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

Size: px
Start display at page:

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

Transcription

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, he collects the information or "facts" (both fundamental and technical) about the company and related matters which may affect the company. Second, he analyzes this information in such a way so as to determine his best estimate (as of today, time "zero") of the stock price at a future date (time "one"). This best estimate is the expected stock price at time one which we denote by P (1). From looking at the P(1) current stock price, P(0), he can estimate an expected return on the stock, Z, which is Z =. P(0) However, his analyst's ob is not finished. Because he recognizes that his information is not perfect (i.e., subect to error, unforeseen events which may occur, etc.), he must also give consideration to the range of possible future prices. In particular, he must estimate how dispersed this range is about his best estimate and how likely is a deviation of a certain size from this estimate. This analysis then gives him an estimate of the deviations of the rate of return from the expected rate and the likelihood of such deviations. Obviously, the better his information, the smaller will be the dispersion and the less risky the investment. Third, armed with his estimates of the expected rate of return and the dispersion, he must make an investment decision and determine how much of the stock to buy or sell. How much will depend on how good the risk-return tradeoff on this stock is in comparison with alternative investments available and on how much money he has to invest (either personally or as a fiduciary). The higher the expected return and the more money he has (or controls), the more of the stock he will want to buy. The larger the dispersion (i.e., the less accurate the information that he has), the smaller the position he will take in the stock. To see how the current market price of the stock is determined, we look at the aggregation of all analysts' estimates, and assume that on the average the market is in equilibrium. I.e., on average, the price will be such that total (desired) demand equals total supply. Analysts' estimates may differ for two reasons: (1) they may have access to different 312

2 Finance Theory amounts of information (although presumably public information is available to all); (2) they may analyze the information differently with regard to its impact on future stock prices. Nonetheless, each analyst comes to a decision as to how much to buy or sell at a given market price, P(0). The aggregation of these decisions gives us the total demand for shares of the company at the price, P(0). Suppose that the price were such that there were more shares demanded than supplied (i.e., it is too low), then one would expect the price to rise, and vice versa, if there were more shares available at a given price than were demanded. Hence, the market price of the stock will reflect a weighted average of the opinions of all analysts. The key question is: what is the nature of this weighting? Because "votes" in the marketplace are cast with dollars, the analysts with the biggest impact will be the ones who control the larger amounts of money, and among these, the ones who have the strongest "opinions" about the stock will be the most important. Note: the ones with the strongest "opinions" have them because (they believe that) they have better information (resulting in a smaller dispersion around their best estimate). Further, because an analyst who consistently overestimates the accuracy of his estimates will eventually lose his customers, one would expect that among the analysts who control large sums, the ones that believe that they have better information, on average, probably do. From all this, we conclude that the market price of the stock will reflect the weighted average of analysts' opinions with heavier weights on the opinions of those analysts with control of more than the average amount of money and with better than average amounts of information. Hence, the estimate of "fair" or "intrinsic" value provided by the market price will be more accurate than the estimate obtained from an average analyst. Now, suppose that you are an analyst and you find a stock whose market price is low enough that you consider it a "bargain" (if you never find this situation, then there is no point being in the analyst business). From the above discussion, there are two possibilities: (1) you do have a bargain your estimate is more accurate than the market's. I.e., you have either better than average information about future events which may affect stock price and/or you do a better than average ob of analyzing information. Or, (2) others have better information than you do or 313

3 Robert C. Merton process available information better, and your "bargain" is not a bargain. One's assessment of which it is, depends on how good the other analysts are relative to oneself. There are important reasons why one would expect the quality of analysts to be high: (1) the enormous rewards to anyone who can consistently beat the average attract large numbers of intelligent people to the business; (2) the relative ease of entry into the (analyst) business implies that competition will force the analysts to get better information and better techniques for processing this information ust to survive; (3) the stock market has been around long enough for these competitive forces to take effect. Unfortunately, the tendency is to underestimate the capabilities of other analysts. Ask any analyst if he is better than average, and invariably he answers "yes." Clearly, this cannot be true for all analysts by the very definition of average. If the analysts are so good, why aren't most of them rich? Precisely because they compete with each other, the market price becomes a better and better estimate of "fair value," and it becomes more difficult to find profit opportunities. To stay ahead, the analyst must develop new ideas continually. As the limiting case of this process, one would expect that as market prices become better estimates of "fair value" in the sense of fully reflecting all relevant known information, the fluctuations of stock prices around the expected "fair return" will be solely the result of unanticipated events and new information. Hence, these fluctuations are random and not forecastable. And it is in this sense that the fluctuations in stock prices can be described by a random walk. This also explains why the performance of most "managed" portfolios will be no better than the performance of an "unmanaged" well-diversified portfolio. In fact, the "unmanaged" portfolio, because it takes market prices as the best estimate of value, is equivalent to a "managed" portfolio whose manager is a no-worse-than-average analyst! The investor who buys such a portfolio is simply "piggy-backing" on the actions taken by active analyst-investors competing with each other. This is essentially the story behind the "Random Walk Theory." It does not imply that a better-than-average analyst cannot make greater than fair returns. It does not imply that all analysts should quit their obs, and in fact, its cornerstone is that enough analysts remain and 314

4 Finance Theory actively compete so that market prices are good estimates of "fair" value. It is only in this way that the "piggy-backing" by investors can be ustified. Further, it does not imply that all investors should hold "unmanaged" portfolios. If an investor can identify an analyst with above-average capabilities and is willing to bear the risk of his capabilities, then a "bargain" can be struck so that both are rewarded for the effort. The theory does imply that to make "extra" profits, one must have superior techniques which process information in a way not generally known in the market and that the longer that the market is in existence, the greater the number of participants, the more difficult it is to make these "extra" profits. An Example to Illustrate the Efficient Market Concept Consider a firm in a cyclical business whose earnings are completely predictable but vary in the following fashion: If the earnings per share this period are $50, then next period's earnings per share will be $100, and if the earnings per share this period are $100, then next period's earnings per share will be $50. I.e., if E t denotes earnings in period t, and if E0 = $50 then E1 =100, E2 = 50, E3 =100,... or E t +1 = E + (-1) 50 t t If the firm pays out all earnings as dividends ( Dt = Et) and if the required return ("fair market return") is 20% per period, then the correct price per share, S t (ex-dividend) is given by = $386.36, S = $363.64, S = $386.36, S = $363.64,... S S t +1 = S t + (-1) t I.e., the return per dollar from investing in the shares from time 0 to time 1, D1 + S Z1 = = =1.20, and from time 1 to time 2, S D2 + S Z2 = = =1.20, and so forth. S

5 Robert C. Merton Suppose that investors are myopic and assume that current earnings (and hence, current dividends) are permanent. I.e., their best guess of future dividends is that they will be equal to ' current dividends. If S t denotes price per share under this belief, then or S S = D 50 D 100 = = $250; = = r.2 r.2 = $500, = D 50 D 100 = = $250; = = r.2 r.2 = $500,... S + = + (-1) 250 ' 0 ' 1 0 S1 ' 2 ' 3 2 S3 ' ' S t 1 t The return per dollar from investing in the shares from time 0 to time 1 under this pricing is ' ' D1 S Z1 = = = ' S or 140% and from time 1 to time 2, ' Z 2 is and it continues to alternate. Z ' ' D2 S2 2 ' S = = = or -40% 316

6 Finance Theory Empirical Studies of Capital Market Theory In Sections IX and X, we developed a theory for the capital markets based on essentially rational behavior and optimal portfolio selection. Specifically, by applying the mean-variance model and aggregating demands, we deduced the Capital Asset Pricing model, which provided a specification for equilibrium expected returns among securities. Based on this model, we deduced a naive or benchmark portfolio strategy. From our analysis of an efficient speculative market, we deduced a rationale for random selection of securities or the naive strategy as possible portfolio strategies. Since these models have important implications for both corporate finance and financial intermediation, it is most important that empirical testing of the models is performed. Basically, there are three questions to be answered: (i) How does the "random walk" theory hold up against the data? (ii) Is the security market line specification a reasonable description of returns on securities? (iii) How does the performance of the naive strategy compare with managed portfolio strategies? 317

7 Robert C. Merton The answer to (i) is simply that a large number of technical trading strategies (filtering, serial correlation, charting services, volume analysis, etc.) have produced no evidence to refute the random walk hypothesis. To the extent that any serial correlation in the returns were present, it was of such small magnitude and "short-lived" nature that no profitable trading was possible. Other studies of brokerage house and general service recommendations, dividend announcements and earning reports have shown no evidence of providing trading profits. "Dart throwing" or more careful random selection of portfolios provide no evidence against the random walk hypothesis. In the study of managed portfolio performance, both the random walk hypothesis and the asset pricing model are implicitly tested. Returns on the "Market" NYSE index: S&P index: value-weighted index of all stocks on the New York Stock Exchange 80% in market value of all securities) Standard & Poors 500-stock index including the largest companies (in 1965 representing 80% of market value of NYSE stocks) Random Selection of Stocks (Fisher & Lorie): Equally-weighted portfolio of all stocks on the New York Stock Exchange Average Return (1-year): including dividends, no taxes, or commissions Years Average Annual Return (Arithmetic Average) Standard Deviation (Annual) % 41.2% % 19.8% % 32.3% 318

8 Finance Theory "Market" (in this sense) was much more volatile in the pre-war versus post-war period. Average Compound Return: including dividends, no taxes, but including purchase commissions: Years Average Compound Return (Geometric Average) % % % All Stocks on the New York Stock Exchange: Value-Weighted Cowles ( ): Average Compound Return: 6.6% Since the Fisher Lorie results for average performance of randomly selected portfolios is as good as managed portfolios on average over the same period, this is additional evidence in favor of the Random Walk. 319

9 Simulated Rate of Return Experience for Successful Market Timing* Monthy Forecasts: P = Probability of Correct Forecast January 1927 December 1978 Market Timing NYSE Per Month P=1.0 P=.90 P=.75 P=.60 P=.50 Stocks Average Rate of Return 2.58% 2.17% 1.56% 0.94% 0.53% 0.85% Standard Deviation 3.82% 3.98% 4.13% 4.19% 4.18% 5.89% Highest Return 38.55% 38.27% 37.61% 36.41% 35.12% 38.55% Lowest Return -0.06% % % % % % Average Compound Return 2.51% 2.10% 1.47% 0.85% 0.44% 0.68% Growth of $1,000 $5,362,212,000 $418,902,144 $9,146,722 $199,718 $15,602 $67,527 Average Annual Compound Return 34.65% 28.32% 19.14% 10.69% 5.41% 8.47% *Buy the market when the forecast is for stocks to do better than bonds. Buy bonds when the forecast is for bonds to do better than stocks. 320

10 Robert C. Merton Average Annual Compound Return on the Market (value-weighted, including reinvesting dividends, no commissions, or taxes) (Scholes) NYSE S&P Average Avg. Excess Average Avg. Excess Years Return Return Return Return Total: % 7.57% 11.63% 7.22% 10 Years: % 10.00% 13.38% 10.25% % 5.15% 9.90% 4.19% 5 Years: % 9.45% 13.50% 10.70% % 10.52% 13.26% 9.79% % 9.70% 12.34% 7.50% % 0.71% 7.52% 0.92% Jensen Performance of Mutual Funds Study Testing 115 Funds ability to Forecast (relative to Security Market Line): Model Specification: Test: Z (t) ~ Z (t) = R(t) + β = R(t) + β [Z [Z ~ M M (t) (t) - R(t)] + α - R(t)] + α (t) (t) + ~ ε (t) E( ~ ε (t)) = 0; Cov( ~ ε (t), ~ εi (t k =1,2,... - k)) = 0 i, =1, Assumes: β is stationary. Suppose not: ~ β (t) = β + U ~ (t) if you can forecast the market, then Cov(U ~, Z ~ M) > 0 which would imply E( estimated β ) < β and biases tests in favor of superior performance (i.e., larger α ). 321

11 Robert C. Merton 115 Funds Studied. Returns net of all costs including management fees. 76 funds had measured α < 0 39 funds had measured α 0 Average α =.011 = 1.1% The statistical significance of the positive α were no more than would have been expected by chance when the true α = average α. Using Returns Gross of Management Fees 55 funds had measured α < 0 60 funds had measured α 0 Average α =.004 = 0.4% Statistical significance of the positive α were no more than would have been expected by change when the true α = 0. Conclusions: Funds taken as a whole do not show evidence of superior forecasting capability; and, of course, do not show evidence of sufficient superior forecasting to cover costs. What about individual funds? Even if funds as a whole do not show evidence of superior forecasting, what about the overtime performance of particular funds? Is it true that funds with observed positive α in the past tend to have positive α in the future? Jensen & Black studied the 115 funds for the years computing the realized α for each year (a total of = 1150 observations). The differential returns were computed gross of management fees. The results were 322

12 Finance Theory Number of Successive Years of Observed Positive "α" Number of Times Observed Percent of Cases Followed by Another Positive "α" % % % % Conclusion: It appears that funds that did well in the past show little evidence of continuing to do so. Jensen also found that there was no significant evidence of serial correlation in the return series in support of the Random Walk Hypothesis. With respect to providing efficient (or well-diversified) portfolios, on average, Jensen found that 85% of the variance of the funds' returns were due to market movements. I.e., σ p (1.085)σ M β p =1.085ρ pm σ p or ρ pm =.9216 Further, on the whole, funds tended to keep about the same level of β p or σ p through time. Overall Summary 1. Over the last forty years, randomly selected portfolios have returns greater than or equal to randomly selected managed portfolios. 2. Most mutual funds are reasonably well diversified (i.e., have reasonably low nonsystematic risk). 3. On average, funds did not perform, before expenses, any better than a naive strategy portfolio with the same beta. 323

13 Robert C. Merton 4. On average, funds did worse, after expenses, than the naive strategy portfolio with the same beta. 5. Few, if any, individual funds showed any consistent performance superior to the naive strategy over time. 6. Most funds spend too much money trying to forecast returns on stocks: either explicitly in analyst salaries and support and implicitly through brokerage commissions and spreads through excess turnover. Investment prescription: Since these results did not include sales commissions on "load" funds which run from 1½ - 8½%, clearly one should buy "no load" funds (with no sales commissions). To achieve an efficient investment strategy, choose a mix of a few well-diversified, no load funds. Select funds with the lowest costs (management fees and turnover). (ii) Testing the Capital Asset Pricing Model (Miller and Scholes; Black-Jensen-Scholes) The capital asset pricing model specifies that E( Z ) = R + β [E(ZM) - R] and E(ZM) > R. I.e., investors are risk-averse; expected excess return on a security is proportional to its beta; it is dependent only on beta; is linear in beta. The Black-Jensen-Scholes paper is one of the most sophisticated tests of the capital asset pricing model. Using monthly returns from on securities, they found the following: 1. The expected return on the market is greater than the riskless rate Z > R). 2. Expected return on individual securities (portfolios) is an increasing function of its beta and the excess returns are linear in beta. 3. Expected return depends on beta. ( M 324

14 Finance Theory 4. The empirical Security Market Line is too "flat." I.e., the returns on "low beta" (β < 1) stocks were higher than predicted by the Capital Asset Pricing Model and the returns on "high beta" (β > 1) stocks were lower than predicted by the Capital Asset Pricing Model. Results 1-3 are consistent with the capital asset pricing model, result 4 is not, and has been the cause for much concern as well as new research in this area. To analyze this problem, BJS constructed a "zero-beta" portfolio by combining stocks only (so it has variance), and this portfolio had realized returns significantly greater than the riskless rate. I.e., Z 0 -β > R where is the expected return on the minimum-variance, zero-beta portfolio constructed from stocks. The specification that they fit was Z - R = β ( ZM - R) + γ( β )( Z 0-β - R), dγ where γ(1) = 0 and < 0. dβ Z 0-β While there are many possible theoretical and empirical explanations for this finding, such analyses are beyond the level of this course. It is evident that the simple form of the Capital Asset Pricing Model as a means for estimating expected returns on individual securities is not sufficient; however, the main results implied by that model (1-3) do seem to describe returns and, as a good approximation, its specification is not unreasonable. 325

Key Concepts and Skills

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

More information

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

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

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

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

Market Efficiency and Behavioral Finance. Chapter 12

Market Efficiency and Behavioral Finance. Chapter 12 Market Efficiency and Behavioral Finance Chapter 12 Market Efficiency if stock prices reflect firm performance, should we be able to predict them? if prices were to be predictable, that would create the

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

Review for Exam 2. Instructions: Please read carefully

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

More information

Lecture 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

Instructor s Manual Chapter 12 Page 144

Instructor s Manual Chapter 12 Page 144 Chapter 12 1. Suppose that your 58-year-old father works for the Ruffy Stuffed Toy Company and has contributed regularly to his company-matched savings plan for the past 15 years. Ruffy contributes $0.50

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

Professionally Managed Portfolios of Exchange-Traded Funds

Professionally Managed Portfolios of Exchange-Traded Funds ETF Portfolio Partners C o n f i d e n t i a l I n v e s t m e n t Q u e s t i o n n a i r e Professionally Managed Portfolios of Exchange-Traded Funds P a r t I : I n v e s t o r P r o f i l e Account

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

The Best of Both Worlds:

The Best of Both Worlds: The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk Jacob Boudoukh 1, Matthew Richardson and Robert F. Whitelaw Stern School of Business, NYU The hybrid approach combines the two most

More information

Prospectus Socially Responsible Funds

Prospectus Socially Responsible Funds Prospectus Socially Responsible Funds Calvert Social Investment Fund (CSIF) Balanced Portfolio Equity Portfolio Enhanced Equity Portfolio Bond Portfolio Money Market Portfolio Calvert Social Index Fund

More information

Black-Scholes-Merton approach merits and shortcomings

Black-Scholes-Merton approach merits and shortcomings Black-Scholes-Merton approach merits and shortcomings Emilia Matei 1005056 EC372 Term Paper. Topic 3 1. Introduction The Black-Scholes and Merton method of modelling derivatives prices was first introduced

More information

FTS Real Time System Project: Portfolio Diversification Note: this project requires use of Excel s Solver

FTS Real Time System Project: Portfolio Diversification Note: this project requires use of Excel s Solver FTS Real Time System Project: Portfolio Diversification Note: this project requires use of Excel s Solver Question: How do you create a diversified stock portfolio? Advice given by most financial advisors

More information

CHAPTER 11: THE EFFICIENT MARKET HYPOTHESIS

CHAPTER 11: THE EFFICIENT MARKET HYPOTHESIS CHAPTER 11: THE EFFICIENT MARKET HYPOTHESIS PROBLEM SETS 1. The correlation coefficient between stock returns for two non-overlapping periods should be zero. If not, one could use returns from one period

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

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

Economia Aziendale online 2000 Web International Business and Management Review

Economia Aziendale online 2000 Web International Business and Management Review Economia Aziendale online 2000 Web International Business and Management Review N. 1/2008 Special Issue 3 rd International Economic Scientific Session International Scientific Conference European Integration

More information

2. How is a fund manager motivated to behave with this type of renumeration package?

2. How is a fund manager motivated to behave with this type of renumeration package? MØA 155 PROBLEM SET: Options Exercise 1. Arbitrage [2] In the discussions of some of the models in this course, we relied on the following type of argument: If two investment strategies have the same payoff

More information

The relationship between exchange rates, interest rates. In this lecture we will learn how exchange rates accommodate equilibrium in

The relationship between exchange rates, interest rates. In this lecture we will learn how exchange rates accommodate equilibrium in The relationship between exchange rates, interest rates In this lecture we will learn how exchange rates accommodate equilibrium in financial markets. For this purpose we examine the relationship between

More information

How to Win the Stock Market Game

How to Win the Stock Market Game How to Win the Stock Market Game 1 Developing Short-Term Stock Trading Strategies by Vladimir Daragan PART 1 Table of Contents 1. Introduction 2. Comparison of trading strategies 3. Return per trade 4.

More information

Glossary of Investment Terms

Glossary of Investment Terms online report consulting group Glossary of Investment Terms glossary of terms actively managed investment Relies on the expertise of a portfolio manager to choose the investment s holdings in an attempt

More information

CHAPTER 20: OPTIONS MARKETS: INTRODUCTION

CHAPTER 20: OPTIONS MARKETS: INTRODUCTION CHAPTER 20: OPTIONS MARKETS: INTRODUCTION PROBLEM SETS 1. Options provide numerous opportunities to modify the risk profile of a portfolio. The simplest example of an option strategy that increases risk

More information

It is a market where current prices reflect/incorporate all available information.

It is a market where current prices reflect/incorporate all available information. ECMC49F Market Efficiency Hypothesis Practice Questions Date: Nov 15, 2005 [1] How to define an efficient market? It is a market where current prices reflect/incorporate all available information. [2]

More information

Five Myths of Active Portfolio Management. P roponents of efficient markets argue that it is impossible

Five Myths of Active Portfolio Management. P roponents of efficient markets argue that it is impossible Five Myths of Active Portfolio Management Most active managers are skilled. Jonathan B. Berk 1 This research was supported by a grant from the National Science Foundation. 1 Jonathan B. Berk Haas School

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

Steve Meizinger. FX Options Pricing, what does it Mean?

Steve Meizinger. FX Options Pricing, what does it Mean? Steve Meizinger FX Options Pricing, what does it Mean? For the sake of simplicity, the examples that follow do not take into consideration commissions and other transaction fees, tax considerations, or

More information

Advantages and disadvantages of investing in the Stock Market

Advantages and disadvantages of investing in the Stock Market Advantages and disadvantages of investing in the Stock Market There are many benefits to investing in shares and we will explore how this common form of investment can be an effective way to make money.

More information

There are two types of returns that an investor can expect to earn from an investment.

There are two types of returns that an investor can expect to earn from an investment. Benefits of investing in the Stock Market There are many benefits to investing in shares and we will explore how this common form of investment can be an effective way to make money. We will discuss some

More information

ANALYSIS AND MANAGEMENT

ANALYSIS AND MANAGEMENT ANALYSIS AND MANAGEMENT T H 1RD CANADIAN EDITION W. SEAN CLEARY Queen's University CHARLES P. JONES North Carolina State University JOHN WILEY & SONS CANADA, LTD. CONTENTS PART ONE Background CHAPTER 1

More information

VALUE ADDED INDEXING SM PERSPECTIVES. Top Ten List: Why Passive Investing Wins SUMMARY:

VALUE ADDED INDEXING SM PERSPECTIVES. Top Ten List: Why Passive Investing Wins SUMMARY: VALUE ADDED INDEXING SM PERSPECTIVES Top Ten List: Why Passive Investing Wins SUMMARY: Too often the active vs. passive investing debate focuses only on performance. While research shows passive strategies

More information

FOR MANY YEARS cconomists, Statisticians, and teachers

FOR MANY YEARS cconomists, Statisticians, and teachers Random Walks in Stock Market Prices by Eugene F. Fama FOR MANY YEARS cconomists, Statisticians, and teachers of finance have been interested in developing and testing models of stock price behavior. One

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

Market Efficiency: Definitions and Tests. Aswath Damodaran

Market Efficiency: Definitions and Tests. Aswath Damodaran Market Efficiency: Definitions and Tests 1 Why market efficiency matters.. Question of whether markets are efficient, and if not, where the inefficiencies lie, is central to investment valuation. If markets

More information

European Options Pricing Using Monte Carlo Simulation

European Options Pricing Using Monte Carlo Simulation European Options Pricing Using Monte Carlo Simulation Alexandros Kyrtsos Division of Materials Science and Engineering, Boston University akyrtsos@bu.edu European options can be priced using the analytical

More information

Benchmarking Low-Volatility Strategies

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

More information

XII. RISK-SPREADING VIA FINANCIAL INTERMEDIATION: LIFE INSURANCE

XII. RISK-SPREADING VIA FINANCIAL INTERMEDIATION: LIFE INSURANCE XII. RIS-SPREADIG VIA FIACIAL ITERMEDIATIO: LIFE ISURACE As discussed briefly at the end of Section V, financial assets can be traded directly in the capital markets or indirectly through financial intermediaries.

More information

CHAPTER 11: THE EFFICIENT MARKET HYPOTHESIS

CHAPTER 11: THE EFFICIENT MARKET HYPOTHESIS CHAPTER 11: THE EFFICIENT MARKET HYPOTHESIS PROBLEM SETS 1. The correlation coefficient between stock returns for two non-overlapping periods should be zero. If not, one could use returns from one period

More information

Exercise Sheet 1. Solution 1.1. One year chart

Exercise Sheet 1. Solution 1.1. One year chart Exercise Sheet 1 Exercies 1.1 Use the monthly data on historical prices in Yahoo to plot the share price of LloydsTSB over the past year. If you had invested 10,000 in LloydsTSB in October 2007 what would

More information

Futures Price d,f $ 0.65 = (1.05) (1.04)

Futures Price d,f $ 0.65 = (1.05) (1.04) 24 e. Currency Futures In a currency futures contract, you enter into a contract to buy a foreign currency at a price fixed today. To see how spot and futures currency prices are related, note that holding

More information

Life Cycle Asset Allocation A Suitable Approach for Defined Contribution Pension Plans

Life Cycle Asset Allocation A Suitable Approach for Defined Contribution Pension Plans Life Cycle Asset Allocation A Suitable Approach for Defined Contribution Pension Plans Challenges for defined contribution plans While Eastern Europe is a prominent example of the importance of defined

More information

Finance 400 A. Penati - G. Pennacchi Market Micro-Structure: Notes on the Kyle Model

Finance 400 A. Penati - G. Pennacchi Market Micro-Structure: Notes on the Kyle Model Finance 400 A. Penati - G. Pennacchi Market Micro-Structure: Notes on the Kyle Model These notes consider the single-period model in Kyle (1985) Continuous Auctions and Insider Trading, Econometrica 15,

More information

Non-FDIC Insured May Lose Value No Bank Guarantee. Time-Tested Investment Strategies for the Long Term

Non-FDIC Insured May Lose Value No Bank Guarantee. Time-Tested Investment Strategies for the Long Term Non-FDIC Insured May Lose Value No Bank Guarantee Time-Tested Investment Strategies for the Long Term Rely on These Four Time-Tested Strategies to Keep You on Course. Buy Right and Sit Tight Keep Your

More information

Tilted Portfolios, Hedge Funds, and Portable Alpha

Tilted Portfolios, Hedge Funds, and Portable Alpha MAY 2006 Tilted Portfolios, Hedge Funds, and Portable Alpha EUGENE F. FAMA AND KENNETH R. FRENCH Many of Dimensional Fund Advisors clients tilt their portfolios toward small and value stocks. Relative

More information

Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate?

Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate? Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate? Emily Polito, Trinity College In the past two decades, there have been many empirical studies both in support of and opposing

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

DETERMINING THE VALUE OF EMPLOYEE STOCK OPTIONS. Report Produced for the Ontario Teachers Pension Plan John Hull and Alan White August 2002

DETERMINING THE VALUE OF EMPLOYEE STOCK OPTIONS. Report Produced for the Ontario Teachers Pension Plan John Hull and Alan White August 2002 DETERMINING THE VALUE OF EMPLOYEE STOCK OPTIONS 1. Background Report Produced for the Ontario Teachers Pension Plan John Hull and Alan White August 2002 It is now becoming increasingly accepted that companies

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

More information

ETF Total Cost Analysis in Action

ETF Total Cost Analysis in Action Morningstar ETF Research ETF Total Cost Analysis in Action Authors: Paul Justice, CFA, Director of ETF Research, North America Michael Rawson, CFA, ETF Analyst 2 ETF Total Cost Analysis in Action Exchange

More information

Test3. Pessimistic Most Likely Optimistic Total Revenues 30 50 65 Total Costs -25-20 -15

Test3. Pessimistic Most Likely Optimistic Total Revenues 30 50 65 Total Costs -25-20 -15 Test3 1. The market value of Charcoal Corporation's common stock is $20 million, and the market value of its riskfree debt is $5 million. The beta of the company's common stock is 1.25, and the market

More information

CAPITAL STRUCTURE AND DIVIDEND POLICY

CAPITAL STRUCTURE AND DIVIDEND POLICY CAPITAL STRUCTURE AND DIVIDEND POLICY Capital Structure In the section of the notes titled Cost of Capital, we examined how the cost of capital is determined. From those notes, you should have discovered

More information

ECON 351: The Stock Market, the Theory of Rational Expectations, and the Efficient Market Hypothesis

ECON 351: The Stock Market, the Theory of Rational Expectations, and the Efficient Market Hypothesis ECON 351: The Stock Market, the Theory of Rational Expectations, and the Efficient Market Hypothesis Alejandro Riaño Penn State University June 8, 2008 Alejandro Riaño (Penn State University) ECON 351:

More information

The efficient market hypothesis and the design of investment activity

The efficient market hypothesis and the design of investment activity The efficient market hypothesis and the design of investment activity 1 How should one design an investment strategy? One option: active trading based on Information ( news ) Market trends ( momentum )

More information

The Conversion of Cooperatives to Publicly Held Corporations: A Financial Analysis of Limited Evidence

The Conversion of Cooperatives to Publicly Held Corporations: A Financial Analysis of Limited Evidence The Conversion of Cooperatives to Publicly Held Corporations: A Financial Analysis of Limited Evidence Robert A. Collins Recent reorganizations of agricultural cooperatives have created concern that the

More information

How to Collect a 162% Cash on Cash Return

How to Collect a 162% Cash on Cash Return How to Collect a 162% Cash on Cash Return Today we are going to explore one of the most profitable, low-risk income strategies I ve come across in my 27 years of trading. This income strategy produced

More information

Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model

Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model Brunel University Msc., EC5504, Financial Engineering Prof Menelaos Karanasos Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model Recall that the price of an option is equal to

More information

Using Duration Times Spread to Forecast Credit Risk

Using Duration Times Spread to Forecast Credit Risk Using Duration Times Spread to Forecast Credit Risk European Bond Commission / VBA Patrick Houweling, PhD Head of Quantitative Credits Research Robeco Asset Management Quantitative Strategies Forecasting

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

Investments, Chapter 4

Investments, Chapter 4 Investments, Chapter 4 Answers to Selected Problems 2. An open-end fund has a net asset value of $10.70 per share. It is sold with a front-end load of 6 percent. What is the offering price? Answer: When

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

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

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

Investing with PredictWallStreet Data September 2013 Update

Investing with PredictWallStreet Data September 2013 Update Investing with PredictWallStreet Data September 2013 Update On Feb 5, 2008, PredictWallStreet released a White Paper entitled: Investing with PredictWallStreet Data. That paper described how we gather

More information

The Evolution of Investing

The Evolution of Investing Bringing the Best of Academic Research to Real-World Investment Strategies The Science of Investing from the Halls of Academia An enormous Industry has developed over the years that s very familiar to

More information

CHARACTERISTICS OF INVESTMENT PORTFOLIOS PASSIVE MANAGEMENT STRATEGY ON THE CAPITAL MARKET

CHARACTERISTICS OF INVESTMENT PORTFOLIOS PASSIVE MANAGEMENT STRATEGY ON THE CAPITAL MARKET Mihaela Sudacevschi 931 CHARACTERISTICS OF INVESTMENT PORTFOLIOS PASSIVE MANAGEMENT STRATEGY ON THE CAPITAL MARKET MIHAELA SUDACEVSCHI * Abstract The strategies of investment portfolios management on the

More information

The essentials of investing for retirement.

The essentials of investing for retirement. The essentials of investing for retirement. Fidelity has been helping people invest for retirement for more than 65 years. Some investors use our actively managed and index mutual funds. Some use our powerful

More information

The Value Line Definitive Guide { Ranking System

The Value Line Definitive Guide { Ranking System The Value Line Definitive Guide{ Ranking System A LETTER FROM IAN GENDLER Investors need to have unbiased and independent research. That is something Value Line subscribers have known for some 80 years.

More information

Madison Investment Advisors LLC

Madison Investment Advisors LLC Madison Investment Advisors LLC Intermediate Fixed Income SELECT ROSTER Firm Information: Location: Year Founded: Total Employees: Assets ($mil): Accounts: Key Personnel: Matt Hayner, CFA Vice President

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: 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

Stock market simulation with ambient variables and multiple agents

Stock market simulation with ambient variables and multiple agents Stock market simulation with ambient variables and multiple agents Paolo Giani Cei 0. General purposes The aim is representing a realistic scenario as a background of a complete and consistent stock market.

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

UBS Global Asset Management has

UBS Global Asset Management has IIJ-130-STAUB.qxp 4/17/08 4:45 PM Page 1 RENATO STAUB is a senior assest allocation and risk analyst at UBS Global Asset Management in Zurich. renato.staub@ubs.com Deploying Alpha: A Strategy to Capture

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

INSURANCE. Life Insurance. as an. Asset Class

INSURANCE. Life Insurance. as an. Asset Class INSURANCE Life Insurance as an Asset Class 16 FORUM JUNE / JULY 2013 Permanent life insurance has always been an exceptional estate planning tool, but as Wayne Miller and Sally Murdock report, it has additional

More information

Valuing Stock Options: The Black-Scholes-Merton Model. Chapter 13

Valuing Stock Options: The Black-Scholes-Merton Model. Chapter 13 Valuing Stock Options: The Black-Scholes-Merton Model Chapter 13 Fundamentals of Futures and Options Markets, 8th Ed, Ch 13, Copyright John C. Hull 2013 1 The Black-Scholes-Merton Random Walk Assumption

More information

Fixed Income Investing

Fixed Income Investing Fixed Income Investing Why Invest in Fixed Income Fixed income securities (bonds) are a fundamental part of an investing plan for most investors. There are many types of bonds along with varied approaches

More information

Proponents of efficient markets argue that it is

Proponents of efficient markets argue that it is Five Myths of Active Portfolio Management Most active managers are skilled. Jonathan B. Berk Proponents of efficient markets argue that it is impossible to beat the market consistently. In support of their

More information

The Performance Of Mutual Funds In The Period 1945-1964

The Performance Of Mutual Funds In The Period 1945-1964 The Performance Of Mutual Funds In The Period 1945-1964 Michael C. Jensen Harvard Business School MJensen@hbs.edu ABSTRACT In this paper I derive a risk-adusted measure of portfolio performance (now known

More information

Non-FDIC Insured May Lose Value No Bank Guarantee. Time-Tested Investment Strategies for the Long Term

Non-FDIC Insured May Lose Value No Bank Guarantee. Time-Tested Investment Strategies for the Long Term Time-Tested Investment Strategies for the Long Term Invest for the Long-Term Stay the Course Through Ups and Downs History shows that the market goes up and the market goes down. While there may be short-term

More information

Active Versus Passive Low-Volatility Investing

Active Versus Passive Low-Volatility Investing Active Versus Passive Low-Volatility Investing Introduction ISSUE 3 October 013 Danny Meidan, Ph.D. (561) 775.1100 Low-volatility equity investing has gained quite a lot of interest and assets over the

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

Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator

Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights

More information

Makeup Exam MØA 155 Financial Economics February 2010 Permitted Material: Calculator, Norwegian/English Dictionary

Makeup Exam MØA 155 Financial Economics February 2010 Permitted Material: Calculator, Norwegian/English Dictionary University of Stavanger (UiS) Stavanger Masters Program Makeup Exam MØA 155 Financial Economics February 2010 Permitted Material: Calculator, Norwegian/English Dictionary The number in brackets is the

More information

CS 522 Computational Tools and Methods in Finance Robert Jarrow Lecture 1: Equity Options

CS 522 Computational Tools and Methods in Finance Robert Jarrow Lecture 1: Equity Options CS 5 Computational Tools and Methods in Finance Robert Jarrow Lecture 1: Equity Options 1. Definitions Equity. The common stock of a corporation. Traded on organized exchanges (NYSE, AMEX, NASDAQ). A common

More information

t = 1 2 3 1. Calculate the implied interest rates and graph the term structure of interest rates. t = 1 2 3 X t = 100 100 100 t = 1 2 3

t = 1 2 3 1. Calculate the implied interest rates and graph the term structure of interest rates. t = 1 2 3 X t = 100 100 100 t = 1 2 3 MØA 155 PROBLEM SET: Summarizing Exercise 1. Present Value [3] You are given the following prices P t today for receiving risk free payments t periods from now. t = 1 2 3 P t = 0.95 0.9 0.85 1. Calculate

More information

Capital Market Theory: An Overview. Return Measures

Capital Market Theory: An Overview. Return Measures Capital Market Theory: An Overview (Text reference: Chapter 9) Topics return measures measuring index returns (not in text) holding period returns return statistics risk statistics AFM 271 - Capital Market

More information

CONFORMED COPY Q.k~c~S ' UNIVERSITY OF PENNSYLVANIA. Philadelphia 4. July 9, 1962. Wharton School of Finance and Commerce

CONFORMED COPY Q.k~c~S ' UNIVERSITY OF PENNSYLVANIA. Philadelphia 4. July 9, 1962. Wharton School of Finance and Commerce CONFORMED COPY Q.k~c~S ' UNIVERSITY OF PENNSYLVANIA Philadelphia 4 Wharton School of Finance and Commerce Securities and Exchange Commission 425 Second St., N. W. Washington 25, D. C. Gentlemen: We are

More information

Journal of Financial and Economic Practice

Journal of Financial and Economic Practice Analyzing Investment Data Using Conditional Probabilities: The Implications for Investment Forecasts, Stock Option Pricing, Risk Premia, and CAPM Beta Calculations By Richard R. Joss, Ph.D. Resource Actuary,

More information

Stock Market Game Test

Stock Market Game Test Stock Market Game Test A test of basic economic concepts and institutions related to saving, investing, risk, the stock market, and productivity 1. A personal investment such as purchasing stocks or corporate

More information

Club. The role of Core Asset Managers in the Global Economy February 2015. Introduction. Content: Yves Choueifaty, 300 Club

Club. The role of Core Asset Managers in the Global Economy February 2015. Introduction. Content: Yves Choueifaty, 300 Club The role of Core Asset Managers in the Global Economy February 2015 Yves Choueifaty, 300 Club The Club Views expressed here are those of the author, who is solely responsible for any errors and omissions.

More information

FREE MARKET U.S. EQUITY FUND FREE MARKET INTERNATIONAL EQUITY FUND FREE MARKET FIXED INCOME FUND of THE RBB FUND, INC. PROSPECTUS.

FREE MARKET U.S. EQUITY FUND FREE MARKET INTERNATIONAL EQUITY FUND FREE MARKET FIXED INCOME FUND of THE RBB FUND, INC. PROSPECTUS. FREE MARKET U.S. EQUITY FUND FREE MARKET INTERNATIONAL EQUITY FUND FREE MARKET FIXED INCOME FUND of THE RBB FUND, INC. PROSPECTUS December 31, 2014 Investment Adviser: MATSON MONEY, INC. 5955 Deerfield

More information

Chapter 9. The Valuation of Common Stock. 1.The Expected Return (Copied from Unit02, slide 39)

Chapter 9. The Valuation of Common Stock. 1.The Expected Return (Copied from Unit02, slide 39) Readings Chapters 9 and 10 Chapter 9. The Valuation of Common Stock 1. The investor s expected return 2. Valuation as the Present Value (PV) of dividends and the growth of dividends 3. The investor s required

More information

Practical aspects of implementing MiFID requirementsin GIPS compositereports

Practical aspects of implementing MiFID requirementsin GIPS compositereports GIPS and MiFID investmentreporting: Practical aspects of implementing MiFID requirementsin GIPS compositereports Zurich, November 15, 2007 Eugene Skrynnyk, UBS Wealth Management November 15, 2007 Agenda

More information

Investing In Volatility

Investing In Volatility Investing In Volatility By: Anish Parvataneni, CFA Portfolio Manager LJM Partners Ltd. LJM Partners, Ltd. is issuing a series a white papers on the subject of investing in volatility as an asset class.

More information

The 50% Indicator Investment Security Analysis. Robert Ruggirello, CFA

The 50% Indicator Investment Security Analysis. Robert Ruggirello, CFA November 11, 2015 The 50% Indicator Investment Security Analysis Robert Ruggirello, CFA Introduction: The 50% Indicator is an investment opportunity available to some NYC Employees. There has been some

More information

Virtual Stock Market Game Glossary

Virtual Stock Market Game Glossary Virtual Stock Market Game Glossary American Stock Exchange-AMEX An open auction market similar to the NYSE where buyers and sellers compete in a centralized marketplace. The AMEX typically lists small

More information