A New Approach to Intertemporal Choice: The Delay Function

The framework of this paper is intertemporal choice, which traditionally has been studied with preference relations and discount functions. However, the interest of econophysics in this topic makes time become a central magnitude. Therefore, the aim of this paper is to introduce the concept of delay function and, by using this tool, to analyze the concept of impatience and the different types of inconsistency. In behavioral finance, consistency is correlated with the concept of symmetry because, in this case, the indifference between two rewards does not change when the same delay is added to their respective availability dates. Moreover, we have shown the way to derive a discount (respectively, delay) function starting from the expression of its corresponding delay (respectively, discount) function by requiring some suitable conditions for this construction. Finally, we have deduced the concept of instantaneous variation rate and Prelec’s measure of inconsistency in terms of the delay function

Essays on endowment fund management

The debate around the perpetual nature of endowment funds from the perspective of current versus future obligations is a major problem that I would like to address in two ways: (i) a macro-level treatment of the simultaneous asset allocation and spending rate with subsistence levels (analogous to the habit formation concept); and (ii) a micro-level analysis of one part of the endowment portfolio with a particular emphasis on the currency hedging decision. The purpose of the third chapter is to illustrate the significance of joint determination of appropriate asset allocation and spending rate decisions, and to describe the behavior of the endowment fund portfolio under certain modeling assumptions, including a sensitivity analysis that evaluates, in particular, the relationship between the spending rate and stock allocation over an extended period of time by changing the values of certain parameters in the model. The fourth chapter tackles the issue of international diversification from the point of view of active currency hedging. The ability to control risk with the possibility of return enhancement is the main reason why institutional investors such as university endowments should worry about the international diversification of investment portfolios. I have concentrated on an area, which has been overlooked by endowment funds for a long time. That is, the introduction of currency hedging in the context of an international portfolio and the provision of some behavioral considerations: first, implicitly, in the framework of the traditional expected utility maximization and then, explicitly, in the disappointment-averse functional context. In both chapters, the discussion is heavily based on the specification of the utility function; i.e., habit formation through the use of a subsistence level in the case of asset allocation and spending rate determination, and behavioral/agency-related formulation of various aversion parameters in the international portfolio management chapter

Portfolio Optimization and Ambiguity Aversion

This thesis analyses whether considering ambiguity aversion in portfolio optimization improves the out-of-sample performance of portfolio optimization approaches. Furthermore, it is assessed which role ambiguity aversion plays in improving the portfolio performance, especially compared with the role of estimation errors. This is done by evaluating the out-of-sample performance of the approach of Garlappi, Uppal and Wang for an investor with multiples priors and aversion to ambiguity compared to other portfolio optimization strategies from the literature not taking ambiguity aversion into account. It is shown that considering ambiguity aversion in portfolio optimization can improve the out-of-sample performance compared to the sample based mean-variance model and the Bayes-Stein model. However, the minimum-variance model and the model of naïve diversification, which are both independent of expected returns, outperform the approach considering ambiguity aversion for most of the empirical applications shown in this thesis. These results indicate that ambiguity aversion does play a role in portfolio optimization, however, estimation errors regarding expected returns overshadow the benefits of optimal asset allocation. Keywords: portfolio choice; asset allocation; estimation error; ambiguity; uncertainty

The demand for broad money (M2) in Botswana

There has been extensive theoretical and empirical research on the subject of demand for money function. This particularly stems from the important role demand for money plays in macroeconomic analysis, especially in the design and implementation of monetary policy. The increase in studies, especially in developing countries, can also be attributed to a number of factors like: the impact of moving towards flexible exchange rate regimes, globalisation of financial markets, ongoing financial liberalisation, innovations in domestic financial products, the advancement in econometrics techniques and other country-specific events. This study estimates and examines the nature and stability of the demand for broad money (M2) in Botswana. This is particularly important in that the usefulness of a money demand function in the conduct of monetary policy depends crucially on its stability. The stability of the money demand function is crucial in that a stable money demand function would mean that the quantity of money is predictably related to a set of key economic variables linking money and the real economic sector. Therefore, this will help central banks to select appropriate monetary policy actions. Based on the findings, the study also proposes policy interventions. The vast majority of the literature on demand for money has underscored the fact that variable selection and representation, and the framework chosen are the two major issues relevant to modelling and estimation of the demand for money function. In modelling and estimating the demand for money function in Botswana, this study surveys a stream of theoretical and empirical literature on money demand in developed and developing countries, including countries that have similar financial sector similar to Botswana. Due consideration is also given to the macroeconomic and financial sector development in Botswana to help in the identification of the variables that are included in the demand for money equation. Most importantly, this helped in getting meaningful results that are free from theoretical and estimation problems. In particular, this study applied the multivariate cointegration approach as proposed by Johansen (1988) and Johansen and Juselius (1990) to estimate the relationship between broad money (M2), real income, interest rate, South African treasury bill rate, inflation rate and US dollar/pula bilateral exchange rate. The study obtains one unique long run relationship between money and the scale and opportunity cost variables. The coefficients of the long run relationship are then modelled along the general to specific approach as proposed by Campos, Ericsson and Hendry (2005). In this type of approach the general model is reduced by sequential elimination of statistically insignificant variables and checking the validity of the reductions at every stage to ensure congruence of the finally selected parsimonious model. In accordance with the economic quantity theory of money, the long run income elasticity obtained is 0.8021, which is close to the value one (unitary) suggested by economic theory. The coefficients of real income, exchange and inflation rate have the expected positive signs and were significant in the long run. Therefore, the long run demand for money (M2) in Botswana was found to be positively affected by real income, inflation rate and exchange rate. The lack of statistical significant of the own rate of money (88 day commercial bank deposit rate) and the foreign opportunity cost variable (South African Treasury bill rate) is attributed to multi-collinearity problems between these two interest rates. This could be caused by the fact that short term rates in Botswana are very responsive to movements in the money markets rates in South Africa. The short run dynamics of the demand for money function shows the slow speed of adjustment to equilibrium of about 2.9 percent in the first quarter and this is reflective of the lack of sufficient availability of banking services and the low returns on financial assets which could allow economic agents to re-establish equilibrium levels of money holdings faster. The final parsimonious model obtained clearly reflects a well specified stable demand for money function. Therefore, based on the findings we can be precise in stating that targeting a monetary aggregate can be a viable policy for the monetary authorities in Botswana

Asymmetry Risk And Asset Pricing

The dissertation primarily focuses on asymmetry risk and its role in asset pricing. Asymmetry risk is a crucial component of systematic risk. However, it does not attract much attention, probably because of the misconception that it is similar to other asymmetry measures (e.g., skewness). Chapter 1 defines the asymmetry risk. The risk indifference curve (RIC) predicts two asymmetry premiums in the return distribution rather than one in the downside. I also derive the risk-neutral measure of asymmetry risk. Chapter 2 empirically investigates the asymmetry beta\u27s return predictability and tail risk hedging ability. Consistent with the risk indifference curve, the asymmetry beta exhibits significant explanation and prediction power for equity risk premiums of US stocks. In addition, low asymmetry beta stocks provide a more effective hedge against crashing markets. Chapter 3 develops the implied market beta based on the risk-neutral measure of the asymmetry risk. The implied market beta is a superior measure of ex-ante beta in that it possesses significant return predictability and hedging ability. The investible option-implied market portfolio built on the implied market beta outperforms the value-weighted market portfolio with better risk-adjusted performance and less downside risk. Overall, the asymmetry risk is a non-negligible systematic risk factor for the market index and individual stocks in physical probability and risk-neutral spaces: the asymmetry beta and AVIX2 own strong return predictability and powerful hedging ability in crashing markets. These results are robust to the risk factors documented in the previous literature

Essays on statistical economics with applications to financial market instability, limit distribution of loss aversion, and harmonic probability weighting functions

This dissertation is comprised of four essays. It develops statistical models of decision making in the presence of risk with applications to economics and finance. The methodology draws upon economics, finance, psychology, mathematics and statistics. Each essay contributes to the literature by either introducing new theories and empirical predictions or extending old ones with novel approaches .The first essay (Chapter II) includes, to the best of our knowledge, the first known limit distribution of the myopic loss aversion (MLA) index derived from micro-foundations of behavioural economics. That discovery predicts several new results. We prove that the MLA index is in the class of α-stable distributions. This striking prediction is upheld empirically with data from a published meta-study on loss aversion; published data on cross-country loss aversion indexes; and macroeconomic loss aversion index data for US and South Africa. The latter results provide contrast to Hofstede's cross-cultural uncertainty avoidance index for risk perception. We apply the theory to information based asset pricing and show how the MLA index mimics information flows in credit risk models. We embed the MLA index in the pricing kernel of a behavioural consumption based capital asset pricing model (B-CCAPM) and resolve the equity premium puzzle. Our theory predicts: (1) stochastic dominance of good states in the B-CCAPM Markov matrix induce excess volatility; and (2) a countercyclical fourfold pattern of risk attitudes. The second essay (Chapter III) introduces a probability model of "irrational exuberance "and financial market instability implied by index option prices. It is based on a behavioural empirical local Lyapunov exponent (BELLE) process we construct from micro-foundations of behavioural finance. It characterizes stochastic stability of financial markets, with risk attitude factors in fixed point neighbourhoods of the probability weighting functions implied by index option prices. It provides a robust early warning system for market crash across different credit risk sources. We show how the model would have predicted the Great Recession of 2008. The BELLE process characterizes Minskys financial instability hypothesis that financial markets transit from financial relations that make them stable to those that make them unstable

On the Formation and Economic Implications of Subjective Beliefs and Individual Preferences

The conceptual framework of neoclassical economics posits that individual decision-making processes can be represented as maximization of some objective function. In this framework, people's goals and desires are expressed through the means of preferences over outcomes; in addition, in choosing according to these objectives, people employ subjective beliefs about the likelihood of unknown states of the world. For instance, in the subjective expected utility paradigm, people linearly combine their probabilistic beliefs and preferences over outcomes to form an expected utility function. Much of the parsimony and power of theoretical economic analysis stems from the striking generality and simplicity of this framework. At the same time, the crucial importance of preferences and beliefs in our conceptual apparatus in combination with the heterogeneity in choice behavior that is observed across many economic contexts raises a number of empirical questions. For example, how much heterogeneity do we observe in core preference or belief dimensions that are relevant for a broad range of economic behaviors? If such preferences and beliefs exhibit heterogeneity, then what are the origins of this heterogeneity? How do beliefs and preferences form to begin with? And how does variation in beliefs and preferences translate into economically important heterogeneity in choice behavior? This thesis is organized around these broad questions and hence seeks to contribute to the goal of providing an improved empirical understanding of the foundations and economic implications of individual decision-making processes. The content of this work reflects the deep belief that understanding and conceptualizing decision-making requires economists to embrace ideas from a broad range of fields. Accordingly, this thesis draws insights and techniques from the literatures on behavioral and experimental economics, cultural economics, household finance, comparative development, cognitive psychology, and anthropology. Chapters 1 through 3 combine methods from experimental economics, household finance, and cognitive psychology to investigate the effects of bounded rationality on the formation and explanatory power of subjective beliefs. Chapters 4 through 6 use tools from cultural economics, anthropology, and comparative development to study the cross-country variation in economic preferences as well as its origins and implications. The formation of beliefs about payoff-relevant states of the world crucially hinges on an adequate processing of incoming information. However, oftentimes, the information people receive is rather complex in nature. Chapters 1 and 2 investigate how boundedly rational people form beliefs when their information is subject to sampling biases, i.e., when the information pieces people receive are either not mutually independent or systematically selected. Chapter 1 is motivated by Akerlof and Shiller's popular narrative that from time to time some individuals or even entire markets undergo excessive belief swings, which refers to the idea that sometimes people are overly optimistic and sometimes overly pessimistic over, say, the future development of the stock market. In particular, Akerlof and Shiller argue that such "exuberance" or excessive pessimism might be driven by the pervasive "telling and re-telling of stories". In fact, many real information structures such as the news media generate correlated rather than mutually independent signals, and hence give rise to severe double-counting problems. However, clean evidence on how people form beliefs in correlated information environments is missing. Chapter 1, which is joint work with Florian Zimmermann, provides clean experimental evidence that many people neglect such double-counting problems in the updating process, so that beliefs are excessively sensitive to well-connected information sources and follow an overshooting pattern. In addition, in an experimental asset market, correlation neglect not only drives overoptimism and overpessimism at the individual level, but also gives rise to a predictable pattern of over- and underpricing. Finally, investigating the mechanisms underlying the strong heterogeneity in the presence of the bias, a series of treatment manipulations reveals that many people struggle with identifying double-counting problems in the first place, so that exogenous shifts in subjects' focus have large effects on beliefs. Chapter 2 takes as starting point the big public debate about increased political polarization in the United States, which refers to the fact that political beliefs tend to drift apart over time across social and political groups. Popular narratives by, e.g., Sunstein, Bishop, and Pariser posit that such polarization is driven by people selecting into environments in which they are predominantly exposed to information that confirms their prior beliefs. This pattern introduces a selection problem into the belief formation process, which may result in polarization if people failed to take the non-representativeness among their signals into account. However, again, we do not have meaningful evidence on how people actually form beliefs in such "homophilous" environments. Thus, Chapter 2 shows experimentally that many people do not take into account how their own prior decisions shape their informational environment, but rather largely base their views on their local information sample. In consequence, beliefs excessively depend on people's priors and tend to be too extreme, akin to the concerns about "echo chambers" driving irrational belief polarization across social groups. Strikingly, the distribution of individuals' naivete follows a pronounced bimodal structure - people either fully account for the selection problem or do not adjust for it at all. Allowing for interaction between these heterogeneous updating types induces little learning: neither the endogenous acquisition of advice nor exogenously induced dissent lead to a convergence of beliefs across types, suggesting that the belief heterogeneity induced by selected information may persist over time. Finally, the paper provides evidence that selection neglect is conceptually closely related to correlation neglect in that both cognitive biases appear to be driven by selective attentional patterns. Taken together, chapters 1 and 2 show that many people struggle with processing information that is subject to sampling issues. What is more, the chapters also show that these biases might share common cognitive foundations, hence providing hope for a unified attention-based theory of boundedly rational belief formation. While laboratory experimental techniques are a great tool to study the formation of beliefs, they cannot shed light on the relationship between beliefs and economically important choices. In essentially all economic models, beliefs mechanically map into choice behavior. However, it is not evident that people's beliefs play the same role in generating observed behavior across heterogeneous individuals: while some people's decision process might be well-approximated by the belief and preference-driven choice rules envisioned by economic models, other people might use, e.g., simple rules of thumb instead, implying that their beliefs should be largely irrelevant for their choices. That is, bounded rationality might not only affect the formation of beliefs, but also the mapping from beliefs to choices. In Chapter 3, Tilman Drerup, Hans-Martin von Gaudecker, and I take up this conjecture in the context of measurement error problems in household finance: while subjective expectations are important primitives in models of portfolio choice, their direct measurement often yields imprecise and inconsistent measures, which is typically treated as a pure measurement error problem. In contrast to this perspective, we argue that individual-level variation in the precision of subjective expectations measures can actually be productively exploited to gain insights into whether economic models of portfolio choice provide an adequate representation of individual decision processes. Using a novel dataset on experimentally measured subjective stock market expectations and real stock market decisions collected from a large probability sample of the Dutch population, we estimate a semiparametric double index model to explore this conjecture. Our results show that investment decisions exhibit little variation in economic model primitives when individuals provide error-ridden belief statements. In contrast, they predict strong variation in investment decisions for individuals who report precise expectation measures. These findings indicate that the degree of precision in expectations data provides useful information to uncover heterogeneity in choice behavior, and that boundedly rational beliefs need not necessarily map into irrational choices. In the standard neoclassical framework, people's beliefs only serve the purpose of achieving a given set of goals. In many applications of economic interest, these goals are well-characterized by a small set of preferences, i.e., risk aversion, patience, and social preferences. Prior research has shown that these preferences vary systematically in the population, and that they are broadly predictive of those behaviors economic theory supposes them to. At the same time, this empirical evidence stems from often fairly special samples in a given country, hence precluding an analysis of how general the variation and predictive power in preferences is across cultural, economic, and institutional backgrounds. In addition, it is conceivable that preferences vary not just at an individual level, but also across entire populations - if so, what are the deep historical or cultural origins of this variation, and what are its (aggregate) economic implications? Chapters 4 through 6 take up these questions by presenting and analyzing the Global Preference Survey (GPS), a novel globally representative dataset on risk and time preferences, positive and negative reciprocity, altruism, and trust for 80,000 individuals, drawn as representative samples from 76 countries around the world, representing 90 percent of both the world's population and global income. In joint work with Armin Falk, Anke Becker, Thomas Dohmen, David Huffman, and Uwe Sunde, Chapter 4 presents the GPS data and shows that the global distribution of preferences exhibits substantial variation across countries, which is partly systematic: certain preferences appear in combination, and follow distinct economic, institutional, and geographic patterns. The heterogeneity in preferences across individuals is even more pronounced and varies systematically with age, gender, and cognitive ability. Around the world, the preference measures are predictive of a wide range of individual-level behaviors including savings and schooling decisions, labor market and health choices, prosocial behaviors, and family structure. We also shed light on the cultural origins of preference variation around the globe using data on language structure. The magnitude of the cross-country variation in preferences is striking and raises the immediate question of what brought it about. Chapter 5 presents joint work with Anke Becker and Armin Falk in which we use the GPS to show that the migratory movements of our early ancestors thousands of years ago have left a footprint in the contemporary cross-country distributions of preferences over risk and social interactions. Across a wide range of regression specifications, differences in preferences between populations are significantly increasing in the length of time elapsed since the respective groups shared common ancestors. This result obtains for risk aversion, altruism, positive reciprocity, and trust, and holds for various proxies for the structure and timing of historical population breakups, including genetic and linguistic data or predicted measures of migratory distance. In addition, country-level preference endowments are non-linearly associated with migratory distance from East Africa, i.e., genetic diversity. In combination with the relationships between language structure and preferences established in Chapter 4, these results point to the importance of very long-run events for understanding the global distribution of some of the key economic traits. Given these findings on the very deep roots of the cross-country variation in preferences, an interesting - and conceptually different - question is whether such country-level preference profiles might have systematic aggregate economic implications. Indeed, according to standard dynamic choice theories, patience is a key driving factor behind the accumulation of productive resources and hence ultimately of income not just at an individual, but also at a macroeconomic level. Using the GPS data on patience, Chapter 6 (joint work with Thomas Dohmen, Armin Falk, David Huffman, and Uwe Sunde) investigates the empirical relevance of this hypothesis in the context of a micro-founded development framework. Around the world, patient people invest more into human and physical capital and have higher incomes. At the macroeconomic level, we establish a significant reduced-form relationship between patience and contemporary income as well as medium- and long-run growth rates, with patience explaining a substantial fraction of development differences across countries and subnational regions. In line with a conceptual framework in which patience drives income through the accumulation of productive resources, average patience also strongly correlates with aggregate human and physical capital accumulation as well as investments into productivity. Taken together, this thesis has a number of unifying themes and insights. First, consistent with the vast heterogeneity in observed choices, people exhibit a large amount of variation in beliefs and preferences, and in how they combine these into choice rules. Second, at least part of this heterogeneity is systematic and has identifyable sources: preferences over risk, time, and social interactions appear to have very deep historical or cultural origins, but also systematically vary with individual characteristics; belief heterogeneity, on the other hand, is partly driven by bounded rationality and its systematic, predictable effects on information-processing. Third, and finally, this heterogeneity in beliefs and preferences is likely to have real economic implications: across cultural and institutional backgrounds, preferences correlate with the types of behaviors that economic models envision them to, not just across individuals, but also at the macroeconomic level; subjective beliefs are predictive of behavior, too, albeit with the twist that certain subgroups of the population do not appear to entertain stable belief distributions to begin with. In sum, (I believe that) much insight is to be gained from further exploring these fascinating topics

Case-Based Decision Theory and Financial Markets

Die Dissertation wendet die fallgestützte Entscheidungstheorie (Case-Based Decision Theory) vorgeschlagen von Gilboa and Schmeidler (1995) auf Entscheidungen in Finanzmärkten an. Betrachtet werden sowohl das individuelle Portfoliowahlproblem eines Investors, wie auch Märkte, in denen fallgestützte Investoren interagieren. Es wird gezeigt, dass fallgestützte Entscheidungen empirisch beobachtete Phänomene, wie Vorhersagbarkeit von Renditen, exzessive Volatilität, Blasen und hohe Handelsfrequenzen erklären kann. Desweiteren wird demonstriert, dass fallgestützte Investoren auch in Märkten mit Erwartungsnutzenmaximierern einen positiven Marktanteil behalten können und Einfluß auf die Preise ausüben

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available