**Interdisciplinary finance**

Teacher: J.V. ANDERSEN

E-mail: jorgen-vitting.andersen@univ-paris1.fr

ECTS: 2.5

Evaluation: Oral through participation + short written take home exam at the end of the course.

Previsional Place and time:

Prerequisites: Primary target of the courses are students having a background in Finance or Economy who want to learn how to apply quantitative and computational techniques using interdisciplinary approaches coming from Physics, Psychology, Sociology, Computer Science. However, since a growing number of students from the Natural Sciences now find work in the financial industry the courses could also be taken by students having a background in Natural Sciences as well as other parts of Social Sciences like Psychology and Sociology (for students having partial quantitative background).

Aim of the course: The aim of the course is three-fold. First part will introduce students to traditional ideas from Finance but with the perspective as well as the tools coming from statistical Physics/Econo-Physics. Second part will introduce the concept of agent based modelling as a tool to understand price formation in financial markets. Finally the third part of the course will introduce the students to classical Behavioral Finance (e.g. Prospect Theory). After the emergence of the credit crisis 2008 behavioral approaches have been more common as a way to get additional understanding of the functioning of financial markets. I will extend the concepts of Behavioral Finance into quantitative methods with broad emphasis on practical applications relevant for investment opportunities as well as investment risks.

All three parts of the course will be relevant for such topics as statistical arbitrage, financial engineering and risk management used by the investment community.

After the course the students will have achieved:

i) A detailed understanding of four of the most well-known Noble Prizes in Finance: Markovitz’s portfolio theory, the CAPM, ARCH/GARCH and Prospect Theory. It is likely that the students already know some, if maybe not all of these topics, still the perspective and tools will be different from what is taught in standard Finance.

ii) Through exercises the ability to construct agent based models which can be used in an understanding of financial markets in general, or to understand high risk periods in particular. The simulation aspect will be important in this part of the course.

iii) A practical understanding of key results from Behavioral Finance. Like e.g. they will be able to analyse a situation and find the reference level in a given situation (Prospect Theory). The understanding of human biases will enable the students to get a more broad assessment of the risks occurring in a given investment situation.

Syllabus: The course will include following 3 topics:

1. Econo-Physics

- Statistics of Real Market Prices

We will first discuss some basic notions in probability theory which then will be applied when it comes to understanding the statistics of real market returns. Different probability distributions, their convolutions, stable distributions and self-similarity will be introduced and applied to understand the formation of financial market data. The emphasis will be to see what real market data tells us and understand how much can be understood in a quantitative framework. Correlations, autocorrelations and how they change in time and across different markets will be discussed.

- Efficient Market Hypothesis and Rational Expectations

Rational expectations theory is the “core” used in most theories of traditional Finance. The efficient market hypothesis will be explained including the traditional view of speculative financial bubbles coming from the theory of rational expectations bubbles. Shortcomings of these ideas and theories will be pointed out during their presentations

- Markovitz Portfolio Theory

This topic will get the student acquainted with how to construct a portfolio according to Markovitz together with knowledge of important limitations of the theory. We will first discuss different risk measures, like the variance, “Value at Risk”, draw ups/draw downs, including temporal aspects of such measures. Then we discuss diversification and correlations before ending up with the formulas for Markovitz portfolio.

- ARCH/GARCH Processes

The statistical properties of ARCH/GARCH processes will be discussed together with empirical observations.

- Higher Order Moments Portfolio Theory

We will discuss how to create a portfolio when some of the assets are “fat-tailed”, something which is beyond the Markovitz portfolio theory. It will be shown how risk has to be redefined and emphasis will be on how to avoid extreme risk scenarios. Theory will be mixed with practical applications.

2. Quantitative Behavioral Finance, Psychology in Finance:

- Prospect Theory (Kahneman and Tversky, Nobel prize Economy 2002)

We will go through all details of Prospect Theory, how it is defined and its practical implications.

- Behavioral Biases in Markets

We will discuss various biases observed in markets like e.g. framing, anchoring, change blindness, overconfidence, the disposition effect, etc. Emphasis will be put on the practical manifestation of such effects in the markets and their implication for investment.

- Introduction of trading algorithms on biases: Sentiments, Anchoring, Change Blindness

Three very different trading algorithms will be introduced analytically together with their implementation on a computer. The main idea is to see how such biases can be detected in financial markets and how to implement and understand investment tools using such biases.-

3 Agent Based Modeling, Sociology in Finance:

- General Introduction to Agent Based Modeling

We will first discuss the general advantages using agent based modeling. The focus will then be on models with heterogeneous agents, like e.g. the El Farol Bar Game, the Minority Game and the $-Game. This part of the course will involve exercises in order to ensure that the students will be able to construct agent based models themselves when the course ends.

- Foundations for Technical Analysis

Various examples will be given to illustrate how the tool of dimensional analysis works to solve problems in Physics. After this short introduction, we will be using dimensional analysis to describe the necessary fundamental principles valid in any theory of technical analysis used to predict future price movements. Theory will be mixed with practical applications showing how to apply technical analysis in financial markets.

- Agent Based Simulations Including Behavioral Biases

Behavioral biases will be introduced in various models of stock markets. Game theoretical results as well as computer simulation techniques will be our main tools.

References:

Books

- “An Introduction to Socio-Finance”, J. Vitting Andersen and A. Nowak (Springer, Berlin 2013). For more information see: http://link.springer.com/book/10.1007%2F978-3-642-41944-7

- “Theory of Financial Risks: From Statistical Physics to Risk Management”, J.-P. Bouchaud and M.Potters, Cambridge University Press 2000.

- "Why Stock Markets Crash: Critical Events in Complex Financial Systems", D. Sornette Princeton University Press 2003.

- "Introduction to Econophysics: Correlations and Complexity in Finance", R. N. Mantegna and H. E. Stanley, Cambridge University Press 2000.

- “Finance”, Handbooks in Operations Research and Management Science Vol.9; R. A. Jarrow, V. Maksimovic, W.T. Ziemba, North-Holland (1995).

-”Thinking, Fast and Slow” , Kahneman, Daniel, New York,Farrar, Straus and Giroux, 2011.

Articles

- “Symmetry and financial markets”,Jørgen Vitting Andersen and Andrzej Nowak, Europhysics Letters (in press 2022), invited “Perspective” article by editor, https://doi.org/10.1209/0295-5075/ac7dfb. Preprint can be downloaded from http://arxiv.org/abs/2007.08475 .

-“Synchronization in human decision-making”, Yi-Fang Liu, Jørgen Vitting Andersen, and Philippe de Peretti, Chaos, Solitons & Fractals 143 110521 (2021) DOI: 10.1016/j.chaos.2020.110521

- “Efficient capital markets: A review of theory and empirical work”, Fama E (1970) J Finance 25:383-417.

- “ Have your Cake and Eat it too : Increasing Returns while Lowering Large Risks ! ”, J. V. Andersen and D. Sornette, Journal of Risk Finance, p. 70 (spring 2001).

- “ fq -Field theory for Portfolio Optimisation : "Fat-Tales" and Non-Linear Correlations ”, D. Sornette, P. Simonetti and J. V. Andersen, Phys. Report 335 (2), 19-92 (2000)

- “Pricing Stocks with Yardsticks and Sentiments”, S. Martinez, J. Vitting Andersen, M. Miniconi, A. Nowak, M. Roszczynska and D. Bree, Algorithmic Finance I, 183-190 (2011).

- “ “Price-Quakes” Shaking the World’s Stock Exchanges”, J. Vitting Andersen, A. Nowak, G. Rotundo, L. Parrot and S. Martinez, PLoS ONE 6 (11): e26472. Doi:10.1371/journal.pone.0026472 (2011). The article can be retrieved from the sites:http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0026472 and http://arxiv.org/abs/0912.3771.

-“Short and Long Term Investor Synchronisation Caused by Decoupling”, M. Roszczynska, A. Nowak, D. Kamieniarz, S. Solomon and J. Vitting Andersen, PLoS ONE 7(2012): e50700.doi:10.1371/journal.pone.0050700. The article can be retrieved from the site: http://dx.plos.org/10.1371/journal.pone.0050700 and http://arxiv.org/abs/0806.2124.

“Rational expectations and stochastic systems”, Roy Cerqueti, Jessica Riccioni and Jørgen Vitting Andersen, submitted to Annals of Operations Research (2022), can be downloaded from https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3965659).

- “Prospect theory: An analysis of decision under risk”, D. Kahneman and A. Tversky Econometrica 47:263-291 (1974).

- “Aspects of Investor Psychology”, D. Kahneman and M. W. Riepe, J Portfolio Management 24:52-65 (1998).

- “On the Psychology of Prediction”, D. Kahneman and A. Tversky, Psychol Rev 80:237-251 (1973). 2010-12-23 6

- “Judgment under Unvertainty: Heuristics and Biases”, A. Tversky A and D Kahneman, Science 185:1124-1131 (1974).

- “Detecting anchoring in financial markets”, J. Vitting Andersen, Journal of Behavioral Finance, Volume 11, Issue 2 April 2010, pages 129-33. The article can be retrieved from the site: http://arxiv.org/abs/0705.3319.

- “Beyond Greed and Fear: Understanding behavioral finance and the psychology of investing”, Shefrin H (2002) Oxford University Press.

- “Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism”, Akerlof GA, Shiller RJ (2009) Princeton University Press

- “Inefficient Markets”, Shleifer A (2000) Oxford University Press.

- “Stock prices and social dynamics”, R. J. Shiller Brookings Pap Eco Ac 2:457-498, (1984)

- “A model of investor sentiment”, N. Barberis, A. Shleifer and R. Vishny, J Fin Econ, 49:307-343 (1998).

- “Minority games: interacting agents in financial Markets”, D. Challet, M. Marsili and Y.-C. Zhang, Oxford University Press (2004).

-“The $-game”, J. V. Andersen and D. Sornette, Eur Phys J B 31:141-145 (2003).

- “ Fundamental Framework for Technical Analysis ”, J. V. Andersen, S. Gluzman and D. Sornette, Eur. Phys. Journal B 14, 579-601 (2000).

-“Market Indicators, Analysis and Performance”, R.J. Bauer and J.R. Dahlquist, Technical J. Wiley, New York, 1999.

- “Regression to the mean: one of the most neglected but important concepts in stock market”, B. I. Murstein, Journal of Behavioral Finance 4:234-237 (2003).

- “Predicting how people play games: reinforcement learning in experimental games with unique, mixed strategy equilibria”, I. Erev and A. E. Roth, Am Econ Rev 88:848-881 (1998).

- “Simple Technical Trading Rules and the Stochastic Properties of Stock Returns”, W. Brock, J.Lakonishok and B. LeBaron, Journal of Finance 47, 1731-1764 (1992)