1 Logistics FI 9100: Theory of Asset Valuation Reza S. Mahani Spring 2007 NOTE: Preliminary and Subject to Revisions Instructor: Reza S. Mahani, Department of Finance, Georgia State University, 1237 RCB building, 35 Broad street, Atlanta, GA 30303, (404) 651-2809, mahani@gsu.edu Office Hours: By appointment Class time: To be determined, tentatively Wednesday 8 12 Class room: To be determined, most probably 1200 RCB 2 Textbooks I will mainly follow this book: [P:06] Pennacchi, G., 2006, Asset Pricing Theory, Unpublished manuscript, Department of Finance, University of Illinois at Urbana-Champaign pdf files: http://www.business.uiuc.edu/gpennacc/fin591.html and chapters of [C:05] Cochrane John H., 2005, Asset Pricing, Princeton University Press [Df:01] Duffie, Darrel, 2001, Dynamic Asset Pricing Theory, Princeton University Press [Dn:90] Dothan, Michael U., 1990, Prices in Financial Markets, Oxford University Press The following books are also recommended: [HL:88] Huang, C.F., and R. Litzenberger, 1988, Foundations for Financial Economics, Prentice Hall [LW:01] LeRoy Stephen F. and Jan Werner, 2001, Principles of Financial Economics, Cambridge University Press J. Ingersoll, 1987, Theory of Financial Decision Making, Rowman and Littlefield. 1
Supplementary materials can be found in: J. Campbell, A. Lo, A. MacKinlay, 1996, The Econometrics of Financial Markets, Princeton University Press. Mas-Colell, A., M. Whinston, and J. Green, 1995, Microeconomics Theory, Oxford University Press, New York. Varian, Hal R., 1992, Microeconomic Analysis, W. W. Norton & Company; 3rd edition Simon, Carl P., and Lawrence Blume, 1994, Mathematics for Economists, W. W. Norton & Company Rudin, W., 1976, Principles of Mathematical Analysis, McGraw Hill, New York. Fleming, Wendell Helms, 1994, Functions of Several Variables, Springer 3 Objective In this course we will study the theoretical foundations of modern financial economics. Students should acquire a clear understanding of the major theoretical results concerning individuals consumption and portfolio decisions under uncertainty and their implications for the valuations of securities. 4 Prerequisites As a Ph.D. seminar on asset pricing theory, this course requires fair understanding of the following mathematical and economic concepts at the minimum: Microeconomics: Basics of preferences and utility function, decision-making under uncertainty, competitive equilibrium at the econ-graduate level (Mas-Colell, Whinston, and Green, 1995: Chapters 1, 2, 3, 6, 10, 19,20 ) Optimization: Basics of optimization, first-order and second-order conditions, Lagrange method for constrained optimization, at the econ-graduate level (Simon and Blume, 1994: Chapters 16 19; Mas-Colell, Whinston, and Green, 1995: Mathematical Appendix; Varian, 1992: Chapter 27; Duffie, 2001: Appendix B) Calculus and real Analysis: One-variable and multi-variable calculus, basics of difference and differential equations, basics of metric spaces (Any undergraduate-level calculus textbook adopted in a good university; Fleming, 1994: Chapters 1 5; Rudin, 1976: Chapters 1 10; Simon and Blume, 1994: Chapters 2 5, 12-15) 2
Probability: Basics of probability theory, expectations, independence, conditioning (Any undergraduate-level probability textbook adopted in a good university; Duffie, 2001: Appendices A, C) Linear Algebra: Matrix operations, vector spaces, projection and orthogonality, (Any undergraduate-level linear algebra textbook adopted in a good university; Simon and Blume, 1994: Chapters 6 11; Varian, 1992: Chapter 26) 5 Structure The course has four parts. The first part covers the single period investment decisions under uncertainty, mean- variance theory, capital market equilibrium, and arbitrage pricing theory. The second and third parts study dynamic investment decisions and equilibrium concept in discrete-time, and in continuous-time, respectively. Finally, the last part consists of student presentation of papers in two recent areas of research in asset pricing: (1) Long-run, consumption-based, asset pricing, and (2) production-based asset pricing. 6 Grading Every week you will have homework assignments from that week s material, and they will be due in the next class. You may work on the homework in groups, but you must hand in your own answers. Homework questions will be graded on a two point scale and they count into 15% of your grade. There will be a closed-book, two-hour, exam at the end of each part (see the tentative schedule). Overall, three exams constitute 3 %15 = %45 of your grade. You are expected to read the reading assignments for a topic beforehand, and actively participate in class discussion. Participation has a 10% weight. Presentations are done during the final week and should accompanied by a short report. Presentation and report counts towards 30% of your grade. 7 Schedule (tentative and subject to change) Note: The mandatory reading for each class is specified by and. Others are recommended. 7.1 Part I: Static Asset Pricing week 1. Decision Making under Uncertainty: Expected utility representations, Risk aversion, Insurance premium certainty equivalent wealth, A simple portfolio choice problem and its comparative statics, Some important utility functions 3
[P:06] Chapter 1 [HL:88] Chapter 1 [LW:01] Chapters 8, 9, 11, 12:.1.3 Cass, D., and J. Stiglitz (1970) The structure of investor preferences and asset returns, and separability in portfolio allocation: a contribution to the pure theory of mutual funds, Journal of Economic Theory, 2, 122 160 [http://cowles.econ.yale.edu/p/cp/p03a/p0329.pdf] Pratt, J. (1964) Risk aversion in the small and in the large, Econometrica, 32, 122 136 Ross, S. (1981) Some stronger measures of risk aversion in the small and large with applications, Econometrica, 49, 621 638 HW [P:06] Chapter 1.4 # 1, 4, 7, 8, 2, 5, 6 week 2. Equilibrium and Arbitrage: Contingent claims, Arbitrage and pricing, Fundamental theorem of asset pricing [Dn:90] Chapters 1, 2 [P:06] Chapter 4.3 [C:05] Chapters 3, 4 (Excluding the continuous-time parts) [Df:01] Chapter 1:.A.E [LW:01] Chapters 1, 2, 3, 4, 5 Arrow, K. (1964) The role of securities in the optimal allocation of riskbearing, Review of Economic Studies, 31, 91 96 [http://links.jstor.org/sici?sici=0034-6 Rubinstein, M. (1974) An aggregation theorem for securities markets, Journal of Financial Economics, 1, 225 244 HW [P:06] Chapter 4.5 # 2, 4 [Df:01] Chapter 1 # 11, 18, 19, 20 week 3. Mean-Variance Portfolio Analysis: Characterization of minimum variance portfolios, Properties of minimum variance portfolios, The case with a riskless asset [P:06] Chapter 2 (Classic/Lagraingian derivation) [C:05] Chapter 5:.2.4 (Modern derivation) [LW:01] Chapters 17, 18 4
[HL:88] Chapter 3 Hansen, L., and S. Richard (1987) The role of conditioning information in deducing testable restrictions implied by asset pricing models, Econometrica, 55, 587 614 Roll, R. (1977) A critique of the asset pricing theory s tests, Journal of Financial Economics, 4, 129 176 (Note the Appendix) HW [P:06] Chapter 2.7 # 2, 3, 6, 4, 5 week 4. Portfolio Separation and the Capital Asset Pricing Model (CAPM): Derivations of the CAPM, One and two-fund separation [P:06] Chapter 3.1 [C:05] Chapter 9:.1.3 (Excluding dynamic programming and cont.-time) [Df:01] Chapter 1.F [LW:01] Chapters 19, 14, 16 [HL:88] Chapter 4:.1.17 Black, F. (1972) Capital market equilibrium with restricted borrowing, Journal of Business, 45, 444 454 Brennan, M. (1971) Capital market equilibrium with diverged borrowing and lending rates, Journal of Financial and Quantitative Analysis, 1197 1205 Ross, S. (1978) Mutual fund separation in financial theory: the separation distributions, Journal of Economic Theory, 17, 254 286 Sharpe, W. (1964) Capital asset prices: a theory of capital market equilibrium under conditions of risk, Journal of Finance, 19, 425 442 HW [P:06] Chapter 3.5 # 1 week 5. Arbitrage Pricing Theory: The linear factor model, An economy with k factors and no residual risk, An economy with k factors and residual risk [P:06] Chapter 3:.2,.3 [C:05] Chapter 9:.4.5 [HL:88] Chapter 4:.18.22 [LW:01] Chapter 20:.1.5 Huberman, G. (1983) A simplified approach to arbitrage pricing theory, Journal of Economic Theory, 28, 1983 1991 5
Ross, S. (1976) Arbitrage Theory of Capital Asset Pricing, Journal of Economic Theory, 13, 341 360 HW [P:06] Chapter 3.5 # 2, 3 week 6. FIRST EXAM, Two hours, Closed-book 7.2 Part II: Dynamic Asset Pricing: Discrete-time week 7. Dynamic Programming and Optimal Consumption and Investment: Dynamic programming, Characterization of optimal consumption and investment policies, [P:06] Chapters 5 [Df:01] Chapter 3:.A.C [HL:88] Chapter 7 * Samuelson, P. (1969) Lifetime portfolio selection by dynamic stochastic programming, Review of Economics and Statistics, 51, 239 246 [http://links.jstor.org/sici?s HW [P:06] Chapters 5.5 # 1, 2, 6.5 # 1 week 8. Dynamic Programming and Equilibrium Valuation: Characterization of Equilibrium, Representative agent revisited, Consumption CAPM [P:06] Chapters 6 [Dn:90] Chapters 2, 3 [Df:01] Chapter 3:.D.E [HL:88] Chapter 7 [C:05] Chapter 9:.1,.2 Campbell, J. (2002) Consumption-based asset pricing, in Handbook of the Economics of Finance, G. Constantinides, M. Harris, and Rene Stulz (eds.), North-Holland Constantinides, G. (1987) Theory of valuation: Overview and recent developments, in Frontiers of Financial Theory, G. Constantinides and S. Bhattacharya (eds.), Rowman and Littlefield, Totowa, New Jersey Epstein, L., S. Zin (1991) Substitution, risk aversion, and the temporal behavior of consumption and asset returns: An empirical analysis, Journal of Political Economy, 99, 263 286 Lucas, R. (1978) Asset prices in an exchange economy, Econometrica, 46, 1426 1446 [http://links.jstor.org/sici?sici=0012-9682%28197811%2946%3a6%3c1429%3a 6
Mehra, R., and E. Prescott (1985) The equity premium puzzle, Journal of Monetary Economics, 15, 145 161 HW [P:06] Chapters 6??? week 9. Martingale Representation Approach: Definition of a martingale, Martingale property of prices and no-arbitrage, The martingale representation technology, Characterization of optimal consumption and investment policies, Asset pricing, The binomial model [Dn:90] Chapter 5 [P:06] Chapters 7 [Df:01] Chapter 2:.A.H [HL:88] Chapter 8 [LW:01] Chapters 22 26 Harrison, M. and D. Kreps (1979) Martingales and arbitrage in multi-period securities markets, Journal of Economic Theory, 20, 381 408 Naik, V. (1995) Finite state securities market models and arbitrage, in Handbooks in OR and MS, Volume 9, R. Jarrow et. al (eds.), Elsevier, North- Holland Cox, J., and S. Ross (1976) The valuation of options for alternative stochastic processes, Journal of Financial Economics, 3, 145 166 Cox, J., S. Ross, and M. Rubinstein (1979) Option pricing: a simplified approach, Journal of Financial Economics, 7, 229 263 HW [P:06] Chapters 7??? week 10. SECOND EXAM, Two hours, Closed-book 7.3 Part III: Dynamic Asset Pricing: Continuous-time week 11. Continuous-Time Methods Dynamic Hedging: [P:06] Chapter 8 [Dn:90] Chapters 7, 8 [Df:01] Appendices D and E [P:06] Chapter 9 [Dn:90] Chapter 9 [Df:01] Chapters 5 7
Black, F., and M. Scholes (1973) The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, 637-654 Merton, C. R. (1973) Theory of Rational Option Pricing, Bell Journal of Economics and Management Science, 4, 141-183 week 12. Martingales, No-arbitrage, and Pricing Kernels: [P:06] Chapter 10:.1.3 [Df:01] Chapters 6 [Dn:90] Chapter 12 Harrison, J. Michael, and Stanley R. Pliska (1981) Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and Their Applications, 11(3), 215 260 Harrison, J. M., and D. Kreps (1979), Martingales and Arbitrage in Multiperiod Securities Markets, Journal of Economic Theory, 20, 381-408 week 13. Optimal Consumption and Investment in Continuous-time: Characterization of optimal consumption and investment policies [P:06] Chapter 12 [Df:01] Chapter 9 Merton, R. (1971) Optimum Consumption and Portfolio Rules in a Continuous Time Model, Journal of Economic Theory, 3, 373-413 Cox, J., and C.-f. Huang (1989) Optimal Consumption and Portfolio Choices when Asset Prices Follow a Diffusion Process, Journal of Economic Theory, 49, 33-83 week 14. Equilibrium in Continuous-time: [P:06] Chapter 13:.1.3 [Df:01] Chapter 10 Merton, R. (1973), An Intertemporal Capital Asset Pricing Model, Econometrica, 41, 867-888 Breeden, C. D. (1979), An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities, Journal of Financial Economics, 7, 265296. 8
Cox, J., J. Ingersoll, and S. Ross (1985) An Intertemporal General Equilibrium Model of Asset Prices, Econometrica, 53, 363 384 Cox, J., J. Ingersoll, and S. Ross (1985) A Theory of the Term Structure of Interest Rates, Econometrica, 53, 385 408 week 15. THIRD EXAM, Two hours, Closed-book 7.4 Part IV: Final Presentations week 16. Long-run Consumption-based and Production-based Asset Pricing: Each student will present a paper, and overall, we will see presentations of 4-5 papers from the following list. (Depending on the number of students in class, I may form groups of two students.) I will assign you the paper (for final presentation) in the first week of class. Starred ( ) articles are more important. Cochrane, John (2006) Financial Markets and the Real Economy, Working Paper Long-run Consumption-based Asset Pricing Epstein, Larry G., and Stanley E. Zin (1989) Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework, Econometrica 57(4), 937 969 Epstein, Larry G., and Stanley E. Zin (1991) Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis, Journal of Political Economy, 99(2), 263 286 Kiku, Dana (2006) Is the Value Premium a Puzzle? Working Paper Hansen, Lars Peter, John C. Heaton, and Nan Li (2005) Consumption Strikes Back? Measuring Long-Run Risk, Working Paper Hansen, Lars Peter, and Jose Scheinkman (2006) Long Term Risk: An Operator Approach, Working Paper Panageas, Stravros, and Jianfeng Yu (2006) Technological Growth, Asset Pricing, and Consumption Risk over Long Horizons, Working Paper Production-based Asset Pricing Cochrane, John H. (1991) Production-Based Asset Pricing and the Link between Stock Returns and Economic Fluctuations, Journal of Finance, 46(1), 209 237 9
Berk, Jonathan B., Richard C. Green, and Vasant Naik (1999) Optimal Investment, Growth Options, and Security Returns, Journal of Finance, 54(5), 1553 1607 Gomes, Joao, Leonid Kogan, and Lu Zhang (2003) Equilibrium Cross Section of Returns, Journal of Political Economy, 111(4), 693 732 Carlson, Murray, Aldai Fisher, and Ron Giammarino (2004) Corporate Investment and Asset Prices Dynamics: Implications for the Cross-section of Returns, Journal of Finance, 59(6), 2577 2603 Panageas, Stavros (2005) The Neoclassical Theory of Investment in Speculative Markets, Working Paper Berk, Jonathan B., Richard C. Green, and Vasant Naik (2004) Valuation and Return Dynamics of New Ventures, Review of Financial Studies, 17(1), 1 35 Zhang, Lu (2005) The Value Premium, Journal of Finance, 60(1), 67 103 10