This study session introduces the common probability distributions used to describe the behavior of random variables, such as asset prices and returns. How to estimate measures of a population (mean, standard deviation) based on a population sample is shown. A framework for hypothesis testing, used for validating dataset hypotheses, follows, along with techniques to accept or reject the assumed hypothesis. The session ends with coverage of technical analysis, a set of tools that uses asset price, trading volume, and other similar data for making investment decisions.

In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

a set is open if it doesn't contain any of its boundary points

La contestation de la Trinité est d’abord, bien entendu, le fait des deux autres religions monothéistes, à savoir le judaïsme et l’islam. C’est là une contestation externe au christianisme, contestation menée au nom du monothéisme justement. À en croire ceux qui s’en font l’écho, embrasser la doctrine trinitaire revient à renoncer à la confession de l’unicité de Dieu. Par suite, l’introduction, au sein du christianisme, de la doctrine de la Trinité trahit le fait qu’il a cessé d’être monothéiste, quoi qu’il en dise.

Trust in the investment profession is only achieved if those practicing within the industry adhere to the highest levels of ethical conduct and behavior. The CFA Institute Code of Ethics and Standards of Professional Conduct (Code and Standards) serve as the ethical foundation for the CFA Institute self-regulatory program.

The Standards of Practice Handbook provides practical application of the Code and Standards by explaining the purpose and scope of each standard, presenting recommended procedures for compliance, and providing examples of each standard in practice.

The Global Investment Performance Standards (GIPS®) establish global standards for performance reporting by investment managers. By providing a consistent set of standards and methodology, GIPS facilitate the fair and accurate comparison of managers around the world, while minimizing the potential for ambiguous or misleading performance reporting practices.

As a candidate in the CFA Program, you are both expected and required to meet high ethical standards. This reading introduces ideas and concepts that will help you understand the importance of ethical behavior in the investment industry. You will be introduced to various types of ethical issues within the investment profession and learn about the CFA Institute Code of Ethics. Subsequently, you will be introduced to a framework as a way to approach ethical decision making.

Imagine that you are employed in the research department of a large financial services firm. You and your colleagues spend your days researching, analyzing, and valuing the shares of publicly traded companies and sharing your investment recommendations with clients. You love your work and take great satisfaction in knowing that your recommendations can help the firm’s investing clients make informed investment decisions that will help them meet their financial goals and improve their lives.

Several months after starting at the firm, you learn that an analyst at the firm has been terminated for writing and publishing research reports that misrepresented the fundamental risks of some companies to investors. You learn that the analyst wrote the reports with the goal of pleasing the management of the companies that were the subjects of the research reports. He hoped that these companies would hire your firm’s investment banking division for its services and he would be rewarded with large bonuses for helping the firm increase its investment banking fees. Some clients bought shares based on the analyst’s reports and suffered losses. They posted stories on the internet about their losses and the misleading nature of the reports. When the media investigated and published the story, the firm’s reputation for investment research suffered. Investors began to question the firm’s motives and the objectivity of its research recommendations. The firm’s investment clients started to look elsewhere for investment advice, and company clients begin to transfer their business to firms with untarnished reputations. With business declining, management is forced to trim staff. Along with many other hard-working colleagues, you lose your job—through no fault of your own.

Imagine how you would feel in this situation. Most people would feel upset and resentful that their hard and honest work was derailed by someone else’s unethical behavior. Yet, this type of scenario is not uncommon. Around the world, unsuspecting employees at such companies as SAC Capital, Stanford Financial Group, Everbright Securities, Enron, Satyam Computer Services, Arthur Andersen, and other large companies have experienced such career setbacks when someone else’s actions destroyed trust in their companies and industries.

Businesses and financial markets thrive on trust—defined as a strong belief in the reliability of a person or institution. In a 2013 study on trust, investors indicated that to earn their trust, the top three attributes of an investment manager should be that it (1) has transparent and open business practices, (2) takes responsible actions to address an issue or crisis, and (3) has ethical business practices. Although these attributes are valued by customers and clients in any industry, this reading will explore why they are of particular importance to the investment industry.

People may think that ethical behavior is simply about following laws, regulations, and other rules, but throughout our lives and careers we will encounter situations in which there is no definitive rule that specifies how to act, or the rules that exist may be unclear or even in conflict with each other. Responsible people, including investment professionals, must be willing and able to identify potential ethical issues and create solutions to them even in the absence of clearly stated rules.

The Standards of Practice Handbook (Handbook) provides guidance to the people who grapple with real ethical dilemmas in the investment profession on a daily basis; the Handbook addresses the professional intersection where theory meets practice and where the concept of ethical behavior crosses from the abstract to the concrete. The Handbook is intended for a diverse and global audience: CFA Institute members navigating ambiguous ethical situations; supervisors and direct/indirect reports determining the nature of their responsibilities to each other, to existing and potential clients, and to the broader financial markets; and candidates preparing for the Chartered Financial Analyst (CFA) examinations.

Recent events in the global financial markets have tested the ethical mettle of financial market participants, including CFA Institute members. The standards taught in the CFA Program and by which CFA Institute members and candidates must abide represent timeless ethical principles and professional conduct for all market conditions. Through adherence to these standards, which continue to serve as the model for ethical behavior in the investment professional globally, each market participant does his or her part to improve the integrity and efficient operations of the financial markets.

The Handbook provides guidance in understanding the interconnectedness of the aspirational and practical principles and provisions of the Code of Ethics and Standards of Professional Conduct (Code and Standards). The Code contains high-level aspirational ethical principles that drive members and candidates to create a positive and reputable investment profession. The Standards contain practical ethical principles of conduct that members and candidates must follow to achieve the broader industry expectations. However, applying the principles individually may not capture the complexity of ethical requirements related to the investment industry. The Code and Standards should be viewed and interpreted as an interwoven tapestry of ethical requirements. Through members’ and candidates’ adherence to these principles as a whole, the integrity of and trust in the capital markets are improved.

I. WHY WERE THE GIPS STANDARDS CREATED?

Institutions and individuals are constantly scrutinizing past investment performance returns in search of the best manager to achieve their investment objectives.

In the past, the investment community had great difficulty making meaningful comparisons on the basis of accurate investment performance data. Several performance measurement practices hindered the comparability of performance returns from one firm to another, while others called into question the accuracy and credibility of performance reporting overall. Misleading practices included:

• Representative Accounts: Selecting a top-performing portfolio to represent the firm’s overall investment results for a specific mandate.

• Survivorship Bias: Presenting an “average” performance history that excludes portfolios whose poor performance was weak enough to result in termination of the firm.

• Varying Time Periods: Presenting performance for a selected time period during which the mandate produced excellent returns or out-performed its benchmark—making comparison with other firms’ results difficult or impossible.

Making a valid comparison of investment performance among even the most ethical investment management firms was problematic. For example, a pension fund seeking to hire an investment management firm might receive proposals from several firms, all using different methodologies for calculating their results.

The GIPS standards are a practitioner-driven set of ethical principles that establish a standardized, industry-wide approach for investment firms to follow in calculating and presenting their historical investment results to prospective clients. The GIPS standards ensure fair representation and full disclosure of investment performance. In other words, the GIPS standards lead investment management firms to avoid misrepresentations of performance and to communicate all relevant information that prospective clients should know in order to evaluate past results.

Preamble—Why Is a Global Investment Performance Standard Needed?

Standardized Investment Performance

Financial markets and the investment management industry have become increasingly global in nature. The growth in the types and number of financial entities, the globalization of the investment process, and the increased competition among investment management firms demonstrate the need to standardize the calculation and presentation of investment performance.

Global Passport

Asset managers and both existing and prospective clients benefit from an established global standard for calculating and presenting investment performance. Investment practices, regulation, performance measurement, and reporting of performance vary considerably from country to country. By adhering to a global standard, firms in countries with minimal or no investment performance standards will be able to compete for business on an equal footing with firms from countries with more developed standards. Firms from countries with established practices will have more confidence in being fairly compared with local firms when competing for business in countries that have not previously adopted performance standards. Performance standards that are accepted globally enable investment firms to measure and present their investment performance so that investors can readily compare investment performance among firms.

Investor Confidence

Investment managers that adhere to investment performance standards help assure investors that the firm’s investment performance is complete and fairly presented. Both prospective and existing clients of investment firms benefit from a global investment performance standard by having a greater degree of confidence in the performance information presented to them.

Objectives

The establishment of a voluntary global investment performance standard leads to an accepted set of best practices for calculating and presenting investment performance that is readily comparable among investment firms, regardless of geographic location. These standards also facilitate a dialogue between investment firms and their existing and prospective clients regarding investment performance.

The goals of the GIPS Executive Committee are:

• To establish investment industry best practices for calculating and presenting investment performance that promote investor interests and instill investor confidence;

• To obtain worldwide acceptance of a single standard for the calculation and presentation of investment performance based on the principles of fair representation and full disclosure;

• To promote the use of accurate and consistent investment performance data;

• To encourage fair, global competition among investment firms without creating barriers to entry; and

• To foster the notion of industry “self-regulation” on a global basis.

Overview

Key features of the GIPS standards include the following:

• The GIPS standards are ethical standards for investment performance presentation to ensure fair representation and full disclosure of investment performance. In order to claim compliance, firms must adhere to the requirements included in the GIPS standards.

• Meeting the objectives of fair representation and full disclosure is likely to require more than simply adhering to the minimum requirements of the GIPS standards. Firms should also adhere to the recommendations to achieve best practice in the calculation and presentation of performance.

• The GIPS standards require firms to include all actual, discretionary, fee-paying portfolios in at least one composite defined by investment mandate, objective, or strategy in order to pre

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As individuals, we often face decisions that involve saving money for a future use, or borrowing money for current consumption. We then need to determine the amount we need to invest, if we are saving, or the cost of borrowing, if we are shopping for a loan. As investment analysts, much of our work also involves evaluating transactions with present and future cash flows. When we place a value on any security, for example, we are attempting to determine the worth of a stream of future cash flows. To carry out all the above tasks accurately, we must understand the mathematics of time value of money problems. Money has time value in that individuals value a given amount of money more highly the earlier it is received. Therefore, a smaller amount of money now may be equivalent in value to a larger amount received at a future date. The time value of money as a topic in investment mathematics deals with equivalence relationships between cash flows with different dates. Mastery of time value of money concepts and techniques is essential for investment analysts.

The reading1 is organized as follows: Section 2 introduces some terminology used throughout the reading and supplies some economic intuition for the variables we will discuss. Section 3 tackles the problem of determining the worth at a future point in time of an amount invested today. Section 4 addresses the future worth of a series of cash flows. These two sections provide the tools for calculating the equivalent value at a future date of a single cash flow or series of cash flows. Sections 5 and 6 discuss the equivalent value today of a single future cash flow and a series of future cash flows, respectively. In Section 7, we explore how to determine other quantities of interest in time value of money problems.

As investment analysts, much of our work includes evaluating transactions involving present and future cash flows. In the reading on the time value of money (TVM), we presented the mathematics needed to solve those problems and illustrated the techniques for the major problem types. In this reading we turn to applications. Analysts must master the numerous applications of TVM or discounted cash flow analysis in equity, fixed income, and derivatives analysis as they study each of those topics individually. In this reading, we present a selection of important TVM applications: net present value and internal rate of return as tools for evaluating cash flow streams, portfolio return measurement, and the calculation of money market yields. Important in themselves, these applications also introduce concepts that reappear in many other investment contexts.

The reading is organized as follows. Section 2 introduces two key TVM concepts, net present value and internal rate of return. Building on these concepts, Section 3 discusses a key topic in investment management, portfolio return measurement. Investment managers often face the task of investing funds for the short term; to understand the choices available, they need to understand the calculation of money market yields. The reading thus concludes with a discussion of that topic in Section 4.

Statistical methods provide a powerful set of tools for analyzing data and drawing conclusions from them. Whether we are analyzing asset returns, earnings growth rates, commodity prices, or any other financial data, statistical tools help us quantify and communicate the data’s important features. This reading presents the basics of describing and analyzing data, the branch of statistics known as descriptive statistics. The reading supplies a set of useful concepts and tools, illustrated in a variety of investment contexts. One theme of our presentation, reflected in the reading’s title, is the demonstration of the statistical methods that allow us to summarize return distributions.1 We explore four properties of return distributions:

• where the returns are centered (central tendency);

• how far returns are dispersed from their center (dispersion);

• whether the distribution of returns is symmetrically shaped or lopsided (skewness); and

• whether extreme outcomes are likely (kurtosis).

These same concepts are generally applicable to the distributions of other types of data, too.

The reading is organized as follows. After defining some basic concepts in Section 2, in Sections 3 and 4 we discuss the presentation of data: Section 3 describes the organization of data in a table format, and Section 4 describes the graphic presentation of data. We then turn to the quantitative description of how data are distributed: Section 5 focuses on measures that quantify where data are centered, or measures of central tendency. Section 6 presents other measures that describe the location of data. Section 7 presents measures that quantify the degree to which data are dispersed. Sections 8 and 9 describe additional measures that provide a more accurate picture of data. Section 10 provides investment applications of concepts introduced in Section 5.

All investment decisions are made in an environment of risk. The tools that allow us to make decisions with consistency and logic in this setting come under the heading of probability. This reading presents the essential probability tools needed to frame and address many real-world problems involving risk. We illustrate how these tools apply to such issues as predicting investment manager performance, forecasting financial variables, and pricing bonds so that they fairly compensate bondholders for default risk. Our focus is practical. We explore in detail the concepts that are most important to investment research and practice. One such concept is independence, as it relates to the predictability of returns and financial variables. Another is expectation, as analysts continually look to the future in their analyses and decisions. Analysts and investors must also cope with variability. We present variance, or dispersion around expectation, as a risk concept important in investments. The reader will acquire specific skills in using portfolio expected return and variance.

The basic tools of probability, including expected value and variance, are set out in Section 2 of this reading. Section 3 introduces covariance and correlation (measures of relatedness between random quantities) and the principles for calculating portfolio expected return and variance. Two topics end the reading: Bayes’ formula and outcome counting. Bayes’ formula is a procedure for updating beliefs based on new information. In several areas, including a widely used option-pricing model, the calculation of probabilities involves defining and counting outcomes. The reading ends with a discussion of principles and shortcuts for counting.

In nearly all investment decisions we work with random variables. The return on a stock and its earnings per share are familiar examples of random variables. To make probability statements about a random variable, we need to understand its probability distribution. A probability distributionspecifies the probabilities of the possible outcomes of a random variable.

In this reading, we present important facts about four probability distributions and their investment uses. These four distributions—the uniform, binomial, normal, and lognormal—are used extensively in investment analysis. They are used in such basic valuation models as the Black–Scholes–Merton option pricing model, the binomial option pricing model, and the capital asset pricing model. With the working knowledge of probability distributions provided in this reading, you will also be better prepared to study and use other quantitative methods such as hypothesis testing, regression analysis, and time-series analysis.

After discussing probability distributions, we end the reading with an introduction to Monte Carlo simulation, a computer-based tool for obtaining information on complex problems. For example, an investment analyst may want to experiment with an investment idea without actually implementing it. Or she may need to price a complex option for which no simple pricing formula exists. In these cases and many others, Monte Carlo simulation is an important resource. To conduct a Monte Carlo simulation, the analyst must identify risk factors associated with the problem and specify probability distributions for them. Hence, Monte Carlo simulation is a tool that requires an understanding of probability distributions.

Before we discuss specific probability distributions, we define basic concepts and terms. We then illustrate the operation of these concepts through the simplest distribution, the uniform distribution. That done, we address probability distributions that have more applications in investment work but also greater complexity.

Each day, we observe the high, low, and close of stock market indexes from around the world. Indexes such as the S&P 500 Index and the Nikkei-Dow Jones Average are samples of stocks. Although the S&P 500 and the Nikkei do not represent the populations of US or Japanese stocks, we view them as valid indicators of the whole population’s behavior. As analysts, we are accustomed to using this sample information to assess how various markets from around the world are performing. Any statistics that we compute with sample information, however, are only estimates of the underlying population parameters. A sample, then, is a subset of the population—a subset studied to infer conclusions about the population itself.

This reading explores how we sample and use sample information to estimate population parameters. In the next section, we discuss sampling—the process of obtaining a sample. In investments, we continually make use of the mean as a measure of central tendency of random variables, such as return and earnings per share. Even when the probability distribution of the random variable is unknown, we can make probability statements about the population mean using the central limit theorem. In Section 3, we discuss and illustrate this key result. Following that discussion, we turn to statistical estimation. Estimation seeks precise answers to the question “What is this parameter’s value?”

The central limit theorem and estimation are the core of the body of methods presented in this reading. In investments, we apply these and other statistical techniques to financial data; we often interpret the results for the purpose of deciding what works and what does not work in investments. We end this reading with a discussion of the interpretation of statistical results based on financial data and the possible pitfalls in this process.

Analysts often confront competing ideas about how financial markets work. Some of these ideas develop through personal research or experience with markets; others come from interactions with colleagues; and many others appear in the professional literature on finance and investments. In general, how can an analyst decide whether statements about the financial world are probably true or probably false?

When we can reduce an idea or assertion to a definite statement about the value of a quantity, such as an underlying or population mean, the idea becomes a statistically testable statement or hypothesis. The analyst may want to explore questions such as the following:

• Is the underlying mean return on this mutual fund different from the underlying mean return on its benchmark?

• Did the volatility of returns on this stock change after the stock was added to a stock market index?

• Are a security’s bid-ask spreads related to the number of dealers making a market in the security?

• Do data from a national bond market support a prediction of an economic theory about the term structure of interest rates (the relationship between yield and maturity)?

To address these questions, we use the concepts and tools of hypothesis testing. Hypothesis testing is part of statistical inference, the process of making judgments about a larger group (a population) on the basis of a smaller group actually observed (a sample). The concepts and tools of hypothesis testing provide an objective means to gauge whether the available evidence supports the hypothesis. After a statistical test of a hypothesis we should have a clearer idea of the probability that a hypothesis is true or not, although our conclusion always stops short of certainty. Hypothesis testing has been a powerful tool in the advancement of investment knowledge and science. As Robert L. Kahn of the Institute for Social Research (Ann Arbor, Michigan) has written, “The mill of science grinds only when hypothesis and data are in continuous and abrasive contact.”

The main emphases of this reading are the framework of hypothesis testing and tests concerning mean and variance, two quantities frequently used in investments. We give an overview of the procedure of hypothesis testing in the next section. We then address testing hypotheses about the mean and hypotheses about the differences between means. In the fourth section of this reading, we address testing hypotheses about a single variance and hypotheses about the differences between variances. We end the reading with an overview of some other important issues and techniques in statistical inference.

Technical analysis has been used by traders and analysts for centuries, but it has only recently achieved broad acceptance among regulators and the academic community. This reading gives a brief overview of the field, compares technical analysis with other schools of analysis, and describes some of the main tools in technical analysis. Some applications of technical analysis are subjective. That is, although certain aspects, such as the calculation of indicators, have specific rules, the interpretation of findings is often subjective and based on the long-term context of the security being analyzed. This aspect is similar to fundamental analysis, which has specific rules for calculating ratios, for example, but introduces subjectivity in the evaluation phase.