The Capital Asset Pricing Model (CAPM)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "The Capital Asset Pricing Model (CAPM)"

Transcription

1 The Capital Asset Pricing Model (CAPM) Tee Kilenthong UTCC c Kilenthong 2016 Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 1 / 36

2 Main Issues What is an equilibrium implication if all investors construct portfolios as we studied? How should we measure risk of any asset? Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 2 / 36

3 CAPM: Simple Derivation The efficient frontier without riskless asset. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 3 / 36

4 CAPM: Simple Derivation The efficient frontier with riskless asset. The straight line is called the capital market line. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 4 / 36

5 CAPM: Simple Derivation The equation of the capital market line is R e = R F + R m R F σ m σ e (1) where σ e is an efficient portfolio on the capital market line. R m R F σ m represents the market price of risk. σ e represents the amount of risk. That is, Expected return = (Market price of risk) (Amount of risk) (2) Problem: This equation does not describe equilibrium return on nonefficient portfolios or individual securities. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 5 / 36

6 Only R i and β i Matter From Single-Index Model, the investor should hold a very well-diversified portfolio. Therefore, only relevant risk is systematic risk measured by β. The only dimensions of a security that need be of concern are expected return R i and β i. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 6 / 36

7 Nonefficient Portfolios and Arbitrage Opportunity From the above figure, one can imagine that they can make money from the following arbitrage strategy: Cash Invested Expected Return β Portfolio C Portfolio D Arbitrage Portfolio Note: we use β P = i X iβ i. Main point: there is a portfolio involving zero risk and zero net investment that has a positive expected return. There is an arbitrage opportunity. This should not be the case in an equilibrium. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 7 / 36

8 Nonefficient Portfolios and Arbitrage Opportunity Therefore, all investors must hold efficient portfolios. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 8 / 36

9 CAPM Equation The security market line can be represented by R i = R F + ( R m R F ) βi (3) Key Insight: systematic risk (measured by β) is the only important ingredient in determining expected returns and that nonsystematic risk plays no role. In other words, investors get rewarded for bearing systematic risk. Important: this implication is empirically testable. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 9 / 36

10 CAPM Equation: Alternative We can represent risk by covariance of asset return and market return: where we use β i = σ im. σm 2 R i = R F + ( Rm R F σ m ) σim σ m (4) Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 10 / 36

11 CAPM: A More Rigorous Derivation Recall: an optimal condition for an efficient portfolio is where σ ki = Cov (R k, R i ). R k R F = λ (X 1 σ 1k X N σ Nk ) (5) Homogeneous expectation implies that the solution to this problem or the optimal portfolio here must be the market portfolio. As a result, R m = N R i X i (6) i=1 Then, we can show that X 1 σ 1k X N σ Nk = Cov (R k, R m ). (7) Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 11 / 36

12 CAPM: A More Rigorous Derivation So, we can write R k R F = λcov (R k, R m ) (8) Since the market portfolio is one of an efficient portfolio, we can write R m R F = λcov (R m, R m ) = λσ 2 m = λ = R m R F σ 2 m (9) Finally we can get the CAPM: R k R F = R m R F σm 2 σ km = ( ) σ km R m R F σm 2 R i R F = ( ) Rm R F βi (10) Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 12 / 36

13 Keys Assumptions for the Derivation of CAPM 1 No transaction costs, no personal income taxes. 2 Perfect competition. 3 Assets are infinitely divisible. 4 Investors have mean-variance preferences. 5 There exist a riskless asset. 6 Homogeneous expectation. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 13 / 36

14 CAPM without Riskless: Simple Derivation Portfolios in expected return β space. This is the case without riskless asset. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 14 / 36

15 CAPM without Riskless: Simple Derivation First, combinations of two risky portfolios lie on a straight line connecting them in expected return β space. Second, consider C and D. Using an arbitrage argument as before, we can show that all portfolios and securities must plot along the straight line, as in the figure. This line can be represented by Our job is to find what are a and b? R i = a + bβ i (11) Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 15 / 36

16 CAPM without Riskless: Simple Derivation Let R Z be the expected return on a zero beta portfolio. This portfolio must also be on the straight line: R Z = a + b 0 = a = R Z (12) Again, the market portfolio must be on the line as well: R m = R Z + b = b = R m R Z (13) Hence, we have an alternative CAPM (without riskless asset): R i = R Z + ( R m R Z ) βi (14) Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 16 / 36

17 CAPM without Riskless: A Rigorous Derivation Recall: an optimal condition for an efficient portfolio is R k R F = λ (X 1σ 1k X N σ Nk ) (15) Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 17 / 36

18 CAPM without Riskless: A Rigorous Derivation Using the result we derived earlier, we can write We then can show that X 1 σ 1k X N σ Nk = Cov (R k, R m ), (16) R k R F = λcov (R k, R m ) (17) R i = R F + ( R m R F ) βi (18) Issue: This equation holds for any zero beta expected return R F. But we should use the least risky zero beta portfolio. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 18 / 36

19 CAPM without Riskless: A Rigorous Derivation The least risky zero beta portfolio is the zero beta portfolio that has the least total risk, the minimum variance zero beta portfolio Z. The CAPM now is R i = R Z + ( Rm R Z ) βi (19) Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 19 / 36

20 Testing CAPM Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 20 / 36

21 Main Issues How can we test CAPM model? Are those tests reliable? Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 21 / 36

22 CAPM is in an Ex-ante Form The basic CAPM model can be written as E (R i ) = R F + β i [E(R m ) R F ] (20) If lending and borrowing at the risk free rate is not possible or there is no risk free rate, then the CAPM becomes E (R i ) = E(R Z ) + β i [E(R m ) E(R Z )] (21) Notice: these models are in an expectation form. This is suppose to be about future values. An expectation means that we are thinking about the situation before the uncertainty is realized. We call this ex-ante. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 22 / 36

23 CAPM is tested using Ex-post Data On the other hand, we usually perform tests of CAPM models using realized (historical) data. These values are said to be ex-post values. How can we justify using ex-post data to test ex-ante model? Defense: using the law of large number, we should be able to estimate consistently (unbiased) the ex-ante expectation using sample mean of ex-post data. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 23 / 36

24 Ex-post test of Ex-ante CAPM model That is, testing a CAPM model is a simultaneous test of all three following hypothesises: 1 The market model holds 2 The CAPM model holds 3 β i is stable over time NOTE: if there is no risk free rate, we will test the following model R it = R Zt + β i [ R mt R Zt ] + ẽ it (22) Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 24 / 36

25 Simple Test of CAPM Sharpe and Cooper (1972) divide stocks into ten portfolios using beta as a criterion. β at each point in time uses past 60 months of data. They also calculate average returns of each portfolio. They then estimate a linear equation with R 2 > R i = β i (23) Key Points: the relationship between return and β is linear. Though the intercept (supposed to represent the risk free rate) is too high. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 25 / 36

26 Simple Test of CAPM Lintner performed a similar but more systematic test of CAPM. First, run a time-series linear regression R it = α i + b i R mt + e it (24) using data of all stocks from 1954 to Then, run a cross-sectional regression R i = a 1 + a 2 b i + a 3 S i + ϵ i (25) where S i = Var(e it ) is the residual variance, representing residual risk. The result shows that a 3 = and statistically significant. This implies that CAPM is violated. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 26 / 36

27 More Advanced Test of CAPM Miller and Scholes Test Black, Jensen, and Scholes Test Fama and MacBeth Test Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 27 / 36

28 Fama and MacBeth Test They use the same procedure as Black et al. to form 20 portfolios. The difference is in the cross-sectional regression: 1 They run R it = ˆγ 0t + ˆγ 1t β i ˆγ 2t β 2 i + ˆγ 3t S et + η it (26) 2 This regression is run each month, month by month. Therefore, they can study how the parameters change over time. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 28 / 36

29 Fama and MacBeth Test This new form allow them to test the following hypotheses: 1 E(ˆγ 3t ) = 0: residual risk does not affect the return 2 E(ˆγ 2t ) = 0: test the linearity structure of CAPM 3 E(ˆγ 1t ) = 0: test the positivity of the price of risk If the first two hold, then we can conclude that a CAPM (either the standard or zero beta version) holds. Table 15.3 confirms that the first two hypothesises hold. In addition, they run a regression without those two terms and get better estimates. We then can conclude that residual risk has no effect. This is the opposite of Litner. the main reason is the measurement error. That is, using portfolios instead of securities reduce the error significantly (use the argument of Miller and Scholes). Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 29 / 36

30 Fama and MacBeth Test Given that a CAPM holds, then we can further distinguish between the standard and zero-beta CAPM using E(ˆγ 0t ) and E(ˆγ 1t ). If the zero beta model is the true model, the deviation of ˆγ 0t from its mean E(R Z ) and the deviation of ˆγ 1t from its mean E(R m ) E(R Z ) must be random. Since we know that E(R Z ) > R F, if E(ˆγ 0t R F ) > 0 and E(ˆγ 1t E(R m ) + R F ) < 0, we will then conclude that the zero beta model is the true model. They find that 1 price of risk is positive, 2 ˆγ 0 is greater than R F and ˆγ 1 is less than R m R F These results support the zero beta CAPM. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 30 / 36

31 Fama and MacBeth Test We can also test if the market operates as a fair game (efficient market). If CAPM is a true model, the expected value of ˆγ 2t and ˆγ 3t at time t + 1 should be zero, regardless of past values. Fama and MacBeth test this implication by looking at the correlation of ˆγ 3t with its lags values. They found that the correlation is not statistically different from zero. They also found a similar result for ˆγ 2t. They then conclude that the market operates as a fair game. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 31 / 36

32 Fama and MacBeth Test of Thailand Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 32 / 36

33 Fama and MacBeth Test of Thailand Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 33 / 36

34 CAPM is Not Testable? If any ex-post mean variance efficient portfolio p selected as the market portfolio, and β are computed using this portfolio as the market proxy, then R i = R ZP + β ip ( Rp R ZP ) (27) must hold. That is, testing CAPM is not meaningful. Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 34 / 36

35 Roll s Proof Consider again the first order condition of an optimal portfolio problem: λ (X 1 σ 1k X N σ kn ) = R k R F (28) Let p be the optimal portfolio, hence we can write λσ kp = R k R F (29) which must be true for any asset or portfolio. That is, it must be true for the optimal portfolio p as well: Hence, we have R i = R F + σkp σ 2 p λσ 2 p = R p R F λ = R p R F σ 2 p ( R p R F ) = RF + β kp ( R p R F ) (30) (31) Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 35 / 36

36 Roll s Proof Using a similar argument as before, we can have a model without riskless: R i = R Zp + β kp ( R p R Zp ) (32) where R Zp is the mean return of the minimum varaince zero beta portfolio. This proves that we can write a zero beta CAPM model with any efficient portfolio as a market proxy. But the true CAPM is the one with the true market portfolio. If we cannot observed the true market portfolio, then we cannot test the CAPM! Tee Kilenthong UTCC The Capital Asset Pricing Model (CAPM) 36 / 36

2. Capital Asset pricing Model

2. Capital Asset pricing Model 2. Capital Asset pricing Model Dr. Youchang Wu WS 2007 Asset Management Youchang Wu 1 Efficient frontier in the presence of a risk-free asset Asset Management Youchang Wu 2 Capital market line When a risk-free

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

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

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

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

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 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

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

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 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

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

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

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

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 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

Lecture 6: Arbitrage Pricing Theory

Lecture 6: Arbitrage Pricing Theory Lecture 6: Arbitrage Pricing Theory Investments FIN460-Papanikolaou APT 1/ 48 Overview 1. Introduction 2. Multi-Factor Models 3. The Arbitrage Pricing Theory FIN460-Papanikolaou APT 2/ 48 Introduction

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

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 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

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

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

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

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

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

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

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

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

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

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

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

1 Capital Asset Pricing Model (CAPM)

1 Capital Asset Pricing Model (CAPM) Copyright c 2005 by Karl Sigman 1 Capital Asset Pricing Model (CAPM) We now assume an idealized framework for an open market place, where all the risky assets refer to (say) all the tradeable stocks available

More information

Chapter 5 Risk and Return ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS

Chapter 5 Risk and Return ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS Chapter 5 Risk and Return ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS 5-1 a. Stand-alone risk is only a part of total risk and pertains to the risk an investor takes by holding only one asset. Risk is

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

CML is the tangent line drawn from the risk free point to the feasible region for risky assets. This line shows the relation between r P and

CML is the tangent line drawn from the risk free point to the feasible region for risky assets. This line shows the relation between r P and 5. Capital Asset Pricing Model and Factor Models Capital market line (CML) CML is the tangent line drawn from the risk free point to the feasible region for risky assets. This line shows the relation between

More information

MODERN PORTFOLIO THEORY AND INVESTMENT ANALYSIS

MODERN PORTFOLIO THEORY AND INVESTMENT ANALYSIS MODERN PORTFOLIO THEORY AND INVESTMENT ANALYSIS EIGHTH EDITION INTERNATIONAL STUDENT VERSION EDWIN J. ELTON Leonard N. Stern School of Business New York University MARTIN J. GRUBER Leonard N. Stern School

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

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

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

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

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 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

D&D, sect : CAPM without risk free asset Main points:

D&D, sect : CAPM without risk free asset Main points: D&D, sect 74 77: CAPM without risk free asset Main points: Consider N risky assets, N > 2, no risk free asset Then the frontier portfolio set is an hyperbola (Mentioned without proof on p 11 of 1 September)

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

Regression Analysis. Pekka Tolonen

Regression Analysis. Pekka Tolonen Regression Analysis Pekka Tolonen Outline of Topics Simple linear regression: the form and estimation Hypothesis testing and statistical significance Empirical application: the capital asset pricing model

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

FINANCIAL ECONOMICS OPTION PRICING

FINANCIAL ECONOMICS OPTION PRICING OPTION PRICING Options are contingency contracts that specify payoffs if stock prices reach specified levels. A call option is the right to buy a stock at a specified price, X, called the strike price.

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

LESSON 29: MARKOWITZ MODEL

LESSON 29: MARKOWITZ MODEL LESSON 29: MARKOWITZ MODEL Harry M. Morkowitz is credited with introducing new concepts of risk measurement and their application to the selection of portfolios. He started with the idea of risk aversion

More information

Simple Linear Regression Chapter 11

Simple Linear Regression Chapter 11 Simple Linear Regression Chapter 11 Rationale Frequently decision-making situations require modeling of relationships among business variables. For instance, the amount of sale of a product may be related

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

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

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

4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4

4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4 4. Simple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/4 Outline The simple linear model Least squares estimation Forecasting with regression Non-linear functional forms Regression

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 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

Positive Weights on the Efficient Frontier

Positive Weights on the Efficient Frontier Positive Weights on the Efficient Frontier Phelim Boyle Wilfrid Laurier University August 2012 Acknowledgments This paper is dedicated to Boyle s Winter 2012 graduate finance class at Wilfrid Laurier University

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

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

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

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

DO NOT COPY PORTFOLIO SELECTION AND THE CAPITAL ASSET PRICING MODEL

DO NOT COPY PORTFOLIO SELECTION AND THE CAPITAL ASSET PRICING MODEL UVA-F-1604 Rev. Mar. 4, 011 PORTFOLIO SELECTION AND THE CAPITAL ASSET PRICING MODEL What portfolio would you recommend to a 8-year-old who has just been promoted to a management position, and what portfolio

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

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

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

Solution Guide to Exercises for Chapter 5 Portfolio selection: the mean-variance model

Solution Guide to Exercises for Chapter 5 Portfolio selection: the mean-variance model THE ECONOMICS O INANCIAL MARKETS R. E. BAILEY Solution Guide to Exercises for Chapter 5 Portfolio selection: the mean-variance model 1. An investor uses the mean-variance criterion for selecting a portfolio

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

OLS is not only unbiased it is also the most precise (efficient) unbiased estimation technique - ie the estimator has the smallest variance

OLS is not only unbiased it is also the most precise (efficient) unbiased estimation technique - ie the estimator has the smallest variance Lecture 5: Hypothesis Testing What we know now: OLS is not only unbiased it is also the most precise (efficient) unbiased estimation technique - ie the estimator has the smallest variance (if the Gauss-Markov

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

Black Scholes Merton Approach To Modelling Financial Derivatives Prices Tomas Sinkariovas 0802869. Words: 3441

Black Scholes Merton Approach To Modelling Financial Derivatives Prices Tomas Sinkariovas 0802869. Words: 3441 Black Scholes Merton Approach To Modelling Financial Derivatives Prices Tomas Sinkariovas 0802869 Words: 3441 1 1. Introduction In this paper I present Black, Scholes (1973) and Merton (1973) (BSM) general

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

WEB APPENDIX. Calculating Beta Coefficients. b Beta Rise Run Y 7.1 1 8.92 X 10.0 0.0 16.0 10.0 1.6

WEB APPENDIX. Calculating Beta Coefficients. b Beta Rise Run Y 7.1 1 8.92 X 10.0 0.0 16.0 10.0 1.6 WEB APPENDIX 8A Calculating Beta Coefficients The CAPM is an ex ante model, which means that all of the variables represent before-thefact, expected values. In particular, the beta coefficient used in

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

CHAPTER 6. Topics in Chapter. What are investment returns? Risk, Return, and the Capital Asset Pricing Model

CHAPTER 6. Topics in Chapter. What are investment returns? Risk, Return, and the Capital Asset Pricing Model CHAPTER 6 Risk, Return, and the Capital Asset Pricing Model 1 Topics in Chapter Basic return concepts Basic risk concepts Stand-alone risk Portfolio (market) risk Risk and return: CAPM/SML 2 What are investment

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

Determination of Forward and Futures Prices

Determination of Forward and Futures Prices Determination of Forward and Futures Prices 3.1 Chapter 3 3.2 Consumption vs Investment Assets Investment assets assets held by significant numbers of people purely for investment purposes Examples: gold,

More information

Risk and Return Models: Equity and Debt. Aswath Damodaran 1

Risk and Return Models: Equity and Debt. Aswath Damodaran 1 Risk and Return Models: Equity and Debt 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

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

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

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, 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

Lesson 5. Risky assets

Lesson 5. Risky assets Lesson 5. Risky assets Prof. Beatriz de Blas May 2006 5. Risky assets 2 Introduction How stock markets serve to allocate risk. Plan of the lesson: 8 >< >: 1. Risk and risk aversion 2. Portfolio risk 3.

More information

LIQUIDITY AND ASSET PRICING. Evidence for the London Stock Exchange

LIQUIDITY AND ASSET PRICING. Evidence for the London Stock Exchange LIQUIDITY AND ASSET PRICING Evidence for the London Stock Exchange Timo Hubers (358022) Bachelor thesis Bachelor Bedrijfseconomie Tilburg University May 2012 Supervisor: M. Nie MSc Table of Contents Chapter

More information

A Review of Cross Sectional Regression for Financial Data You should already know this material from previous study

A Review of Cross Sectional Regression for Financial Data You should already know this material from previous study A Review of Cross Sectional Regression for Financial Data You should already know this material from previous study But I will offer a review, with a focus on issues which arise in finance 1 TYPES OF FINANCIAL

More information

PASS Sample Size Software. Linear Regression

PASS Sample Size Software. Linear Regression Chapter 855 Introduction Linear regression is a commonly used procedure in statistical analysis. One of the main objectives in linear regression analysis is to test hypotheses about the slope (sometimes

More information

Portfolio Analysis. M. Kateregga

Portfolio Analysis. M. Kateregga Portfolio Analysis M. Kateregga November 21, 2014 @ AIMS South Africa Outline Introduction The Optimization Problem Return of a Portfolio Variance of a Portfolio Portfolio Optimization in n-stocks case

More information

M.I.T. Spring 1999 Sloan School of Management 15.415. First Half Summary

M.I.T. Spring 1999 Sloan School of Management 15.415. First Half Summary M.I.T. Spring 1999 Sloan School of Management 15.415 First Half Summary Present Values Basic Idea: We should discount future cash flows. The appropriate discount rate is the opportunity cost of capital.

More information

THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING

THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING 1. Introduction The Black-Scholes theory, which is the main subject of this course and its sequel, is based on the Efficient Market Hypothesis, that arbitrages

More information

Mean-Variance Portfolio Analysis and the Capital Asset Pricing Model

Mean-Variance Portfolio Analysis and the Capital Asset Pricing Model Mean-Variance Portfolio Analysis and the Capital Asset Pricing Model 1 Introduction In this handout we develop a model that can be used to determine how a risk-averse investor can choose an optimal asset

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

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

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

Financial Econometrics Jeffrey R. Russell Final Exam

Financial Econometrics Jeffrey R. Russell Final Exam Name Financial Econometrics Jeffrey R. Russell Final Exam You have 3 hours to complete the exam. Use can use a calculator. Try to fit all your work in the space provided. If you find you need more space

More information

Practice Set #4 and Solutions.

Practice Set #4 and Solutions. FIN-469 Investments Analysis Professor Michel A. Robe Practice Set #4 and Solutions. What to do with this practice set? To help students prepare for the assignment and the exams, practice sets with solutions

More information

Investment decisions are based on the risk-return patterns. Appropriate measures of risk and return are of great concern to

Investment decisions are based on the risk-return patterns. Appropriate measures of risk and return are of great concern to Investment decisions are based on the risk-return patterns. Appropriate measures of risk and return are of great concern to investors. CAPM, based on market beta, addresses this concern quite well. But,

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

15.401 Finance Theory

15.401 Finance Theory Finance Theory MIT Sloan MBA Program Andrew W. Lo Harris & Harris Group Professor, MIT Sloan School Lecture 13 14 14: : Risk Analytics and Critical Concepts Motivation Measuring Risk and Reward Mean-Variance

More information

ECON4510 Finance Theory Lecture 7

ECON4510 Finance Theory Lecture 7 ECON4510 Finance Theory Lecture 7 Diderik Lund Department of Economics University of Oslo 11 March 2015 Diderik Lund, Dept. of Economics, UiO ECON4510 Lecture 7 11 March 2015 1 / 24 Market efficiency Market

More information

Journal of Financial and Strategic Decisions Volume 13 Number 1 Spring 2000

Journal of Financial and Strategic Decisions Volume 13 Number 1 Spring 2000 Journal of Financial and Strategic Decisions Volume 13 Number 1 Spring 2000 ESTIMATING SYSTEMATIC RISK: THE CHOICE OF RETURN INTERVAL AND ESTIMATION PERIOD Phillip R. Daves *, Michael C. Ehrhardt * and

More information

Basic Financial Tools: A Review. 3 n 1 n. PV FV 1 FV 2 FV 3 FV n 1 FV n 1 (1 i)

Basic Financial Tools: A Review. 3 n 1 n. PV FV 1 FV 2 FV 3 FV n 1 FV n 1 (1 i) Chapter 28 Basic Financial Tools: A Review The building blocks of finance include the time value of money, risk and its relationship with rates of return, and stock and bond valuation models. These topics

More information

An Overview of Asset Pricing Models

An Overview of Asset Pricing Models An Overview of Asset Pricing Models Andreas Krause University of Bath School of Management Phone: +44-1225-323771 Fax: +44-1225-323902 E-Mail: a.krause@bath.ac.uk Preliminary Version. Cross-references

More information