This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev, Pirogov and Schenk-Hoppé, Proceedings of the American Mathematical Society 139, 1061-1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived, extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness.
Wealth Management besteht aus einer Reihe von Dienstleistungen zum Aufbau und der nachhaltigen Verwaltung von Vermögen. In diesem Artikel konzentriere ich mich auf den Aspekt des Portfolio Managements, vernachlässige dabei jedoch die wichtigen legalen und steuerlichen Aspekte.
Die Finanzkrise von 1998 hat traditionelle Theorien über Investition, Risiko, Korrelation und Diversifikation in den Grundfesten erschüttert. Mittlerweile ist klar, dass die Standardabweichung alleine ein ungenügendes Mass des Risikos darstellt und dass traditionelle Investitionsstrategien, die sich auf die Annahmen und Vorhersagen des sogenannten Capital Asset Pricing Models stützen, überholt sind (sicherlich wird niemand mehr die Annahme von normalverteilten Renditen wirklich ernst nehmen).
Alternative Ansätze, welche auf der Verhaltensökonomie aufbauen, scheinen einige der Probleme des traditionellen Ansatzes zu lösen - aber auch hier fehlt letztendlich der explizite Zusammenhang zwischen Preisen auf Finanzmärkten und gesamtwirtschaftlicher Aktivität. In Zeiten normaler öko‐nomischer Aktivität ist dies nicht allzu problematisch, aber es ist zu bezweifeln, dass wir uns (schon) wieder in solch „normalen“ Zeiten befinden. Um eine kohärente Theorie der optimalen Portfolio-Verwaltung zu entwickeln, muss man zunächst erklären, wie es regelmässig zu Finanzkrisen kommen kann.
Using an experimental analysis of a simple monetary economy as a basis, we argue that a monetary system can be more stable than one would expect from individual rationality. We show that positive reciprocity stabilizes the monetary system, provided every participant considers the feedback of his choice to the stationary equilibrium. If, however, the participants do not play stationary strategies and some participants notoriously refuse to accept money, then due to negative reciprocity their behavior will eventually induce a break-down of the monetary system.
We consider a repeated stochastic coordination game with imperfect public monitoring. In the game any pattern of coordinated play is a perfect Bayesian Nash equilibrium. Moreover, standard equilibrium selection arguments either have no bite or they select an equilibrium that is not observed in actual plays of the game. We give experimental evidence for a unique equilibrium selection and explain this very robust finding by equilibrium selection based on behavioral arguments, in particular focal point analysis, probability matching and overconfidence. Our results have interesting applications in finance because the observed equilibrium exhibits momentum, reversal and excess volatility. Moreover, the results may help to explain why technical analysis is a commonly observed investment style.
The paper first shows that financial market equilibria need not to exist if agents possess cumulative prospect theory preferences with piecewise-power value functions. This is due to the boundary behavior of the cumulative prospect theory value function, which might cause an infinite short-selling problem. But even when a nonnegativity constraint on final wealth is added, non-existence can occur due to the non-convexity of CPT preferences, which might cause discontinuities in the agents' demand functions. This latter observation also implies that concavification arguments which has been used in portfolio allocation problems with CPT preferences do not apply to our general equilibrium setting with finite many agents. Existence of equilibria is established when non-negativity constraints on final wealth are imposed and there is a continuum of agents in the market. However, if the original prospect theory is used instead of cumulative prospect theory, then other discontinuity problems can cause non-existence of market equilibria even in this case.
In a dynamic general equilibrium model, we derive conditions for a mutual fund separation property by which the savings decision is separated from the asset allocation decision. With logarithmic utility functions, this separation holds for any heterogeneity in discount factors, while the generalization to constant relative risk aversion holds only for homogeneous discount factors but allows for any heterogeneity in endowments. The logarithmic case provides a general equilibrium foundation for the growth-optimal portfolio literature. Both cases yield equilibrium asset pricing formulas that allow for investor heterogeneity, in which the return process is endogenous and asset prices are determined by expected discounted relative dividends. Our results have simple asset pricing implications for the time series as well as the cross section of relative asset prices. It is found that on data from the Dow Jones Industrial Average, a risk aversion smaller than in the logarithmic case fits best.
More and more academic journals are adopting an open access policy by which articles are accessible free of charge, while publication costs are recovered through author fees. We study the consequences of this open access policy on the quality standard of an electronic academic journal. If the journal's objective were to maximize social welfare, open access would be optimal. However, we show that if the journal has a different objective (such as maximizing readers' utility, the impact of the journal, or its profit), open access tends to induce it to choose a quality standard below the socially efficient level.
This paper presents an equilibrium model that provides a rational explanation for two features of data that have been considered puzzling: The positive relation between US dividend yields and nominal interest rates, often called the Fed-model, and the time-varying correlation of US stock and bond returns. Key ingredients are time-varying first and second moments of consumption growth, inflation, and dividend growth in conjunction with Epstein-Zin and Weil recursive preferences. Historically in the US, inflation has signalled low future consumption growth. The representative agent therefore dislikes positive inflation shocks and demands a positive risk premium for holding assets that are poor inflation hedges, such as equity and nominal bonds. As a result, risk premiums on equity and nominal bonds comove positively through their exposure to macroeconomic volatility. This generates a positive correlation between dividend yields and nominal yields and between stock and bond returns. High levels of macro volatility in the late 1970s and early 1980s caused stock and bond returns to comove strongly. The subsequent moderation in aggregate economic risk has brought correlations lower. The model is able to produce correlations that can switch sign by including the covariances between consumption growth, inflation, and dividend growth as state variables.
We analyze the attractiveness of investment strategies over a variety of investment horizons from the viewpoint of an investor with preferences described by Cumulative Prospect Theory (CPT), currently the most prominent descriptive theory for decision making under uncertainty. A bootstrap technique is applied using historical return data of 1926–2008. To allow for variety in investors’ preferences, we conduct several sensitivity analyses and further provide robustness checks for the results. In addition, we analyze the attractiveness of the investment strategies based on a set of experimentally elicited preference parameters. Our study reveals that strategy attractiveness substantially depends on the investment horizon. While for almost every preference parameter combination a bond strategy is preferred for the short run, stocks show an outperformance for longer horizons. Portfolio insurance turns out to be attractive for almost every investment horizon. Interestingly, we find probability weighting to be a driving factor for insurance strategies’ attractiveness.
