Multi-period Setting Research Articles

A new, transitive productivity index

The Malmquist productivity index is not transitive. This paper argues that, instead of trying to accommodate this two-period concept to a multi-period setting, it is preferable to look at the measurement of productivity, efficiency, and technical change in a multi-period setting from the outset. A new, transitive productivity index is developed with as by-product a measure of the non-neutrality of technical change. The various indices are illustrated on panel data of Swedish pharmacies.

Implications of Economic Income for Earnings Usefulness Judgments

Various studies consider the ex ante (pre‐decision) or ex post (post‐decision) uses of accounting information (e.g., Demski, 1974; Beaver and Demski, 1979; Beaver, 1981). Although these uses are distinct conceptually, the same information can be pertinent to both uses in multiperiod settings (see, e.g., the discussion in Demski, 1974). Also, several manuscripts (e.g., Beaver and Demski, 1979; Beaver, 1981; Vickrey, 1984; Miller and Rock, 1985) suggest that the abnormal security returns related to earnings can be partial functions of both ex ante probability revision and ex post state revelation in multiperiod settings. This article demonstrates that if the ex ante and ex post uses of information are linked empirically, then the returns/earnings studies may have: (a) misconstrued the usefulness of earnings, and (b) ignored the separate issues of the usefulness of earnings in ex ante probability revision and in ex post state revelation. It should aid in eliminating these deficiencies by motivating returns/earnings studies that investigate the extent to which the abnormal returns related to earnings are partial functions of ex ante probability revision and ex post state revelation. Studies of this type have great potential for enhancing our understanding of the effects of earnings.

Executive incentive compensation and earnings manipulation in a multi-period setting

This study examines in a multi-period setting how trading of equity securities by managers and the awarding of such securities to managers affects earnings manipulation. The study explores the effect of an executive incentive compensation plan, comprised of bonus and equity holdings, on the reporting strategy of the manager under different degrees of market efficiency. The findings indicate that insider trading provides an informative signal about the direction of earnings manipulation. Furthermore, the results confirm that the choice of compensation scheme by owners tends to affect earnings manipulation.

The effect of uncertain inflation on firm value in a multiperiod economy

We model firm value in a multiperiod setting with uncertain inflation and show that real rates of return on the firm's securities are intertemporally dependent. The model also predicts an inverse intertemporal relationship between the real rate of return and the lagged value of Tobin'sq. We report empirical evidence in support of the hypothesized relationship. The model could explain the mean-reverting property of long-horizon stock returns reported in recent studies.

Dynamic Asset Pricing Theory.

Dynamic Asset Pricing Theory is a textbook for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimaltiy, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. For simplicity, all continuous-time models are based on Brownian motion. Applications include term structure models, derivative valuation and hedging methods, and dynamic programming algorithms for portfolio choice and optimal exercise of American options. Numerical methods covered include Monte Carlo simulation and finite-difference solvers for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. This second edition is substantially longer, while still retaining the consciseness for which the first edition was praised. All chapters from the first edition have been revised. Two new chapters have been added on term structure modeling and on derivative securities. References have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains the definitive textbook in the field.

Volatility, information and noise trading

Abstract We construct a dynamic competitive model where price volatility comes from both information arrival and noise trading. We first show that in the absence of noise trading, there exists a fully revealing equilibrium, thus extending a well-known result to a multiperiod setting. Informational efficiency implies that price variations are serially uncorrelated and that volatility over time sums up to a constant. Thus a permanent increase in price volatility cannot be accounted for strictly in terms of an increase in information producing activities. In this context, information arrival at time 0 is welfare reducing (the Hirshleifer effect). We then study the effects of noise trading on the equilibrium prices. With noise trading, more information may mean less volatility as improved information places rational agents in a better position to counteract the actions of noise traders. We find that, in principle, significant episodes of noise trading can be identified as they translate into a negative correlation in price changes and that, under plausible hypotheses, more information is beneficiary in that it reduces the (net) welfare loss due to noise trading.

An Analysis of the Determination of Deutsche Mark/French Franc Exchange Rate in a Discrete-Time Target-Zone Model

Following Krugman (1 99 I), recent models of exchange rates within a target zone have paid particular attention to the effect of the band on exchange rate expectations (see, for example, Miller and Weller, I 989 and Froot and Obstfeld, I 989). The basic idea is that the band, as long as it is credible, has a stabilising effect on the exchange rate not only because the authorities, when necessary, would control the fundamentals in order to contain the movements of the exchange rate, but also because expectations are influenced by the band. These studiesby employing the continuous-time stochastic setting of regulated Brownian motion, familiar from option-pricing theory (cf. Merton, 1973), have also made a significant contribution to the theoretical analysis of the exchange rate. The advantage of the continuous-time framework is that, in a multiperiod setting, it makes the analysis of bands algebraically more manageable than a discrete formulation. To illustrate the approach consider the following simple model from the literature:

Further Ambiguity When Performance Is Measured by the Security Market Line

AbstractThis paper employs the optimality conditions for expected utility and mean‐variance portfolio problems to examine the ambiguities associated with the security market line criterion both at a point in time and through time. At a point in time, we show that the security market line criterion can be irrelevant, even in meanvariance economies. In a multiperiod setting, we show that the analysis of performance based on portfolio choice is inconsistent with the analysis based on return generating models. Empirical work suggests that the inconsistency can lead to dramatically different estimates of a security's required return.

The dynamic structure of optimal debt contracts

Abstract In a two-period model of costly state verification, the optimal contract is characterized and shown to exist. The optimal contract is interpreted as a bond contract. The model extends the result of one-period models that the verification region must be a left-tail interval to a multi-period setting. Conditions are identified for the optimal contract to exhibit features such as call (prepayment) option, coupon payment, or sinking fund. The optimality of certain bond covenants such as “refinancing covenants” and “dividends covenants” is also studied.

Optimal Internal Control Strategy under Dynamic Conditions

The importance of optimal allocations of resources to the internal control effort of firms is necessary in a competitive environment following some initiatives mandating such efforts. Viewing the internal control effectiveness as a stock variable affecting the net benefits of the firm, we address the issue of the optimal path internal control outlays in a multiperiod setting. Our analysis highlights some interrelationships among the parameters in the model, in addition to providing a cross-point solution for switching to lower levels of outlays.

Consumer Welfare Under the Adjustable‐Rate Mortgage: Some Empirical Evidence

The theoretical literature on the economics of mortgage choice holds that consumer‐borrower preference for the ARM depends largely on the FRM‐ARM rate differential. However, there is no empirical evidence as to whether consumers are better off, worse off, or left indifferent with the choice of the ARM relative to the alternative FRM. This paper estimates the windfall gain or loss induced by the FRM‐ARM rate differential in a multiperiod setting. The major results are as follows: (1) on the average consumer‐borrowers reap windfall gain from the use of ARM, (2) but some individual consumers had windfall loss, (3) consumers with ARMs that have periodic interest‐rate caps have significantly higher windfall gain than consumers whose ARMs have no periodic rate caps, and (4) the level of the windfall gain (loss) appears to be correlated with the slope of the yield curve and the level of interest rate.

Debt and taxes: A multiperiod investigation

This paper extends the Miller bond market equilibrium analysis to a multiperiod setting. From the model developed we derive several predictions relating optimal financial leverage to firm characteristics and to the business cycle. The analysis also reveals some interesting determinants of the market value of the tax subsidy associated with corporate debt.

A Test of the Hotelling Valuation Principle

Time-series tests of the Hotelling r-percent rule for natural resource prices have not been strongly supportive, but the tests and the data are subject to serious difficulties. We propose here an alternative testing strategy based on another but less widely known implication of the Hotelling model. We test this implication, which we call the Hotelling Valuation Principle, by regressing the market values of the reserves of a sample of U.S. domestic oiland gas-producing companies on their estimated Hotelling values. We find that the estimated Hotelling values account for a significant portion of the observed variations in market values and that the Hotelling measures are better indicators of the market values of petroleum properties than two widely cited publicly available alternative appraisals.

The Use of Market Data and Accounting Data in Hedging Against Consumer Price Inflation

This paper examines the use of alternative information sets in the construction of inflation hedge portfolios. The study is motivated by consideration of the investor's problem in a multiperiod world. Several authors (e.g., Merton [1973] and Breeden [1979]) have shown that in a multiperiod setting, optimal investment behavior will, in general, involve holding portfolios that can be used to hedge against changes in certain relevant states of nature. One potentially relevant state of nature is the rate of inflation in general prices (Jones [1982] and Elton, Gruber, and Rentzler [1983]). In contrast to prior related research, the empirical results indicate that it is possible to construct inflation hedge portfolios successfully, if certain accounting information is used. However, portfolios constructed on the basis of historical security price information do not serve as effective hedges. One contribution of this paper is to demonstrate the potential usefulness of accounting information to a price-taking investor. Although financial statements play an important role in the setting of equilibrium

Optimal multi-period insurance contracts

Abstract In multi-period insurance contracts (such as automobile insurance contracts), unlike single-period ones, the premiums that the insured must pay increase whenever he files a claim. Hence, the buyer faces a problem that is absent in one-period models, namely: he must determine for which damages he should file a claim and for which he should not. The optimal claims policy of the buyer is presented for a large class of insurance contracts. It is shown that the buyer will file a claim only if it is larger than some critical value. Based on this it is shown that the buyer prefers a contract that provides full coverage above a deductible for damages that exceed his critical value. In this case the optimal contract is not unique since the buyer is indifferent to the form of the contract for damages below his critical value. It is shown, however, that as in one-period models (Arrow (1963, 1974)) there exists an optimal contract that provides full coverage above a deductible. In multi-period setting, however, the buyer will file a claim only if the damage is sufficiently higher than the deductible. It is also shown that the buyer prefers a strictly positive deductible. Unlike the one-period case (Mossin (1968)), this result holds true even if the premium rates equal the expected payments.

The Time Pattern of Hedging and the Volatility of Futures Prices

The paper proposes a multi-period model of hedging which allows for a futures position to be revised within the cash holding period. Within this framework, we assess the robustness of the two-period theory of hedging when generalized to many periods. We characterize the normal time path of a hedge and the way it is affected by the requirement that futures accounts mark to market daily. Finally we show how the resolution of production uncertainty over time affects hedging behavior and determines the volatility of futures prices. In the large literature on hedging in futures markets the principal analytical accounts of hedging are framed in a two trade date setting. An agent commits himself now to a future purchase or sale of a good whose cash price later is uncertain. This risk is hedged by purchase or sale of an appropriate number of futures contracts and holding this futures position until the cash transaction is realized. In the present paper we formulate a multi-period model of hedging which allows for the futures position to be revised within the cash holding period. The resulting analysis captures an important institutional reality that is absent in a two trade date model, namely the fact that the day to day fluctuations of the futures price will generate a series of random cash flows over the period during which a futures position is held. This is due to the requirement that futures accounts mark to market daily. Within this framework we address a number of issues. First we assess the robustness of the two period theory of hedging when generalized to many periods. Second we characterize the normal time path of a hedge and contrast futures and forward contracts from the perspective of an individual hedger. Finally, we show how the resolution of production uncertainty over time affects hedging behaviour and determines the volatility of futures prices. While the literature on asset demand in a multiperiod setting is large, futures markets are specifically treated in a limited number of studies. Grauer and Litzenberger (1976) are concerned principally with characterizing the relation of spot and futures prices in a for a storable, periodically produced commodity. They offer a rationale for positive stock holding in markets where spot price exceeds the futures price. Richard and Sundaresan (1980) are also concerned primarily with characterizing price behaviour. Since they posit identical consumers, in equilibrium individual holdings of futures are zero. There is no hedging activity in the sense that we understand it. Breeden (1980b) analyzes the optimal futures position sizes in a multiperiod setting. His framework is more general than ours in that his is a multi-good, multi-asset model where preferences

Strategic behavior and regulation research in accounting

Abstract This paper focuses on models of political behavior that implicitly or explicitly form the foundation for empirical economic consequences studies in accounting. The studies that have appeared adopt a single-period of single-agendum-item perspective. This paper discusses differences in rational political behavior that arise naturally in single-period versus multiperiod settings. The behavioral implications of varying configurations of available information on agents' “ preferences” are also considered. Because of the tremendously complex empirical domain being studied, examples are relied on heavily to motivate the discussion rather than engaging in a formal modeling exercise.

A General Mean-Variance Approximation to Expected Utility for Short Holding Periods

The mean-variance model is precisely consistent with the expected utility hypothesis only in the special cases of normally distributed security returns or quadratic utility functions. There is little evidence, however, that security returns follow normal distributions (see [13] for references) and quadratic preferences can be shown to generate implausible results, exhibiting increasing absolute risk aversion in the Pratt [ll]–Arrow [1, 2] sense and displaying negative marginal utility after some finite wealth level. In addition, Hakansson [4] has shown that single–period, mean-variance-efficient portfolios can have disastrous consequences over time—even when return distributions are stationary. Such criticisms of the mean-variance approach within the Von Neumann-Morgenstern framework have prompted several writers to suggest that investors maximize the expected value of utility functions with more “realistic” properties, while others have criticized the single-period focus of the model. One popular alternative utility function is the logarithmic function which exhibits decreasing absolute risk aversion and (conveniently) leads to myopic decision processes through time (i.e., investors treat each period as if it were the last, basing investment decisions on that period's wealth and return distributions only [8, 4]). (Other utility functions with constant relative risk aversion—such as the power function—also imply myopic decision rules within a multiperiod setting.)

THE MULTI-PERIOD CONSUMPTION INVESTMENT PROBLEM AND SINGLE PERIOD ANALYSIS

IN recent years multi-period consumption investment models have received increasing attention in the economic literature. This represents a departure from economists' early preoccupation with single-period models. Given the vast number of normative and descriptive models which have been derived based on the assumption that single-period decisions were appropriate, it would be fortuitous if the multi-period formulation of the problem led to results which were consistent with those produced by single-period models. The purpose of this paper is to synthesize the work that has been done on the multi-period consumption-investment decision in order to examine the implications for the validity of single-period models in the multi-period setting. Throughout this paper we will assume that the investor's objective is maximization of multi-period consumption. This objective function is sufficiently general to encompass all multi-period objective functions.'