OF CONTINGENT CLAIMS AND THE MODIGLIANI-MILLER THEOREM*

Abstract A general formula is derived for the price of a security whose value under specified conditions is a known function of the value of another security. Although the formula can be derived using the arbitrage technique of Black and Scholes, the alternative approach of continuous-time portfolio strategies is used instead. This alternative derivation allows the resolution of some controversies surrounding the Black and Scholes methodology. Specifically, it is demonstrated that the derived pricing formula must be continuous with continuous first derivatives, and that there is not a ‘pre-selection bias’ in the choice of independent variables used in the formula. Finally, the alternative derivation provides a direct proof of the Modigliani-Miller theorem even when there is a positive probability of bankruptcy.

A Functional Perspective of Financial Intermediation

New financial product designs, improved computer and telecommunications technology, and advances in the theory of finance have led to dramatic and rapid changes in the structure of global financial markets and institutions. This paper offers a functional perspective as the conceptual framework for analyzing the dynamics of institutional changes in financial intermediation and uses a series of examples to illustrate the range of institutional change that is likely to occur. These examples are used to frame the managerial issues surrounding the production process for intermediaries and to discuss the regulatory process for those intermediaries.

Dividend Behavior for the Aggregate Stock Market

We develop and estimate a model of the dynamic behavior of aggregate corporate dividends as a function of the change in permanent earnings of firms. Although structured along the lines of the Lintner-Brittain-FamaBabiak models of individual-firm dividend behavior, the model uses changes in stock prices instead of accounting earnings to measure permanent earnings changes. The performance of the model is compared with both the accounting earnings-based models and the trend-autoregressive model associated with Shiller (1981a).