Chapter 7 Portfolio Theory and Other Asset Pricing Models

Size: px
Start display at page:

Download "Chapter 7 Portfolio Theory and Other Asset Pricing Models"

Transcription

1 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 risky if held in isolation may have little, or even no risk if held in a well-diversified portfolio. The feasible, or attainable, set represents all portfolios that can be constructed from a given set of stocks. This set is only efficient for part of its combinations. n efficient portfolio is that portfolio which provides the highest expected return for any degree of risk. lternatively, the efficient portfolio is that which provides the lowest degree of risk for any expected return. The efficient frontier is the set of efficient portfolios out of the full set of potential portfolios. On a graph, the efficient frontier constitutes the boundary line of the set of potential portfolios. b. n indifference curve is the risk/return trade-off function for a particular investor and reflects that investor's attitude toward risk. The indifference curve specifies an investor's required rate of return for a given level of risk. The greater the slope of the indifference curve, the greater is the investor's risk aversion. The optimal portfolio for an investor is the point at which the efficient set of portfolios--the efficient frontier--is just tangent to the investor's indifference curve. This point marks the highest level of satisfaction an investor can attain given the set of potential portfolios. nswers and Solutions: 7-1

2 c. The Capital sset Pricing Model (CPM) is a general equilibrium market model developed to analyze the relationship between risk and required rates of return on assets when they are held in well-diversified portfolios. The SML is part of the CPM. The Capital Market Line (CML) specifies the efficient set of portfolios an investor can attain by combining a risk-free asset and the risky market portfolio M. The CML states that the expected return on any efficient portfolio is equal to the riskless rate plus a risk premium, and thus describes a linear relationship between expected return and risk. d. The characteristic line for a particular stock is obtained by regressing the historical returns on that stock against the historical returns on the general stock market. The slope of the characteristic line is the stock's beta, which measures the amount by which the stock's expected return increases for a given increase in the expected return on the market. The beta coefficient (b) is a measure of a stock's market risk. It measures the stock's volatility relative to an average stock, which has a beta of 1.0. e. rbitrage Pricing Theory (PT) is an approach to measuring the equilibrium risk/return relationship for a given stock as a function of multiple factors, rather than the single factor (the market return) used by the CPM. The PT is based on complex mathematical and statistical theory, but can account for several factors (such as GNP and the level of inflation) in determining the required return for a particular stock. The Fama-French 3-factor model has one factor for the excess market return (the market return minus the risk free rate), a second factor for size (defined as the return on a portfolio of small firms minus the return on a portfolio of big firms), and a third factor for the book-to-market effect (defined as the return on a portfolio of firms with a high book-to-market ratio minus the return on a portfolio of firms with a low bookto-market ratio). Most people don t behave rationally in all aspects of their personal lives, and behavioral finance assumes that investors have the same types of psychological behaviors in their financial lives as in their personal lives. 7- Security is less risky if held in a diversified portfolio because of its lower beta and negative correlation with other stocks. In a single-asset portfolio, Security would be more risky because > B and CV > CV B. nswers and Solutions: 7 -

3 SOLUTIONS TO END-OF-CHPTER PROBLEMS 7-1 b i = ρ im ( i / M ) = 0.70(0.40/0.0) = r i = r RF + (r 1 r RF )b i1 + (r j r RF )b ij = ( )(0.7) + ( )(0.9) = 0.1 = 1%. 7-3 r i = r RF + a i + b i (r M r RF ) + c i (r SMB ) + d i (r HML ) = 5% + 0.0% + 1.(10% - 5%) + (-0.4)(3.%) + 1.3(4.8%) = 15.96% 7-4 r^p = w r^ + (1 w ) r^b = 0.30(1%) (18%) = 16.0% p = w + (1 w ) B + w (1 w )ρ B B = (0.3 )(0.4 ) + (0.7 )(0.6 ) + (0.3)(0.7)(0.)(0.4)(0.6) = = = = 45.9% ρimi 7-5 a. ri = rrf + (rm rrf )bi = rrf + (rm rrf ). M r M rrf b. CML: r p = rrf + p. M rm r RF SML: ri = rrf + rimi. M With some arranging, the similarities between the CML and SML are obvious. When in this form, both have the same market price of risk, or slope, (r M - r RF )/ M. The measure of risk in the CML is p. Since the CML applies only to efficient portfolios, p not only represents the portfolio's total risk, but also its market risk. However, the SML applies to all portfolios and individual securities. Thus, the appropriate risk measure is not i, the total risk, but the market risk, which in this form of the SML is r im i, and is less than for all assets except those which are perfectly positively correlated with the market, and hence have r im = nswers and Solutions: 7-3

4 7-6 a. Using the CPM: r i = r RF + (r M - r RF )b i = 7% + (1.1)(6.5%) = 14.15% b. Using the 3-factor model: r i = r RF + (r M r rf )b i + (r SMB )c i + (r HML )d i = 7% + (1.1)(6.5%) + (5%)(0.7) + (4%)(-0.3) = 16.45% 7-7 a. plot of the approximate regression line is shown in the following figure: 30 r X (%) r Y Using Excel, the regression equation estimates are: Beta = 0.56; Intercept = 0.037; R = nswers and Solutions: 7-4

5 b. The arithmetic average return for Stock X is calculated as follows: ( ) r vg = = 10.6%. 7 The arithmetic average rate of return on the market portfolio, determined similarly, is 1.1%. For Stock X, the estimated standard deviation is 13.1 percent: ( ) + ( ) ( ) X = = 13.1%. The standard deviation of returns for the market portfolio is similarly determined to be.6 percent. The results are summarized below: Stock X Market Portfolio verage return, r vg 10.6% 1.1% Standard deviation, Several points should be noted: (1) M over this particular period is higher than the historic average M of about 15 percent, indicating that the stock market was relatively volatile during this period; () Stock X, with X = 13.1%, has much less total risk than an average stock, with vg =.6%; and (3) this example demonstrates that it is possible for a very low-risk single stock to have less risk than a portfolio of average stocks, since X < M. c. Since Stock X is in equilibrium and plots on the Security Market Line (SML), and given the further assumption that r X = r X and r M = r M --and this assumption often does not hold--then this equation must hold: r X = r RF + (r r RF )b X. This equation can be solved for the risk-free rate, r RF, which is the only unknown: 10.6 = r 10.6 = r 0.44r r RF RF RF RF + (1.1 r r = = 3.8/ 0.44 RF = 8.6%. )0.56 RF nswers and Solutions: 7-5

6 d. The SML is plotted below. Data on the risk-free security (b RF = 0, r RF = 8.6%) and Security X (b X = 0.56, r X = 10.6%) provide the two points through which the SML can be drawn. r M provides a third point. r(%) k(%) 0 k M = 1.1% r X k X = = 10.6% r RF = 8.6% k RF = Beta e. In theory, you would be indifferent between the two stocks. Since they have the same beta, their relevant risks are identical, and in equilibrium they should provide the same returns. The two stocks would be represented by a single point on the SML. Stock Y, with the higher standard deviation, has more diversifiable risk, but this risk will be eliminated in a well-diversified portfolio, so the market will compensate the investor only for bearing market or relevant risk. In practice, it is possible that Stock Y would have a slightly higher required return, but this premium for diversifiable risk would be small. nswers and Solutions: 7-6

7 7-8 a. The regression graph is shown above. Using a spreadsheet, we find b = 0.6. rk S y (%) (%) k M (%) r M (%) -15 b. Because b = 0.6, Stock Y is about 6 percent as volatile as the market; thus, its relative risk is about 6 percent of that of an average firm. c. 1. Total risk ( ) would be greater because the second term of the firm's risk equation, Y Y M Y = b + ey, would be greater.. CPM assumes that company-specific risk will be eliminated in a portfolio, so the risk premium under the CPM would not be affected. d. 1. The stock's variance would not change, but the risk of the stock to an investor holding a diversified portfolio would be greatly reduced.. It would now have a negative correlation with r M. 3. Because of a relative scarcity of such stocks and the beneficial net effect on portfolios that include it, its "risk premium" is likely to be very low or even negative. Theoretically, it should be negative. nswers and Solutions: 7-7

8 SOLUTION TO SPREDSHEET PROBLEM 7-9 The detailed solution for the spreadsheet problem is available in the file Solution for FM1 Ch 07 P09 Build a Model.xls on the textbook s Web site. nswers and Solutions: 7-8

9 MINI CSE To begin, briefly review the Chapter 6 Mini Case. Then, extend your knowledge of risk and return by answering the following questions. a. Suppose asset has an expected return of 10 percent and a standard deviation of 0 percent. sset B has an expected return of 16 percent and a standard deviation of 40 percent. If the correlation between and B is 0.35, what are the expected return and standard deviation for a portfolio comprised of 30 percent asset and 70 percent asset B? nswer: rˆ P = w rˆ + (1 w ) rˆ = 0.3(0.1) + 0.7(0.16) = 0.14= 14.%. B p = = W 0.3 = (0. + (1 W ) ) (0.4 B + W (1 W ) ρ B ) + (0.3)(0.7)(0.35)(0.)(0.4) b. Plot the attainable portfolios for a correlation of Now plot the attainable portfolios for correlations of +1.0 and nswer: B 0% pb = +0.35: ttainable Set of Risk/Return Combinations Expected return 15% 10% 5% 0% 0% 10% 0% 30% 40% Risk, sigma p Mini Case: 7-9

10 ρ B = +1.0: ttainable Set of Risk/Return Combinations 0% Expected return 15% 10% 5% 0% 0% 10% 0% 30% 40% Risk, p ρ B = -1.0: ttainable Set of Risk/Return Combinations 0% Expected return 15% 10% 5% 0% 0% 10% 0% 30% 40% Risk, p Mini Case: 7-10

11 c. Suppose a risk-free asset has an expected return of 5 percent. By definition, its standard deviation is zero, and its correlation with any other asset is also zero. Using only asset and the risk-free asset, plot the attainable portfolios. nswer: ttainable Set of Risk/Return Combinations with Risk-Free sset 15% Expected return 10% 5% 0% 0% 5% 10% 15% 0% Risk, p Mini Case: 7-11

12 d. Construct a reasonable, but hypothetical, graph which shows risk, as measured by portfolio standard deviation, on the x axis and expected rate of return on the y axis. Now add an illustrative feasible (or attainable) set of portfolios, and show what portion of the feasible set is efficient. What makes a particular portfolio efficient? Don't worry about specific values when constructing the graph merely illustrate how things look with "reasonable" data. nswer: Expected Portfolio Return Expected Portfolio ^ Return, k ^ p r P Efficient Set (,B) B C D E Feasible, or ttainable, Set risk, Risk, P p The figure above shows the feasible set of portfolios. The points B, C, D, and E represent single securities (or portfolios containing only one security). ll the other points in the shaded area, including its boundaries, represent portfolios of two or more securities. The shaded area is called the feasible, or attainable, set. The boundary B defines the efficient set of portfolios, which is also called the efficient frontier. Portfolios to the left of the efficient set are not possible because they lie outside the attainable set. Portfolios to the right of the boundary line (interior portfolios) are inefficient because some other portfolio would provide either a higher return with the same degree of risk or a lower level of risk for the same rate of return. Mini Case: 7-1

13 e. Now add a set of indifference curves to the graph created for part B. What do these curves represent? What is the optimal portfolio for this investor? Finally, add a second set of indifference curves which leads to the selection of a different optimal portfolio. Why do the two investors choose different portfolios? Expected Portfolio Return, Expected Portfolio ^ Return, k^ p r p B I B I B1 C I 3 I D Optimal Portfolio Investor B I 1 E Optimal Portfolio Investor risk, Risk, P p nswer: The figure above shows the indifference curves for two hypothetical investors, and B. To determine the optimal portfolio for a particular investor, we must know the investor's attitude towards risk as reflected in his or her risk/return tradeoff function, or indifference curve. Curves I a1, I a, and I a3 represent the indifference curves for individual, with the higher curve (I a3 ) denoting a greater level of satisfaction (or utility). Thus, I a3 is better than I a for any level of risk. The optimal portfolio is found at the tangency point between the efficient set of portfolios and one of the investor's indifference curves. This tangency point marks the highest level of satisfaction the investor can attain. The arrows point toward the optimal portfolios for both investors and B. The investors choose different optimal portfolios because their risk aversion is different. Investor chooses the portfolio with the lower expected return, but the riskiness of that portfolio is also lower than investor's B optimal portfolio, because investor a is more risk averse. Mini Case: 7-13

14 f. What is the capital asset pricing model (CPM)? What are the assumptions that underlie the model? nswer: The Capital sset Pricing Model (CPM) is an equilibrium model which specifies the relationship between risk and required rates of return on assets when they are held in well-diversified portfolios. The CPM requires an extensive set of assumptions: ll investors are single-period expected utility of terminal wealth maximizers, who choose among alternative portfolios on the basis of each portfolio's expected return and standard deviation. ll investors can borrow or lend an unlimited amount at a given risk-free rate of interest. Investors have homogeneous expectations (that is, investors have identical estimates of the expected values, variances, and covariances of returns among all assets). ll assets are perfectly divisible and perfectly marketable at the going price, and there are no transactions costs. There are no taxes. ll investors are price takers (that is, all investors assume that their own buying and selling activity will not affect stock prices). The quantities of all assets are given and fixed. Mini Case: 7-14

15 g. Now add the risk-free asset. What impact does this have on the efficient frontier? Expected Portfolio Return, Expected Portfolio Return, ^ k ^ p r p Z B M kr RF Risk, p nswer: The risk-free asset by definition has zero risk, and hence = 0%, so it is plotted on the vertical axis. Now, given the possibility of investing in the risk-free asset, investors can create new portfolios that combine the risk-free asset with a portfolio of risky assets. This enables them to achieve any combination of risk and return that lies along any straight line connecting r RF with any portfolio in the feasible set of risky portfolios. However, the straight line connecting r RF with m, the point of tangency between the line and the portfolio's efficient set curve, is the one that all investors would choose. Since all portfolios on the line r RF mz are preferred to the other risky portfolio opportunities on the efficient frontier B, the points on the line r RF mz now represent the best attainable combinations of risk and return. ny combination under the r RF mz line offers less return for the same amount of risk, or offers more risk for the same amount of return. Thus, everybody wants to hold portfolios which are located on the r RF mz line. Mini Case: 7-15

16 h. Write out the equation for the capital market line (CML) and draw it on the graph. Interpret the CML. Now add a set of indifference curves, and illustrate how an investor's optimal portfolio is some combination of the risky portfolio and the risk-free asset. What is the composition of the risky portfolio? nswer: The line r RF mz in the figure above is called the capital market line (CML). It has an M / intercept of r RF and a slope of r rrf ) market line may be expressed as follows: ( r M rrf CML: r p = rrf + p. M M. Therefore the equation for the capital The CML tells us that the expected rate of return on any efficient portfolio (that is, any portfolio on the CML) is equal to the risk-free rate plus a risk premium, and the risk premium is equal to ( r M rrf ) / M multiplied by the portfolio's standard deviation, p. Thus, the CML specifies a linear relationship between expected return and risk, with the slope of the CML being equal to the expected return on the market portfolio of risky stocks, r M, minus the risk-free risk, rate, P rrf, which is called the market risk premium, all divided by the standard deviation of returns on the market portfolio, m. ^ Expected Rate of Return, Expected Rate ^ ^ of Return, r p k p I 3 I I 1 CML r RF k RF Optimal Portfolio p Risk, p Mini Case: 7-16

17 The figure above shows a set of indifference curves (i 1, i, and i 3 ), with i 1 touching the CML. This point of tangency defines the optimal portfolio for this investor, and he or she will buy a combination of the market portfolio and the riskfree asset. The risky portfolio, m, must contain every asset in exact proportion to that asset's fraction of the total market value of all assets; that is, if security g is x percent of the total market value of all securities, x percent of the market portfolio must consist of security g. i. What is a characteristic line? How is this line used to estimate a stock s beta coefficient? Write out and explain the formula that relates total risk, market risk, and diversifiable risk. nswer: Betas are calculated as the slope of the characteristic line, which is the regression line formed by plotting returns on a given stock on the y axis against returns on the general stock market on the x axis. In practice, 5 years of monthly data, with 60 observations, would be used, and a computer would be used to obtain a least squares regression line. The relationship between stock J's total risk, market risk, and diversifiable risk can be expressed as follows: TOTL RISK = VRINCE = MRKET RISK + DIVERSIFIBLE RISK J = b J M + Here J is the variance or total risk of stock j, is the variance of the market, b M j is stock J's beta coefficient, and ej is the variance of stock J's regression error term. If stock J is held in isolation, then the investor must bear its total risk. However, when stock J is held as part of a well-diversified portfolio, the regression error term, ej is driven to zero; hence, only the market risk remains. ej j. What are two potential tests that can be conducted to verify the CPM? What are the results of such tests? What is roll s critique of CPM tests? nswer: Since the CPM was developed on the basis of a set of unrealistic assumptions, empirical tests should be used to verify the CPM. The first test looks for stability in historical betas. If betas have been stable in the past for a particular stock, then its historical beta would probably be a good proxy for its ex-ante, or expected beta. Empirical work concludes that the betas of individual securities are not good estimators of their future risk, but that betas of portfolios of ten or more randomly selected stocks are reasonably stable, hence that past portfolio betas are good estimators of future portfolio volatility. Mini Case: 7-17

18 The second type of test is based on the slope of the SML. s we have seen, the CPM states that a linear relationship exists between a security's required rate of return and its beta. Further, when the SML is graphed, the vertical axis intercept should be r RF, and the required rate of return for a stock (or portfolio) with beta = 1.0 should be r m, the required rate of return on the market. Various researchers have attempted to test the validity of the CPM model by calculating betas and realized rates of return, plotting these values in graphs, and then observing whether or not (1) the intercept is equal to r RF, () the regression line is linear, and (3) the SML passes through the point b = 1.0, r m. Evidence shows a more-or-less linear relationship between realized returns and market risk, but the slope is less than predicted. Tests that attempt to assess the relative importance of market and company-specific risk do not yield definitive results, so the irrelevance of diversifiable risk specified in the CPM model can be questioned. Roll questioned whether it is even conceptually possible to test the CPM. Roll showed that the linear relationship which prior researchers had observed in graphs resulted from the mathematical properties of the models being tested, hence that a finding of linearity proved nothing about the validity of the CPM. Roll's work did not disprove the CPM theory, but he did show that it is virtually impossible to prove that investors behave in accordance with the theory. In general, evidence seems to support the CPM model when it is applied to portfolios, but the evidence is less convincing when the CPM is applied to individual stocks. Nevertheless, the CPM provides a rational way to think about risk and return as long as one recognizes the limitations of the CPM when using it in practice. k. Briefly explain the difference between the CPM and the arbitrage pricing theory (PT). nswer: The CPM is a single-factor model, while the rbitrage Pricing Theory (PT) can include any number of risk factors. It is likely that the required return is dependent on many fundamental factors such as the GNP growth, expected inflation, and changes in tax laws, and that different groups of stocks are affected differently by these factors. Thus, the apt seems to have a stronger theoretical footing than does the CPM. However, the apt faces several major hurdles in implementation, the most severe being that the apt does not identify the relevant factors--a complex mathematical procedure called factor analysis must be used to identify the factors. To date, it appears that only three or four factors are required in the apt, but much more research is required before the apt is fully understood and presents a true challenge to the CPM. Mini Case: 7-18

19 l. Suppose you are given the following information. The beta of company, b i, is 0.9, the risk free rate, r RF, is 6.8%, and the expected market premium, r M -r RF, is 6.3%. Because your company is larger than average and more successful than average (i.e., it has a lower book-to-market ratio), you think the Fama-French 3- factor model might be more appropriate than the CPM. You estimate the additional coefficients from the Fama-French 3-factor model: the coefficient for the size effect, C i, is -0.5, and the coefficient for the book-to-market effect, d i, is 0.3. If the expected value of the size factor is 4% and the expected value of the book-to-market factor is 5%, what is the required return using the Fama- French 3-factor model? (assume that i = 0.0.) What is the required return using CPM? nswer: The Fama-French model: r i = r RF + (r m - r RF )b i + (r smb )c i + (r hmb )d j r i = 6.8% + (6.3%)(0.9) + (4%)(-0.5) + (5%)(-0.3) = 8.97% The CPM: r i = r rf + (r m - r rf )b i r i = 6.8% + (6.3%)(0.9) = 1.47% Mini Case: 7-19

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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

1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises.

1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises. 1. Solutions to PS 1: 1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises. 7. The bill has a maturity of one-half year, and an annualized

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

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

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

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

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

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

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

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

Econ 422 Summer 2006 Final Exam Solutions

Econ 422 Summer 2006 Final Exam Solutions Econ 422 Summer 2006 Final Exam Solutions This is a closed book exam. However, you are allowed one page of notes (double-sided). Answer all questions. For the numerical problems, if you make a computational

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 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

CHAPTER 6: RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS

CHAPTER 6: RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS CHAPTER 6: RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS PROBLEM SETS 1. (e). (b) A higher borrowing is a consequence of the risk of the borrowers default. In perfect markets with no additional

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

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 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

Diversification and the Risk-Return Trade-Off

Diversification and the Risk-Return Trade-Off Diversification and the Risk-Return Trade-Off Dr. Patrick Toche References : Zvi Bodie, Alex Kane, Alan Marcus, Investments, McGraw-Hill/Irwin. The relevant chapters of this textbook will be followed closely

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

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

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

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

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

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

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 2 Portfolio Management and the Capital Asset Pricing Model

Chapter 2 Portfolio Management and the Capital Asset Pricing Model Chapter 2 Portfolio Management and the Capital Asset Pricing Model In this chapter, we explore the issue of risk management in a portfolio of assets. The main issue is how to balance a portfolio, that

More information

Cost of Capital Presentation for ERRA Tariff Committee Dr. Konstantin Petrov / Waisum Cheng / Dr. Daniel Grote April 2009 Experience you can trust.

Cost of Capital Presentation for ERRA Tariff Committee Dr. Konstantin Petrov / Waisum Cheng / Dr. Daniel Grote April 2009 Experience you can trust. Cost of Capital Presentation for ERRA Tariff Committee Dr. Konstantin Petrov / Waisum Cheng / Dr. Daniel Grote April 2009 Experience you can trust. Agenda 1.Definition of Cost of Capital a) Concept and

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 13 Composition of the Market Portfolio 1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z,

Chapter 13 Composition of the Market Portfolio 1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z, Chapter 13 Composition of the arket Portfolio 1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z, and a riskless government security. Evaluated at current prices in

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

2. Mean-variance portfolio theory

2. Mean-variance portfolio theory 2. Mean-variance portfolio theory (2.1) Markowitz s mean-variance formulation (2.2) Two-fund theorem (2.3) Inclusion of the riskfree asset 1 2.1 Markowitz mean-variance formulation Suppose there are N

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

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

Chapter 11. Topics Covered. Chapter 11 Objectives. Risk, Return, and Capital Budgeting

Chapter 11. Topics Covered. Chapter 11 Objectives. Risk, Return, and Capital Budgeting Chapter 11 Risk, Return, and Capital Budgeting Topics Covered Measuring Market Risk Portfolio Betas Risk and Return CAPM and Expected Return Security Market Line CAPM and Stock Valuation Chapter 11 Objectives

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

A reading prepared by Pamela Peterson Drake

A reading prepared by Pamela Peterson Drake Risk, return, and diversification A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction 2. Diversification and risk 3. Modern portfolio theory 4. Asset pricing models 5. Summary 1.

More information

Optimal Risky Portfolios Chapter 7 Investments Bodie, Kane and Marcus

Optimal Risky Portfolios Chapter 7 Investments Bodie, Kane and Marcus Optimal Risky ortfolios Section escription 7.0 Introduction 7.1 iversification and ortfolio Risk 7. ortfolios of Two Risky Assets 7.3 Asset Allocation with Stocks, Bonds and Bills 7.4 The Markowitz ortfolio

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

Chapter 11. Topics Covered. Chapter 11 Objectives. Risk, Return, and Capital Budgeting

Chapter 11. Topics Covered. Chapter 11 Objectives. Risk, Return, and Capital Budgeting Chapter 11 Risk, Return, and Capital Budgeting Topics Covered Measuring Market Risk Portfolio Betas Risk and Return CAPM and Expected Return Security Market Line CAPM and Stock Valuation Chapter 11 Objectives

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

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

One Period Binomial Model

One Period Binomial Model FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 One Period Binomial Model These notes consider the one period binomial model to exactly price an option. We will consider three different methods of pricing

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

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

15 Solution 1.4: The dividend growth model says that! DIV1 = $6.00! k = 12.0%! g = 4.0% The expected stock price = P0 = $6 / (12% 4%) = $75.

15 Solution 1.4: The dividend growth model says that! DIV1 = $6.00! k = 12.0%! g = 4.0% The expected stock price = P0 = $6 / (12% 4%) = $75. 1 The present value of the exercise price does not change in one hour if the risk-free rate does not change, so the change in call put is the change in the stock price. The change in call put is $4, so

More information

Chapter 1. Introduction to Portfolio Theory. 1.1 Portfolios of Two Risky Assets

Chapter 1. Introduction to Portfolio Theory. 1.1 Portfolios of Two Risky Assets Chapter 1 Introduction to Portfolio Theory Updated: August 9, 2013. This chapter introduces modern portfolio theory in a simplified setting where there are only two risky assets and a single risk-free

More information

Equity Risk Premium Article Michael Annin, CFA and Dominic Falaschetti, CFA

Equity Risk Premium Article Michael Annin, CFA and Dominic Falaschetti, CFA Equity Risk Premium Article Michael Annin, CFA and Dominic Falaschetti, CFA This article appears in the January/February 1998 issue of Valuation Strategies. Executive Summary This article explores one

More information

15.433 Investments. Assignment 1: Securities, Markets & Capital Market Theory. Each question is worth 0.2 points, the max points is 3 points

15.433 Investments. Assignment 1: Securities, Markets & Capital Market Theory. Each question is worth 0.2 points, the max points is 3 points Assignment 1: Securities, Markets & Capital Market Theory Each question is worth 0.2 points, the max points is 3 points 1. The interest rate charged by banks with excess reserves at a Federal Reserve Bank

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

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

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

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

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

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 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

On Black-Scholes Equation, Black- Scholes Formula and Binary Option Price

On Black-Scholes Equation, Black- Scholes Formula and Binary Option Price On Black-Scholes Equation, Black- Scholes Formula and Binary Option Price Abstract: Chi Gao 12/15/2013 I. Black-Scholes Equation is derived using two methods: (1) risk-neutral measure; (2) - hedge. II.

More information

1 Capital Allocation Between a Risky Portfolio and a Risk-Free Asset

1 Capital Allocation Between a Risky Portfolio and a Risk-Free Asset Department of Economics Financial Economics University of California, Berkeley Economics 136 November 9, 2003 Fall 2006 Economics 136: Financial Economics Section Notes for Week 11 1 Capital Allocation

More information

Chapter 8 Risk and Return

Chapter 8 Risk and Return Chapter 8 Risk and Return LEARNING OBJECTIVES (Slides 8-2 & 8-3) 1. Calculate profits and returns on an investment and convert holding period returns to annual returns. 2. Define risk and explain how uncertainty

More information

Midterm Exam:Answer Sheet

Midterm Exam:Answer Sheet Econ 497 Barry W. Ickes Spring 2007 Midterm Exam:Answer Sheet 1. (25%) Consider a portfolio, c, comprised of a risk-free and risky asset, with returns given by r f and E(r p ), respectively. Let y be the

More information

AN OVERVIEW OF FINANCIAL MANAGEMENT

AN OVERVIEW OF FINANCIAL MANAGEMENT CHAPTER 1 Review Questions AN OVERVIEW OF FINANCIAL MANAGEMENT 1. Management s basic, overriding goal is to create for 2. The same actions that maximize also benefits society 3. If businesses are successful

More information

Mid-Term Spring 2003

Mid-Term Spring 2003 Mid-Term Spring 2003 1. (1 point) You want to purchase XYZ stock at $60 from your broker using as little of your own money as possible. If initial margin is 50% and you have $3000 to invest, how many shares

More information

An Introduction to Portfolio Theory

An Introduction to Portfolio Theory An Introduction to Portfolio Theory John Norstad j-norstad@northwestern.edu http://www.norstad.org April 10, 1999 Updated: November 3, 2011 Abstract We introduce the basic concepts of portfolio theory,

More information

Chapter 10. Chapter 10 Topics. Recent Rates

Chapter 10. Chapter 10 Topics. Recent Rates Chapter 10 Introduction to Risk, Return, and the Opportunity Cost of Capital Chapter 10 Topics Rates of Return Risk Premiums Expected Return Portfolio Return and Risk Risk Diversification Unique & Market

More information

Chapter 5 Uncertainty and Consumer Behavior

Chapter 5 Uncertainty and Consumer Behavior Chapter 5 Uncertainty and Consumer Behavior Questions for Review 1. What does it mean to say that a person is risk averse? Why are some people likely to be risk averse while others are risk lovers? A risk-averse

More information

Regression Analysis Prof. Soumen Maity Department of Mathematics Indian Institute of Technology, Kharagpur. Lecture - 2 Simple Linear Regression

Regression Analysis Prof. Soumen Maity Department of Mathematics Indian Institute of Technology, Kharagpur. Lecture - 2 Simple Linear Regression Regression Analysis Prof. Soumen Maity Department of Mathematics Indian Institute of Technology, Kharagpur Lecture - 2 Simple Linear Regression Hi, this is my second lecture in module one and on simple

More information

Holding Period Return. Return, Risk, and Risk Aversion. Percentage Return or Dollar Return? An Example. Percentage Return or Dollar Return? 10% or 10?

Holding Period Return. Return, Risk, and Risk Aversion. Percentage Return or Dollar Return? An Example. Percentage Return or Dollar Return? 10% or 10? Return, Risk, and Risk Aversion Holding Period Return Ending Price - Beginning Price + Intermediate Income Return = Beginning Price R P t+ t+ = Pt + Dt P t An Example You bought IBM stock at $40 last month.

More information

The number of mutual funds has grown dramatically in recent

The number of mutual funds has grown dramatically in recent Risk-Adjusted Performance of Mutual Funds Katerina Simons Economist, Federal Reserve Bank of Boston. The author is grateful to Richard Kopcke and Peter Fortune for helpful comments and to Jay Seideman

More information

PART IV INFORMATION, MARKET FAILURE, AND THE ROLE OF GOVERNMENT CHAPTER 16 GENERAL EQUILIBRIUM AND ECONOMIC EFFICIENCY

PART IV INFORMATION, MARKET FAILURE, AND THE ROLE OF GOVERNMENT CHAPTER 16 GENERAL EQUILIBRIUM AND ECONOMIC EFFICIENCY PART IV INFORMATION, MARKET FAILURE, AND THE ROLE OF GOVERNMENT CHAPTER 6 GENERAL EQUILIBRIUM AND ECONOMIC EFFICIENCY QUESTIONS FOR REVIEW. Why can feedback effects make a general equilibrium analysis

More information

approach and the Price of securities

approach and the Price of securities 10 28 Class 9: The portfolio approach and the Price of securities Problems with the portfolio approach CAPM; Rise of the passive investor; What happens when new information comes in; Another no trade result?

More information