Exact arbitrage, well-diversified portfolios and asset pricing in large markets

For a market with an atomless continuum of assets, we formulate the intuitive idea of a “well-diversified” portfolio, and present a notion of “exact arbitrage”, strictly weaker than the more conventional notion of “asymptotic arbitrage”, and necessary and sufficient for the validity of an APT pricing formula. Our formula involves “essential” risk, one based on a specific index portfolio constructed from factors and factor loadings that are endogenously extracted to satisfy an optimality property involving a finite number of factors. We illustrate how our results can be translated to markets with a large but finite number of assets.     

Cooperation through imitation

This paper characterizes long-run outcomes for broad classes of symmetric games, when players select actions on the basis of average historical performance. Received wisdom suggests that when agent's interests are partially opposed, behavior is excessively competitive: “keeping up with the Jones' ” lowers everyones' welfare. Here, we study the long-run consequences of imitative behavior when agents have sufficiently long memories and evaluate past actions in terms of (weighted) average payoff. Imitation robustly leads to cooperative outcomes (with highest symmetric payoffs) in the long run. Furthermore, lengthening memory reinforces this effect. This provides a rationale, for example, for collusive cartel-like behavior without collusive intent.     

Evolutionary stable stock markets

Summary. This paper shows that a stock market is evolutionary stable if and only if stocks are evaluated by expected relative dividends. Any other market can be invaded in the sense that there is a portfolio rule that, when introduced on the market with arbitrarily small initial wealth, increases its market share at the incumbents expense. This mutant portfolio rule changes the asset valuation in the course of time. The stochastic wealth dynamics in our evolutionary stock market model is formulated as a random dynamical system. Applying this theory, necessary and sufficient conditions are derived for the evolutionary stability of portfolio rules when relative dividend payoffs follow a stationary Markov process. These local stability conditions lead to a unique evolutionary stable portfolio rule according to which assets are evaluated by expected relative dividends (with respect to the objective probabilities).Received: 7 October 2003, Revised: 18 January 2005, JEL Classification Numbers: G11, D52, D81. Correspondence to: Klaus Reiner Schenk-HoppéWe are grateful to Jarrod Wilcox and William Ziemba for valuable comments. Financial support by the national center of competence in research Financial Valuation and Risk Management is gratefully acknowledged. The national centers in research are managed by the Swiss National Science Foundation on behalf of the federal authorities.     

When does the majority become a majority? Empirical analysis of the time at which main market adopters purchase the bulk of our sales

The idea of a dual-market structure in the early stages of a product's life cycle has become one of the most widely accepted ideas among new product marketing practitioners in the past decade. Concepts such as “Early Market/Main Market” and “Visionaries/Pragmatists” have entered the lexicon of high-tech executives to express the notion that the market for new products is composed of early and main markets with a discontinuity in the diffusion process in between them. Moreover, these concepts have been at least partially tested and verified in the marketing academic literature in the past few years.We extend this branch of research by investigating the timing issues in dual-market cases. We define Change-of-Dominance Time (CD-Time) as the number of years it takes main market adopters to outnumber early market adopters. We empirically investigate this timing issue on a comprehensive data set of new product sales in the consumer electronics industry. We find that regarding explanatory determinants of CD-Time, external influence, such as advertising, to the early market is the most important explanatory variable.We examine the relationship between CD-Time and other early product life cycle phenomena: Takeoff, Saddle, and Rogers' size of adopter categories. We found relatively high correlations between these phenomena and CD-Time.The answer to the question “When does the majority become a majority?” is indeed “at 16%”! In a dual-market setting, the average time at which the main market outnumbers the early market is when 16% of the market has already adopted the product. In terms of time, in 75% of the cases the majority becomes a majority in 5 to 10 years.     

Are stocks desirable in tax-deferred accounts?

Existing literature suggests that, in order to maximize the tax benefit of retirement accounts, investors should follow a “pecking order” location rule of placing highly taxed assets (e.g., bonds) in a tax-deferred account and lightly taxed assets (e.g., stocks) in a taxable account. Empirical evidence, however, documents that a large number of investors violate this rule. In this paper, we show that such violations can be optimal for risk-averse investors who face portfolio constraints. In particular, while the strategy of placing bonds in the tax-deferred account maximizes the expected level of tax benefit, it may lead to volatile benefits under different realizations of stock returns. By holding a similar portfolio in both accounts, investors can achieve a more balanced growth in the two accounts, minimize the likelihood of violating the constraints in the future and hence “smooth” the volatility of the tax benefit. For some risk-averse investors, this smoothing motive can lead to the observed violation of the pecking order location rule. Our model predicts that such violations are more likely when future tax benefits are more volatile, which can occur, for example, when: (i) the tax rate differential across assets increases over time due either to tax law changes or to tax bracket changes for investors; (ii) asset returns are more volatile; and (iii) investors anticipate large future liquidity needs.     

Optimizing the shares of native tree species in forest plantations with biased financial parameters

Addressing uncertainty is a key requirement to follow the principle of precaution in sustainable ecosystem management. The maximization of worst-case outcomes according to the “maximin” decision rule, based on the two parameters mean and variance of a financial indicator, is a prominent approach to integrate uncertainty in decision-making. In forestry, the problem of selecting the optimum tree species combination for a forest plantation investment can be seen as a problem of optimal portfolio selection, to be solved according to the “maximin” decision rule. Yet, it is well known that portfolios computed from expected means and variances are highly sensitive to changes in the estimated parameters. The financial results may be poor if we rely too much on the historical data. This paper tests an extended worst-case model that considers a lower bound for the expected mean net present value (NPV) of a tree species portfolio and an upper bound for its variance. Biased expected mean NPVs, variances and correlations for the tree species Picea abies [L.] Karst. (Spruce) and Fagus sylvatica L. (Beech) were used to test the variability of the resulting tree species portfolios (27 scenarios). A comprehensive simulated data set, which was adopted from an existing study and defined as the independent reference, served to evaluate the financial performance of the tree species portfolios obtained from optimization with the biased data. Compared with the results of classical worst-case optimization instances, it was feasible to reduce the variability of tree species shares effectively when the optimization was carried out with the extended worst-case approach. Furthermore, the financial performance of this approach was better when tested with the independent data. The worst-case forest NPVs achieved with the extended approach were on average 10% (statistical confidence 0.95) or 147% (statistical confidence 0.99) greater in comparison to the results of the classical approach. The influence of the uncertainty parameter selection was tested and the results were discussed against the controversial viewpoints on the usefulness of the “information-gap decision theory”. Finally, the significance of our results for sustainable ecosystem management is pointed out.     

The analysis of a price war strategy under market demand growth

We use the finite repeated Prisoners' Dilemma game model herein to discuss how firms choose their optimal strategy under a price war with market demand growth. This model has two players: one is an R-type player and the other is a TFT-type player. Each player has two strategies to choose from: a preemption strategy and a “wait” strategy. Our results indicate that: (i) if the probability that the opponent is an R-type (TFT-type) player is high, then the time when the opponent adopts a preemption strategy will be early (late); (ii) Market demand growth is an incentive for cooperation among firms; (iii) if the market demand growth rate is high, then the R-type player will not have an evolutionary advantage. We use the competition between cell phone manufacturing firms Nokia and Motorola in China as an example. When Nokia is an R-type player and adopts a preemption strategy, Motorola should preferably use a preemption strategy rather than a “wait” strategy. However, as a TFT-type player, this will benefit Motorola under the situation of market demand growth.     

Consistent representative democracy

We study axioms which define “representative democracy” in an environment in which agents vote over a finite set of alternatives. We focus on a property that states that whether votes are aggregated directly or indirectly makes no difference. We call this property representative consistency. Representative consistency formalizes the idea that a voting rule should be immune to gerrymandering. We characterize the class of rules satisfying unanimity, anonymity, and representative consistency. We call these rules “partial priority rules.” A partial priority rule can be interpreted as a rule in which each agent can “veto” certain alternatives. We investigate the implications of imposing other axioms to the list specified above. We also study the partial priority rules in the context of specific economic models.     

Imitation processes with small mutations

This note characterizes the impact of adding rare stochastic mutations to an “imitation dynamic,” meaning a process with the properties that absent strategies remain absent, and non-homogeneous states are transient. The resulting system will spend almost all of its time at the absorbing states of the no-mutation process. The work of Freidlin and Wentzell [Random Perturbations of Dynamical Systems, Springer, New York, 1984] and its extensions provide a general algorithm for calculating the limit distribution, but this algorithm can be complicated to apply. This note provides a simpler and more intuitive algorithm. Loosely speaking, in a process with K strategies, it is sufficient to find the invariant distribution of a K×K Markov matrix on the K homogeneous states, where the probability of a transit from “all play i” to “all play j” is the probability of a transition from the state “all agents but 1 play i, 1 plays j” to the state “all play j”.     

An equilibrium model of a second economy market in a centrally planned economy

We study a CPE in which an identical good is sold on the official market (OM) and a “second economy” market (SEM ). Planners set parameters. Managers divide inputs between markets to maximize expected utility of wealth. Consumers are expected utility maximizers who purchase the good on the OM or SEM. On the OM, excess demand exists at the non-Walrasian price; delivery date is stochastic. The SEM offers immediate availability. Our solution concept involves the rational expectations of managers, the consistency of consumers' decisions, and a market-clearing SEM. We solve for SEM price and supply and investigate various comparative statics.     

Government funding strategy in technology programs

Industrial R&D in a market economy is mainly implemented in the private sector, therefore public funding is a very important tool of government to guide private R&D activities. This paper investigates the experience of funding national programs in a number of industrialized countries, and reaches some preliminary conclusions: (a) To reduce opportunistic behavior and ingrain intrinsic incentive in firms, both competition and cost-sharing principles should be used concurrently in underwriting firms' R&D projects. (b) Competition principles can be applied across many candidate projects around the same time or a series of one-of-a-kind projects over a longer time horizon. (c) The major threat to application of competition principles is that there is no “real competition” due to few qualified candidates in specific technological fields or in some, especially small, countries. (d) In practice, the appropriate cost-sharing level is difficult to determine. Fifty-fifty is used as a rule of thumb in many countries to simplify the decision making and circumvent “bounded rationality.” (e) Full cost endorsement may be another “quantum” alternative for projects urged by government but not felt to be very relevant by firms.     

Can Japan succeed in “Chigyo-ka” (intelprise-formation)?

There are two aspects in today's information revolution that started in the late 1970s. The first is an aspect referred to as “the third industrial revolution,” which triggers the transition to the “21st century system of Industrialization.” The information revolution in this sense brings the creation of new “breakthrough industries (new multimedia industries).” And the second aspect of the information revolution possesses the characteristics of both a technological revolution and a social revolution and brings about the arrival of the third phase of the historical evolutionary process of the modern civilization, which proceeds through three phases, namely “militarization, industrialization, and then informatization.”If the bearers of modern industrialization are a “group of enterprises” that have been engaged in the race in order to gain “wealth” (generalized means of exchange/exploitation power), and if these enterprises' activities have been exercised in the world market where their products have been sold, then it is appropriate to call the bearers of informatization a “group of intelprises.” They will be engaged in the race to gain “wisdom” (generalized means of persuasion/induction power), then stages of their activities can be called a “global intelplace” where “sharables,” that is, information and knowledge, will be disseminated. And now, toward the 21st century, the third phase of modernization, which can be called the “informatization/intelprise formation” or the “wisdom game” (intellectualism), is about to begin.Japan's “ie society (a society based on the ie principle—literally, it means “house” but here it is interpreted as cultural principle for organizing a society), which has been going through the process of evolution on the Japan Archipelago, has developed a network-based organization with little stratification within its infrastructure. In this sense, Japanese society can be characterized as a “network-oriented society” in which intelprises and an intelplace in the broad sense have functioned as the essential components of the society since Middle Ages. In general, an intelplace and intelprises that operate actively within this framework serve as the flexible bases for different types of social relations and institutions, such as states and markets and eventually integrate these into the society to a certain extent. In fact, it took place quite regularly during the modernization “in the narrow sense,” or Westernization of Japanese society after the Meiji Restoration. There exist some problems, however. Some of the characteristics found in Japanese society may become obstacles to activities aimed at the sharing and promotion of information and knowledge in the global intelplace and Japanese participation in the “wisdom game.” Badly needed are serious efforts for Japanese intelprise-formation to reduce these obstacles as much as possible.     

Does the road to serfdom lead to the Servile State?

Hilaire Belloc's The Servile State is often seen as an antisocialist tract arguing that “socialism is slavery.” It is typically assumed that an appreciation and defense of free market capitalism, as well as a general dislike of government intervention must motivate the its thesis. Nevertheless The Servile State is an argument against what Belloc saw as unbridled capitalism not collectivism. Belloc defines capitalism to mean a state in which there is a skewed distribution of wealth in society where the majority of people are dispossessed, proletariat, and a minority makes up the capitalist, property owning class. For Belloc capitalism is an inherently unstable system and servile measures arise to ameliorate insecurity and instability.     

A model of “coupled” technology transfer : A logistic curve approach

This article presents a mathematical model relating to the technology transfer problem. The origin of the problem stems from the existing trade-offs between the strategies of “technological progressiveness” and “static efficiency” employed by firms or countries defined as “leaders” and “followers,” respectively. The formulation of the model is based on the assumption that the technological development of a firm or a country follows a logistic growth curve when related to a specific technology. During the process of a “coupled” technology transfer, the development of the follower changes and its behavior is described by a first order nonhomogenous deferential equation. Different scenarios of the “coupled” technology transfer between the leader and the follower are being discussed.     

On optimality in collective institutional choice

Conditions are investigated under which democratic choice of the division of land between collective and “private” use and of the distribution of collective income between “needs” and “work” payments will produce a Pareto-optimal land allocation and optimal collective labor incentives. Sen's optimal rule for the degree of “needs” distribution is found to result from self-interested voting on this parameter when the distribution of labor inputs is unskewed or when votes are weighted by labor contributions. This in turn increases the optimality of land allocation, which can be further improved by a simple rental scheme. J. Comp. Econ., Dec. 1981, 5(4), pp. 392–403. Brown University, Providence, Rhode Island.     

A Primer on Logistic Growth and Substitution: The Mathematics of the Loglet Lab Software

This article describes the mathematics underlying the Loglet Lab software package for loglet analysis. “Loglet analysis” refers to the decomposition of growth and diffusion into S-shaped logistic components, roughly analogous to wavelet analysis, popular for signal processing and compression. The term “loglet” joins “logistic” and “wavelet.” Loglet analysis comprises two models: the first is the component logistic model, in which autonomous systems exhibit logistic growth. The second is the logistic substitution model, which models the effects of competitions within a market. An appendix describes the current status of the software.     

Conceptions of the dual economy

Due to the current labor market problems and to the increase in personal “free time,” the “other half” of the economy is attracting increased attention: the household economy, the informal sector, black labor, the shadow economy, etc. The purpose of this paper is to summarize the current terminology and conceptual diversity in this field, in order to clarify the notions and thus the theoretical approaches which are a prerequisite for further work at the present stage of research.     

On the utility premium of Friedman and Savage

We re-examine the utility premium of Friedman–Savage [Friedman, Milton and Savage, Leonard J., “The Utility Analysis of Choices Involving Risk.” Journal of Political Economy 56, 1948, pp. 279–304.]. This measure is useful in understanding risky choices. For instance its reaction to an increased wealth equates to a precautionary demand for saving. We also analyze its two components.     

Evolutionary stability and lexicographic preferences

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. Econ. Theory 57, 278–305) are limit Nash equilibria. Modified evolutionary stability differs from “lexicographic evolutionarily stability” (defined by extending the common characterization of evolutionary stability to lexicographic preferences) in the order in which limits in the payoff space and the space of invasion barriers are taken.     

The role of factor substitution in the theory of economic growth and income distribution: Two examples

While much empirical evidence suggests that the Cobb–Douglas production function may be a reasonable benchmark for aggregate analysis, we argue that the practice, particularly prevalent in contemporary growth theory, of adopting the Cobb–Douglas technology, may lead to misleading implications. Using two examples, we show that key implications of the models are highly sensitive to small deviations of the elasticity of substitution from unity. The first employs the standard neoclassical model and emphasizes the sensitivity of the speed of convergence to small changes in the elasticity of substitution. This in turn has profound consequences for wealth and income distribution. The second deals with foreign aid and highlights how the relative merits of “tied” versus “untied” aid are also very sensitive to the elasticity of substitution.