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UNIVERSITY OF LJUBLJANA FACULTY OF ECONOMICS Matjaž Steinbacher SIMULATING PORTFOLIOS BY USING MODELS OF SOCIAL NETWORKS Doctoral Dissertation Ljubljana, 2012 AUTHORSHIP STATEMENT The undersigned MATJAŽ STEINBACHER, a student at the University of Ljubljana, Faculty of Economics, (hereafter: FELU), declare that I am the author of the doctoral dissertation entitled SIMULATING PORTFOLIOS BY USING MODELS OF SOCIAL NETWORKS, written under supervision of Dr. HARRY M. MARKOWITZ. In accordance with the Copyright and Related Rights Act (Official Gazette of the Republic of Slovenia, Nr. 21/1995 with changes and amendments) I allow the text of my doctoral dissertation to be published on the FELU website. I further declare • the text of my doctoral dissertation to be based on the results of my own research; • the text of my doctoral dissertation to be language-edited and technically in adherence with the FELU’s Technical Guidelines for Written Works which means that I o cited and / or quoted works and opinions of other authors in my doctoral dissertation in accordance with the FELU’s Technical Guidelines for Written Works and o obtained (and referred to in my doctoral dissertation) all the necessary permits to use the works of other authors which are entirely (in written or graphical form) used in my text; • to be aware of the fact that plagiarism (in written or graphical form) is a criminal offence and can be prosecuted in accordance with the Copyright and Related Rights Act (Official Gazette of the Republic of Slovenia, Nr. 21/1995 with changes and amendments); • to be aware of the consequences a proven plagiarism charge based on the submitted doctoral dissertation could have for my status at the FELU in accordance with the relevant FELU Rules on Doctoral Dissertation. Date of public defense: OCTOBER 25, 2012 Committee Chair: MARKO PAHOR, PhD Supervisor: HARRY M. MARKOWITZ, PhD Member: VLADIMIR BATAGELJ, PhD Ljubljana, October/15/2012 Author’s signature: _________________ ii SIMULIRANJE PORTFELJEV Z UPORABO OMREŽNIH MODELOV Matjaž Steinbacher POVZETEK Vprašanje, s katerim se na finančnih trgih srečujejo investitorji in ga tudi rešujejo, je, kako na učinkovit način upravljati s premoženjem. V tem procesu pomeni izbor portfelja izbiro med mnogimi stohastičnimi alternativami, ki so posameznim agentom na voljo v času. Disertacija je ilustracija vedenjske dinamične igre sočasnih potez igralcev v negotovem svetu trgov kapitala. Model predstavlja aplikacijo socialnih omrežij v ekonomiji in vsebuje agente in njihove preference, vrednostne funkcije, povezave med agenti in nabor akcij za posameznega agenta. V modelu se vedenjske finance nanašajo na psihologijo izbora agentov. V igrah uporabim tako zaupljive, kot tudi nezaupljive agente. Temeljna metodološka značilnost disertacije je ta, da interakcija med agenti privede do kompleksnega vedenja celotne skupine, ki ga brez uporabe pristopa, ki vključuje interakcijo med agenti, ni mogoče pojasniti. V prvem delu (poglavje 5) pokažem, na kakšen način donosi in raven tveganja posameznih portfeljev vplivajo na njihov izbor v preprosti igri z dvema vrednostnima papirjema. Simulacije izvedem v dveh različnih okoliščinah: najprej z netveganim in tveganim vrednostnim papirjem, nato še z dvema tveganima vrednostnima papirjema. Rezultati pokažejo, pod katerimi okoliščinami se agenti odločijo za mešane portfelje tveganega in netveganega vrednostnega papirja. Simulacije še pokažejo, da je za nemoten potek izbora nujno potrebno zagotavljanje likvidnosti. Vključitev šoka v proces izbora pokaže, da v kolikor jakost šoka ni premočna, je njegov učinek zgolj kratkoročen. V drugem delu (poglavja 6-8) razširim osnovni okvir in se lotim iger z mnogoterimi alternativami. Četudi imajo agenti v modelu omejeno védenje o donosih vrednostnih papirjev, svoje portfelje pa izbirajo na podlagi realiziranih donosov, pa so portfelje kljub temu sposobni izbrati skladno s hipotezo učinkovite meje. Nekoliko bolj razpršeni izbor nezaupljivih agentov je posledica njihove nezmožnosti igranja načela “zmagovalec pobere vse,” četudi so sposobni identificati iste “zmagovalce” kot zaupljivi agenti. Omenjena ugotovitev je podprta tako v bikovskem kot tudi medvedjem trendu, četudi v bikovskem trendu agenti prevzemajo več tveganja, kar je skladno s teoretičnimi predvidevanji. Agenti ne preferirajo preveč razpršenih portfeljev, ampak portfelje dveh vrednostnih papirjev, ki so zgrajeni okrog najbolj zaželenega posamičnega vrednostnega papirja. Testi konsistentnosti, opravljeni s pomočjo koficienta variacije in metode Monte Carlo, pokažejo, da so najbolj konsistentno izbrani bodisi najbolj bodisi najmanj zaželeni portfelji. Ti testi še pokažejo, da so zaupljivi agenti bolj konsistentni pri svojih odločitvah kot nezaupljivi agenti. Simulacije z novicami so navrgle dve skupini zmagovalnih portfeljev: portfelje iz učinkovite meje oz. iz njene okolice, in diverzificirane portfelje, katerih izbor je pozitivno koreliran s številom objavljenih nenegativnih novic. Ključne besede: večperiodni izbor portfelja, navidezni finančni trgi, družbena omrežja, razvojne omrežne igre, informacije in védenje, komuniciranje, zaupljivost, ocenjevano učenje. iii iv SIMULATING PORTFOLIOS BY USING MODELS OF SOCIAL NETWORKS Matjaž Steinbacher SUMMARY The problem that financial agents address and solve is how to manage assets efficiently. This involves choosing from different types of stochastic alternatives that are available over time. The dissertation is an application of a dynamic behavioral-based and a simultaneous-move game in a stochastic environment that is run on a network. The model includes agents and their preferences, value functions, relations among agents and the set of actions for each agent. The notion of behavioral finance is on the psychology of agents’ decision-making. In the games, I use unsuspicious and suspicious agents. A fundamental methodological premise of the dissertation is that interaction and information sharing lead to complex collective behavior associated with non-linear dynamics, which can only be explanied with an interaction-based approach. In the first part of the simulation games (Chapter 5), I demonstrate how returns and risk affect portfolio selection in a very simple two-asset game. Games are simulated under two different environments: with riskless and risky asset, and in the environment of two risky assets. I present the conditions, under which agents select mixed portfolios. Games of this part also demonstrated that preserving liquidity is essential for the selection process to work smoothly. It has been demonstrated that one-time shocks affect the selection process in the short run but not over the longer run unless the magnitude is very large. In the second part of Chapters 6-8, I extend the basic framework and consider multiple-asset games. Here, I examine the selections in the context of the efficient frontier theory. Although agents follow only the returns of the portfolios they have and make decisions based on realized returns, it has been demonstrated that they are capable of investing according to the efficient frontier hypothesis. The slightly more dispersed selection by suspicious agents is a consequence of their slight failure to conduct a “winner takes all” principle, even though they identify the same “winners” as unsuspicious agents do. This conclusion is supported in both bull and bear markets, except that agents take on more risk in the former, which is consistent with the theory. Agents do not prefer excessively diversified portfolios, but two- asset portfolios with the most desired individual stock in the center. Consistency tests, tested by the coefficient of variability and Monte Carlo simulations, demonstrate that agents behave the most consistently on the most desired or the least desired choices. In addition, unsuspicious agents were more consistent in their selections than suspicious agents were. In the presence of news and returns, two groups of portfolios seemed to be the winners. As before, the first group consisted from the efficient frontier portfolios, or portfolios from its closest neighborhood. The second group of selected portfolios was stimulated by the number of non-negative news and included highly diversified portfolios. Keywords: multiperiod portfolio selection, stochastic finance, artificial markets, social networks, evolutionary games on networks, information and knowledge, communication, suspiciousness, reinforcement learning. v vi Acknowledgement I would like to thank to everyone who has been involved in this dissertation in any way, especially to my supervisor Harry Markowitz and my brothers, Matej and Mitja. I would also like to acknowledge the contribution of Didier Sornette, John Cochrane and Terrance Odean, whose suggestions to one of my papers proved to be beneficiary also for the dissertation. It is a great pleasure to acknowledge my debt to them. I have benefited from comments of seminar participants at the ETH Zürich, Department of Management, Technology, and Economics, Chair of Entrepreneurial Risks, of March 25, 2011. The dissertation was presented at the 18th International Conference on Computing in Economics and Finance, organized by the Society for Computational Economics, June 27-29, 2012 (Prague, Czech Republic). I thank Vladimir Batagelj for his valuable suggestions on how to improve the chapter on social networks, and Marko Pahor for his suggestions on how to improve the structure of some chapters which in the end contributed to the quality of the present dissertation.

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