Empirical Financial Economics Asset pricing and Mean Variance Efficiency.

Slides:



Advertisements
Similar presentations
Tests of Static Asset Pricing Models
Advertisements

Chapter 9: Factor pricing models
Capital Asset Pricing Model
COMM 472: Quantitative Analysis of Financial Decisions
Lecture 12: Stochastic Discount Factor and GMM Estimation
LECTURE 8 : FACTOR MODELS
Investment Science D.G. Luenberger
Behavioral Finance and Asset Pricing What effect does psychological bias (irrationality) have on asset demands and asset prices?
Capital Asset Pricing Model and Single-Factor Models
L18: CAPM1 Lecture 18: Testing CAPM The following topics will be covered: Time Series Tests –Sharpe (1964)/Litner (1965) version –Black (1972) version.
The Capital Asset Pricing Model
Théorie Financière Risk and expected returns (2) Professeur André Farber.
LECTURE 7 : THE CAPM (Asset Pricing and Portfolio Theory)
Diversification and Portfolio Management (Ch. 8)
Empirical Financial Economics 5. Current Approaches to Performance Measurement Stephen Brown NYU Stern School of Business UNSW PhD Seminar, June
FINANCE 9. Optimal Portfolio Choice Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2007.
Empirical Financial Economics 4. Asset pricing and Mean Variance Efficiency Stephen Brown NYU Stern School of Business UNSW PhD Seminar, June
FINANCE 10. Capital Asset Pricing Model Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2007.
AN INTRODUCTION TO PORTFOLIO MANAGEMENT
FINANCE 10. Risk and expected returns Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2006.
Lecture: 4 - Measuring Risk (Return Volatility) I.Uncertain Cash Flows - Risk Adjustment II.We Want a Measure of Risk With the Following Features a. Easy.
Duan Wang Center for Polymer Studies, Boston University Advisor: H. Eugene Stanley.
Portfolio Theory & Capital Asset Pricing Model
Tests of linear beta pricing models (I) FINA790C Spring 2006 HKUST.
Empirical Financial Economics 2. The Efficient Markets Hypothesis - Generalized Method of Moments Stephen Brown NYU Stern School of Business UNSW PhD Seminar,
AN INTRODUCTION TO PORTFOLIO MANAGEMENT
Expected Utility, Mean-Variance and Risk Aversion Lecture VII.
Investments, 8 th edition Bodie, Kane and Marcus Slides by Susan Hine McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights.
This module identifies the general determinants of common share prices. It begins by describing the relationships between the current price of a security,
The Equity Premium Puzzle Bocong Du November 18, 2013 Chapter 13 LS 1/25.
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Chapter 9 Capital Asset Pricing.
Investment Analysis and Portfolio Management
The Capital Asset Pricing Model (CAPM)
Risk and Return CHAPTER 5. LEARNING OBJECTIVES  Discuss the concepts of portfolio risk and return  Determine the relationship between risk and return.
Chapter 13 CAPM and APT Investments
Lecture #3 All Rights Reserved1 Managing Portfolios: Theory Chapter 3 Modern Portfolio Theory Capital Asset Pricing Model Arbitrage Pricing Theory.
Modern Portfolio Theory. History of MPT ► 1952 Horowitz ► CAPM (Capital Asset Pricing Model) 1965 Sharpe, Lintner, Mossin ► APT (Arbitrage Pricing Theory)
Lecture 10 The Capital Asset Pricing Model Expectation, variance, standard error (deviation), covariance, and correlation of returns may be based on.
© Markus Rudolf Page 1 Intertemporal Surplus Management BFS meeting Internet-Page: Intertemporal Surplus Management 1. Basics.
L8: Consumption Based CAPM1 Lecture 8: Basics of Consumption-based Models The following topics will be covered: Overview of Consumption-based Models –Basic.
The Arbitrage Pricing Model Lecture XXVI. A Single Factor Model  Abstracting away from the specific form of the CAPM model, we posit a single factor.
Online Financial Intermediation. Types of Intermediaries Brokers –Match buyers and sellers Retailers –Buy products from sellers and resell to buyers Transformers.
Risk and Return Professor Thomas Chemmanur Risk Aversion ASSET – A: EXPECTED PAYOFF = 0.5(100) + 0.5(1) = $50.50 ASSET – B:PAYS $50.50 FOR SURE.
A 1/n strategy and Markowitz' problem in continuous time Carl Lindberg
Computational Finance 1/34 Panos Parpas Asset Pricing Models 381 Computational Finance Imperial College London.
Derivation of the Beta Risk Factor
Finance 300 Financial Markets Lecture 3 Fall, 2001© Professor J. Petry
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 24-1 Portfolio Performance Evaluation.
Chapter 6 Market Equilibrium. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. The seminal work of Sharpe (1964) and Lintner.
Generalised method of moments approach to testing the CAPM Nimesh Mistry Filipp Levin.
Risk and Return: Portfolio Theory and Assets Pricing Models
INVESTMENTS | BODIE, KANE, MARCUS Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin CHAPTER 9 The Capital Asset.
McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Corporate Finance Ross  Westerfield  Jaffe Seventh Edition.
Managing Portfolios: Theory
Chapter 7 An Introduction to Portfolio Management.
McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Corporate Finance Ross  Westerfield  Jaffe Seventh Edition.
The Farm Portfolio Problem: Part I Lecture V. An Empirical Model of Mean- Variance Deriving the EV Frontier –Let us begin with the traditional portfolio.
1 CAPM & APT. 2 Capital Market Theory: An Overview u Capital market theory extends portfolio theory and develops a model for pricing all risky assets.
Estimating standard error using bootstrap
Optimal Risky Portfolios
Capital Market Theory: An Overview
The Capital Asset Pricing Model
6 Efficient Diversification Bodie, Kane and Marcus
Theory of Capital Markets
Asset Pricing and Skewness
Chapter 7 Implications of Existence and Equivalence Theorems
Corporate Finance Ross  Westerfield  Jaffe
Optimal Risky Portfolios
Figure 6.1 Risk as Function of Number of Stocks in Portfolio
Capital Asset Pricing Model
Presentation transcript:

Empirical Financial Economics Asset pricing and Mean Variance Efficiency

Eigenvalues and Eigenvectors  Eigenvalues and eigenvectors satisfy  Eigenvectors diagonalize covariance matrix

Normal Distribution results  Basic result used in univariate tests:

Multivariate Normal results  Direct extension to multivariate case:

Mean variance facts

The geometry of mean variance Note: returns are in excess of the risk free rate

Tests of Mean Variance Efficiency  Mean variance efficiency implies CAPM  For Normal with mean and covariance matrix, is distributed as noncentral Chi Square with degrees of freedom and noncentrality

MacBeth T 2 test  Regress excess return on market excess return  Define orthogonal return  Market efficiency implies, estimate.

MacBeth T 2 test (continued)  The T 2 test statistic is distributed as noncentral Chi Square with m degrees of freedom and noncentrality parameter  The quadratic form is interpreted as the Sharpe ratio of the optimal orthogonal portfolio  This is interpreted as a test of Mean Variance Efficiency  Gibbons Ross and Shanken adjust for unknown Gibbons, M, S. Ross and J. Shanken, 1989 A test of the efficiency of a given portfolio Econometrica 57,

The geometry of mean variance Note: returns are in excess of the risk free rate

Multiple period consumption- investment problem  Multiperiod problem:  First order conditions:  Stochastic discount factor interpretation:

Stochastic discount factor and the asset pricing model  If there is a risk free asset:  which yields the basic pricing relationship

Stochastic discount factor and mean variance efficiency  Consider the regression model  The coefficients are proportional to the negative of minimum variance portfolio weights, so

The geometry of mean variance Note: returns are in excess of the risk free rate

Hansen Jagannathan Bounds  Risk aversion times standard deviation of consumption is given by:  “Equity premium puzzle”: Sharpe ratio of market implies a risk aversion coefficient of about 50  Consider

Non negative discount factors  Negative discount rates possible when market returns are high  Consider a positive discount rate constraint:

Stochastic discount factor and the asset pricing model  If there is a risk free asset:  which yields the basic pricing relationship

Where does m come from?  Stein’s lemma  If the vector f t+1 and r t+1 are jointly Normal  Taylor series expansion  Linear term: CAPM, higher order terms?  Put option payoff

Multivariate Asset Pricing  Consider  Unconditional means are given by  Model for observations is

Principal Factors  Single factor case  Define factor in terms of returns  What factor maximizes explained variance?  Satisfied by with criterion equal to

Principal Factors  Multiple factor case  Covariance matrix  Define and the first columns  Then  This is the “principal factor” solution  Factor analysis seeks to diagonalize  Satisfied by with criterion equal to

Importance of the largest eigenvalue

The Economy What does it mean to randomly select security i? Restrictive? Harding, M., 2008 Explaining the single factor bias of arbitrage pricing models in finite samples Economics Letters 99,

k Equally important factors  Each factor is priced and contributes equally (on average) to variance:  Eigenvalues are given by

Important result  The larger the number of equally important factors, the more certain would a casual empirical investigator be there was only one factor!

Numerical example

What are the factors?  Where W is the Helmert rotation: The average is one and the remaining average to zero

Implications for pricing  Regress returns on factor loadings  Suppose k factors are priced:  Only one factor will appear to be priced!

Application of Principal Components Yield curve factors: level, slope and curvature

A more interesting example Yield curve factors: level, slope and curvature

Application of Principal Components Procedure: 1.Estimate B* using principal components 2.Choose an orthogonal rotation to minimize a function that penalizes departures from

Conclusion  Mean variance efficiency and asset pricing  Important role of Sharpe ratio  Implicit assumption of Multivariate Normality  Limitations of data driven approach