Doctoral School of Business and Management   

Department of Finance

Supervisor: Dr. Andor György

The Marriage of Behavioral Finance and Financial Mathematics

Introducing the research area

During my research, I search for the driving factors behind models in financial mathematics using theories and empirical findings of psychology, cognitive neurology and experimental economics. These mathematical models often represent the behavioral patterns as irrational consequences and anomalies; however, in fact, these patterns constitute an integral part of the actual human behavior, and hence the functioning of markets. In my research project, I focus on implementing these phenomena, and extending the boundaries of currently used mathematical models.

Brief introduction of the research place

The research is conducted at Investments Group within the Department of Finance at BME GTK. The goal of this research group is to better understand the behavior of capital markets and pricing. Its diversity properly reflects its interconnectedness within the university, which is well-reflected by the fact that many of the undergraduate and graduate students come from different majors, such as computer science, applied mathematics and economics.

 

The history and context of the current research project

The issue of pricing of capital assets dates back to a long time ago. Although, trading is essentially the result of overproduction and appeared in ancient societies, the first concentrated institutions of capital exchange had not appeared until the 1500s. In line with an increase in flow of capital, methodology and theory related to capital market analysis had also undergone major changes.

In the 1700s, economics theory appeared in Adam Smith’s findings, and in the late 1800s and early 1900s, financial mathematics and empirical results brought about significant improvements in the methodology related to the analysis of financial processes. The main assumptions, that is, investors’ economic rationality and random walk models of prices survived without any serious alternative until the 1970s. From that time on, however, several behavioral and cognitive psychological evidence came to light that contrasted the well-defined axioms of the von Neumann-Morgenstern Expected Utility Theory, which latter were essential in economic modeling.

One of the most significant results was documenting the generality of the utility model of Kahneman and Tversky, the Prospect Theory, the frame dependence and the behavioral heuristics. From the 1990s onwards, in addition to cognitive psychology, neuro-economics provided further evidence in favor of the irrational, emotional thinking in decision-making processes. Although the relevance of this evidence has been accepted in academy, capital asset pricing models used in practice still refrain from including the phenomena mentioned above.

 

The research goal, open questions

Which processes reflect individuals' not purely rational behavior? How do these processes reflect the patterns measured in experimental tests that contradict the paradigms of  the Expected Utility Theory? What anomalies cause the results of cognitive psychology, and with which mathematical models can these patterns be described? How can we detect the specific impact of irrational decision-making mechanisms separately for individuals and as an aggregate effect? How can we define the market price of asset by knowing individuals' preferences and decision-making mechanisms?

In my analyses, I search for the answers to these questions, through which one could provide more precise pricing both for cross-sectional analysis and for the time series dynamics. Therefore, they lead to both a better understanding of the current structure and prediction of the future movements in capital markets; hence, the findings would aid both regulation and policy making and individuals’ portfolio allocation decisions.

Methodology

My research activity targets the inclusion of the above-mentioned phenomena in financial mathematics from two aspects. On the one hand, I would like to focus on the underlying behavioral phenomena behind the empirically well-performing mathematical models. Two of my studies deal with the dynamics of volatility (the standard deviation of returns in a given period) in capital markets: in the first one (Ormos and Timotity, 2016a), derived from option prices, by measuring the difference between ex-ante expected and ex-post realized volatility I filter out the irrational behavior, which arises due to the anchoring heuristic in investors’ estimates for the future; in another study (Ormos and Timotity, 2016b), assuming that individuals behave according to Prospect Theory, I examine individual investors’ transactions with the aim of explaining the asymmetry present in volatility dynamics. This study can also explain the asymmetric pattern of two of the best-performing volatility models, in particular the T-GARCH and E-GARCH models.

On the other hand, in addition to explaining the high predictive performance of current model, I also aim at creating novel frameworks. Several papers related to this goal have already been published. My article on market microstructure (Ormos and Timotity, 2016c) examines the Budapest Stock Exchange microstructure during the 2008 crisis, in which I present the dynamics of the market share of each investor group. The novelty of this microstructural model is that I extend the structure, in addition to rational investors, market makers and noise traders, with a well-defined heuristic class of investors that is motivated by the anchoring heuristic. From a slightly different topic, but also based on the anchoring heuristic, I create an equilibrium asset pricing model based on a new risk measure, the Expected Downside Risk (EDR) (Ormos and Timotity, 2016d). Within the framework of this model, the most irrealistic assumptions of standard pricing models (such as normality returns, the existence of price-taking and risk-averse investors, as well as unlimited leverage) can be relaxed; therefore, the whole framework becomes much more general. The empirical test of this latter model is carried out for European capital markets (Ormos and Timotity, 2016e), as well as the dynamics of the risk-return relationship in this setting, derived from the principles of expected utility (Ormos and Timotity, 2016f).

In addition to the aforementioned applications of financial mathematics, other topics are also part of my research. In these studies I aim at clarifying and discovering the rules governing the behavior of individuals. For example, in a study currently under review (Ormos and Timotity, 2016g), I separate the effects of revenge and sensitivity to fairness in allocations decision using a repeated ultimatum game.

 

Results so far

It is clear – in the light of the results we obtained so far – that behavioral effects play an important role in asset price dynamics. The studies published in Economic Systems (Ormos and Timotity, 2016a) and SSRN (Ormos and Timotity, 2016b) present that mental framing and anchoring to past performance significantly affect the financial mathematical models often defined as random walk. Due to these behavioral patterns the volatility process becomes somewhat predictable, hence, it does not follow Brownian motion or AR (1) process as commonly assumed. I provide evidence that the T-GARCH and E-GARCH models can be derived analytically; hence, the patterns measured only in empirics so far are finding their theoretical foundations as well.

My results published in the Finance Research Letters (Ormos and Timotity, 2016c) reveal that heuristic investors driven by the anchoring heuristic follow a contrarian strategy and constitute a significant part of the market microstructure. Moreover, the proportion of this group before, during and after the 2008 crisis stays at constant levels, suggesting that these investors are independent from the rational and noise trader classes, and form a general and robust attribute of market structure both in cross-sectional and time series analysis.

My study published in Economic Modeling. (Ormos and Timotity, 2016d) shows that with a shift in risk measure to EDR, the currently used asset pricing models can be generalized, the most unrealistic assumptions can be relaxed, and a theoretically consistent model can be constructed. The study published in Empirica (Ormos and Timotity, 2016e) provides a clear support to the theoretical advantage and generalizability of the model from the empirical side as well, as both developed (France, Germany and the United Kingdom) and developing capital markets (Hungary, Czech Republic and Poland) show a better performance in predicting the expected return with EDR compared to alternatives risk measures used in practice. Related to this model, in one of my working papers (Ormos and Timotity, 2016f) I also find theoretical and empirical evidence that both positive and negative relationship between risk and required return can be derived analytically and measured empirically. These results are in line with findings in experimental economics, which latter have documented both the risk-seeking (negative relationship between risk and expected return) and risk-averse behavior (positive relationship between risk and expected return).

In my paper focusing on the effect decomposition in ultimatum games (Ormos and Timotity, 2016g), I show that, in contrast to existing literature, instead of the sensitivity to fairness, hunger for revenge is the dominant driving factor behind the positive and negative reciprocity documented in repeated ultimatums games.

Expected impact and further research

The use of my theoretical model in practice would be an ideal impact. The EDR-based asset pricing model would allow more precise estimations of expected returns and risks; and therefore, the regulatory side could advise its use in the risk analytics of institutions participating in capital markets. At an individual’s level, the generalized theory offers a better, more accurate optimal portfolio allocation, so that individual investors could then invest into a more efficient portfolio subject to their constraints.

On the other hand, I would also like to bolster further support to the observed asset price dynamics and behavioral patterns from alternative approaches. For example, testing the models both in experimental setting and also using neuro-economics, a recently emerged interdisciplinary science, might help in understanding the decision-making mechanisms and the biological (neurological) basis of the observed patterns.

Publications, references, links

Ormos, M., Timotity, D. (2016a). Unravelling the asymmetric volatility puzzle: A novel explanation of volatility through anchoring. Economic Systems.

Ormos, M., Timotity, D. (2016b). Microfoundations of Heteroscedasticity: A Loss-Aversion-Based Explanation of Asymmetric GARCH Models. Available at SSRN 2736390.

Ormos, M., Timotity, D. (2016c). Market microstructure during financial crisis: Dynamics of informed and heuristic-driven trading. Finance Research Letters.

Ormos, M., Timotity, D. (2016d). Generalized asset pricing: Expected Downside Risk-based equilibrium modeling. Economic Modeling., 52, 967–980.

Ormos, M., Timotity, D. (2016e). Expected downside risk and asset prices: characteristics of emerging and developed European markets. Empirica, 1–18.

Ormos, M., Timotity, D. (2016f). The case of “Less is more” Modeling. risk-preference with Expected Downside Risk. dx.doi.org/10.13140/RG.2.1.1617.3685

Ormos, M., Timotity, D. (2016g). Sense of fairness or hunger for revenge? It does make a difference. dx.doi.org/10.13140/RG.2.1.5025.2409