Three essays on the psychology of investment and financial markets

Préface My thesis consists of three essays where I consider equilibrium asset prices and investment strategies when the market is likely to experience crashes and possibly sharp windfalls. Although each part is written as an independent and self contained article, the papers share a common behavioral approach in representing investors preferences regarding to extremal returns. Investors utility is defined over their relative performance rather than over their final wealth position, a method first proposed by Markowitz (1952b) and by Kahneman and Tversky (1979), that I extend to incorporate preferences over extremal outcomes. With the failure of the traditional expected utility models in reproducing the observed stylized features of financial markets, the Prospect theory of Kahneman and Tversky (1979) offered the first significant alternative to the expected utility paradigm by considering that people focus on gains and losses rather than on final positions. Under this setting, Barberis, Huang, and Santos (2000) and McQueen and Vorkink (2004) were able to build a representative agent optimization model which solution reproduced some of the observed risk premium and excess volatility. The research in behavioral finance is relatively new and its potential still to explore. The three essays composing my thesis propose to use and extend this setting to study investors behavior and investment strategies in a market where crashes and sharp windfalls are likely to occur. In the first paper, the preferences of a representative agent, relative to time varying positive and negative extremal thresholds are modelled and estimated. A new utility function that conciliates between expected utility maximization and tail-related performance measures is proposed. The model estimation shows that the representative agent preferences reveals a significant level of crash aversion and lottery-pursuit. Assuming a single risky asset economy the proposed specification is able to reproduce some of the distributional features exhibited by financial return series. The second part proposes and illustrates a preference-based asset allocation model taking into account investors crash aversion. Using the skewed t distribution, optimal allocations are characterized as a resulting tradeoff between the distribution four moments. The specification highlights the preference for odd moments and the aversion for even moments. Qualitatively, optimal portfolios are analyzed in terms of firm characteristics and in a setting that reflects real-time asset allocation, a systematic over-performance is obtained compared to the aggregate stock market. Finally, in my third article, dynamic option-based investment strategies are derived and illustrated for investors presenting downside loss aversion. The problem is solved in closed form when the stock market exhibits stochastic volatility and jumps. The specification of downside loss averse utility functions allows corresponding terminal wealth profiles to be expressed as options on the stochastic discount factor contingent on the loss aversion level. Therefore dynamic strategies reduce to the replicating portfolio using exchange traded and well selected options, and the risky stock.

A balance of questions: what can we ask of climate change economics?

The standard approach to the economics of climate change, which has its best known implementation in Nordhaus's DICE and RICE models (well described in Nordhaus's 2008 book, A Question of Balance) is not well equipped to deal with the possibility of catastrophe, since we are unable to evaluate a risk averse representative agent's expected utility when there is any signi cant probability of zero consumption. Whilst other authors attempt to develop new tools with which to address these problems, the simple solution proposed in this paper is to ask a question that the currently available tools of climate change economics are capable of answering. Rather than having agents optimally choosing a path (that differs from the recommendations of climate scientists) within models which cannot capture the essential features of the problem, I argue that economic models should be used to determine the savings and investment paths which implement climate targets that have been suggested in the physical science literature.

Price Transmission and Effects of Exchange Rates on Domestic Commodity Prices via Offshore and Currency Hedging

The framework presents how trading in the foreign commodity futures market and the forward exchange market can affect the optimal spot positions of domestic commodity producers and traders. It generalizes the models of Kawai and Zilcha (1986) and Kofman and Viaene (1991) to allow both intermediate and final commodities to be traded in the international and futures markets, and the exporters/importers to face production shock, domestic factor costs and a random price. Applying mean-variance expected utility, we find that a rise in the expected exchange rate can raise both supply and demand for commodities and reduce domestic prices if the exchange rate elasticity of supply is greater than that of demand. Whether higher volatilities of exchange rate and foreign futures price can reduce the optimal spot position of domestic traders depends on the correlation between the exchange rate and the foreign futures price. Even though the forward exchange market is unbiased, and there is no correlation between commodity prices and exchange rates, the exchange rate can still affect domestic trading and prices through offshore hedging and international trade if the traders are interested in their profit in domestic currency. It illustrates how the world prices and foreign futures prices of commodities and their volatility can be transmitted to the domestic market as well as the dynamic relationship between intermediate and final goods prices. The equilibrium prices depends on trader behaviour i.e. who trades or does not trade in the foreign commodity futures and domestic forward currency markets. The empirical result applying a two-stage-least-squares approach to Thai rice and rubber prices supports the theoretical result.

Information Design

There are two ways of creating incentives for interacting agents to behave in a desired way. One is by providing appropriate payoff incentives, which is the subject of mechanism design. The other is by choosing the information that agents observe, which we refer to as information design. We consider a model of symmetric information where a designer chooses and announces the information structure about a payoff relevant state. The interacting agents observe the signal realizations and take actions which affect the welfare of both the designer and the agents. We characterize the general finite approach to deriving the optimal information structure for the designer - the one that maximizes the designer's ex ante expected utility subject to agents playing a Bayes Nash equilibrium. We then apply the general approach to a symmetric two state, two agent, and two actions environment in a parameterized underlying game and fully characterize the optimal information structure: it is never strictly optimal for the designer to use conditionally independent private signals; the optimal information structure may be a public signal or may consist of correlated private signals. Finally, we examine how changes in the underlying game affect the designer's maximum payoff. This exercise provides a joint mechanism/information design perspective.

Why do scientists migrate? A diffusion model

The article is intended to improve our understanding of the reasons underlying the intellectual migration of scientists from well-known cognitive domains to nascent scientific fields. To that purpose we present, first, a number of findings from the sociology of science that give different insights about this phenomenon. We then attempt to bring some of these insights together under the conceptual roof of an actor-based approach linking expected utility and diffusion theory. Intellectual migration is regarded as the rational choice of scientists who decide under uncertainty and on the base of a number of decision-making variables, which define probabilities, costs, and benefits of the migration.

Evolving from inferences to decisions in the interpretation of scientific evidence

Le travail d'un(e) expert(e) en science forensique exige que ce dernier (cette dernière) prenne une série de décisions. Ces décisions sont difficiles parce qu'elles doivent être prises dans l'inévitable présence d'incertitude, dans le contexte unique des circonstances qui entourent la décision, et, parfois, parce qu'elles sont complexes suite à de nombreuse variables aléatoires et dépendantes les unes des autres. Etant donné que ces décisions peuvent aboutir à des conséquences sérieuses dans l'administration de la justice, la prise de décisions en science forensique devrait être soutenue par un cadre robuste qui fait des inférences en présence d'incertitudes et des décisions sur la base de ces inférences. L'objectif de cette thèse est de répondre à ce besoin en présentant un cadre théorique pour faire des choix rationnels dans des problèmes de décisions rencontrés par les experts dans un laboratoire de science forensique. L'inférence et la théorie de la décision bayésienne satisfont les conditions nécessaires pour un tel cadre théorique. Pour atteindre son objectif, cette thèse consiste de trois propositions, recommandant l'utilisation (1) de la théorie de la décision, (2) des réseaux bayésiens, et (3) des réseaux bayésiens de décision pour gérer des problèmes d'inférence et de décision forensiques. Les résultats présentent un cadre uniforme et cohérent pour faire des inférences et des décisions en science forensique qui utilise les concepts théoriques ci-dessus. Ils décrivent comment organiser chaque type de problème en le décomposant dans ses différents éléments, et comment trouver le meilleur plan d'action en faisant la distinction entre des problèmes de décision en une étape et des problèmes de décision en deux étapes et en y appliquant le principe de la maximisation de l'utilité espérée. Pour illustrer l'application de ce cadre à des problèmes rencontrés par les experts dans un laboratoire de science forensique, des études de cas théoriques appliquent la théorie de la décision, les réseaux bayésiens et les réseaux bayésiens de décision à une sélection de différents types de problèmes d'inférence et de décision impliquant différentes catégories de traces. Deux études du problème des deux traces illustrent comment la construction de réseaux bayésiens permet de gérer des problèmes d'inférence complexes, et ainsi surmonter l'obstacle de la complexité qui peut être présent dans des problèmes de décision. Trois études-une sur ce qu'il faut conclure d'une recherche dans une banque de données qui fournit exactement une correspondance, une sur quel génotype il faut rechercher dans une banque de données sur la base des observations faites sur des résultats de profilage d'ADN, et une sur s'il faut soumettre une trace digitale à un processus qui compare la trace avec des empreintes de sources potentielles-expliquent l'application de la théorie de la décision et des réseaux bayésiens de décision à chacune de ces décisions. Les résultats des études des cas théoriques soutiennent les trois propositions avancées dans cette thèse. Ainsi, cette thèse présente un cadre uniforme pour organiser et trouver le plan d'action le plus rationnel dans des problèmes de décisions rencontrés par les experts dans un laboratoire de science forensique. Le cadre proposé est un outil interactif et exploratoire qui permet de mieux comprendre un problème de décision afin que cette compréhension puisse aboutir à des choix qui sont mieux informés. - Forensic science casework involves making a sériés of choices. The difficulty in making these choices lies in the inévitable presence of uncertainty, the unique context of circumstances surrounding each décision and, in some cases, the complexity due to numerous, interrelated random variables. Given that these décisions can lead to serious conséquences in the admin-istration of justice, forensic décision making should be supported by a robust framework that makes inferences under uncertainty and décisions based on these inferences. The objective of this thesis is to respond to this need by presenting a framework for making rational choices in décision problems encountered by scientists in forensic science laboratories. Bayesian inference and décision theory meets the requirements for such a framework. To attain its objective, this thesis consists of three propositions, advocating the use of (1) décision theory, (2) Bayesian networks, and (3) influence diagrams for handling forensic inference and décision problems. The results present a uniform and coherent framework for making inferences and décisions in forensic science using the above theoretical concepts. They describe how to organize each type of problem by breaking it down into its différent elements, and how to find the most rational course of action by distinguishing between one-stage and two-stage décision problems and applying the principle of expected utility maximization. To illustrate the framework's application to the problems encountered by scientists in forensic science laboratories, theoretical case studies apply décision theory, Bayesian net-works and influence diagrams to a selection of différent types of inference and décision problems dealing with différent catégories of trace evidence. Two studies of the two-trace problem illustrate how the construction of Bayesian networks can handle complex inference problems, and thus overcome the hurdle of complexity that can be present in décision prob-lems. Three studies-one on what to conclude when a database search provides exactly one hit, one on what genotype to search for in a database based on the observations made on DNA typing results, and one on whether to submit a fingermark to the process of comparing it with prints of its potential sources-explain the application of décision theory and influ¬ence diagrams to each of these décisions. The results of the theoretical case studies support the thesis's three propositions. Hence, this thesis présents a uniform framework for organizing and finding the most rational course of action in décision problems encountered by scientists in forensic science laboratories. The proposed framework is an interactive and exploratory tool for better understanding a décision problem so that this understanding may lead to better informed choices.

Do the Wealthy Risk More Money? An Experimental Comparison

Are poor people more or less likely to take money risks than wealthy folks? We find that risk attraction is more prevalent among the wealthy when the amounts of money at risk are small (not surprising, since ten dollars is a smaller amount for a wealthy person than for a poor one), but, interestingly, for the larger amounts of money at risk the fraction of the nonwealthy displaying risk attraction exceeds that of the wealthy. We also replicate our previous finding that many people display risk attraction for small money amounts, but risk aversion for large ones. We argue that preferences yielding risk attraction for small money amounts, together with risk aversion for larger amounts, at all levels of wealth, while contradicting the expected utility hypothesis, may be well-defined, independently of reference points, on the choice space.

The value of useless information

There are many situations in which individuals have a choice of whether or notto observe eventual outcomes. In these instances, individuals often prefer to remainignorant. These contexts are outside the scope of analysis of the standard vonNeumann-Morgenstern (vNM) expected utility model, which does not distinguishbetween lotteries for which the agent sees the final outcome and those for which hedoes not. I develop a simple model that admits preferences for making an observationor for remaining in doubt. I then use this model to analyze the connectionbetween preferences of this nature and risk-attitude. This framework accommodatesa wide array of behavioral patterns that violate the vNM model, and thatmay not seem related, prima facie. For instance, it admits self-handicapping, inwhich an agent chooses to impair his own performance. It also accommodatesa status quo bias without having recourse to framing effects, or to an explicitdefinition of reference points. In a political economy context, voters have strictincentives to shield themselves from information. In settings with other-regardingpreferences, this model predicts observed behavior that seems inconsistent witheither altruism or self-interested behavior.

Crime and punishment: Further results

I consider a general specification of criminals' objective functionand argue that, when the general non-expected utility theory issubstituted for the traditional expected utility theory, thehigh-fine-low-probability result (Becker, 1968) only holds underspecific and strong restrictions.

The gain-loss asymmetry and single-self preferences

Kahneman and Tversky asserted a fundamental asymmetry between gains and losses, namely a reflection effect which occurs when an individual prefers a sure gain of $ pz to anuncertain gain of $ z with probability p, while preferring an uncertain loss of $z with probability p to a certain loss of $ pz.We focus on this class of choices (actuarially fair), and explore the extent to which thereflection effect, understood as occurring at a range of wealth levels, is compatible with single-self preferences.We decompose the reflection effect into two components, a probability switch effect,which is compatible with single-self preferences, and a translation effect, which is not. To argue the first point, we analyze two classes of single-self, nonexpected utility preferences, which we label homothetic and weakly homothetic. In both cases, we characterize the switch effect as well as the dependence of risk attitudes on wealth.We also discuss two types of utility functions of a form reminiscent of expected utility but with distorted probabilities. Type I always distorts the probability of the worst outcome downwards, yielding attraction to small risks for all probabilities. Type II distorts low probabilities upwards, and high probabilities downwards, implying risk aversion when the probability of the worst outcome is low. By combining homothetic or weak homothetic preferences with Type I or Type II distortion functions, we present four explicit examples: All four display a switch effect and, hence, a form of reflection effect consistent a single self preferences.

Asset pricing implications of benchmarking: A two-factor CAPM

In this paper we consider the equilibrium effects of an institutionalinvestor whose performance is benchmarked to an index. In a partialequilibrium setting, the objective of the institutional investor is modeledas the maximization of expected utility (an increasing and concave function,in order to accommodate risk aversion) of final wealth minus a benchmark.In equilibrium this optimal strategy gives rise to the two-beta CAPM inBrennan (1993): together with the market beta a new risk-factor (that wecall active management risk) is brought into the analysis. This new betais deffined as the normalized (to the benchmark's variance) covariancebetween the asset excess return and the excess return of the market overthe benchmark index. Different to Brennan, the empirical test supports themodel's predictions. The cross-section return on the active management riskis positive and signifficant especially after 1990, when institutionalinvestors have become the representative agent of the market.

Do the eealthy risk more money? An experimental comparison

Are poor people more or less likely to take money risks than wealthy folks?We find that risk attraction is more prevalent among the wealthy when theamounts of money at risk are small (not surprising, since ten dollars is asmaller amount for a wealthy person than for a poor one), but, interestingly,for the larger amounts of money at risk the fraction of the nonwealthydisplaying risk attraction exceeds that of the wealthy.We also replicate our previous finding that many people display riskattraction for small money amounts, but risk aversion for large ones. Weargue that preferences yielding risk attraction for small money amounts,together with risk aversion for larger amounts, at all levels of wealth, while contradicting the expected utility hypothesis, may be well-defined,independently of reference points, on the choice space.

Portfolio choice beyond the traditional approach

This paper surveys asset allocation methods that extend the traditional approach. An important feature of the the traditional approach is that measures the risk and return tradeoff in terms of mean and variance of final wealth. However, there are also other important features that are not always made explicit in terms of investor s wealth, information, and horizon: The investor makes a single portfolio choice based only on the mean and variance of her final financial wealth and she knows the relevant parameters in that computation. First, the paper describes traditional portfolio choice based on four basic assumptions, while the rest of the sections extend those assumptions. Each section will describe the corresponding equilibrium implications in terms of portfolio advice and asset pricing.

Reflections on gains and losses: A 2x2x7 experiment

We test whether risk attitudes change when losses instead of gains areinvolved. The study of gain-loss asymmetries has been largely confinedto reflected choices, where all the money amounts of a positiveprospect are multiplied by minus one. We define the decomposition reflection = translation + probability switch, and experimentally findboth a translation effect (risk attraction becomes more frequent whengains are translated into losses) and a probability switch effect (riskattraction becomes more frequent when the probability of the best outcomedecreases). Surprisingly, the switch effect is somewhat stronger than thetranslation effect, negating a conventional reflection effect when onestarts with choices between gains with a low probability of the bestoutcome. We conclude by arguing that, while both the translation effectand the switch effect contradict the expected utility hypothesis, thetranslation effect implies a deeper violation of standard preference theory.

Intergenerational justice when future worlds are uncertain

Let there be a positive (exogenous) probability that, at each date, the human species will disappear.We postulate an Ethical Observer (EO) who maximizes intertemporal welfare under thisuncertainty, with expected-utility preferences. Various social welfare criteria entail alternativevon Neumann- Morgenstern utility functions for the EO: utilitarian, Rawlsian, and an extensionof the latter that corrects for the size of population. Our analysis covers, first, a cake-eating economy(without production), where the utilitarian and Rawlsian recommend the same allocation.Second, a productive economy with education and capital, where it turns out that the recommendationsof the two EOs are in general different. But when the utilitarian program diverges, thenwe prove it is optimal for the extended Rawlsian to ignore the uncertainty concerning the possibledisappearance of the human species in the future. We conclude by discussing the implicationsfor intergenerational welfare maximization in the presence of global warming.