Little attention has been given to the behavior of option portfolio risk across different portfolio sizes, perhaps because many individuals view unhedged long option positions as too risky for rational investor consideration. It appears possible, however, to combine long option positions with less risky assets to produce portfolios with favorable risk-return characteristics [10].

This paper presents a multiperiod model of a deposit-type mutual financial institution and analyzes the manager's capital accumulation and deposit pricing decisions under uncertainty. The model is meant to describe a mutual savings and loan association (SLA) or a credit union in which there are no stockholders and nominal ownership is widely diffused (see [12] and [14]). The resulting paucity of monitoring gives rise to an agency problem (see [13]) in which the manager maximizes his multiperiod expected discounted utility with minimal intervention from nominal owners.

Considerable attention has been focused recently on models of firms under uncertainty in which there is an incomplete set of securities markets. In these models, each firm can issue only one security and consumers can generate consumption plans only through the purchase of firms' securities. Consequently, if the economy is competitive, each stockholder of a firm will impute the same value to the firm in equilibrium, where this value is given by the market price of the firm's security. However, stockholders will not, in general, have the same implicit prices for state-contingent consumption. Since the financial market is said to be incomplete if the number of independent securities is less than the number of states of nature, consumers cannot hedge perfectly, whichimplies that unconstrained Pareto-optimal allocations are not generally attainable (see [2] and [3]). Finally, it is unclear what firms' objectives should be in these models because profit maximization is not well defined; firms' profits in different states cannot be aggregated into a single index. It is still generally accepted, however, that firms should operate in their own stockholders'interests, a necessary condition for allocative efficiency.

In a paper published in 1978, Levy [5] proposed a general capital asset pricing model (GCAPM), which he obtained by maximizing investors' utility when the number of securities held in each investor's portfolio is constrained. Although Levy's resultant asset pricing model is somewhat different in appearance than the asset pricing model proposed by Mao [8] in 1971, it can be shown that both models are not only quite comparable in content but that both result in some very promising theoretical and empirical implications. Thus, the purpose of this paper is twofold. First, these two important contributions to the literature on asset pricing in imperfect markets will be compared and contrasted. Second, it will be shown that both models can yield a “clinical” form of the traditional CAPM, which appears to be more desirable for empirical testing purposes.

The theory of portfolio selection and diversification developed by Markowitz [22] and Tobin [33] was based primarily on the criterion of meanvariance (MV) efficiency. The objective was to select an efficient set of portfolios from which every risk averter will choose the optimal portfolio which maximizes his expected utility. The MV criterion is the appropriate rule either for the case in which the utility function is quadratic or if the returns are normally distributed and risk aversion is assumed.

This paper serves as an intuitive companion piece to a more technical paper in which Forsythe and Suchanek (F–S) introduce a model which demonstrates “the impossibility of efficient decision rules for firms in competitive stock market economies.” F–S are to be commended for undertaking this effort. The major theme of this paper appears to be that “inefficient equilibria are generic to competitive stock market economies.” This is contrary to the general belief that not only do complete financial markets but also a wide variety of incomplete financial markets guarantee efficient financial equilibria. The F–S model claims to demonstrate otherwise.

This paper has two purposes. First, we model a key decision for international banks using data on the foreign direct investment (FDI) behavior of foreign banks in Japan and California. Second, we examine the utility of linear discriminant analysis and maximum likelihood logit analysis as statistical techniques for relating a qualitative dependent variable to a vector of independent variables.

This paper differentiates between country risk--the probability that a country will default on its obiigations--and two forms of international banking risk: (1) the extent to which a bank's foreign activities affect the cost of equity capital; and (2) the extent to which a bank's foreign activities affect the probability of bankruptcy. The paper focuses on the latter form of international banking risk.

Using Chebyshev's Inequality, it is pointed out that the risk of bankruptcy is influenced by the mean as well as the variance of the return distribution. Consequently, restrictions on the (international) composition of a bank's portfolio may increase rather than reduce the probability of bankruptcy.

Recently, a debate has developed in both the theoretical and applied statistical literature regarding the appropriateness of various techniques in analytical models with limited (particularly, 0-1) dependent variables. In financial research, limited dependent variable models usually arise in one of two ways:

1. classification (or discrimination)--assigning observations to discrete, a priori determined groups, or

2. regression--relating a qualitative dependent variable to one or more independent variables (which may or may not be qualitative).

Recent developments in the finance literature dealing with the valuation of contingent claims have been triggered by Black and Scholes [2] with their valuation of European options on corporate stocks. The type of valuation model derived by Black and Scholes is attractive because it is independent of preferences. This independence is possible due to the fact that the contingent claims are usually assumed to be contingent on traded assets or traded state variables. For example, a European call option is a claim contingent on the value of the corresponding stock. To maintain the independence of the claim from preferences, however, some variables have to be discarded and considered as constants. For example, the rate of interest, which is not a traded state variable, is considered a constant in most of the literature (see Black and Scholes [2], Merton [11], and Ingersoll [9]). Though this approximation might not cause important discrepancies in the case of corporate liabilities and options on corporate liabilities, the effect of such an approximation on the value of default-free bonds and options on default-free bonds is more important since these liabilities depend only on the rate of interest.

It is often desirable to know whether or not a risky asset's beta coefficient has changed and, if so, at what point in time the change occurred. For example, this knowledge is of obvious importance to beta-using security analysts and portfolio managers. As another example, a given theory may imply that a particular firm's beta should have changed at different points in time. Investigators may want to test such a hypothesis. Furthermore, tests are frequently performed on the effects of events on residuals of the market model, tests requiring the assumption of beta stability. For these, and possibly other reasons, it is useful to be able to detect that a change in beta did, in fact, take place as well as, in some instances, identifying the point in time at which the change took place.

In a seminal paper in 1963, Frederick S. Hillier alerted the finance community to the importance of including probabilistic information in the process of investment decision-making [4]. The method proposed and demonstrated by Hillier introduced the use of additional information regarding the probability distributions governing three measures of investment merit: present worth; internal rate of return; and uniform annual cost. He showed that by assessing investment merit only on the basis of a measure of central tendency, crucial information regarding dispersion, hence risk, was ignored and investments were not evaluated accurately. By incorporating the amount of risk involved in terms of the probability distribution of the present worth, the internal rate of return, or uniform annual cost, a firm's management can make more sound decisions regarding risky investment proposals. Since this important paper was published, a virtual revolution has occurred in finance, particularly in the area of risk assessment. Indeed, under modern capital asset pricing theory, the dispersion in the probability distribution of future cash flows is an irrelevant statistic. Instead, as the theory goes, a project's systematic risk, as indexed by its “beta,” is the only relevant measure of risk. This disparity between modern capital asset pricing theory and the type of analysis that follows from the Hillier approach will be addressed in detail in Section III. We will show that under conditions in which dispersion is regarded as the relevant measure of risk, the Hillier approach provides a reasonable approximation of the dispersion arising from the multiperiod framework.

The concept of immunization is currently one of the most widely discussed innovations in bond portfolio management. The interest in immunization, which allows one to nearly guarantee a minimum return performance over a specified investment horizon, is due in large measure to the desire on the part of bond managers to reduce the risk which has accompanied the recent swings in interest rates.

The investment performance of professionally managed portfolios, in general, and mutual funds, in particular, has been the subject of considerable attention in finance. Fama [9] has suggested that overall portfolio performance be broken down in such a manner that the individual sources of performance can be identified. Two basic sources are: (1) the ability of the portfolio manager to forecast price movements of individual common stocks relative to stocks in general (selectivity or microforecasting); and (2) the ability to forecast the direction of the stock market relative to fixed income securities (timing or macroforecasting).

A number of studies have compared the investment risk of various industries and of various individual corporations in developed countries (DCs). The purpose of this paper is to compare investment risk in DCs with less developed countries (LDCs). The variance of returns to investment in common stocks provides a natural measure of investment risk and will be used in this study. Studies in LDCs include work of Levy and Sarnat [12], [13]. Errunza [3], [4], and Lessard [11]. Levy and Sarnat and Errunza found low economy-wide investment risk on an average for LDCs (relative to DCs), with stock indices being used as surrogates for economy-wide risk. These results are not unambiguous, however, because there are probable difficulties due to infrequent trading and averaging in the broad market indices used in the above studies. Hence, we use a sample of the largest corporations that suffer little, if at all, from thin trading and/or averaging.

Corporate pension plans represent a large and growing force in the capital market. Their promised benefits comprise a large portion of the expected retirement income of millions of employees. Because of this importance, and because of some widely publicized abuses and scandals, these plans were the subject of increased governmental regulation in the 1970s. One outgrowth of this has been the Employee Retirement Income Security Act (ERISA) under which the Pension Benefit Guarantee Corporation (PBGC) provides insurance of pension benefits. The objective of this paper is to develop a multiperiod model of the pension plan in order (1) to evaluate the robustness of prior analyses of the wealth transfers caused by the passage of ERISA among workers, firms, and the PBGC; (2) to characterize the nature of a PBGC insurance scheme which could, if it were so desired, reduce the potential liability of the PBGC; and (3) to serve as a prototype for modeling the multiperiod pension plan.

Bawa [3] has argued that mean-lower partial moment portfolio selection rules are more general than mean-variance rules in that they rely on fewer restrictive assumptions regarding investor utility functions and/or distributions of security returns. As with the mean-variance model, it is possible to formulate equilibrium security prices under the assumption that expected utility-maximizing investors utilize mean-lower partial moment portfolio selection rules. This paper has investigated the empirical relationship between the resultant mean-lower partial moment pricing model and the long established mean-variance pricing model.

The issue of capital structure has been intensively examined in the finance literature, particularly after the appearance of the landmark 1958 paper by Modigliani and Miller [8], hereafter MM. In that paper, MM derived a relationship in terms of the expected return on equity of a levered and unlevered firm, known as MM Proposition II. Their analysis was extended later by researchers such as Hamada [5] and Rubinstein [9] who derived the corresponding relationship in terms of the systematic risk (beta). Both these risk-return relationships have been derived for the case of perfect capital markets and the case in which corporate income taxes are the only type of market imperfection. Although effects of other types of market imperfections such as personal income taxes and bankruptcy costs have been examined in numerous studies, neither MM Proposition II nor the “beta” relationship were extended to include the effects of personal income taxes and bankruptcy costs.

Security behavior in bull and bear markets has received some attention in recent years. Fabozzi and Francis [5] first documented evidence that security betas are not influenced by the alternating forces of bull and bear markets. Their subsequent study of mutual fund betas also indicated that mutual funds generally respond indifferently to bull and bear market conditions. Using the concept of bull and bear market variations, Kim and Zumwa1t [9] developed and tested the risk premiums associated with the upside and the downside portions of returns variation. They concluded that investors expect to receive a risk premium for downside risk and pay a premium for upside variation of returns. From their results, Kim and Zumwalt [9] suggested that the down-market beta measuring downside risk (downside variation of returns) may be a more appropriate measure of portfolio risk than the single beta in the market model.

While the literature in finance is replete with studies on stock betas, bond betas have, to this day, not attracted much attention. This is quite understandable because much of the finance literature addresses stock betas in the context of the single period Capital Asset Pricing Model (CAPM). In the single period model, the risk-free rate (if it exists) is assumed to be constant over the period in question. Since the interest rate is fixed and investors are required to hold these default-free bonds over the entire period, interest rate risk, and, consequently, systematic risk for bonds do not exist. However, if the constant risk-free rate assumption is relaxedand investors are allowed to trade “intra period,” (say continuously), Merton [4] has argued that an Intertemporal Capital Asset Pricing Model can be derived. Using Merton's framework, Jarrow [3] has recently derived a systematic risk measure for bonds. The primary intent of this paper is to investigate the effect of yield changes on the systematic risk of bonds. As we will demonstrate, the impact of yield changes on bond betas depends on several (sometimes complex) relationships between yields, duration, and bond prices. We derive conditions under which bond betas increase/decrease and show that the elasticity of duration with respect to yields and the sign of the initial beta of a bond will determine the manner in which yield changes affect bond betas.