NASD licenses brokers and handles the punishment for violators of its prescribed fair practices. Basically, the y are fully computerized trading networks that match buy and sell orders from investors without the use of a dealer. ECNs offer the possibility of very quick execution, low costs, trading after the exchanges are closed, and anonymity.
The NYSE was seeking a way to offer its customers almost instantaneous execution of orders, which some institutional investors want. They probably also realized that the future of trading is going to more heavily emphasize this type of trading. An OTC security today is an unlisted security not trading on an exchange. Nasdaq trades listed securities, and in January was approved by the SEC to become an exchange. OTC securities typically involve very small, relatively unknown companies.
Almost all stock price indices today are market value weighted indexes, or capitalization weighted. The exception is the DJIA, a price-weighted index. The price weighted procedure is a holdover from the 19th Century, when the Dow Jones Industrial Average was started. All price indexes created today are market-value weighted indexes. These measures are the two most often-used indicators of what stocks in general are doing. Blue chip stocks are large, well-established and well-known companies with long records of earnings and dividends.
They are typically traded on the NYSE. It is, in effect, a non- American world index. Blocks are defined as transactions involving at least 10, shares. Large-block activity on the NYSE is an indicator of institutional investor participation in equity trading.
The total number of large-block transactions has increased over the years on the NYSE. It now describes itself as a hybrid market because it can offer trading using the traditional specialist system, or trading using the fully computerized ECN technology, which offers very quick execution. The NYSE has approximately 2, common stocks listed.
Nasdaq typically has more, although the number has declined in recent years. In- house trading refers to internal trading by fund managers within one company without the use of a broker or an exchange. Traders agree to buy and sell in- house, or cross- trade, perhaps at the next closing price. Fidelity Investments operates an in- house trading system for its own funds because of the large amount of buying and selling it does every day.
Large international investors will benefit from in-house trading. All federal, agency, and municipal bonds trade OTC, and most corporates. Growth stocks are the most likely stocks to split. As high-priced stocks split and their prices decline, they lose relative importance in the DJIA, which is a price-weighted series. High-price stocks carry more weight than do low-priced stocks in such a series.
The price of Altria is much higher than the price of Pfizer as of early Thus, a 10 percent change in Altria would have a larger impact. This can be shown by constructing a simple example of price X number of shares for each stock. Presumably, if you owned a portfolio of large cap stocks you would prefer to see both indexes moving in a similar manner, which would then be more reassuring as to how your own portfolio was performing.
The DJIA will reflect the performance of the large stocks in that index. This problem illustrates how stock splits can affect a price-weighted average. With an unchanged divisor of 15, the average would of course decrease, in this case to This material typically is of great interest to most students, and instructors must decide how much time and effort to devote to it.
Chapter 5 devotes considerable attention to the major aspects of brokerage transactions. An important part of this discussion centers on brokers themselves, a subject which tends to interest students. The chapter discussion explains what brokers do, the types of brokerage operations full-service vs.
The remainder of the brokerage transaction discussion covers the major points that students need to know. These include the types of brokerage accounts, commissions, investing without a broker, how orders work, the types of orders, clearing procedures, using the internet, and so forth. Instructors will wish to vary their discussions of this material depending upon student knowledge, interest, time availability, and current discussions in the popular press.
There are numerous interesting illustrations that can be given of brokerage costs, how orders work, market orders versus limit orders, and so forth. The popular press regularly has articles that would be appropriate for class discussion. Chapter 5 contains a thorough discussion of investor protection in the markets, a topic of concern to many investors.
This covers not only federal legislation and the SEC but also self- regulation by the stock exchanges, including the latest measures on the NYSE such as trading halts and sidecars. The role of the NASD in regulating brokers and dealers also is covered. The remainder of the chapter is devoted to margin trading and short selling. These are important subjects, and ones that many students have difficulty understanding, particularly short selling.
Instructors should spend a reasonable amount of time on these concepts. To explain the mechanics of securities trading, such as brokerage transactions, margin trading and short selling. To provide an overview of how markets are regulated. The intent is to present this material in a concise format, and illustrate it with examples. Exhibit contains a brief description of the major legislative acts regulating the securities markets.
This material can be very tedious when presented as regular text. This presentation better allows instructors to devote as much, or as little, time as they desire. Exhibit is a detailed discussion of how short selling works. Many students have difficulty understanding exactly how one sells short.
Exhibit presents the details of short selling. Box Inserts Box discusses possible careers in the financial services industry, with primary emphasis on brokers. It is based on material from the Department of Labor. Thus, an investor who wants to be certain of quickly establishing a position in a stock or getting out of a stock will probably want to use a market order.
A limit order specifies a particular price to be met or bettered. The purchase or sale will occur only if the broker obtains that price, or betters it. Therefore, an investor can attempt to pay no more than a certain price in a purchase, or receive no less than a certain price in a sale; a completed transaction, however, cannot be guaranteed. A stop order specifies a certain price at which a market order takes effect. The exact price specified in the stop order is not guaranteed, and may no t be realized.
Limit orders are placed on opposite sides of the current market price of a stock from stop orders. Quoting prices in cents has generally lowered the spread on stocks, thereby helping investors. Margin is the equity that a customer has in a transaction. The Board of Governors of the Federal Reserve System sets the initial margin, which is the percentage of the value of a securities transaction that the purchaser must pay at the time of the transaction. Completion, however, may result in significantly different rates paid by the customer.
Actual margin between the initial and maintenance margins results in a restricted account where no additional margin purchases are allowed. If the actual margin declines below the maintenance margin, a margin call results, requiring the investor to put up additional cash or securities or be sold out by the brokerage firm.
If an investor sells short, he or she is usually selling a security that is not owned. The broker borrows the security from another customer who owns it , and lends it to the short seller who must subsequently replace it. In effect, the investor from whom the security is borrowed never knows it since his or her monthly statement continues to reflect a long position.
Short sales on the exchanges are permitted at the last trade price only if that price equaled or exceeded the last price before it. Otherwise, the seller must wait for an uptick. This restriction does not apply to Nasdaq stocks. A sell limit order and a buy stop order are above the current market price. A buy limit order and a sell stop order are below the current market price. The margin requirement for U. With a wrap account, investors with large sums to invest use a broker as a consultant to choose an outside money manager from a list provided by the broker.
All costs are wrapped in one fee--the cost of the broker-consultant, the money manager, and transactions costs. Investors can visit an office, call a broker at one of these firms, or use their internet facilities. Internet only discount brokers offer bare-bones brokerage commissions but less in the way of services.
Many of these firms tend to be quite small relative to the major discount brokers. More than companies offer dividend reinvestment plans, whereby dividends can be used to purchase additional shares of the company paying the dividend.
Many companies now offer direct purchase stock plans, allowing investors to purchase shares directly from the company. Exxon Mobil is a good example. Investors can open a direct-purchase account with Exxon to buy its stock. The role of specialists is critical on an auction market such as the NYSE.
They are expected to maintain a fair and orderly market in those stocks assigned to them, often going against the market. As brokers, specialists maintain the limit book, which records all limit orders. The commission brokers leave the limit orders with the specialist to be filled when possible, paying a specialist a fee to do this.
The specialist will buy from commission brokers with orders to sell and sell to those with orders to buy, hoping to profit by a favorable spread between the two sides. Both of these terms apply to limit orders. An open order remains in effect for six months unless canceled or renewed. A day order is effective for only one day. The mission of the SEC is to administer laws in the securities field and to protect investors and the public in securities transactions.
In general, it administers all securities laws. All brokers must register with the NASD in order to trade securities. The NASD can fine an individual. Penalties can be appealed to the SEC, which suspends the monetary penalties until resolution. Investors are interested in margin accounts because such accounts permit the magnification of gains but also losses.
The risks are obvious. If the transaction goes against the investor, the percentage losses are doubled, and interest costs must still be paid. Investors are required to have margin accounts for some transactions, such as short sales. Short sales account for less than 10 percent of all reported sales. The basis of regulation of mutual funds is the Investment Company Act of This federal act has been incredibly successful in regulating the investment company industry, providing almost total confidence in investors as to the operations of investment companies.
The Investors Advisors Act of simply requires would-be investment advisors to fill out a form and pay a fee to register with the SEC. There are no education or competency requirements. Therefore, investors have no assurances as to the abilities of people offering advice.
Investors may choose to use a full-service broker for several reasons. First, they may have confidence in a particular broker and wish to have the personal contact implied in such a relationship. Second, they can seek, and obtain, advice from the broker, and by extension, the entire resources of a firm such as Merrill Lynch. Fourth, full-service brokers may offer a wider range of services than many discount brokers, and investors needing such services will want to have them available.
The SEC does not provide assurances to investors when an IPO is marketed in terms of being able to tell investors that the company will be successful. The SEC does ensure that the company selling the new securities has complied with various accounting and legal provisions, thereby hopefully preventing the sale of new securities based upon fraudulent or misleading information.
The specialist system on the exchanges assigns stocks to specialist firms, who then make a market in the stock. Specialists buy from and sell to the public to maintain an orderly market in the stock. The system has worked well over the years, and has provided some notable successes in maintaining orderly markets. For example, in the great crash of October 19, , specialists remained at their posts, trading stocks and providing liquidity. Dealers in the Nasdaq stock market make markets in stocks, buying from investors and selling to them from their inventory.
Thus, they have a vested interest in each transaction, and in the spread between the bid and asked price. Investigations in the s revealed that these spreads often were too wide relative to what should be expected. In most cases, these spreads have narrowed since these investigations.
It can be used to curb speculative activity in the stock market. Marked to the market means that overnight each margin account is checked by the brokerage firm to see if it is in compliance with all margin requirements. If not, adjustments will have to be made. A short seller must have a margin account. Return and risk are the key elements of investment decisions--in effect, everything else revolves around these two factors.
It makes sense, therefore, to analyze and discuss these concepts in detail. Chapter 6 focuses only on understanding and measuring realized returns and wealth. This allows students to concentrate on this one issue in a comprehensive manner. All of the equations for calculating the various types of returns needed in a b asic Investments course are included in this chapter.
Beginning students are unlikely to use anything beyond what is contained here with regard to realized returns. Chapter 6 provides a complement to Chapter 7, which covers expected returns and risk and the basic calculations of portfolio theory. Thus, in Chapter 6 we analyze and calculate realized returns, while in Chapter 7 we analyze and calculate expected returns, based on probability distributions.
This discussion centers on the definition and meaning of return and risk including the components of return, the sources of risk, and types of risk. The emphasis is on how to both understand and measure return and risk. Considerable attention is devoted to explaining the total return TR , return relative RR , and cumulative wealth calculations, which are used throughout this text and are exactly comparable to the definitions used in such prominent sources as the Ibbotson Associates Yearbook.
Numerous examples are presented. The discussion of returns measures facilitates the presentation of the data on rates of return and wealth indexes. This data is both important as benchmarks and interesting it can be the basis of lively class discussion. The data used here were collected and calculated by the author, and correspond closely with the Ibbotson data.
The use of the geometric mean is fully explored, along with wealth indexes. Although challenging, this material is important. Calculations include measuring the yield component and capital gains component of total returns and cumulative wealth separately, measures of inflation- adjusted returns, and risk premiums.
Definitions of risk are presented and discussed. While examples include calculating the standard deviation, the emphasis here is on understanding and using it. This chapter contains an extensive problem set. To illustrate the use of such measures as the geometric mean and standard deviation. To present the well-known data on rates of return for major financial assets for long periods of time. To present and illustrate virtually all the calculations needed for a thorough understanding of return and risk.
This is an important calculation for the entire course, and students should be very comfortable with doing such calculations. Figure shows the spread in returns for the major financial assets covered in Table Figure shows cumulative wealth indices for the major financial assets since the beginning of Instructors may wish to emphasize how these values are calculated which is covered in the chapter.
Calculated total returns for each year are presented. These data were calculated and compiled by Jack Wilson and Charles Jones, and have been used in several articles. Tables and involve the calculation and interpretation of the arithmetic and geometric means using TRs.
Instructors should stress the meaning of the geometric mean. Table for historical data shows calculations for the standard deviation and can be handled by students on their own or emphasized by instructors to the extent thought necessary. Table is an important table on rates of return and should be used as a transparency for class discussion.
This table is important for numerous reasons: investors need to know the historical return series for benchmark purposes, it illustrates the nature of the return--risk tradeoff, and it allows you to talk about the variability in returns over time by analyzing the arithmetic and geometric means as well as the standard deviations presented in the table.
Key differences include a start date at the beginning of , and the use of more stocks for the years than the 90 stocks which Ibbotson Associates uses. Box Inserts There are no box inserts for Chapter 6. Historical returns are realized returns, such as those reported by Ibbotson Associates. Expected returns are returns expected to occur in the future.
They are the most likely returns for the future, although they may not actually be realized because of risk. A Total Return can be calculated for any asset for any holding period. Both monthly and annual TRs are often calculated, but any desired period of time can be used. Total return for any security consists of an income yield component and a capital gain or loss component. While either component can be zero for a given security over a specified time period, only the capital change component can be negative.
Return relative adds 1. The geometric mean is a better measure of the change in wealth over more than a single period. Over multiple periods the geometric mean indicates the compound rate of return, or the rate at which an invested dollar grows, and takes into account the variability in the returns. The geometric mean is always less than the arithmetic mean because it allows for the compounding effect--the earning of interest on interest.
The arithmetic mean should be used when describing the average rate of return without considering compounding. It is the best estimate of the rate of return for a single period. Thus, in estimating the rate of return for common stocks for next year, we use the arithmetic mean and not the geometric mean. The reason is that because of variability in the returns, we will have to earn, on average, the arithmetic rate in order to achieve a rate of growth which is given by the smaller geometric mean.
See Equation Knowing the arithmetic mean and the standard deviation for a series, the geometric mean can be approximated. An equity risk premium is the difference between stocks and a risk-free rate proxied by the return on Treasury bills.
It represents the additional compensation, on average, for taking the risk of equities rather than buying Treasury bills. As Table shows, the risk standard deviation of all common stocks for the period was Therefore, common stocks are clearly more risky than bonds, as they should be since larger returns would be expected to be accompanied by larger risks over long periods of time.
Market risk is the variability in returns due to fluctuations in the overall market. It includes a wide range of factors exogenous to securities themselves. Business risk is the risk of doing business in a particular industry or environment. Interest rate risk and inflation risk are clearly directed related. Interest rates and inflation generally rise and fall together.
Systematic risk: market risk, interest rate risk, inflation risk, exchange rate risk, and country risk. Nonsystematic risk: business risk, financial risk, and liquidity risk. Country risk is the same thing as political risk. The United States can be used as a benchmark with which to judge other countries on a relative basis. Canada would be considered to have relatively low country risk although some of the separation issues that have occurred there have probably increased the risk for Canada.
Mexico seems to be on the upswing economically, but certainly has its risk in the form of nationalized industries, overpopulation, and other issues. Mexico also experienced a dramatic devaluation of the peso. The return on the Japanese investment is now worth less in dollars.
The percentage of the original investment after the curre ncy risk is accounted for is 0. Risk is the chance that the actual outcome from an investment will differ from the expected outcome. Risk is often associated with the dispersion in the likely outcomes. Dispersion refers to variability, and the standard deviation is a statistical measure of variability or dispersion. Beta, discussed in Chapter 9, is a relative measure of the risk of an individual security in relation to the overall market, which has a beta of 1.
Betas have intuitive meaning only in relation to the benchmark of 1. It measures the level rather than changes in wealth. The geometric mean is the nth root of the cumulative wealth index. Alternatively, adding 1. You cannot validly compare an year mean return with recent return figures because of inflation premiums. The expected return on common stocks may be higher than the historical realized mean because of a higher inflation premium at a minimum.
The proper comparison is either between the historical returns on both stocks and bonds or the current expected returns on both stocks and bonds. Dividing 1. The two components of the cumulative wealth index are the yield income component and the price change capital gain or loss component. Multiplying these two components together produces cumulative wealth.
Knowing one of these components, the other can be calculated by dividing the known component into the cumulative wealth index number. These relationships are not linear, nor is there any reason why they should be. The risk on common stocks relative to bonds has been more than twice as great. This means that a loss occurred. An index number less than 1. The capital gain component for bonds over some very long periods of time has, in fact, been less than 1.
CFA Purchasing power risk is the risk of inflation reducing the returns on various investments. One should look at the total return of equities on a price level adjusted basis. Interest Rate Risk is a rise in the level of interest rates that depresses the prices of fixed income instruments and frequently causes lower prices for equities. Interest rate volatility and uncertainty are both relevant.
Stock prices tend to go down in anticipation of a downturn in the business cycle. Factors affecting the business cycle include the impact of monetary policy, changes in technology, and changes in supply of raw materials. Attempting to correctly forecast the turning point in a business cycle and the factors that affect a business cycle can reduce the business risk. Market Risk is the general risk associated with fluctuations in the stock market. When the stock market declines, most stocks go down.
While a low beta for a stock or a defensive stock position may reduce the volatility, the stock market has a pervasive influence on individual stocks. Exchange rate risk is the potential decline in investment value due to a decline in the currency in which the shares or bonds are held. Regulatory risk is the risk of an unanticipated change in the regulation of factors that affect investments such as changes in tax policy.
Political risk is the unanticipated change in investment environment due to a change in political parties or a change of view of the current political party. A CFA This is a good opportunity for instructors to point out how TRs for a company can fluctuate violently from year-to-year.
This shows dramatically the risk of common stocks as well as the opportunities for large returns. Refer to Equation for the standard deviation formula. NOTE: We use n-1 in the calculation. There are 85 years for the period Jan. First, raise 3. NOTE: Obviously, we must put the two components of cumulative wealth on the same basis. Converting the geometric mean for the yield component to cumulative wealth, we have 1.
The CWI for this or any other financial asset series is the product of the two components. NOTE: The numbe rs here are made-up, and clearly not realistic. They are for illustration purposes only. The two ways to calculate inflation-adjusted returns are: 1. Using a spreadsheet package, enter the 5 TRs from Table for the years as Return Relatives.
Round the returns to two decimal places. The program should calculate the geometric mean as Taking the fifth root of the wealth index using a calculator produces a result of. The calculated results are: Arithmetic Mean This is because of the good years in the s that were more similar than in a typical 10 or 11 year period. Also, there were only two negative years during this period, whereas the historical norm for many years was 3 negative years out of 10 this did not occur in the s.
Changing the value from This is obviously because the dispersion is reduced. This value moves closer to the mean. First, convert the TRs to Return Relatives:. Multiply these RRs together to obtain. The cumulative wealth for the s was 1. Divide this result by. Take the 5th root of this result to obtain 1. Subtract the 1. Thus, the geometric mean for the last 5 years must be Cumulative wealth for the first 5 years is.
Cumulative wealth for 10 years, given a geometric mean of Take the 4th root of 3. Therefore, the geometric mean of the remaining 4 years must be Knowing these two items, the geometric mean for the total return and the geometric mean for the dividend yield component, we can calculate the other component of total return. The linkage between the geometric mean and the arithmetic mean is given, as an approximation, by Equation As the standard deviation of the series increases, holding the arithmetic mean constant, the geometric mean decreases.
Variability matters! This organization allows the reader to focus on expected return and risk in Chapter 7 where portfolio theory, which is based on expected returns, is developed. Chapter 7 covers basic portfolio theory, allowing students to be exposed to the most important, basic concepts of diversification, Markowitz portfolio theory, and capital market theory relatively early in the semester.
They can then use these concepts throughout the remaining chapters. For example, it is very useful to know the implications of saying that stock A is very highly correlated with stock C, or with the market. Chapter 7 serves as an introduction to portfolio theory, centering on the important building blocks of the Markowitz model.
Students learn about such well known concepts as diversification, efficient portfolios, the risk of the portfolio, covariances, and so forth. The first part of the chapter discusses the estimation of individual security return and risk, which provides the basis for considering portfolio return and risk in the next section.
It begins with a discussion of uncertainty, and develops the concept of a probability distribution. The important calculation of expected value, or, as used here, expected return, is presented, as is the equation for standard deviation. The next part of the chapter presents the Markowitz model along the standard dimensions of efficient portfolios, the inputs needed, and so forth. The discussion first examines expected portfolio return and risk.
The portfolio risk discussion shows why portfolio risk is not a weighted average of individual security risks, which leads directly into a discussion of analyzing portfolio risk. The concept of risk reduction is illustrated for the cases of independent returns the insurance principle , random diversification, and Markowitz diversification. Correlation coefficients and covariances are explained in detail.
This is a very standard discussion. The calculation of portfolio risk is explained in two stages, starting with the two-security case and progressing to the n-security case. Sufficient detail is provided in order for stude nts to really understand the concept of calculating portfolio risk using the Markowitz model, and why the problem of a large number of covariances is significant. Efficient portfolios are explained and illustrated in brief fashion, which sets the stage for a more thorough discussion in Chapter 8.
To fully explain the concepts of expected return and risk for portfolios based on correlations and covariances. To present the basics of Markowitz portfolio theory, with an emphasis on portfolio risk. As such, they can be referred to directly or instructors can substitute their own figures and examples without any loss of continuity. Figure illustrates a discrete and a continuous probability distribution. Figure illustrates the concept of risk reduction when returns are independent.
Risk continues to decline as the number of observations increase. Table illustrates the calculation of standard deviation when probabilities are involved. Table shows the expected standard deviation of annual portfolio returns for various numbers of stocks in a portfolio. Table illustrates the variance-covariance matrix involved in calculating the standard deviation of a portfolio of two securities and of four securities.
The point illustrated is that the number of covariances involved increases quickly as more securities are considered. Box Inserts Box is an interesting discussion of risk, and how best to understand it. It was written by Peter Bernstein, a well-known investments professional. Historical returns are realized returns, such as those reported by Ibbotson Associates and Wilson and Jones in Chapter 6 Table Expected returns are ex ante returns--they are the most likely returns for the future, although they may not actually be realized because of risk.
The expected return for one security is determined from a probability distribution consisting of the likely outcomes, and their associated probabilities, for the security. The weights used are the percentages of total investable funds invested in each security. The basis of portfolio theory is that the whole is not equal to the sum of its parts, at least with respect to risk. Portfolio risk, as measured by the standard deviation, is not equal to the weighted sum of the individual security standard deviations.
The reason, of course, is that the covariances must be accounted for. In the Markowitz model, three factors determine portfolio risk: individual variances, the covariances between securities, and the weights percentage of investable funds given to each security. The Markowitz approach is built around return and risk. The return is, in effect, the mean of the probability distributions, and variance is a proxy for risk. Efficient portfolios, a key concept, are defined on the basis of return and risk--that is, mean and variance.
A stock with a large risk standard deviation could be desirable if it has high negative correlation with other stocks. This will lead to large negative covariances which help to reduce the portfolio risk. The covariance is an absolute measure of risk.
Markowitz was the first to formally develop the concept of portfolio diversification. He showed quantitatively why, and how, portfolio diversification works to reduce the risk of a portfolio to an investor. In effect, he showed that diversification involves the relationships among securities. The expected return for a portfolio of securities is calculated exactly as the expected return for a portfolio of 2 securities--namely, as a weighted average of the individual security returns.
With securities, the weights for each of the securities would be very small. Each security in a portfolio, in terms of dollar amounts invested, is a percentage of the total dollar amount invested in the portfolio. This percentage is a weight, and the general assumption is that these weights sum to 1. The expected return for a portfolio must be between the lowest expected return for a security in the portfolio and the highest expected return for a security in the portfolio.
The exact position depends upon the weights of each of the securities. Naive or random diversification refers to the act of randomly diversifying without regard to relevant investment characteristics such as expected return and industry classification. For 10 securities, there would be n n-1 covariances, or With 30 securities, there would be terms in the variance-covariance matrix. Of these terms, 30 would be variances, and n n - 1 , or , would be covariances. Of the covariances, are unique.
The correlation coefficient is more useful in explaining diversification concepts because it is a relative measure of association between security returns--we always know the boundaries of the association. Investors should typically expect stock and bond returns to be positively related, as well as bond and bill returns.
Note, however, that correlations can change depending upon the time period used to measure the correlation. Stocks and gold have been negatively related, and stocks and real estate are typically negatively related. No—their systematic risk differs, and they should priced in relation to their systematic risk But this may not be the highest return. The choice between BC and CD would depend on the investor's risk-return tradeoff. We will confirm the expected return for the third case shown in the table-- 0.
Each of the other expected returns in column 1 are calculated exactly the same way. We will confirm the portfolio variance for the third case, 0. Each of the other portfolio variances in column 2 are calculated exactly the same way. Knowing the variance for any combination of portfolio weights, the sta ndard deviation is, of course, simply the square root. Thus, for the case of 0.
Chapter 8 concludes this discussion by analyzing the efficient frontier, global diversification considerations, the Single Index Model simplification of the efficient frontier, and asset allocation considerations. This organizational structure allows students to concentrate on the efficient frontier itself because the basic details of the Markowitz analysis were covered in Chapter 7.
Chapter 8 begins by discussing the steps involved in building a portfolio of financial assets. The first step is to use the Markowitz portfolio selection model to choose an efficient portfolio. The efficient set of portfolios is explained in detail, including the necessary information about indifference curves.
This discussion concludes with matching indifference curves preferences with the efficient set possibilities. Important points about the Markowitz analysis that often cause confusion are explained. Alternative methods of obtaining the efficient frontier via the Single Index Model are noted. This model is developed in some detail. Multi- index models are also considered. This discussion includes an analysis of selecting optimal asset classes rather than individual assets with the Markowitz model.
This topic is considered in detail because it is a good illustration of the usefulness of the Markowitz analysis. With relatively few asset classes, as opposed to individual stocks, the Markowitz model can be implemented relatively easily. To outline and describe the steps involved in building an efficient portfolio. To present the concept of asset allocation in detail.
To show how total risk can be broken into two components. Figure illustrates indifference curves. Figure shows how a portfolio on the efficient frontier is selected. Figure illustrates the Single Index Model, including the difference between the actual return and the estimated return.
Figure illustrates the application of the Markowitz technique to asset classes by showing a traditional and nontraditional frontier. Figure illustrates the division of total risk into systematic and nonsystematic risk. Figure illustrates the number of securities needed to adequately diversify. Table shows an example of calculating efficient portfolios using the Markowitz optimization technique. Table shows the geometric mean return and risk combinations for bonds and stocks for the two most recent years periods ending in Box Inserts Box illustrates how one large retirement fund manager explains the value of asset allocation to investors using model portfolios diversified among five asset classes.
The number of covariances needed for securities with the Sharpe model is The vertical axis of the efficient frontier is expected return. The horizontal axis is risk, as measured by standard deviation. There are many portfolios on the Markowitz efficient frontier, depending on how precise one wishes to be. For example, an efficient frontier could be calculated using one percentage point intervals for expected return, or one-tenth of a percent intervals.
Regardless, there are many portfolios on the efficient frontier. The Markowitz efficient set consists of those portfolios dominating the feasible set of portfolios that could be attained. It is described by a curve, as opposed to a straight line. Rational investors seek efficient portfolios because these portfolios promise maximum expected return for a specified level of risk, or minimum risk for a specified expected return.
An indifference curve describes investor preferences for risk and return. Each indifference curve represents all combinations of portfolios that are equally desirable to a particular investor given the return and risk involved. Thus, an investor's risk aversion would be reflected in his or her indifference curve.
The curves for all risk-averse investors will be upward-sloping, but the shapes of the curves can vary depending on risk preferences. In recent years, the correlations among stocks of different countries have gone up. These correlations increased significantly starting in The immediate benefits of risk reduction by adding stocks with lower correlations have been reduced.
Investors should not ignore international diversification. The correlations could become somewhat lower in the future, although as the world economy becomes more integrated, this is less and less likely. However, there should always be opportunities for investors in the stocks of other countries, and they should be looking for these opportunities. The purpose of the Single Index Model is to simplify the calculations needed in the Markowitz model in order to obtain the efficient set of portfolios.
This is accomplished by reducing the number of covariances to the number of securities being considered, which in turn reduces the total number of pieces of data needed to carry out the analysis. The key assumption of the SIM is that securities are related only in their common response to the return on the market. The two components are market risk systematic risk plus company-specific risk nonsystematic risk. Multi- index models were found not to work better ex-ante, which is the more important consideration for investors.
It is believed by many to be the most important decision an investor can make, and this is particularly true for large institutional investors. When more asset classes are involved, the efficient frontier often improves. This is because there are more opportunities for low correlations between asset classes, and even negative correlations. As we add securities to a portfolio, the total risk of the portfolio declines rapidly, but then levels off and at some point will not decline a noticeable amount.
Diversification works extremely well in reducing part of the risk of a portfolio, but it cannot eliminate all of the risk because diversification cannot eliminate market risk. There are clearly limits to diversification because it cannot eliminate market risk. The effects of diversification are both immediate and dramatic.
The traditional beliefs about diversification, popularized by Evans and Archer in the s, was that something like securities provided most of the diversification benefits that could be obtained. In round numbers, call it 20 stocks. In round numbers, call it 50 stocks. Chapter 9 also contains some important concepts relevant to a better understanding of s uch topics as systematic and nonsystematic risk and beta.
The first part of Chapter 9 outlines the necessary assumptions to derive capital market theory and introduces the concept of equilibrium in the capital markets. Important related concepts are introduced and discussed, primarily the market portfolio. Both its importance and its composition are considered. Using the concepts developed to this point, the equilibrium risk--return tradeoff is analyzed in detail.
The capital market line is developed and illustrated. This line applies to efficient portfolios, with the slope of the line showing the market price of risk for efficient portfolios. The equation is explained, and certain points about the line are emphasized. The security market line is developed next. The equation is developed, and beta as a measure of volatility is considered in some detail.
The process of identifying undervalued and overvalued securities using the SML follows this discussion. Problems in estimating the SML are described, and this leads into a detailed discussion of the accuracy of beta estimates and tests of the CAPM. The characteristic line is also explained. The chapter concludes with a thorough discussion of Arbitrage Pricing Theory in terms of what beginners need to know.
Although this concept probably has not advanced in terms of being widely used in the investments world as much as some have predicted, it is an important development that can be used for discussion purposes if the instructor so chooses. Factor models are explained as part of this discussion. A reasonably detailed discussion on understanding the APT is included. Consistent with the emphasis in this text, the use of APT in investment decisions is considered.
Students should be able to see how the model could be applied in actual practice. To discuss related issues such as what beta measures and the problems with estimating beta, systematic and nonsystematic risk, problems in testing asset pricing models, and so forth. To provide the necessary information about APT, including what it means and how it could be used to make investment decisions.
As such, they are interchangeable with virtually any other comparable figures that an instructor may already have developed. They are not unique although they are keyed to the discussion in the text in terms of points on the graph, etc. Figure shows the Markowitz efficient frontier and the borrowing and lending possibilities resulting from introducing a risk-free asset. Figure shows the efficient frontier with a risk-free borrowing and lending rate.
The important point is that the Markowitz efficient frontier, which is an arc, now becomes a straight line. Figure shows the capital market line and the components of its slope. It is important to emphasize that standard deviation is on the horizontal axis and to emphasize what the slope of this line measures. Figure illustrates different betas—the higher the beta, the steeper the line. Figure shows the SML. The emphasis now is on beta as the measure of risk on the horizontal axis.
Figure illustrates how an overvalued and an undervalued security can be identified by using the SML. It could be pointed out here that in some sense this is how to think of modern security analysis--the search for securities not on the equilibrium tradeoff that should exist. Figure shows the characteristic line for Coca-Cola, using monthly data. There are no tables in Chapter 9. Box Inserts There are no box inserts in Chapter 9.
Lending possibilities change part of the Markowitz efficient frontier from an arc to a straight line. The straight line extends from RF, the risk- free rate of return, to M, the market portfolio. This new opportunity set, which dominates the old Markowitz efficient frontier, provides investors with various combinations of the risky asset portfolio M and the riskless asset. Borrowing possibilities complete the transformation of the Markowitz efficient frontier into a straight line extending from RF through M and beyond.
Investors can use borrowed funds to lever their portfolio position beyond point M, increasing the expected return and risk beyond that available at point M. Under the CAPM, all investors hold the market portfolio because it is the optimal risky portfolio. Because it produces the highest attainable return for any given risk level, all rational investors will seek to be on the straight line tangent to the efficient set at the steepest point, which is the market portfolio.
In theory, the market portfolio portfolio M is the portfolio of all risky assets, both financial and real, in their proper proportions. Such a portfolio would be completely diversified; however, it is a risky portfolio. In equilibrium, all risky assets must be in portfolio M because all investors are assumed to hold the same risky portfolio. If they do, in equilibrium this portfolio must be the market portfolio consisting of all risky assets. The slope of the CML is the market price of risk for efficient portfolios; that is, it indicates the equilibrium price of risk in the market.
It shows the additional return that the market demands for each percentage increase in a portfolio's risk. The CML extends from RF, the risk-free asset, through M, the market portfolio of all risky securities weighted by their respective market values. This portfolio is efficient, and the CML consists of combinations of this portfolio and the risk-free asset.
All asset combinations on the CML are efficient portfolios consisting of M and the risk-free asset. The contribution of each security to the standard deviation of the market portfolio depends on the size of its covariance with the market portfolio. Therefore, investors consider the relevant measure of risk for a security to be its covariance with the market portfolio. Using some methodology such as the dividend valuation model to estimate the expected returns for securities, investors can compare these expected returns to the required returns obtained from the SML.
Securities whose expected returns plot above the SML are undervalued because they offer more expected return than investors require; if they plot below the SML, they are overvalued because they do not offer enough expected return for their level of risk. When a security is recognized by investors as undervalued, they will purchase it because it offers more return than required, given its risk.
This demand will drive up the price of the security as more of it is purchased. The return will be driven down until it reaches the level indicated by the SML as appropriate for its degree of risk. The difficulties involved in estimating a security's beta include deciding on the number of observations and the length of the periods to use in calculating the beta.
The regression estimate of beta is only an estimate of the true beta, and subject to error. Also, the beta is not perfectly stationary over time. The major problem in testing capital market theory is that the theory is formulated ex- ante, concerning what is expected to happen. Costs are forever. The lower your costs, the greater your share of an investment's return. And research suggests that lower-cost investments have tended to outperform higher-cost alternatives.
To hold onto even more of your return, manage for tax efficiency. You can't control the markets, but you can control the bite of costs and taxes. Investing can provoke strong emotions. In the face of market turmoil, some investors may find themselves making impulsive decisions or, conversely, becoming paralyzed, unable to implement an investment strategy or rebalance a portfolio as needed. Discipline and perspective can help them remain committed to a long-term investment program through periods of market uncertainty.
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