on 05-Feb-2018 (Mon)

The most regularly tra ded structure in the inflation-linke d swaps market, and particularly in the inter-dealer market, is the zer o coupon inflation swap. One counterparty agre es to pay the cumulative percentage increase in the price index over the tenor of the s wap (with some lag on the referenc e index, similar to cash securities) , and the other pays a comp ounded fixed rate. There ar e no exchanges until the maturity of the swap, or in other words it is a zero coupon transaction

Riemann's definition of integral starts with the construction of a sequence of easily calculated areas that converge to the integral of a given function.

We say that the Lebesgue integral of the measurable function f exists, or is defined if at least one of and is finite:

The formula for the dot product of the vectors is \( uv = \|u\| \|v \| \cos θ. \)

if a and b are orthogonal, then the angle between them is 90° and

Calculus has two major branches,

1. differential calculus (concerning rates of change and slopes of curves),^[2] and
2. integral calculus (concerning accumulation of quantities and the areas under and between curves).^[3]

These two branches are related to each other by the fundamental theorem of calculus.

Calculus of variations is a field of mathematical analysis that

1. uses variations, which are small changes in functions and functionals, to
2. find maxima and minima of functionals, which are mappings from a set of functions to the real numbers.

elementary calculus is about infinitesimally small changes in the values of functions without changes in the function itself, calculus of variations is about infinitesimally small changes in the function itself, which are called variations.

Composition of the Board of Directors A board of directors is the central pillar of the governance structure, serves as the link between shareholders and managers, and acts as the shareholders' internal monitoring tool within the company. The structure and composition of a board of directors vary across countries and companies. The number of directors may vary, and the board typically includes a mix of expertise levels, backgrounds, and competencies. Board members must have extensive experience in business, education, the professions and/or public service so they can make informed decisions about the company's future. If directors lack the skills, knowledge and expertise to conduct a meaningful review of the company's activities, and are unable to conduct in-depth evaluations of the issues affecting the company's business, they are more likely to defer to management when making decisions. Executive (internal) directors are employed by the company and are typically members of senior management. Non-executive (external) directors have limited involvement in daily operations but serve an important oversight role. In a classified or staggered board, directors are typically elected in two or more classes, serving terms greater than one year. Proponents argue that by staggering the election of directors, a certain level of continuity and skill is maintained. However, staggered terms make it more difficult for shareholders to make fundamental changes to the composition and behavior of the board and could result in a permanent impairment of long-term shareholder value.

Stakeholder relationships and corporate governance are continually shaped and influenced by a variety of market and non-market factors.

Market Factors
Shareholder engagement involves a company's interactions with its shareholders. It can provide benefits that include building support against short-term activist investors, countering negative recommendations from proxy advisory firms, and receiving greater support for management's position.

Shareholder activism encompasses a range of strategies that may be used by shareholders seeking to compel a company to act in a desired manner. It can take any of several forms: proxy battles, public campaigns, shareholder resolutions, litigation, and negotiations with management.

Corporate takeovers can happen in different ways: proxy contest or proxy fight, tender offer, hostile takeover, etc. The justification for the use of various anti-takeover defenses should rest on the support of the majority of shareholders and on the demonstration that preservation of the integrity of the company is in the long-term interests of shareholders.

Non-Market Factors

These factors include the legal environment, the media, and the corporate governance industry itself.

In portfolio management Fixed-income securities are a way by which investors can prepare to fund, with some degree of safety, known future obligations such as tuition payments or pension obligations.

The correlations of fixed-income securities with common shares vary, but adding fixed-income securities to portfolios including common shares is usually an effective way of obtaining diversification benefits.

Executive (internal) directors are employed by the company and are typically members of senior management. Non-executive (external) directors have limited involvement in daily operations but serve an important oversight role.

In a classified or staggered board, directors are typically elected in two or more classes, serving terms greater than one year. Proponents argue that by staggering the election of directors, a certain level of continuity and skill is maintained. However, staggered terms make it more difficult for shareholders to make fundamental changes to the composition and behavior of the board and could result in a permanent impairment of long-term shareholder value.

A staggered board of directors (also known as a classified board) is a board that is made up of different classes of directors. Usually, there are three classes, with each class serving for a different term length than the other. Elections for the directors of staggered boards usually happen on an annual basis. At each election, shareholders are asked to vote to fill whatever positions of the board are vacant, or up for re-election. Terms of service for elected directors vary, but one-, three- and five-year terms are common.

Information on corporate governance policies and board composition can be found in a public company's proxy statement. Generally, proponents of staggered boards sight two main advantages that staggered boards have over traditionally elected boards: board continuity and anti-takeover provisions - hostile acquirers have a difficult time gaining control of companies with staggered boards. Opponents of staggered boards, however, argue that they are less accountable to shareholders than annually elected boards and that staggering board terms tends to breed a fraternal atmosphere inside the boardroom that serves to protect the interests of management above those of shareholders. (To learn more, read Governance Pays, The Basics Of Corporate Structure and What Are Corporate Actions?)

A structure for a board of directors in which a portion of the directors serve for different term lengths, depending on their particular classification. Under a classified system, directors serve terms usually lasting between one and eight years; longer terms are often awarded to more senior board positions (i.e. chairman of the corporate governance committee).

Classified boards are often referred to as "staggered boards", although staggered boards and classified boards have somewhat different structures. Staggered boards need not be classified, but classified boards are inherently staggered.

A proxy statement is a document containing the information the Securities and Exchange Commission (SEC) requires companies to provide to shareholders so shareholders can make informed decisions about matters that will be brought up at an annual or special stockholder meeting. Issues covered in a proxy statement can include proposals for new additions to the board of directors, information on directors' salaries, information on bonus and options plans for directors, and any declarations made by the company's management.

Stakeholder relationships and corporate governance are continually shaped and influenced by a variety of market and non-market factors.

Market Factors
Shareholder engagement involves a company's interactions with its shareholders. It can provide benefits that include building support against short-term activist investors, countering negative recommendations from proxy advisory firms, and receiving greater support for management's position.

Shareholder activism encompasses a range of strategies that may be used by shareholders seeking to compel a company to act in a desired manner. It can take any of several forms: proxy battles, public campaigns, shareholder resolutions, litigation, and negotiations with management.

Corporate takeovers can happen in different ways: proxy contest or proxy fight, tender offer, hostile takeover, etc. The justification for the use of various anti-takeover defenses should rest on the support of the majority of shareholders and on the demonstration that preservation of the integrity of the company is in the long-term interests of shareholders.

Non-Market Factors

These factors include the legal environment, the media, and the corporate governance industry itself.

All businesses and investors manage risk in the choices they make, even if not conciously. Business and investing are about allocating resources and capital to chosen risks. In their decision process, businesses and investors may take steps to avoid some risks, pursue the risks that provide the highest rewards, and measure and mitigate their exposure to these risks as necessary. Risk management processes and tools make difficult business and financial problems easier to address. Risk is not just a matter of fate; it can be actively controled with decisions, within a risk management framework. Risk is an integral part of the business or investment process. Even in the earliest models of modern portfolio theory, such as mean–variance portfolio optimization and the capital asset pricing model, investment return is linked directly to risk but requires that risk be managed optimally. Proper identification and measurement of risk, and keeping risks aligned with the goals of the enterprise, are key factors in managing businesses and investments. Good risk management results in a higher chance of a preferred outcome—more value for the company or portfolio or more utility for the individual.

Portfolio managers need to be familiar with risk management not only to improve the portfolio’s risk–return outcome, but also because of two other ways in which they use risk management at an enterprise level. First, they help to manage their own companies that have their own enterprise risk issues. Second, many portfolio assets are claims on companies that have risks. Portfolio managers need to evaluate the companies’ risks and how those companies are addressing them.

This reading takes talks about the risk management of enterprises in general and portfolio risk management. The principles underlying portfolio risk management are generally applicable to the risk management of financial and non-financial institutions as well.

The concept of risk management applies to individuals. Although many large entities formally practice risk management, most individuals practice it informally and disorderly, oftentimes responding to risk events after they occur, and they ignore more subtle risks often. Many individuals simply do not view risk management as a formal, systematic process that would help them achieve not only their financial goals but also the ultimate end result of happiness, or maximum utility as economists like to call it, but they should.

Although the primary focus of this reading is on institutions, we will also cover risk management as it applies to individuals. We will show that many common themes underlie risk management—themes that are applicable to both organizations and individuals.

Although often viewed as defensive, risk management is a valuable offensive weapon in the manager’s arsenal. In the quest for preferred outcomes, such as higher profit, returns, or share price, management does not usually get to choose the outcomes but does choose the risks it takes in pursuit of those outcomes. The choice of which risks to undertake through the allocation of its scarce resources is the key tool available to management. An organization with a comprehensive risk management culture in place, in which risk is integral to every key strategy and decision, should perform better in the long-term, in good times and bad, as a result of better decision making.

The fact that all businesses and investors engage in risky activities (i.e., activities with uncertain outcomes) raises a number of important questions. The questions that this reading will address include the following:

• What is risk management, and why is it important?

• What risks does an organization (or individual) face in pursuing its objectives?

• How are an entity’s goals affected by risk, and how does it make risk management decisions to produce better results?

• How does risk governance guide the risk management process and risk budgeting to integrate an organization’s goals with its activities?

• How does an organization measure and evaluate the risks it faces, and what tools does it have to address these risks?

The answers to these questions collectively help to define the process of risk management.

Ethics is the study of moral principles used to make good choices.

• Ethical principles are beliefs regarding what is good, acceptable, or responsible behavior, and what is bad, unacceptable, or forbidden behavior. They provide guidance for our behavior.

• Ethical conduct is behavior that follows moral principles.

• Ethical actions are those actions that are perceived as beneficial and conform to

  the ethical expectations of society.

Ethics encompass a set of moral principles (code of ethics) and standards of conduct that provide guidance for our behavior. Violations can harm the community in a variety of ways.

A profession is:

• based on specialized knowledge and skills.

• based on service to others.

• practiced by members who share and agree to adhere to a common code of

  ethics.

A profession's code of ethics:

• communicates the shared principles and expected behaviors of its members.

• generates confidence not only among members of the organization but also

  among non-members (clients, prospective clients, and/or the general public).

A profession may adopt standards of conduct to enhance and clarify the code of ethics.

Challenges to ethical behavior include:

• the overconfidence bias. Most of us simply assume that we are good people and will therefore make sound ethical decisions. This overconfidence in one's own moral compass can lead to making decisions without serious ethical reflection.

• situational influences, which are external factors such as environmental or cultural elements. They can motivate individuals to act in their short-term interests without recognizing the long-term risks or consequences for themselves and others. Examples include financial rewards, prestige, and loyalty to employer and colleagues.

High ethical standards are important for the investment industry and investment professionals. This is because the industry is built almost entirely on trust. Trust is important in the investment industry for several reasons:

• The nature of the client relationship

• Differences in knowledge and access to information

• The nature of investment products and services

Clients must trust investment professionals to use their specialized skills and knowledge to serve clients and protect client assets. All stakeholders will gain long-term benefits when investment professionals adhere to high ethical standards.

Laws often codify ethical actions that lead to better outcomes for society or specific groups of stakeholders. Legal and ethical conduct often coincide, but they are not always the same.

• Some legal behaviors are not considered ethical.

• Some ethical behaviors may not be legal in certain countries.

Laws and regulations are not always the best mechanism to reduce unethical behavior. They often lag behind current circumstances; legal standards are often created to address past ethical failings and do not provide guidance for an evolving and increasingly complex world. In addition, new laws designed to reduce or eliminate conduct that adversely affects the markets can create opportunities for different but similarly problematic conduct. Investment professionals should act beyond legal standards, making good judgments and responsible choices even in the absence of clear laws or rules.

The CFA Institute Ethical Decision-Making Framework is a tool for analyzing and evaluating ethical scenarios in the investment profession. The Identify-Consider-Act- Reflect framework advances a decision-making structure for situations that often fall outside the clear confines of "right" and "wrong."

Neither a linear model nor a checklist, the framework provides a summary of the key elements of making ethical decisions. The framework is offered with the understanding that there likely will be additional influences, conflicts, and actions unique to each ethical scenario and beyond those detailed in the framework.

Identify: ethical principles, duties to others (to whom do you owe a duty?), important facts, conflicts of interest.

Consider: situational Influences, alternative actions, additional guidance.
Act: make a decision or elevate the issue to a higher authority.
Reflect: What did you learn? The lessons you learn will help you reach ethical decisions more quickly in the future

The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.

Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields.

In mathematics, a metric space is a set for which distances between all members of the set are defined. Those distances, taken together, are called a metric on the set. A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces.

In a topological space, a closed set can be defined as a set which contains all its limit points.

A norm must also satisfy certain properties pertaining to scalability and additivity which are given in the formal definition below.

Among the topologies of vector spaces, those that are defined by a norm or inner product are more commonly used, as having a notion of distance between two vectors.

The sequence x_n is shown in blue. The two red curves approach the limit superior and limit inferior of x_n, shown as dashed black lines. In this case, the sequence accumulates around the two limits. The superior limit is the larger of the two, and the inferior limit is the smaller of the two. The inferior and superior limits agree if and only if the sequence is convergent (i.e., when there is a single limit).

El entrenador de Manchester United cree que no hay "mucho entusiasmo" de la hinchada, aunque los futbolistas "les gusta jugar" en casa.

Vladimir Arnold once said: "Kolmogorov – Poincaré – Gauss – Euler – Newton, are only five lives separating us from the source of our science".

To assign a value to the integral of the indicator function 1_S of a measurable set S consistent with the given measure μ, the only reasonable choice is to set:

Notice that the result may be equal to +∞ , unless μ is a finite measure.

A finite linear combination of indicator functions

where the coefficients a_k are real numbers and the sets S_k are measurable, is called a measurable simple function.

Credit risk refers to the risk that a borrower may not repay a loan and that the lender may lose the principal of the loan or the interest associated with it. Credit risk arises because borrowers expect to use future cash flows to pay current debts; it's almost never possible to ensure that borrowers will definitely have the funds to repay their debts. Interest payments from the borrower or issuer of a debt obligation are a lender's or investor's reward for assuming credit risk.

This reading covers basic principles of credit analysis, which may be broadly defined as the process by which credit risk is evaluated.

Readers will be introduced to the definition of credit risk, the interpretation of credit ratings, the four Cs of traditional credit analysis, and key financial measures and ratios used in credit analysis. The reading explains, among other things, how to compare bond issuer creditworthiness within a given industry as well as across industries and how credit risk is priced in the bond market.

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 measure 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.