# Financial Economics 2015/2016

## Table of Contents

## Structure of the course

- Teaching load: 63 hours (ECTS credits 9)
- Main lecturer: BOTTAZZI Giulio
- Teaching assistant: GIACHINI Daniele
- Guest lecturer and experts: TBA
- Semester: Spring
- Keywords: financial economics, general equilibrium, arbitrage, asset pricing, optimization
- Outline: This course aims to provide a wide theoretical foundation to the most widespread notions and tools in modern finance, including present value theory, real interest rates, arbitrage pricing, portfolio allocation and mean-variance analysis.
- Objectives: The students should understand the theoretical justification of interest rate and yield curve. The students should become acquainted with the notion of arbitrage and equilibrium prices in different market settings. They should be able to solve the problem of portfolio optimization and mean-variance analysis in rather general terms.
- Description: General equilibrium, no arbitrage in risk less economies, real interest rate and the interest rate curve. Arbitrage in security markets, state prices, complete and incomplete markets, valuation functional and the fundamental theorem of finance. Choices under uncertainty, expected utility theory and risk aversion. Portfolio choices, optimal portfolio with multiple risky assets. General equilibrium under uncertainty. Pricing kernel and mean-variance analysis. OPTIONAL: behavioral finance, asset prices under ambiguity, evolutionary finance and the market selection hypothesis.
- Prerequisites: The course requires a knowledge of linear algebra (linear space, linear map, basis, inversion, eigenvectors and eigensystems), calculus (differential analyses of function of many real variables and static optimization) and, to a lesser extent, probability theory. Some basic knowledge of the theory of choice under uncertainty (expected utility theory) and economic equilibrium are in general considered understood and only cursorily reviewed.
- Final exam: the get the final grading students are required to pass a final written exam. At least one trial exam will be organized to test your level of preparation. Students get extra points for completing their homework during the course.
- Course web page: http://cafim.sssup.it/~giulio/teaching.html

## Course material

Lecture notes will be made available to all students. The syllabus (see below) contains references to specific parts of the books. Each week, students will be assigned a few examples and exercises as homework. The following week, the teaching assistant will collect the students papers and review the exercises.

- Textbooks:
- [LRW]
- Principles of Financial Economics, S.F. LeRoy and J. Werner
- [FBJ]
- Foundations of Financial Markets and Institutions, Fabozzi, Modigliani and Jones

- Further references and Optional readings:
- [MWG]
- Microeconomic Theory, A. Mas-Colell, M. D. Whinston, and J. R. Green
- [CN]
- Quantitative Financial Economics, K. Cuthbertson and D. Nitzsche
- [HR]
- Financial Economics, T. Hens and M. O. Rieger
- [ES]
- Ambiguity and Asset Markets, L. G. Epstein and M. Schneider, NBER paper;
- [Hu]
- Options, Futures and Other Derivatives, J. C. Hull (7th ed.)
- [Ni]
- The Ascent of Money: A Financial History of the World, Niall Ferguson
- [Eco]
- Guide to the Financial Markets, The Economist

- Prerequisites suggested reading (only relevant parts): C. P. Simon, L. E. Blume, Mathematics for Economists, H. R. Varian Microeconomic Analysis.

## Syllabus

List of topics with reference to the textbooks. Each item roughly corresponds to one or two lectures.

- Introduction: the structure of the course and its textbooks; the role of financial institutions slides (Textbooks sections: [FBJ] Ch. 1, 2 and 3; [Ni] Ch. 1; [Eco] Ch 1). The first building blocks: Walras market clearing condition and utility theory.
- The notion of economic equilibrium; Two agents, two goods, one date model. The role of prices.
- Two date model. Spot and forward market. Financial equilibrium. Present value prices and economic equilibrium. Redundant contracts; the role of arbitrage in setting princes;
- Real and nominal interest rate; The role of inflation; (Textbooks sections: [FBJ] Ch. 4 and 5)
- A second look at intertemporal allocation in a one good two date model: the role of preferences and endowments. Pricing of future contracts (Textbooks sections: [Hu] Sections from 4.1 to 4.8 and from 6.1 to 6.3 [Ni] Ch. 2)
- The multi-period case and the role of the yield curve. Pricing loans and fixed income securities.
- Structure of security markets with uncertainty; complete markets and redundant assets; (Textbook sections: [LRW] 1.1, 1.2)
- Structure of security markets: Left and right matrix inverse; payoff pricing correspondence; the Law of One Price; state claims and state prices (Textbook sections: [LRW] 1.6, 2.1, 2.3, 2.4, 2.5)
- Arbitrage and valuation: strong and weak arbitrage; positive pricing; the payoffs convex cone; Farkas' Lemma; the valuation functional and strong arbitrage; Stiemke's Lemma; the valuation functional and arbitrage; (Textbook sections: [LRW] 3.2, 3.3, 3.4, 3.5, 5.1)
- Arbitrage and valuation: the fundamental theorem of finance; multiplicity of valuation functional; values bound; risk neutral probabilities; (Textbook sections: [LRW] 5.2, 5.3, 5.5, 6.3, 6.4, 6.5, 6.6, 6.7;)
- Valuation of derivatives in a two date model: forward and future; put and call options. Practical example: from option price to risk-neutral measure (The software used is octave. Data courtesy of yahoo!finance) (Textbook sections: see the discussion of forward and future contracts in [Hu] Ch.1-3)
- Brief history of risk and uncertainty in Economics
- Choices under uncertainty: consumption and portfolio choices, Expected Utility Theory, separable and time invariant utilities; risk aversion; absolute and relative risk aversion coefficients; certainty equivalent; concave transformation; comparison of utility functions (Textbook sections: [LRW] 9.2, 9.3, 9.4, 9.5, 9.6, 9.8; the proves of the theorems can also be found in [MWG] Ch.6 Sec.B; further examples are discussed in [CN] Ch.1 Sec.3-5)
- Portfolio optimization: first order conditions; arbitrage and optimal portfolio, optimal consumption, prices and returns. (Textbook sections: [LRW] 1.4, 1.5, 2.6, 3.6, 11.1, 11.2; see [CN] Ch.15 for an introductory discussion of the problem)
- Portfolio optimization with one risky security: impact of wealth on optimal investment; exercises (Textbook sections: [LRW ]12.2)
- Portfolio optimization with several risky securities: from consumption to investment optimization; risk-return trade off; optimal portfolio under fair pricing; (Textbook sections: [LRW] 13.2, 13.3, 13.4, 9.9, 13.6)
- Economic equilibrium with uncertanty; representative agent model; equilibrium sufficient conditions; equilibrium and arbitrage (Textbook sections: [LRW] 1.7, 1.8, 1.9, 2.4, 3.7)
- Economic equilibrium: example with heterogeneous agents, log-utilities and Arrow securities.
- Mean variance analysis and the Markowitz economy
- Consumption based security pricing; a first derivation of CAPM; the social planner problem; equilibrium and Pareto optimality, first and second welfare theorems; (Textbook sections: 14.2, 14.3, 14.5, 15.2, 15.3, 15.4, 15.5, without theorem 15.5.1)
- Practical example: mean-variance efficient frontier from empirical data; (The software used is octave. Data courtesy of yahoo!finance)
- CAPM (Textbook sections: chapter 19 all, theorems without proof; ; see also the discussion in [CN] Ch.15 Sec. 3-5)
- A short introduction to continuous time option pricing (by a guest lecturer)
- Two seminars on empirical problems in finance (guest experts)