CLASS 4: ASSEt pricing. The Intertemporal Model. Theory and Experiment
|
|
- Ira Booker
- 5 years ago
- Views:
Transcription
1 CLASS 4: ASSEt pricing. The Intertemporal Model. Theory and Experiment
2 Lessons from the 1- period model If markets are complete then the resulting equilibrium is Paretooptimal (no alternative allocation could make everyone better off). Pareto optimality implies existed of a representative agent (with a utility function that is a weighted average of the individual investors utility functions) and state prices are proportional to that agent s marginal utility at that state s aggregate wealth. Consequently, the higher the risk aversion of the representative agent, the higher the risk premium (the difference between the return on the market portfolio and the return on a risk-free security) in the market. In the quadratic utility (CAPM) version of the model risk aversion is represented by the quadratic term coefficient. 2
3 Infinite horizon: The Lucas model Equilibrium notions: Radner Equilibrium, rational expectations, dynamic completeness Preserves the main cross-sectional prediction of the 1-period model that the higher the risk aversion the higher the risk premium. Delivers time-series predictions about prices (returns) as functions of the fundamentals. More precisely prices move with economic fundamentals and the co-movement is stronger the higher the risk aversion. Representative agent? Pareto Optimality? 3
4 The lucas model: AN example Setting (Lucas original - stationary in levels!!!) Stationary, infinite horizon setting; infinite-lived agents with time-separable utility Two assets: - Atreethatpays$0 of $1 with equal chance (i.i.d.) - A (consol) bond that pays $0.50 each period Equal number of two types of agents: Type I receives income of $15 in even periods (2,4,...) and Type II receives income of $15 in odd periods (total income is constant over time!) Type I starts with 10 trees and 0 bonds; Type II with 0 trees and 10 bonds Assets pay their dividend before a (trading) period starts; investors receive their income at that time as well Dividends/income is perishable ( cash ) 4
5 The lucas model: AN example Simple, but still complex enough to get transparent and rich predictions Cross-sectional: (Assuming risk aversion), tree is less expensive than bond (tree has higher consumption beta ) Intertemporal: price levels move with fundamentals the level of dividends of the tree Cross-sectional and intertemporal predictions reinforce each other Consumption ( cash ) is perfectly (rank-)correlated across states in equilibrium Pareto optimality reached through dynamic completeness; investors fully insure income fluctuations by trading continuously desired experimentally: trade is in subjects interest 5 Sophisticated price risk hedging...
6 No Trading PERIOD State H L L H L H Initial Holdings Tree Bond Dividends Tree $1*10=10 $0*10=0 $0*10=0 $1*10=10 $0*10=0 $1*10=10 Bond $0.5*0=0 $0.5*0=0 $0.5*0=0 $0.5*0=0 $0.5*0=0 $0.5*0=0 Income Initial Cash $10 (=10+0+0) Trade $15 (=0+0+15) $0 (=0+0+0) $25 (= ) $0 (=0+0+0) $25 (= ) Tree Bond Cash Change $0 $0 $0 $0 $0 $0 Final Holdings Tree Bond CASH $ $ $ $ $ 0.00 $ 25.00
7 ! trading!"#$%&)(& PERIOD State H L L H L H Initial Holdings Tree Bond Dividends Tree $1*10=10 $0*5=0 $0*6=0 $1*4=4 $0*5=0 $1*3=3 Bond $0.5*0=0 $0.5*5=2.5 $0.5*6=3 $0.5*4=2 $0.5*6=3 $0.5*4=2 Income $0 $15 $0 $15 $0 $15 Initial Cash $10 (=10+0+0) Trade $17.5 (= ) $3 (=0+3+0) $21 (=4+2+15) $3 (=0+3+0) $20 (=3+2+15) Tree Bond Cash Change $0 -$5 +$10 -$7.5 +$10 -$5 Final Holdings Tree Bond CASH $ $ $ $ $ $ 15.00! 7
8 The lucas model: AN Mathematically example Investor maximizes lifetime consumption: 1X t max 1 u(c(t)) t=1 subject to a budget constraint on consumption c(t), income/dividends and investment (in bonds and trees) First-order conditions from optimal (p(t + 1) + d(t + 1)) I (t)] = p(t), where I (t) is information up to t (basically, only the dividend on the tree in period t), p and d denote prices and dividends, respectively Key: price anticipations are perfect (Radner 1972) 8
9 The lucas model: AN example Numerical Example: Log Utility, = 5/6 Prices: State Tree Bond ( Equity Premium ($)) High (0.62) Low (0.42) (Di erence) (0.83) (1.03) (0.20) In terms of returns, bigger equity premium in Low state: State Tree Bond ( Equity Premium (%)) High 3.4% -0.5% (3.9%) Low 55% 49% (6%) 9
10 The lucas model: AN example Numerical Example: Log Utility, = 5/6 Holdings and Trading (Type I, who do not receive income in odd periods): Period Tree Bond (Total) Odd (8.19) Even (9.81) (Trade in Odd) (+5.54) (-7.16) Remarks: Consumption smoothing to the point that each Type consumes a fixed fraction of total available dividend ( cash ) (Sophisticated trading: buy the tree to hedge price risk) Lots of trading, desired experimentally (see also 10 Crockett-Du y, 2010)
11 The lucas model: in the laboratory Inducing Consumption Smoothing In The Laboratory At the end of each trading period, we roll a (twelve-sided) die If outcome is either 7 or 8, then we terminate the replication and subjects take home the cash they are holding at that moment; trees and bonds are taken away If the outcome is anything else, cash is forfeited and we move to the subsequent period, carrying over trees and bonds, which pay dividends that become cash (in addition to any income) Unlike Crockett-Du y (2010),whousenonlinearpayo s 11 in order to induce smoothing...
12 The lucas model: in the laboratory Implementing A Stationary, Infinite-Horizon Setting In The Laboratory Technique: - Infinite Horizon: the twelve-sided die has positive probability of continuing the replication - Stationarity: if a replication has not terminated when the end of the experimental session (fixed duration) has been reached, then subjects get to keep the cash for that period The latter works because of the time-separability of preferences in the Lucas model and our assumption of 12 i.i.d. dividends!
13 The lucas model: in the laboratory Implementing A Stationary, Infinite-Horizon Setting In The Laboratory Technique: - Infinite Horizon: the twelve-sided die has positive probability of continuing the replication - Stationarity: if a replication has not terminated when the end of the experimental session (fixed duration) has been reached, then subjects get to keep the cash for that period The latter works because of the time-separability of preferences in the Lucas model and our assumption of 13 i.i.d. dividends!
14 Design summary Possible Termination of Session *If termination--keep CASH *If continuation--lose CASH, carry over Trees and Bonds Possible Termination of Session *If termination--keep CASH *If continuation--lose CASH, carry over Trees and Bonds Income Dividends from initial allocation of Trees and Bonds Income Dividends from carried over allocation of Trees and Bonds Etc. Period 1 Period 2 Period 3 Trade to a final allocation of Trees, Bonds, and CASH Trade to a final allocation of Trees, Bonds, and CASH 14
15 Trading platform 15
16 Sessions Session Place Replication Periods Subject Number (Total, Min, Max) Count 1 Caltech 4 (14, 1, 7) 16 2 Caltech 2 (13, 4, 9) 12 3 UCLA 3 (12, 3, 6) 30 4 UCLA 2 (14, 6, 8) 24 5 Caltech 2 (12, 2, 10) 20 6 Utah 2 (15, 6, 9) 24 (Overall) 15 (80, 1, 10) 16
17 Prices Tree Bond Equity Price Price Premium ($) Mean St. Dev High (State) Low (State) Di erence
18 Prices Correlation between the Equity Premium in each replication and the price differential between high/low dividend periods (what was the theoretical prediction here???) Tree Bond Correlation (St. Err.) (0.40) (0.40) 18
19 Prices Figure 2: Time series of Tree (solid line) and Bond (dashed line) transaction prices; averages per period. Session numbers underneath line segments refer to Table Price Period 19
20 Prices and fundamentals A stochastic drift model influenced by tree dividend best describes price evolution: Explanatory Tree Price Change Bond Price Change Variables Estim. (95% CI) Estim. (95% CI) State: (None=0; 0.19 (0.08, 0.29) 0.10 (-0.03, 0.23) High-to-Low=-1, Low-to-High=+1) R Autocor. (s.e. 0.13)
21 (Pareto) efficiency Consumption ($) Consumption Ratio Type High Low High Low I (19.75) 7.64 (4.69) 1.01 (0.52) 1.62 (3.26) II (10.25) (15.31) Type Odd Even I 7.69 (2.41) (20.65) II (20) (5) Positive rank correlation of end-of-period cash (vs. autarky) Sharing (of total cash) much closer to equal 21
22 What is happening Subjects did not hedge price risk (much) they did not expect prices to move with fundamentals Resulting equilibrium is VERY di erent from Lucas model!... but very much like in our experiments (stochastic drift, etc.) (Significant correlation between prices and fundamentals cannot easily be detected in rounds) 22
23 Price expectations Adam, Marcet and Nicolini (2012) also point out that even with only small mistakes in expectations about prices (assuming everyone knows underlying dividend processes!), equilibrium prices may look very di erent from the Lucas equilibrium much more like in the real world. But Adam, Marcet and Nicolini (2012) do not point out that equilibrium allocations could still be pretty much the same as in the Lucas equilibrium and close to optimal!... because our agents trade consistent with their expectations, and their expectations are almost self-fulfilling. 23
24 Price expectations Figure 3: Time series of period-average Tree (red line) and Bond (blue line) transaction price changes. Changes are concatenated across all replications and all sesions, but exclude inter-replication observations. State is indicated by black solid line on top; state = 2 when High (tree dividend equals $1); state = 0 when Low (tree dividend equals $0) price change (blue; red) and state (black) bond tree period 24
25 Price expectations Figure 4: Simulated equilibrium Tree (blue line) and Bond (green line) prices, first 100 periods. State is indicated by red solid line on bottom; state = 1 when High (tree dividend equals $1); state = 0 when Low (tree dividend equals $0). Equilibrium is based on (false) agent beliefs that the past prices are the best prediction of future prices. 25
26 In conclusion The cross-sectional pricing implications of the Lucas model are born out in the experimental data The intertemporal variation (predictability) in asset prices is far less than predicted (given cross-sectional di erence) Subjects seem to have anticipated this and therefore reduce their demands to hedge against price risk; still, these anticipations are inconsistent in equilibrium (prices will and do depend on tree dividends even if this is not anticipated...) Nevertheless, the risk sharing properties of the Lucas equilibrium emerge: allocations are OK even if prices are wrong in one important dimension... 26
Experiments On The Lucas Asset Pricing Model
Experiments On The Lucas Asset Pricing Model Elena Asparouhova Peter Bossaerts Nilanjan Roy William Zame October 13, 2012 Abstract This paper reports on experimental tests of the Lucas asset pricing model
More informationExperiments With The Lucas Asset Pricing Model
Experiments With The Lucas Asset Pricing Model Elena Asparouhova Peter Bossaerts Nilanjan Roy William Zame July 11, 2012 Abstract For over thirty years, the model of Lucas (1978) has been the platform
More informationExperiments With The Lucas Asset Pricing Model
Experiments With The Lucas Asset Pricing Model Elena Asparouhova Peter Bossaerts Nilanjan Roy William Zame December 5, 2011 Abstract For over thirty years, the model of Lucas (1978) has been the platform
More informationConsumption and Portfolio Choice under Uncertainty
Chapter 8 Consumption and Portfolio Choice under Uncertainty In this chapter we examine dynamic models of consumer choice under uncertainty. We continue, as in the Ramsey model, to take the decision of
More informationSlides III - Complete Markets
Slides III - Complete Markets Julio Garín University of Georgia Macroeconomic Theory II (Ph.D.) Spring 2017 Macroeconomic Theory II Slides III - Complete Markets Spring 2017 1 / 33 Outline 1. Risk, Uncertainty,
More informationFINANCE RESEARCH SEMINAR SUPPORTED BY UNIGESTION
FINANCE RESEARCH SEMINAR SUPPORTED BY UNIGESTION ʺExperiments on the Lucas Asset Pricing Modelʺ with Elena Asparouhov, Peter Bossaerts, Nilanjan Roy Prof. William Zame UCLA, Department of Economics Abstract
More information29 Week 10. Portfolio theory Overheads
29 Week 1. Portfolio theory Overheads 1. Outline (a) Mean-variance (b) Multifactor portfolios (value etc.) (c) Outside income, labor income. (d) Taking advantage of predictability. (e) Options (f) Doubts
More informationINTERTEMPORAL ASSET ALLOCATION: THEORY
INTERTEMPORAL ASSET ALLOCATION: THEORY Multi-Period Model The agent acts as a price-taker in asset markets and then chooses today s consumption and asset shares to maximise lifetime utility. This multi-period
More informationGraduate Macro Theory II: Two Period Consumption-Saving Models
Graduate Macro Theory II: Two Period Consumption-Saving Models Eric Sims University of Notre Dame Spring 207 Introduction This note works through some simple two-period consumption-saving problems. In
More information1 Asset Pricing: Bonds vs Stocks
Asset Pricing: Bonds vs Stocks The historical data on financial asset returns show that one dollar invested in the Dow- Jones yields 6 times more than one dollar invested in U.S. Treasury bonds. The return
More informationProblem set 1 Answers: 0 ( )= [ 0 ( +1 )] = [ ( +1 )]
Problem set 1 Answers: 1. (a) The first order conditions are with 1+ 1so 0 ( ) [ 0 ( +1 )] [( +1 )] ( +1 ) Consumption follows a random walk. This is approximately true in many nonlinear models. Now we
More informationJaksa Cvitanic. Joint with: Elena Asparouhova, Peter Bossaerts, Jernej Copic, Brad Cornell, Jaksa Cvitanic, Debrah Meloso
Delegated Portfolio Management: Theory and Experiment Jaksa Cvitanic Joint with: Elena Asparouhova, Peter Bossaerts, Jernej Copic, Brad Cornell, Jaksa Cvitanic, Debrah Meloso Goals To develop a theory
More informationIdiosyncratic risk, insurance, and aggregate consumption dynamics: a likelihood perspective
Idiosyncratic risk, insurance, and aggregate consumption dynamics: a likelihood perspective Alisdair McKay Boston University June 2013 Microeconomic evidence on insurance - Consumption responds to idiosyncratic
More informationTOBB-ETU, Economics Department Macroeconomics II (ECON 532) Practice Problems III
TOBB-ETU, Economics Department Macroeconomics II ECON 532) Practice Problems III Q: Consumption Theory CARA utility) Consider an individual living for two periods, with preferences Uc 1 ; c 2 ) = uc 1
More informationDynamic Replication of Non-Maturing Assets and Liabilities
Dynamic Replication of Non-Maturing Assets and Liabilities Michael Schürle Institute for Operations Research and Computational Finance, University of St. Gallen, Bodanstr. 6, CH-9000 St. Gallen, Switzerland
More informationBooms and Busts in Asset Prices. May 2010
Booms and Busts in Asset Prices Klaus Adam Mannheim University & CEPR Albert Marcet London School of Economics & CEPR May 2010 Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of
More informationInterest Rates and Currency Prices in a Two-Country World. Robert E. Lucas, Jr. 1982
Interest Rates and Currency Prices in a Two-Country World Robert E. Lucas, Jr. 1982 Contribution Integrates domestic and international monetary theory with financial economics to provide a complete theory
More informationExercises on chapter 4
Exercises on chapter 4 Exercise : OLG model with a CES production function This exercise studies the dynamics of the standard OLG model with a utility function given by: and a CES production function:
More informationHomework 3: Asset Pricing
Homework 3: Asset Pricing Mohammad Hossein Rahmati November 1, 2018 1. Consider an economy with a single representative consumer who maximize E β t u(c t ) 0 < β < 1, u(c t ) = ln(c t + α) t= The sole
More informationChapter 9 Dynamic Models of Investment
George Alogoskoufis, Dynamic Macroeconomic Theory, 2015 Chapter 9 Dynamic Models of Investment In this chapter we present the main neoclassical model of investment, under convex adjustment costs. This
More informationThe Capital Asset Pricing Model in the 21st Century. Analytical, Empirical, and Behavioral Perspectives
The Capital Asset Pricing Model in the 21st Century Analytical, Empirical, and Behavioral Perspectives HAIM LEVY Hebrew University, Jerusalem CAMBRIDGE UNIVERSITY PRESS Contents Preface page xi 1 Introduction
More informationNon-Time-Separable Utility: Habit Formation
Finance 400 A. Penati - G. Pennacchi Non-Time-Separable Utility: Habit Formation I. Introduction Thus far, we have considered time-separable lifetime utility specifications such as E t Z T t U[C(s), s]
More information1 Consumption and saving under uncertainty
1 Consumption and saving under uncertainty 1.1 Modelling uncertainty As in the deterministic case, we keep assuming that agents live for two periods. The novelty here is that their earnings in the second
More informationBehavioral Finance and Asset Pricing
Behavioral Finance and Asset Pricing Behavioral Finance and Asset Pricing /49 Introduction We present models of asset pricing where investors preferences are subject to psychological biases or where investors
More informationAccounting for Patterns of Wealth Inequality
. 1 Accounting for Patterns of Wealth Inequality Lutz Hendricks Iowa State University, CESifo, CFS March 28, 2004. 1 Introduction 2 Wealth is highly concentrated in U.S. data: The richest 1% of households
More informationConsumption and Asset Pricing
Consumption and Asset Pricing Yin-Chi Wang The Chinese University of Hong Kong November, 2012 References: Williamson s lecture notes (2006) ch5 and ch 6 Further references: Stochastic dynamic programming:
More informationBUSM 411: Derivatives and Fixed Income
BUSM 411: Derivatives and Fixed Income 3. Uncertainty and Risk Uncertainty and risk lie at the core of everything we do in finance. In order to make intelligent investment and hedging decisions, we need
More informationAdvanced Modern Macroeconomics
Advanced Modern Macroeconomics Asset Prices and Finance Max Gillman Cardi Business School 0 December 200 Gillman (Cardi Business School) Chapter 7 0 December 200 / 38 Chapter 7: Asset Prices and Finance
More informationConvergence of Life Expectancy and Living Standards in the World
Convergence of Life Expectancy and Living Standards in the World Kenichi Ueda* *The University of Tokyo PRI-ADBI Joint Workshop January 13, 2017 The views are those of the author and should not be attributed
More informationINTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS. Jakša Cvitanić and Fernando Zapatero
INTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS Jakša Cvitanić and Fernando Zapatero INTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS Table of Contents PREFACE...1
More informationContinuous time Asset Pricing
Continuous time Asset Pricing Julien Hugonnier HEC Lausanne and Swiss Finance Institute Email: Julien.Hugonnier@unil.ch Winter 2008 Course outline This course provides an advanced introduction to the methods
More informationContinuous Time Research and Development Investment and Innovation: Effects on Price and Dividend Paths *
Continuous Time Research and Development Investment and Innovation: Effects on Price and Dividend Paths * by Thomas A. Rietz ** July 997 Working Paper #33 Abstract Here, I solve a general equilibrium,
More informationLecture 2, November 16: A Classical Model (Galí, Chapter 2)
MakØk3, Fall 2010 (blok 2) Business cycles and monetary stabilization policies Henrik Jensen Department of Economics University of Copenhagen Lecture 2, November 16: A Classical Model (Galí, Chapter 2)
More informationARCH Models and Financial Applications
Christian Gourieroux ARCH Models and Financial Applications With 26 Figures Springer Contents 1 Introduction 1 1.1 The Development of ARCH Models 1 1.2 Book Content 4 2 Linear and Nonlinear Processes 5
More informationLecture Quantitative Finance Spring Term 2015
and Lecture Quantitative Finance Spring Term 2015 Prof. Dr. Erich Walter Farkas Lecture 06: March 26, 2015 1 / 47 Remember and Previous chapters: introduction to the theory of options put-call parity fundamentals
More informationModeling Capital Market with Financial Signal Processing
Modeling Capital Market with Financial Signal Processing Jenher Jeng Ph.D., Statistics, U.C. Berkeley Founder & CTO of Harmonic Financial Engineering, www.harmonicfinance.com Outline Theory and Techniques
More informationDynamic Macroeconomics
Chapter 1 Introduction Dynamic Macroeconomics Prof. George Alogoskoufis Fletcher School, Tufts University and Athens University of Economics and Business 1.1 The Nature and Evolution of Macroeconomics
More informationOnline Appendix: Extensions
B Online Appendix: Extensions In this online appendix we demonstrate that many important variations of the exact cost-basis LUL framework remain tractable. In particular, dual problem instances corresponding
More informationEndogenous employment and incomplete markets
Endogenous employment and incomplete markets Andres Zambrano Universidad de los Andes June 2, 2014 Motivation Self-insurance models with incomplete markets generate negatively skewed wealth distributions
More informationUncertainty in Equilibrium
Uncertainty in Equilibrium Larry Blume May 1, 2007 1 Introduction The state-preference approach to uncertainty of Kenneth J. Arrow (1953) and Gérard Debreu (1959) lends itself rather easily to Walrasian
More informationFoundations of Asset Pricing
Foundations of Asset Pricing C Preliminaries C Mean-Variance Portfolio Choice C Basic of the Capital Asset Pricing Model C Static Asset Pricing Models C Information and Asset Pricing C Valuation in Complete
More informationMultiperiod Market Equilibrium
Multiperiod Market Equilibrium Multiperiod Market Equilibrium 1/ 27 Introduction The rst order conditions from an individual s multiperiod consumption and portfolio choice problem can be interpreted as
More informationAsset Pricing and Portfolio. Choice Theory SECOND EDITION. Kerry E. Back
Asset Pricing and Portfolio Choice Theory SECOND EDITION Kerry E. Back Preface to the First Edition xv Preface to the Second Edition xvi Asset Pricing and Portfolio Puzzles xvii PART ONE Single-Period
More informationReal Options and Game Theory in Incomplete Markets
Real Options and Game Theory in Incomplete Markets M. Grasselli Mathematics and Statistics McMaster University IMPA - June 28, 2006 Strategic Decision Making Suppose we want to assign monetary values to
More information1. Money in the utility function (start)
Monetary Policy, 8/2 206 Henrik Jensen Department of Economics University of Copenhagen. Money in the utility function (start) a. The basic money-in-the-utility function model b. Optimal behavior and steady-state
More informationStock Price, Risk-free Rate and Learning
Stock Price, Risk-free Rate and Learning Tongbin Zhang Univeristat Autonoma de Barcelona and Barcelona GSE April 2016 Tongbin Zhang (Institute) Stock Price, Risk-free Rate and Learning April 2016 1 / 31
More informationSupplement to the lecture on the Diamond-Dybvig model
ECON 4335 Economics of Banking, Fall 2016 Jacopo Bizzotto 1 Supplement to the lecture on the Diamond-Dybvig model The model in Diamond and Dybvig (1983) incorporates important features of the real world:
More informationAsset Pricing and Equity Premium Puzzle. E. Young Lecture Notes Chapter 13
Asset Pricing and Equity Premium Puzzle 1 E. Young Lecture Notes Chapter 13 1 A Lucas Tree Model Consider a pure exchange, representative household economy. Suppose there exists an asset called a tree.
More informationEC 324: Macroeconomics (Advanced)
EC 324: Macroeconomics (Advanced) Consumption Nicole Kuschy January 17, 2011 Course Organization Contact time: Lectures: Monday, 15:00-16:00 Friday, 10:00-11:00 Class: Thursday, 13:00-14:00 (week 17-25)
More informationMacroeconomics 2. Lecture 12 - Idiosyncratic Risk and Incomplete Markets Equilibrium April. Sciences Po
Macroeconomics 2 Lecture 12 - Idiosyncratic Risk and Incomplete Markets Equilibrium Zsófia L. Bárány Sciences Po 2014 April Last week two benchmarks: autarky and complete markets non-state contingent bonds:
More informationThe stochastic discount factor and the CAPM
The stochastic discount factor and the CAPM Pierre Chaigneau pierre.chaigneau@hec.ca November 8, 2011 Can we price all assets by appropriately discounting their future cash flows? What determines the risk
More informationMacroeconomics: Fluctuations and Growth
Macroeconomics: Fluctuations and Growth Francesco Franco 1 1 Nova School of Business and Economics Fluctuations and Growth, 2011 Francesco Franco Macroeconomics: Fluctuations and Growth 1/54 Introduction
More information1. Cash-in-Advance models a. Basic model under certainty b. Extended model in stochastic case. recommended)
Monetary Economics: Macro Aspects, 26/2 2013 Henrik Jensen Department of Economics University of Copenhagen 1. Cash-in-Advance models a. Basic model under certainty b. Extended model in stochastic case
More informationProblem Set 5 Answers. ( ) 2. Yes, like temperature. See the plot of utility in the notes. Marginal utility should be positive.
Business John H. Cochrane Problem Set Answers Part I A simple very short readings questions. + = + + + = + + + + = ( ). Yes, like temperature. See the plot of utility in the notes. Marginal utility should
More informationFinancial Mathematics III Theory summary
Financial Mathematics III Theory summary Table of Contents Lecture 1... 7 1. State the objective of modern portfolio theory... 7 2. Define the return of an asset... 7 3. How is expected return defined?...
More informationAppendix: Common Currencies vs. Monetary Independence
Appendix: Common Currencies vs. Monetary Independence A The infinite horizon model This section defines the equilibrium of the infinity horizon model described in Section III of the paper and characterizes
More information14.02 Principles of Macroeconomics Solutions to Problem Set # 2
4.02 Principles of Macroeconomics Solutions to Problem Set # 2 September 25, 2009 True/False/Uncertain [20 points] Please state whether each of the following claims are True, False or Uncertain, and provide
More informationProblem Set 4 Answers
Business 3594 John H. Cochrane Problem Set 4 Answers ) a) In the end, we re looking for ( ) ( ) + This suggests writing the portfolio as an investment in the riskless asset, then investing in the risky
More informationUnderstanding the Distributional Impact of Long-Run Inflation. August 2011
Understanding the Distributional Impact of Long-Run Inflation Gabriele Camera Purdue University YiLi Chien Purdue University August 2011 BROAD VIEW Study impact of macroeconomic policy in heterogeneous-agent
More informationNBER WORKING PAPER SERIES 'LUCAS' IN THE LABORATORY. Elena Asparouhova Peter Bossaerts Nilanjan Roy William Zame
NBER WORKING PAPER SERIES 'LUCAS' IN THE LABORATORY Elena Asparouhova Peter Bossaerts Nilanjan Roy William Zame Working Paper 19068 http://www.nber.org/papers/w19068 NATIONAL BUREAU OF ECONOMIC RESEARCH
More informationLucas In The Laboratory
Lucas In The Laboratory Elena Asparouhova Peter Bossaerts Nilanjan Roy William Zame May 27, 2014 ABSTRACT This paper studies the empirical relevance of the Lucas asset pricing model in a controlled setting
More informationE ects of di erences in risk aversion on the. distribution of wealth
E ects of di erences in risk aversion on the distribution of wealth Daniele Coen-Pirani Graduate School of Industrial Administration Carnegie Mellon University Pittsburgh, PA 15213-3890 Tel.: (412) 268-6143
More informationSTATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Spring, 2013
STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics Spring, 2013 Section 1. (Suggested Time: 45 Minutes) For 3 of the following 6 statements,
More informationFiscal Policy and Economic Growth
Chapter 5 Fiscal Policy and Economic Growth In this chapter we introduce the government into the exogenous growth models we have analyzed so far. We first introduce and discuss the intertemporal budget
More informationAsset Pricing under Information-processing Constraints
The University of Hong Kong From the SelectedWorks of Yulei Luo 00 Asset Pricing under Information-processing Constraints Yulei Luo, The University of Hong Kong Eric Young, University of Virginia Available
More information11/6/2013. Chapter 17: Consumption. Early empirical successes: Results from early studies. Keynes s conjectures. The Keynesian consumption function
Keynes s conjectures Chapter 7:. 0 < MPC < 2. Average propensity to consume (APC) falls as income rises. (APC = C/ ) 3. Income is the main determinant of consumption. 0 The Keynesian consumption function
More informationCorporate Risk Measures and Real Options Extended Abstract
Corporate Risk Measures and Real Options Extended Abstract Yuanshun Li Gordon Sick February 11, 2013 Rogers School of Business, Ryerson University Haskayne School of Business, University of Calgary 1 Abstract
More informationMarket Survival in the Economies with Heterogeneous Beliefs
Market Survival in the Economies with Heterogeneous Beliefs Viktor Tsyrennikov Preliminary and Incomplete February 28, 2006 Abstract This works aims analyzes market survival of agents with incorrect beliefs.
More informationAutarky vs Openness in a Neoclassical Growth Model. George Alogoskoufis Athens University of Economics and Business
Autarky vs Openness in a Neoclassical Growth Model! George Alogoskoufis Athens University of Economics and Business Financial Autarky vs Openness During the 1950s and the 1960s the domestic financial systems
More informationIntertemporally Dependent Preferences and the Volatility of Consumption and Wealth
Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth Suresh M. Sundaresan Columbia University In this article we construct a model in which a consumer s utility depends on
More informationPortfolio Investment
Portfolio Investment Robert A. Miller Tepper School of Business CMU 45-871 Lecture 5 Miller (Tepper School of Business CMU) Portfolio Investment 45-871 Lecture 5 1 / 22 Simplifying the framework for analysis
More informationCHAPTER 8 Risk and Rates of Return
CHAPTER 8 Risk and Rates of Return Stand-alone risk Portfolio risk Risk & return: CAPM The basic goal of the firm is to: maximize shareholder wealth! 1 Investment returns The rate of return on an investment
More informationConsumption-Savings Decisions and State Pricing
Consumption-Savings Decisions and State Pricing Consumption-Savings, State Pricing 1/ 40 Introduction We now consider a consumption-savings decision along with the previous portfolio choice decision. These
More informationOptimization 101. Dan dibartolomeo Webinar (from Boston) October 22, 2013
Optimization 101 Dan dibartolomeo Webinar (from Boston) October 22, 2013 Outline of Today s Presentation The Mean-Variance Objective Function Optimization Methods, Strengths and Weaknesses Estimation Error
More information1 Non-traded goods and the real exchange rate
University of British Columbia Department of Economics, International Finance (Econ 556) Prof. Amartya Lahiri Handout #3 1 1 on-traded goods and the real exchange rate So far we have looked at environments
More informationMacro II. John Hassler. Spring John Hassler () New Keynesian Model:1 04/17 1 / 10
Macro II John Hassler Spring 27 John Hassler () New Keynesian Model: 4/7 / New Keynesian Model The RBC model worked (perhaps surprisingly) well. But there are problems in generating enough variation in
More informationP2.T5. Market Risk Measurement & Management. Bruce Tuckman, Fixed Income Securities, 3rd Edition
P2.T5. Market Risk Measurement & Management Bruce Tuckman, Fixed Income Securities, 3rd Edition Bionic Turtle FRM Study Notes Reading 40 By David Harper, CFA FRM CIPM www.bionicturtle.com TUCKMAN, CHAPTER
More informationStock Prices and the Stock Market
Stock Prices and the Stock Market ECON 40364: Monetary Theory & Policy Eric Sims University of Notre Dame Fall 2017 1 / 47 Readings Text: Mishkin Ch. 7 2 / 47 Stock Market The stock market is the subject
More informationGeneral Examination in Macroeconomic Theory SPRING 2014
HARVARD UNIVERSITY DEPARTMENT OF ECONOMICS General Examination in Macroeconomic Theory SPRING 2014 You have FOUR hours. Answer all questions Part A (Prof. Laibson): 48 minutes Part B (Prof. Aghion): 48
More informationMicroeconomics of Banking: Lecture 3
Microeconomics of Banking: Lecture 3 Prof. Ronaldo CARPIO Oct. 9, 2015 Review of Last Week Consumer choice problem General equilibrium Contingent claims Risk aversion The optimal choice, x = (X, Y ), is
More informationOptimal Taxation : (c) Optimal Income Taxation
Optimal Taxation : (c) Optimal Income Taxation Optimal income taxation is quite a different problem than optimal commodity taxation. In optimal commodity taxation the issue was which commodities to tax,
More informationMean-Variance Analysis
Mean-Variance Analysis Mean-variance analysis 1/ 51 Introduction How does one optimally choose among multiple risky assets? Due to diversi cation, which depends on assets return covariances, the attractiveness
More informationMulti-armed bandit problems
Multi-armed bandit problems Stochastic Decision Theory (2WB12) Arnoud den Boer 13 March 2013 Set-up 13 and 14 March: Lectures. 20 and 21 March: Paper presentations (Four groups, 45 min per group). Before
More informationResolution of a Financial Puzzle
Resolution of a Financial Puzzle M.J. Brennan and Y. Xia September, 1998 revised November, 1998 Abstract The apparent inconsistency between the Tobin Separation Theorem and the advice of popular investment
More informationNotes on Syllabus Section VI: TIME AND UNCERTAINTY, FUTURES MARKETS
Economics 200B UCSD; Prof. R. Starr, Ms. Kaitlyn Lewis, Winter 2017; Syllabus Section VI Notes1 Notes on Syllabus Section VI: TIME AND UNCERTAINTY, FUTURES MARKETS Overview: The mathematical abstraction
More informationPlaying games with transmissible animal disease. Jonathan Cave Research Interest Group 6 May 2008
Playing games with transmissible animal disease Jonathan Cave Research Interest Group 6 May 2008 Outline The nexus of game theory and epidemiology Some simple disease control games A vaccination game with
More informationFINAL Exam: Economics 463, Labor Economics Fall 2003 in R. Butler s class YOUR NAME: Section I (60 points) Questions 1-20 (3 points each)
FINAL Exam: Economics 463, Labor Economics Fall 2003 in R. Butler s class YOUR NAME: Section I (60 points) Questions 1-20 (3 points each) Section II (20 points) Questions 21-24 (5 points each) Section
More informationIntroduction: A Shortcut to "MM" (derivative) Asset Pricing**
The Geneva Papers on Risk and Insurance, 14 (No. 52, July 1989), 219-223 Introduction: A Shortcut to "MM" (derivative) Asset Pricing** by Eric Briys * Introduction A fairly large body of academic literature
More informationGroupe de Travail: International Risk-Sharing and the Transmission of Productivity Shocks
Groupe de Travail: International Risk-Sharing and the Transmission of Productivity Shocks Giancarlo Corsetti Luca Dedola Sylvain Leduc CREST, May 2008 The International Consumption Correlations Puzzle
More informationExpected Return and Portfolio Rebalancing
Expected Return and Portfolio Rebalancing Marcus Davidsson Newcastle University Business School Citywall, Citygate, St James Boulevard, Newcastle upon Tyne, NE1 4JH E-mail: davidsson_marcus@hotmail.com
More informationProblem Set 3. Thomas Philippon. April 19, Human Wealth, Financial Wealth and Consumption
Problem Set 3 Thomas Philippon April 19, 2002 1 Human Wealth, Financial Wealth and Consumption The goal of the question is to derive the formulas on p13 of Topic 2. This is a partial equilibrium analysis
More informationCapital markets liberalization and global imbalances
Capital markets liberalization and global imbalances Vincenzo Quadrini University of Southern California, CEPR and NBER February 11, 2006 VERY PRELIMINARY AND INCOMPLETE Abstract This paper studies the
More informationTopic 3: International Risk Sharing and Portfolio Diversification
Topic 3: International Risk Sharing and Portfolio Diversification Part 1) Working through a complete markets case - In the previous lecture, I claimed that assuming complete asset markets produced a perfect-pooling
More informationSignal or noise? Uncertainty and learning whether other traders are informed
Signal or noise? Uncertainty and learning whether other traders are informed Snehal Banerjee (Northwestern) Brett Green (UC-Berkeley) AFA 2014 Meetings July 2013 Learning about other traders Trade motives
More information1 Modelling borrowing constraints in Bewley models
1 Modelling borrowing constraints in Bewley models Consider the problem of a household who faces idiosyncratic productivity shocks, supplies labor inelastically and can save/borrow only through a risk-free
More informationOPTIMAL MONETARY POLICY FOR
OPTIMAL MONETARY POLICY FOR THE MASSES James Bullard (FRB of St. Louis) Riccardo DiCecio (FRB of St. Louis) Swiss National Bank Research Conference 2018 Current Monetary Policy Challenges Zurich, Switzerland
More informationMacroeconomic Cycle and Economic Policy
Macroeconomic Cycle and Economic Policy Lecture 1 Nicola Viegi University of Pretoria 2016 Introduction Macroeconomics as the study of uctuations in economic aggregate Questions: What do economic uctuations
More informationAdvanced International Macroeconomics Session 5
Advanced International Macroeconomics Session 5 Nicolas Coeurdacier - nicolas.coeurdacier@sciencespo.fr Master in Economics - Spring 2018 International real business cycles - Workhorse models of international
More informationNotes on Intertemporal Optimization
Notes on Intertemporal Optimization Econ 204A - Henning Bohn * Most of modern macroeconomics involves models of agents that optimize over time. he basic ideas and tools are the same as in microeconomics,
More informationIntermediary Asset Pricing
Intermediary Asset Pricing Z. He and A. Krishnamurthy - AER (2012) Presented by Omar Rachedi 18 September 2013 Introduction Motivation How to account for risk premia? Standard models assume households
More information