2. Capital Asset pricing Model

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "2. Capital Asset pricing Model"

Transcription

1 2. Capital Asset pricing Model Dr. Youchang Wu WS 2007 Asset Management Youchang Wu 1

2 Efficient frontier in the presence of a risk-free asset Asset Management Youchang Wu 2

3 Capital market line When a risk-free asset exists, i.e., when a capital market is introduced, the efficient frontier is linear. This linear frontier is called capital market line The capital market line touches the efficient frontier of the risky assets only at the tangency portfolio The optimal portfolio of any investor with mean-variance preference can be constructed using the risk-free asset and the tangency portfolio, which contains only risky assets (Two-fund separation) All investors with a mean-variance preference, independent of their risk attitudes, hold the same portfolio of risky assets. The risk attitude only affects the relative weights of the risk-free asset and the risky portfolio Asset Management Youchang Wu 3

4 Market price of risk The equation for the capital market line E( rt ) rf E ( r P ) = r f + σ ( r p σ ( r ) T The slope of the capital market line represents the best risk-return trade-off that t is available on the market Without the risk-free asset, the marginal rate of substitution between risk and return will be different across investors After introducing i the risk-free asset, it will be the same for all investors. Almost all investors benefit from introducing the risk-free asset (capital market) Reminiscent of the Fisher Separation Theorem? ) Asset Management Youchang Wu 4

5 Remaining questions What would be the tangency portfolio in equilibrium? CML describes the risk-return relation for all efficient portfolios, but what is the equilibrium relation between risk and return for inefficient portfolios or individual assets? What if the risk-free asset does not exist? Asset Management Youchang Wu 5

6 CAPM If everybody holds the same risky portfolio, then the risky portfolio must be the MARKET portfolio, i.e., the value-weighted portfolio of all securities (demand must equal supply in equilibrium!). It follows that the market portfolio is a frontier portfolio. According to Property III of portfolio frontier (discussed last time), we must have E( r ) = r f + β [ E( r ) r ], where β = COV( r m f, r m 2 ) / σ ( r This is the famous CAPM independently derived by Treynor(1961), Sharpe (1964), Lintner(1965) and Mossin (1966) E(r m )-r f is called market risk premium. An asset s risk premium is given by its beta time the market risk premium. m ) Asset Management Youchang Wu 6

7 Underlying assumptions Mean-variance preference Homogeneous beliefs among investors regarding the planning horizon and the distribution of security returns No market frictions: no transaction costs, no tax, no restriction on short selling, no information cost etc. Asset Management Youchang Wu 7

8 Intuition for CAPM Since everybody holds the market portfolio, the risk of an individual asset is characterized by its contribution to variance of the market portfolio instead of its own variance. The contribution of an individual security to the variance of market portfolio is determined by its covariance with the market portfolio n n 2 2 σ ( rm ) σ ( r m ) = wiw COV ( ri, r ) => = w i= 1 = 1 2COV The part of an asset ss risk that is correlated with the market portfolio, the systematic risk, cannot be diversified away; thus, investors need to be compensated for bearing it. The part of an asset ss risk that is not correlated with the market portfolio, the unsystematic risk, can be diversified away; thus, bearing unsystematic risk need not be rewarded, and therefore, an asset s unsystematic risk does not affect its risk premium. i ( r i, r m ) Asset Management Youchang Wu 8

9 CAPM vs Property III Property III is a mathematical property of portfolio frontier that holds for any return distribution. CAPM is an asset pricing relation derived using economic reasoning. It specifies how risk and return are related in equilibrium. Asset returns under CAPM are not exogenously given. They are endogenously determined d in market equilibrium. i If the CAPM does not hold, i.e., market portfolio is not mean-variance efficient, then demand does not equal supply for some assets. The prices of such assets as well as other assets must change, therefore the whole return distribution will change This process will continue until we converge to an return distribution that makes the market portfolio mean-variance efficient. Asset Management Youchang Wu 9

10 Security market line E(r) Capital market line E(r) Security market line E(r m ) E(r m ) r f r f σ β=1 β Asset Management Youchang Wu 10

11 SML vs CML Capital market line describes the efficient frontier in the presence of a risk-free asset. It specifies the equilibrium relation between return and total risk of efficient portfolio. Security market line describes the equilibrium relation between return and systematic risk for all assets or portfolios Asset Management Youchang Wu 11

12 Portfolio beta CAPM holds both for individual assets and portfolios of assets The beta of a portfolio is simply the weighted average beta of each individual assets in the portfolio, this is because COV( r p, r m ) = COV( n i= 1 w r, r i i m ) n i= 1 w COV( r where w i is the weight of asset i in portfolio p. Asset Management Youchang Wu 12 = i i, r m )

13 Zero-beta CAPM What if there is no risk-free asset? Each investor will hold a different frontier portfolio depending on his own risk attitude According to Property I of portfolio frontier, the aggregate of each investor s portfolio, i.e., the market portfolio, is also a frontier portfolio By Property III of portfolio frontier, it follows that the linear relation between expected return and beta with respect to the market portfolio must hold. This argument leads to the zero-beta CAPM (Black 1972): E r ) = E( r ) + β [ E( r ) E( r )] ( z m z where r z is the return of a zero-beta portfolio Asset Management Youchang Wu 13

14 Implications for investment CAPM solves three most important t issues in investment t simultaneously: Where to invest? Invest in the market portfolio and risk-free asset! How to value an asset? Estimated the beta of this asset and discount all the future cash flows generated by this asset using a discount rate given by CAPM! How to evaluate investment performance? Adust the performance by beta! Not surprisingly this is regarded as one of the greatest results in finance But how does it fit the real world? Numerous studies have tried to answer this question Asset Management Youchang Wu 14

15 Earlier empirical tests of CAPM Cross-sectional sectional test First estimate the beta by running the following time-serise regression r t = α + β r + ε Then run the following (out of sample) cross-sectional regression mt r = γ + γ β + γ CHAR + = 0 1 γ 2 where CHAR is a charateristic of stock unrelated to CAPM such firm size, idiosyncratic risk CAPM predicts that γ 0 =risk free rate, γ 1 =market risk premium, and γ 2 =0 Tests are usually based on portfolio returns to avoid measurement errors in estimated t betas. Supportive results are reported by Fama and MacBeth (1974) t e Asset Management Youchang Wu 15

16 Earlier empirical tests of CAPM (2) Time series test r t r = α + β ( r r ) + ε f mt f t Prediction of CAPM: α is zero for every stock or portfolio Black, Jensen and Scholes (1972) reect the standard CAPM in favor of the zero-beta CAPM Asset Management Youchang Wu 16

17 Roll s critique Roll (1977) argues that CAPM is inherently untestable The only economic prediction of CAPM is that the market portfolio is mean-variance efficient The linear return/beta relation can be found in any sample irrespective of how returns are determined in the market (All we need is to identify an index portfolio which is ex post efficient) All existing tests only tell us whether the market proxy used by researchers are efficient or not, they say nothing about the efficiency of the market portfolio itself A true market portflio should include all assets (human capital etc) and is unobservable, therefore CAPM is untestable Asset Management Youchang Wu 17

18 Roll s critique (2) Roll (1978) further argues that using CAPM to measure performance is problematic If performance is measure relative to an index that is ex post efficient, then from PIII of porftolio frontier, all portfolios will be on the security market line (no performance) If performance is measured relative to an ex post inefficient index, then any ranking of portfolio performance is possible depending on which inefficient index has been chosen Asset Management Youchang Wu 18

19 Findings from more recent tests The relation between beta and return is weak at best (Fama and French 1992) Size effect: small stocks outperform large stocks (Banz 1981,Fama and French 1992) Book-to-market k t effect: stocks with high h book-tomarket equity ratios outperform stocks with low book-to-market ratios (Fama and French 1992) Momentum effect: Stocks outperforming in the last 3-12 months tend to outperform in the following 3-12 months (Jegadeesh and Titman 1993). Asset Management Youchang Wu 19

20 Possible explanations for empirical shortcomings of CAPM Measurement errors Measurement errors in beta Measurement errors in expected return (survivorship bias) Behavioral biases of investors Small investors are subect to many behavioral biases Institutional investors are subect to agency issues Missing risk factors People do not ust hold bonds and stocks Therefore they do not ust care about an asset s covariance with a market index They also care about its covariance with other components (such as human capital) of their true portfolio This means we have to consider other risk factors as well Asset Management Youchang Wu 20

21 Summary CAPM is an elegant model that gives simple answers to several key issues in finance The real prediction of CAPM is that the market portfolio is mean-variance efficient. Empirical results should be interpreted with great caution in the light of Roll s critique Asset Management Youchang Wu 21

Lecture 2: Equilibrium

Lecture 2: Equilibrium Lecture 2: Equilibrium Investments FIN460-Papanikolaou Equilibrium 1/ 33 Overview 1. Introduction 2. Assumptions 3. The Market Portfolio 4. The Capital Market Line 5. The Security Market Line 6. Conclusions

More information

THE CAPITAL ASSET PRICING MODEL

THE CAPITAL ASSET PRICING MODEL THE CAPITAL ASSET PRICING MODEL Szabolcs Sebestyén szabolcs.sebestyen@iscte.pt Master in Finance INVESTMENTS Sebestyén (ISCTE-IUL) CAPM Investments 1 / 30 Outline 1 Introduction 2 The Traditional Approach

More information

The Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) The Capital Asset Pricing Model (CAPM) Tee Kilenthong UTCC c Kilenthong 2016 Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 1 / 36 Main Issues What is an equilibrium implication if all investors

More information

This is the trade-off between the incremental change in the risk premium and the incremental change in risk.

This is the trade-off between the incremental change in the risk premium and the incremental change in risk. I. The Capital Asset Pricing Model A. Assumptions and implications 1. Security markets are perfectly competitive. a) Many small investors b) Investors are price takers. Markets are frictionless a) There

More information

is dead in the context of empirical models of assets returns. Rhys Frake Word count: 2997

is dead in the context of empirical models of assets returns. Rhys Frake Word count: 2997 Present a critique of the Capital Asset Pricing Model, and hence discuss the claim that beta is dead in the context of empirical models of assets returns. Rhys Frake 0937708 Word count: 2997 1 P a g e

More information

CAPM, Arbitrage, and Linear Factor Models

CAPM, Arbitrage, and Linear Factor Models CAPM, Arbitrage, and Linear Factor Models CAPM, Arbitrage, Linear Factor Models 1/ 41 Introduction We now assume all investors actually choose mean-variance e cient portfolios. By equating these investors

More information

Capital Market Equilibrium and the Capital Asset Pricing Model

Capital Market Equilibrium and the Capital Asset Pricing Model Capital Market Equilibrium and the Capital Asset Pricing Model Econ 422 Investment, Capital & Finance Spring 21 June 1, 21 1 The Risk of Individual Assets Investors require compensation for bearing risk.

More information

Chap 3 CAPM, Arbitrage, and Linear Factor Models

Chap 3 CAPM, Arbitrage, and Linear Factor Models Chap 3 CAPM, Arbitrage, and Linear Factor Models 1 Asset Pricing Model a logical extension of portfolio selection theory is to consider the equilibrium asset pricing consequences of investors individually

More information

Capital Asset Pricing Model. Joel Barber. Department of Finance. Florida International University. Miami, FL 33199

Capital Asset Pricing Model. Joel Barber. Department of Finance. Florida International University. Miami, FL 33199 Capital Asset Pricing Model Joel Barber Department of Finance Florida International University Miami, FL 33199 Capital Asset Pricing Model Mean-variance efficient risky portfolio For each asset j =1, 2,...,

More information

Chapter 7 Portfolio Theory and Other Asset Pricing Models

Chapter 7 Portfolio Theory and Other Asset Pricing Models Chapter 7 Portfolio Theory and Other sset Pricing Models NSWERS TO END-OF-CHPTER QUESTIONS 7-1 a. portfolio is made up of a group of individual assets held in combination. n asset that would be relatively

More information

Module 7 Asset pricing models

Module 7 Asset pricing models 1. Overview Module 7 Asset pricing models Prepared by Pamela Peterson Drake, Ph.D., CFA Asset pricing models are different ways of interpreting how investors value investments. Most models are based on

More information

Portfolio Performance Measures

Portfolio Performance Measures Portfolio Performance Measures Objective: Evaluation of active portfolio management. A performance measure is useful, for example, in ranking the performance of mutual funds. Active portfolio managers

More information

The CAPM & Multifactor Models

The CAPM & Multifactor Models The CAPM & Multifactor Models Business Finance 722 Investment Management Professor Karl B. Diether The Ohio State University Fisher College of Business Review and Clarification In the last few lectures

More information

The Tangent or Efficient Portfolio

The Tangent or Efficient Portfolio The Tangent or Efficient Portfolio 1 2 Identifying the Tangent Portfolio Sharpe Ratio: Measures the ratio of reward-to-volatility provided by a portfolio Sharpe Ratio Portfolio Excess Return E[ RP ] r

More information

The Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) Prof. Alex Shapiro Lecture Notes 9 The Capital Asset Pricing Model (CAPM) I. Readings and Suggested Practice Problems II. III. IV. Introduction: from Assumptions to Implications The Market Portfolio Assumptions

More information

Econ 424/Amath 462 Capital Asset Pricing Model

Econ 424/Amath 462 Capital Asset Pricing Model Econ 424/Amath 462 Capital Asset Pricing Model Eric Zivot August 15, 2013 SI Model and Efficient Portfolios assets with returns iid ( 2 ) R = Σ = 1. = 2 1 1..... 1 2 1. Assume risk-free asset with return

More information

Capital Asset Pricing Model Econ 487

Capital Asset Pricing Model Econ 487 Capital Asset Pricing Model Econ 487 Outline CAPM Assumptions and Implications CAPM and the Market Model Testing the CAPM Conditional CAPM CAPM Readings Zivot, Ch. 8 (pp. 185-191) (page # s at top of page)

More information

The basic CAPM model assumes the existence of a risk free asset and we assume this in the current

The basic CAPM model assumes the existence of a risk free asset and we assume this in the current Chapter III Basics of the Capital Asset Pricing Model The Capital Asset Pricing Model (CAPM) is the most popular model of the determination of expected returns on securities and other financial assets

More information

CHAPTER 10 RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM)

CHAPTER 10 RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM) CHAPTER 10 RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM) Answers to Concepts Review and Critical Thinking Questions 1. Some of the risk in holding any asset is unique to the asset in question.

More information

Journal of Exclusive Management Science May 2015 -Vol 4 Issue 5 - ISSN 2277 5684

Journal of Exclusive Management Science May 2015 -Vol 4 Issue 5 - ISSN 2277 5684 Journal of Exclusive Management Science May 2015 Vol 4 Issue 5 ISSN 2277 5684 A Study on the Emprical Testing Of Capital Asset Pricing Model on Selected Energy Sector Companies Listed In NSE Abstract *S.A.

More information

Lecture 1: Asset Allocation

Lecture 1: Asset Allocation Lecture 1: Asset Allocation Investments FIN460-Papanikolaou Asset Allocation I 1/ 62 Overview 1. Introduction 2. Investor s Risk Tolerance 3. Allocating Capital Between a Risky and riskless asset 4. Allocating

More information

CHAPTER 9: THE CAPITAL ASSET PRICING MODEL

CHAPTER 9: THE CAPITAL ASSET PRICING MODEL CHAPTER 9: THE CAPITAL ASSET PRICING MODEL PROBLEM SETS 1. E(r P ) = r f + β P [E(r M ) r f ] 18 = 6 + β P(14 6) β P = 12/8 = 1.5 2. If the security s correlation coefficient with the market portfolio

More information

This paper is not to be removed from the Examination Halls

This paper is not to be removed from the Examination Halls ~~FN3023 ZA d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON FN3023 ZA BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences,

More information

CFA Examination PORTFOLIO MANAGEMENT Page 1 of 6

CFA Examination PORTFOLIO MANAGEMENT Page 1 of 6 PORTFOLIO MANAGEMENT A. INTRODUCTION RETURN AS A RANDOM VARIABLE E(R) = the return around which the probability distribution is centered: the expected value or mean of the probability distribution of possible

More information

Received: August 25, 2015 Accepted: Jan. 18, 2016 Published: January 18, 2016

Received: August 25, 2015 Accepted: Jan. 18, 2016 Published: January 18, 2016 Validity of Capital Assets Pricing Model (CAPM) (Empirical Evidences from Amman Stock Exchange) Ahmad Alqisie (Corresponding Author) Faculty of Business and Finance, the World Islamic Sciences & Education

More information

The Capital Asset Pricing Model

The Capital Asset Pricing Model Finance 400 A. Penati - G. Pennacchi The Capital Asset Pricing Model Let us revisit the problem of an investor who maximizes expected utility that depends only on the expected return and variance (or standard

More information

CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNS

CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNS CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNS Note: For end-of-chapter-problems in Chapter 13, the focus is on the estimation procedure. To keep the exercise feasible the sample was limited to returns

More information

How Many Days Equal A Year? Non-trivial on the Mean-Variance Model

How Many Days Equal A Year? Non-trivial on the Mean-Variance Model How Many Days Equal A Year? Non-trivial on the Mean-Variance Model George L. Ye, Dr. Sobey School of Business Saint Mary s University Halifax, Nova Scotia, Canada Christine Panasian, Dr. Sobey School of

More information

The Risk-Free Rate s Impact on Stock Returns with Representative Fund Managers

The Risk-Free Rate s Impact on Stock Returns with Representative Fund Managers School of Economics and Management Department of Business Administration FEKN90 Business Administration- Degree Project Master of Science in Business and Economics Spring term of 2013 The Risk-Free Rate

More information

Models of Risk and Return

Models of Risk and Return Models of Risk and Return Aswath Damodaran Aswath Damodaran 1 First Principles Invest in projects that yield a return greater than the minimum acceptable hurdle rate. The hurdle rate should be higher for

More information

A Two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes

A Two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes A Two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes Y. Malevergne 1,2 & D. Sornette 1 1 ETH Zurich, Chair of Entrepreneurial Risks Switzerland 2 EM-Lyon Business School France

More information

The CAPM (Capital Asset Pricing Model) NPV Dependent on Discount Rate Schedule

The CAPM (Capital Asset Pricing Model) NPV Dependent on Discount Rate Schedule The CAPM (Capital Asset Pricing Model) Massachusetts Institute of Technology CAPM Slide 1 of NPV Dependent on Discount Rate Schedule Discussed NPV and time value of money Choice of discount rate influences

More information

Asset Pricing Models and Industry Sorted Portfolios

Asset Pricing Models and Industry Sorted Portfolios Asset Pricing Models and Industry Sorted Portfolios Author: Marijn de Vries ANR: 264141 Faculty: Faculty of Economics and Business studies Programme: Bedrijfseconomie Supervisor: Jiehui Hu MSc Date: 7/6/2012

More information

13. und 14. Mai 2014 BAI Alternative Investor Conference (AIC)

13. und 14. Mai 2014 BAI Alternative Investor Conference (AIC) NEWSLETTER Februar 2014 Diesen Termin sollten Sie sich nicht entgehen lassen! 13. und 14. Mai 2014 BAI Alternative Investor Conference (AIC) www.ai-conference.com Ort: IHK, Frankfurt Inhalt Leitartikel...

More information

ON THE RISK ADJUSTED DISCOUNT RATE FOR DETERMINING LIFE OFFICE APPRAISAL VALUES BY M. SHERRIS B.A., M.B.A., F.I.A., F.I.A.A. 1.

ON THE RISK ADJUSTED DISCOUNT RATE FOR DETERMINING LIFE OFFICE APPRAISAL VALUES BY M. SHERRIS B.A., M.B.A., F.I.A., F.I.A.A. 1. ON THE RISK ADJUSTED DISCOUNT RATE FOR DETERMINING LIFE OFFICE APPRAISAL VALUES BY M. SHERRIS B.A., M.B.A., F.I.A., F.I.A.A. 1. INTRODUCTION 1.1 A number of papers have been written in recent years that

More information

Solution: The optimal position for an investor with a coefficient of risk aversion A = 5 in the risky asset is y*:

Solution: The optimal position for an investor with a coefficient of risk aversion A = 5 in the risky asset is y*: Problem 1. Consider a risky asset. Suppose the expected rate of return on the risky asset is 15%, the standard deviation of the asset return is 22%, and the risk-free rate is 6%. What is your optimal position

More information

THE ELASTICITY OF THE PRICE OF A STOCK AND ITS BETA

THE ELASTICITY OF THE PRICE OF A STOCK AND ITS BETA THE ELASTICITY OF THE PRICE OF A STOCK AND ITS BETA Cyriac ANTONY MPh, Lecturer (Selection Grade) in Statistics, Sacred Heart College Thevara, Kochi, India E-mail: cyriacantony2003@yahoo.co.in E.S. JEEVANAND

More information

Testing the CAPM. Karl B. Diether. Fisher College of Business. Karl B. Diether (Fisher College of Business) Testing the CAPM 1 / 29

Testing the CAPM. Karl B. Diether. Fisher College of Business. Karl B. Diether (Fisher College of Business) Testing the CAPM 1 / 29 Testing the CAPM Karl B. Diether Fisher College of Business Karl B. Diether (Fisher College of Business) Testing the CAPM 1 / 29 Testing the CAPM: Background CAPM is a model It is useful because it tells

More information

The capital asset pricing model (CAPM) of William Sharpe (1964) and John

The capital asset pricing model (CAPM) of William Sharpe (1964) and John Journal of Economic Perspectives Volume 18, Number 3 Summer 2004 Pages 25 46 The Capital Asset Pricing Model: Theory and Evidence Eugene F. Fama and Kenneth R. French The capital asset pricing model (CAPM)

More information

Part III. Equilibrium Pricing

Part III. Equilibrium Pricing Part III Equilibrium Pricing Chapter 7: The Capital Asset Pricing Model: Another View About Risk 7. Introduction The CAPM is an equilibrium theory built on the premises of Modern Portfolio Theory. It is,

More information

HOW MODERN IS MODERN PORTFOLIO THEORY?

HOW MODERN IS MODERN PORTFOLIO THEORY? Section for Building and Real Estate Economics Department of Real Estate and Construction Management School of Architecture and the Built Environment Royal Institute of Technology HOW MODERN IS MODERN

More information

AFM 472. Midterm Examination. Monday Oct. 24, 2011. A. Huang

AFM 472. Midterm Examination. Monday Oct. 24, 2011. A. Huang AFM 472 Midterm Examination Monday Oct. 24, 2011 A. Huang Name: Answer Key Student Number: Section (circle one): 10:00am 1:00pm 2:30pm Instructions: 1. Answer all questions in the space provided. If space

More information

Chapter 11, Risk and Return

Chapter 11, Risk and Return Chapter 11, Risk and Return 1. A portfolio is. A) a group of assets, such as stocks and bonds, held as a collective unit by an investor B) the expected return on a risky asset C) the expected return on

More information

Review for Exam 2. Instructions: Please read carefully

Review for Exam 2. Instructions: Please read carefully Review for Exam Instructions: Please read carefully The exam will have 1 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation questions.

More information

FE670 Algorithmic Trading Strategies. Stevens Institute of Technology

FE670 Algorithmic Trading Strategies. Stevens Institute of Technology FE670 Algorithmic Trading Strategies Lecture 6. Portfolio Optimization: Basic Theory and Practice Steve Yang Stevens Institute of Technology 10/03/2013 Outline 1 Mean-Variance Analysis: Overview 2 Classical

More information

Chapter 7 Risk, Return, and the Capital Asset Pricing Model

Chapter 7 Risk, Return, and the Capital Asset Pricing Model Chapter 7 Risk, Return, and the Capital Asset Pricing Model MULTIPLE CHOICE 1. Suppose Sarah can borrow and lend at the risk free-rate of 3%. Which of the following four risky portfolios should she hold

More information

skiena

skiena Lecture 19: The Capital Assets Pricing Model Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena The Capital Asset Pricing

More information

I.e., the return per dollar from investing in the shares from time 0 to time 1,

I.e., the return per dollar from investing in the shares from time 0 to time 1, XVII. SECURITY PRICING AND SECURITY ANALYSIS IN AN EFFICIENT MARKET Consider the following somewhat simplified description of a typical analyst-investor's actions in making an investment decision. First,

More information

Chapter 5. Conditional CAPM. 5.1 Conditional CAPM: Theory. 5.1.1 Risk According to the CAPM. The CAPM is not a perfect model of expected returns.

Chapter 5. Conditional CAPM. 5.1 Conditional CAPM: Theory. 5.1.1 Risk According to the CAPM. The CAPM is not a perfect model of expected returns. Chapter 5 Conditional CAPM 5.1 Conditional CAPM: Theory 5.1.1 Risk According to the CAPM The CAPM is not a perfect model of expected returns. In the 40+ years of its history, many systematic deviations

More information

The Capital Asset Pricing Model. Capital Budgeting and Corporate Objectives

The Capital Asset Pricing Model. Capital Budgeting and Corporate Objectives The Capital Asset Pricing odel Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Overview Utility and risk aversion» Choosing efficient

More information

Active Management in Swedish National Pension Funds

Active Management in Swedish National Pension Funds STOCKHOLM SCHOOL OF ECONOMICS Active Management in Swedish National Pension Funds An Analysis of Performance in the AP-funds Sara Blomstergren (20336) Jennifer Lindgren (20146) December 2008 Master Thesis

More information

The CAPM: Theory and Evidence

The CAPM: Theory and Evidence Amos Tuck School of Business at Dartmouth College Working Paper No. 03-26 Center for Research in Security Prices (CRSP) University of Chicago Working Paper No. 550 The CAPM: Theory and Evidence Eugene

More information

ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS

ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS Masters in Business Administration (MBA) Offered by the Departments of: Business Administration & Marketing and Communication PORTFOLIO ANALYSIS AND MANAGEMENT

More information

Review for Exam 2. Instructions: Please read carefully

Review for Exam 2. Instructions: Please read carefully Review for Exam 2 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems You are not responsible for any topics that are not covered in the lecture note

More information

Lecture Notes 8. Index Models. I. Readings and Suggested Practice Problems. III. Why the Single Index Model is Useful?

Lecture Notes 8. Index Models. I. Readings and Suggested Practice Problems. III. Why the Single Index Model is Useful? Prof. Alex Shapiro Lecture Notes 8 Index Models I. Readings and Suggested Practice Problems II. A Single Index Model III. Why the Single Index Model is Useful? IV. A Detailed Example V. Two Approaches

More information

Lecture 2: Delineating efficient portfolios, the shape of the meanvariance frontier, techniques for calculating the efficient frontier

Lecture 2: Delineating efficient portfolios, the shape of the meanvariance frontier, techniques for calculating the efficient frontier Lecture 2: Delineating efficient portfolios, the shape of the meanvariance frontier, techniques for calculating the efficient frontier Prof. Massimo Guidolin Portfolio Management Spring 2016 Overview The

More information

Cost of equity estimation

Cost of equity estimation MSc in Finance & International Business Authors: Anna Kwiatkowska Magdalena Mazuga Academic Advisor: Frank Pedersen Cost of equity estimation Application of the Capital Asset Pricing Model on the Warsaw

More information

INVESTMENTS Classes 8 & 9: The Equity Market Cross Sectional Variation in Stock Returns. Spring 2003

INVESTMENTS Classes 8 & 9: The Equity Market Cross Sectional Variation in Stock Returns. Spring 2003 15.433 INVESTMENTS Classes 8 & 9: The Equity Market Cross Sectional Variation in Stock Returns Spring 2003 Introduction Equities are common stocks, representing ownership shares of a corporation. Two important

More information

Capital Asset Pricing Model Homework Problems

Capital Asset Pricing Model Homework Problems Capital Asset Pricing Model Homework Problems Portfolio weights and expected return 1. Consider a portfolio of 300 shares of firm A worth $10/share and 50 shares of firm B worth $40/share. You expect a

More information

TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II + III

TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II + III TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II III Instructions 1. Only one problem should be treated on each sheet of paper and only one side of the sheet should be used. 2. The solutions folder

More information

Chapter 7 Risk and Return: Portfolio Theory and Asset Pricing Models ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 7 Risk and Return: Portfolio Theory and Asset Pricing Models ANSWERS TO END-OF-CHAPTER QUESTIONS Chapter 7 Risk and Return: Portfolio Theory and Asset Pricing odels ANSWERS TO END-OF-CHAPTER QUESTIONS 7-1 a. A portfolio is made up of a group of individual assets held in combination. An asset that

More information

Capital Allocation Between The Risky And The Risk- Free Asset. Chapter 7

Capital Allocation Between The Risky And The Risk- Free Asset. Chapter 7 Capital Allocation Between The Risky And The Risk- Free Asset Chapter 7 Investment Decisions capital allocation decision = choice of proportion to be invested in risk-free versus risky assets asset allocation

More information

Estimating the NER equity beta based on stock market data a response to the AER draft decision A report for the JIA

Estimating the NER equity beta based on stock market data a response to the AER draft decision A report for the JIA Estimating the NER equity beta based on stock market data a response to the AER draft decision A report for the JIA Dr. Tom Hird Professor Bruce D. Grundy January 2009 Table of Contents Executive summary

More information

Use the table for the questions 18 and 19 below.

Use the table for the questions 18 and 19 below. Use the table for the questions 18 and 19 below. The following table summarizes prices of various default-free zero-coupon bonds (expressed as a percentage of face value): Maturity (years) 1 3 4 5 Price

More information

CHAPTER 9 THE CAPITAL ASSET PRICING MODEL

CHAPTER 9 THE CAPITAL ASSET PRICING MODEL CHAPTER 9 THE CAPITAL ASSET PRICING MODEL THE CAPITAL ASSET PRICING MODEL The Capital Asset Pricing Model Extensions of the APM The CAPM and Liquidity THE CAPITAL ASSET PRICING MODEL The capital asset

More information

Benchmarking Low-Volatility Strategies

Benchmarking Low-Volatility Strategies Benchmarking Low-Volatility Strategies David Blitz* Head Quantitative Equity Research Robeco Asset Management Pim van Vliet, PhD** Portfolio Manager Quantitative Equity Robeco Asset Management forthcoming

More information

Investigation on the Under and Overvalued Stocks of PSU Banks Quoted on NSE

Investigation on the Under and Overvalued Stocks of PSU Banks Quoted on NSE Investigation on the Under and Overvalued Stocks of PSU Banks Quoted on NSE Rachna Agrawal Associate Professor, Department of Management Studies, YMCA University of Science & Technology, Faridabad, Haryana.

More information

The Capital Asset Pricing Model Theory, Econometrics, and Evidence

The Capital Asset Pricing Model Theory, Econometrics, and Evidence HA Almen 6. Semester Bachelor thesis Author: Magnus David Sander Jensen Supervisor: David Sloth Pedersen The Capital Asset Pricing Model Theory, Econometrics, and Evidence S. 2011 Department of Business

More information

Testing the CAPM Model -- A study of the Chinese Stock Market

Testing the CAPM Model -- A study of the Chinese Stock Market UMEÅ University U.S.B.E Master Thesis Testing the CAPM Model -- A study of the Chinese Stock Market Author: Xi Yang Supervisor: Jörgen Hellström Donghui Xu ACKNOWLEDGMENT Initially, we would like to express

More information

LECTURE 17: RISK AND DIVERSIFICATION

LECTURE 17: RISK AND DIVERSIFICATION LECTURE 17: RISK AND DIVERSIFICATION I. STUDENT LEARNING OBJECTIVES A. Risk aversion B. Investment implications of risk aversion C. Standard deviation as a measure of risk for individual securities and

More information

EMPIRICAL TESTING OF CAPITAL ASSET PRICING MODEL

EMPIRICAL TESTING OF CAPITAL ASSET PRICING MODEL EPIRICAL TESTING OF CAPITAL ASSET PRICING ODEL Theriou. N 1 Aggelidis. V. 2 Spiridis. T. 3 Abstract The present study examines the CAP in the Athens Stock Exchange (ASE) using the Black, Jensen and ScholesBJS

More information

Exchange Risk versus the Value Factor In International Asset Pricing

Exchange Risk versus the Value Factor In International Asset Pricing Exchange Risk versus the Value Factor In International Asset Pricing Hong Wu Division of Economics and Finance College of Business & Economics West Virginia University Morgantown, WV 26506-6025 hwu3@wvu.edu

More information

The use of CAPM and Fama and French Three Factor Model: portfolios selection

The use of CAPM and Fama and French Three Factor Model: portfolios selection Belen Blanco (Spain) The use of CAPM and Fama and French Three Factor Model: portfolios selection Abstract This work tests the American NYSE market, the expected returns of a portfolios selection according

More information

CHAPTER 10. Capital Markets and the Pricing of Risk. Chapter Synopsis

CHAPTER 10. Capital Markets and the Pricing of Risk. Chapter Synopsis CHAPE 0 Capital Markets and the Pricing of isk Chapter Synopsis 0. A First Look at isk and eturn Historically there has been a large difference in the returns and variability from investing in different

More information

Chapter 5. Risk and Return. Copyright 2009 Pearson Prentice Hall. All rights reserved.

Chapter 5. Risk and Return. Copyright 2009 Pearson Prentice Hall. All rights reserved. Chapter 5 Risk and Return Learning Goals 1. Understand the meaning and fundamentals of risk, return, and risk aversion. 2. Describe procedures for assessing and measuring the risk of a single asset. 3.

More information

Answers to Concepts in Review

Answers to Concepts in Review Answers to Concepts in Review 1. A portfolio is simply a collection of investments assembled to meet a common investment goal. An efficient portfolio is a portfolio offering the highest expected return

More information

Lecture 05: Mean-Variance Analysis & Capital Asset Pricing Model (CAPM)

Lecture 05: Mean-Variance Analysis & Capital Asset Pricing Model (CAPM) Lecture 05: Mean-Variance Analysis & Capital Asset Pricing Model (CAPM) Prof. Markus K. Brunnermeier Slide 05-1 Overview Simple CAPM with quadratic utility functions (derived from state-price beta model)

More information

CHAPTER 7: OPTIMAL RISKY PORTFOLIOS

CHAPTER 7: OPTIMAL RISKY PORTFOLIOS CHAPTER 7: OPTIMAL RIKY PORTFOLIO PROLEM ET 1. (a) and (e).. (a) and (c). After real estate is added to the portfolio, there are four asset classes in the portfolio: stocks, bonds, cash and real estate.

More information

Risk (beta), Return & Capital Budgeting Chpt. 12: problems 2,6,9,13,15. I. Applications of CAPM. 1) risk premium

Risk (beta), Return & Capital Budgeting Chpt. 12: problems 2,6,9,13,15. I. Applications of CAPM. 1) risk premium Risk (beta), Return & Capital Budgeting Chpt. 12: problems 2,6,9,13,15 I. Applications of CAPM 1) risk premium estimate from historical data (Ibbotson) 2) risk free rate Tbill vs. Tbond, consistent with

More information

The Capital Asset Pricing Model

The Capital Asset Pricing Model Journal of Economic Perspectives Volume 18, Number 3 Summer 2004 Pages 3 24 The Capital Asset Pricing Model André F. Perold A fundamental question in finance is how the risk of an investment should affect

More information

The Capital Asset Pricing Model: Some Empirical Tests

The Capital Asset Pricing Model: Some Empirical Tests The Capital Asset Pricing Model: Some Empirical Tests Fischer Black* Deceased Michael C. Jensen Harvard Business School MJensen@hbs.edu and Myron Scholes Stanford University - Graduate School of Business

More information

Key Concepts and Skills

Key Concepts and Skills Chapter 10 Some Lessons from Capital Market History Key Concepts and Skills Know how to calculate the return on an investment Understand the historical returns on various types of investments Understand

More information

SAMPLE MID-TERM QUESTIONS

SAMPLE MID-TERM QUESTIONS SAMPLE MID-TERM QUESTIONS William L. Silber HOW TO PREPARE FOR THE MID- TERM: 1. Study in a group 2. Review the concept questions in the Before and After book 3. When you review the questions listed below,

More information

Chapter 5. Risk and Return. Learning Goals. Learning Goals (cont.)

Chapter 5. Risk and Return. Learning Goals. Learning Goals (cont.) Chapter 5 Risk and Return Learning Goals 1. Understand the meaning and fundamentals of risk, return, and risk aversion. 2. Describe procedures for assessing and measuring the risk of a single asset. 3.

More information

Lecture 3: CAPM in practice

Lecture 3: CAPM in practice Lecture 3: CAPM in practice Investments FIN460-Papanikolaou CAPM in practice 1/ 59 Overview 1. The Markowitz model and active portfolio management. 2. A Note on Estimating β 3. Using the single-index model

More information

Finance Homework p. 65 (3, 4), p. 66-69 (1, 2, 3, 4, 5, 12, 14), p. 107 (2), p. 109 (3,4)

Finance Homework p. 65 (3, 4), p. 66-69 (1, 2, 3, 4, 5, 12, 14), p. 107 (2), p. 109 (3,4) Finance Homework p. 65 (3, 4), p. 66-69 (1, 2, 3, 4, 5, 12, 14), p. 107 (2), p. 109 (3,4) Julian Vu 2-3: Given: Security A Security B r = 7% r = 12% σ (standard deviation) = 35% σ (standard deviation)

More information

DOES IT PAY TO HAVE FAT TAILS? EXAMINING KURTOSIS AND THE CROSS-SECTION OF STOCK RETURNS

DOES IT PAY TO HAVE FAT TAILS? EXAMINING KURTOSIS AND THE CROSS-SECTION OF STOCK RETURNS DOES IT PAY TO HAVE FAT TAILS? EXAMINING KURTOSIS AND THE CROSS-SECTION OF STOCK RETURNS By Benjamin M. Blau 1, Abdullah Masud 2, and Ryan J. Whitby 3 Abstract: Xiong and Idzorek (2011) show that extremely

More information

Mean Variance Analysis

Mean Variance Analysis Mean Variance Analysis Karl B. Diether Fisher College of Business Karl B. Diether (Fisher College of Business) Mean Variance Analysis 1 / 36 A Portfolio of Three Risky Assets Not a two risky asset world

More information

LESSON 28: CAPITAL ASSET PRICING MODEL (CAPM)

LESSON 28: CAPITAL ASSET PRICING MODEL (CAPM) LESSON 28: CAPITAL ASSET PRICING MODEL (CAPM) The CAPM was developed to explain how risky securities are priced in market and this was attributed to experts like Sharpe and Lintner. Markowitz theory being

More information

CHAPTER 5 Risk and Rates of Return. Tasks: Risk and Rate of Return. Stand-alone risk Portfolio risk Risk & return: CAPM / SML

CHAPTER 5 Risk and Rates of Return. Tasks: Risk and Rate of Return. Stand-alone risk Portfolio risk Risk & return: CAPM / SML Assist. Assist. Prof. Prof. Dr. Dr. Şaban Çelik Yaşar University Faculty of Economics and Administrative Sciences Department of 015/016 Fall Semester : Izmir- Turkey Risk andrate Rate of Return of Return

More information

A Mean-Variance Framework for Tests of Asset Pricing Models

A Mean-Variance Framework for Tests of Asset Pricing Models A Mean-Variance Framework for Tests of Asset Pricing Models Shmuel Kandel University of Chicago Tel-Aviv, University Robert F. Stambaugh University of Pennsylvania This article presents a mean-variance

More information

The Size Effect and the Capital Asset Pricing Model. Nikhil Gupta ECON 381: Econometrics Advisor: Prof. Gary Krueger

The Size Effect and the Capital Asset Pricing Model. Nikhil Gupta ECON 381: Econometrics Advisor: Prof. Gary Krueger The Size Effect and the Capital Asset Pricing Model Nikhil Gupta ECON 381: Econometrics Advisor: Prof. Gary Krueger I. Introduction The Capital Asset Pricing Model (CAPM) is one of the most widely used

More information

Estimation of the Mean Variance Portfolio Model

Estimation of the Mean Variance Portfolio Model Estimation of the Mean Variance Portfolio Model In the mean variance framework, the optimal portfolio weight vector, x, is a function of the investor s preference parameters, c, and the first two moments

More information

Optimal Debt-to-Equity Ratios and Stock Returns

Optimal Debt-to-Equity Ratios and Stock Returns Utah State University DigitalCommons@USU All Graduate Plan B and other Reports Graduate Studies 3-2014 Optimal Debt-to-Equity Ratios and Stock Returns Courtney D. Winn Utah State University Follow this

More information

Empirical Researches of the Capital Asset Pricing Model and the Fama-French Three-factor Model on the U.S. Stock Market

Empirical Researches of the Capital Asset Pricing Model and the Fama-French Three-factor Model on the U.S. Stock Market Mälardalens University Västerås, 2013-06-04 The School of Business, Society and Engineering (EST) Division of Economics Bachelor Thesis in Economics Supervisor: Clas Eriksson Empirical Researches of the

More information

The performance of the S&P Global Luxury Index compared to the MSCI World Index, during the financial crisis.

The performance of the S&P Global Luxury Index compared to the MSCI World Index, during the financial crisis. The performance of the S&P Global Luxury Index compared to the MSCI World Index, during the financial crisis. An analysis of 80 luxury goods companies around the world Name: Laura van Ballegooijen Student

More information

A Panel Data Analysis of Corporate Attributes and Stock Prices for Indian Manufacturing Sector

A Panel Data Analysis of Corporate Attributes and Stock Prices for Indian Manufacturing Sector Journal of Modern Accounting and Auditing, ISSN 1548-6583 November 2013, Vol. 9, No. 11, 1519-1525 D DAVID PUBLISHING A Panel Data Analysis of Corporate Attributes and Stock Prices for Indian Manufacturing

More information

ผ ช วยศาสตราจารย ดร.ส ล กษมณ ภ ทรธรรมมาศ

ผ ช วยศาสตราจารย ดร.ส ล กษมณ ภ ทรธรรมมาศ การบรรยายว ชาการเร อง AEC Portfolio Investment ห วข อเร อง AEC Capital Asset Pricing Models ผ บรรยาย ผ ช วยศาสตราจารย ดร.ส ล กษมณ ภ ทรธรรมมาศ จ ดโดย คณะพาณ ชยศาสตร และการบ ญช มหาว ทยาล ยธรรมศาสตร ร วมก

More information

CHAPTER 11: ARBITRAGE PRICING THEORY

CHAPTER 11: ARBITRAGE PRICING THEORY CHAPTER 11: ARBITRAGE PRICING THEORY 1. The revised estimate of the expected rate of return on the stock would be the old estimate plus the sum of the products of the unexpected change in each factor times

More information

Wel Dlp Portfolio And Risk Management

Wel Dlp Portfolio And Risk Management 1. In case of perfect diversification, the systematic risk is nil. Wel Dlp Portfolio And Risk Management 2. The objectives of investors while putting money in various avenues are:- (a) Safety (b) Capital

More information