Plymouth State UniversityCollege of Business Administration

BU 5120 Financial Analysis

This is the START page for the MBA graduate course in finance, online, with Professor Harding.

Below are the links to the course modules:1) SYLLABUS: A general orientation to the course2) CONTENT: An overview of the course content3) LESSONS: A listing of the weekly lessons for the course4) EXERCISES: The detailed instructions for student exercises 5) READINGS: A list of the readings for the course6) ROSTER: Students currently enrolled with email addresses Registered students must use Moodle 1) to get access to some of the readings, 2) to submit exercises, and 3) to review their grade book. To get to Moodle: Go to: my.plymouth.eduLogin: PSUusernamePassword: ****** Go to: myCoursesClick on: BU5120 Fin Analysis and Decision Making

OVERVIEW OF COURSE CONTENT: The content of this course is broad in its attempt to at least identify all the major areas of finance. Beyond that, some selected topics are explored in greater depth. There are also discussions of the relationships between financial issues that, to the casual observer, may otherwise appear to be unrelated.

Content Modules: 1. Corporate Finance: The course opens with a brief review of the nature of finance, noting the objective of the firm, followed by a discussion on corporate finance, the functions of the financial manager (concentrating on the sources and uses of funding) and an exercise in the financial analysis of the firm. (See also: capital structure, cash flow mgt, capital budgeting, and dividend policy)

INTRODUCTION to FINANCEThis course opens with a brief introduction to the nature of the discipline of finance in which the connection between the academic discipline of finance and the firm (corporation, enterprise, business) is established. Also, the connection between finance and other disciplines (economics, accounting, psychology, mathematics) is noted below.

NATURE of FINANCE: The nature of the broad discipline of finance may be regarded from two slightly different perspectives: That is, we might regard finance 1) as an academic study or 2) as a professional activity with a particular set of skills. Further, we should note 3) the relationship between finance and other disciplines, and finally, 4) an old reading that still has startling relevance is provided that begins to address how the practice of finance strengthens (and weakens) our social fabric.

1) Academic DisciplineAs a field of academic study, the primary focus of finance is often on the firm and the financial management of the firm because such a large proportion of the total wealth in an economy is created within the context of the firm (i.e. the enterprise, the corporation, the business, the private sector, etc.). For this reason, introductory finance courses are variously known as financial management, corporate finance or managerial finance.

However, a secondary academic perspective is external to the firm and focuses on individuals and institutions that participate in the capitalization of the firm through the purchase of equity securities (stocks) or debt instruments (bonds). As an academic study this second perspective is referred to as investing or portfolio management.

There is yet a third perspective in the academic discipline of finance that regards the activities engaged in by financial professionals who design new contracts (financial engineering), institutions that lend and borrow capital (investment banking), and others who take speculative positions based on the performance of other instruments (institutional finance). And in addition, more specialized courses, for example in international finance, financial modeling, and financial accounting, cover various niches of finance in greater detail.

2) Profession

As a professional activity, the practitioner needs to understand the nature of corporations, the laws (regulations, standards, protocols) governing financial activities, the mathematics of the instruments, the accounting standards adopted by the firm, and the economic theories that are inherent in the actual management of the firm and the management of funds outside the firm.

The particular skill set required to successfully participate in the financial profession include many of those universally found in other professions, for example the ability to work with others, the ability to communicate clearly in writing and discourse, and the ability to develop and practice productive work habits. However, some skill sets are more essential to finance than to some other professions, for example - the quantitative skills of mathematics and quantitative modeling (see also financial models) and the skilled use of information technology. Here is an employment advertisement for an investment analyst.

Investments Analyst – 05016700

Job DescriptionApply Online

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DescriptionThe Citigroup Private Bank serves the financial needs of high net worth individuals around the world. Our Private Bankers play a central role in delivering personalized, effective, and insightful financial solutions to meet client needs. Globally, The Citigroup Private Bank has more than 4,000 employees in 90 offices, located in 58 cities (30 countries and territories), and manages more than $100 billion of client business volumes. Principal investment centers include: New York, London, Switzerland, Jersey, Hong Kong, Singapore and Tokyo. Through its product and service offerings, and by functioning as the gateway to the resources of the Citigroup companies, the Private Bank provides clients with comprehensive investment and banking choices. Products and Services include Investment Services, Global Trading Services, Risk Management, Credit and Lending, Alternative Investments, Real Estate Services, Traditional Banking Services, Trust Services, Global Wealth Structuring and Art Advisory.

Specifications / Qualifications

The Investment Management Organization manages assets across all asset classes for Institutional, Private Bank, International Retail and HNW, and U.S. Retail and High Net Worth businesses.

Role:

The Analyst is responsible to participate in research and modeling work on various traditional and alternative asset classes. Will perform evaluation of products for inclusion in asset allocation models. Develops and maintains proprietary optimization and simulation models. Participates in asset allocation related projects with private bank, institutional and retail clients. Provides general support of private

bank and consumer bank with respect to risk management, portfolio analytics, attribution analysis, and other general investment topics. Participates in marketing efforts and client meetings

Education and Experience:

MBA in finance/quantitative field, and/or CFA. Five to ten years experience in portfolio management or quantitative analysis (specific work in asset allocation a plus) required. Quantitative background and programming skills (VBA and Matlab at a minimum) required.

Other qualifications:

The ideal candidate will possess:

Financial expertise: A practical understanding of financial principles and portfolio management concepts; familiarity with, risk and valuation models.

Statistical understanding: Statistical methods must be understood well enough to judge their efficacy and drawbacks in specific circumstances; must be comfortable dealing with numerical and statistical concepts.

Computer understanding: Comfortable with statistical analysis and analytic programming; familiarity with commercial analytic packages (e.g., VBA, MATLAB).

Profile

Job Function Investment Management

Location North America-US-NY-New York

Employee Status Full-time

Job Level Team Leader

Education Level Master's Degree (Approx 18 years of Educ)

Shift Day Job

Employee Type Regular

Exempt Status Exempt

Travel Yes, 25 % of the Time

Additional Information

Posting Date July 19, 2005

Number of Positions 1

Relocation

Yes

Business Area

Private Bank - Global Wealth Management

Alternate Requisition Number

Replacement

Brief Description of the Organization

The Citigroup Private Bank serves the financial needs of high net worth individuals around the world. Our Private Bankers play a central role in delivering personalized, effective, and insightful financial solutions to meet client needs. Globally, The Citigroup Private Bank has more than 4,000 employees in 90 offices, located in 58 cities (30 countries and territories), and manages more than $100 billion of client business volumes. Principal investment centers include: New York, London, Switzerland, Jersey, Hong Kong,

Singapore and Tokyo. Through its product and service offerings, and by functioning as the gateway to the resources of the Citigroup companies, the Private Bank provides clients with comprehensive investment and banking choices. Products and Services include Investment Services, Global Trading Services, Risk Management, Credit and Lending, Alternative Investments Real Estate Services, Traditional Banking Services, Trust Services, Global Wealth

Office Location / Address

CGC, NEW YORK

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3) Other DisciplinesFinance has clear connections with other disciplines (e.g. law, marketing, information technology), but often the distinction between finance and economics, and between finance and accounting gets fuzzy. Finance has sometimes been considered a sub-type, a "grubby off-spring", of economics, owing to finance's pre-occupation with actually making money for the practitioner. Economics, on the other hand, tends to be more of an intellectual pursuit, seeking understanding of the cause and effect relationships among variables.

The relationship between finance and accounting is similar, except that accounting is the more mundane number-crunching activity that compiles the necessary statements for the higher-order financial types. [The allusion to any actual superiority of one discipline over another is purely artistic license used to illustrate a point.]

Psychology has more recently joined forces with finance as both disciplines strive to understand the markets which are an aggregate of individuals making financial choices. Within the last decade, the discipline of behavioral finance has emerged as a combination of these two disciplines. Finally, mathematics, the pure science, provides the tools for financial calculations.

4) Ethics and Finance: In other cultures and in other times, the charging of interest was immoral and illegal. Lending money to a neighbor was considered acceptable, but charging interest on the loan was considered harvesting money from a source into which no labor was provided. Ergo, interest must have come from the Devil. Times and culture have changed to where charging interest is fair play, yet there are still ample opportunities to take unethical advantage of our imperfect economic system. Harry Markowitz has some thoughtful comments on "Markets and Morality".

CORPORATE FINANCE The focus on the corporation is pursued further with a reading on the objective of the firm, followed by a discussion on the functions of the financial manager, concentrating on the sources and uses of funding, and an exercise in the financial analysis of the firm. (see also: capital structure, capital budgeting and dividend policy)

THE OBJECTIVE OF THE FIRM

The following is from chapter one in the text, Financial Management and Policy, by James C. Van Horne, Copyright 1974 by Prentice-Hall. It is classic finance.

In this [course], we assume that the objective of the firm is to maximize its value to its shareholders. Value is represented by the market price of the company’s common stock which, in turn, is a reflection of the firm’s investment, financing, and dividend decisions.

Profit Maximization vs. Wealth Maximization Frequently, maximization of profits is regarded as the proper objective of the firm, but it is not as inclusive a goal as that of maximizing shareholder wealth. For one thing, total profits are not as important as earnings per share. A firm could always raise total profits by issuing stock and using the proceeds to invest in Treasury bills. Even maximization of earnings per share, however, is not a fully appropriate objective, partly because it does not specify the timing or duration of expected returns. Is the investment project that will produce $100,000 return 5 years from now more valuable than the project that will produce annual returns of $15,000 in each of the next 5 years? An answer to this question depends upon the time value of money to the firm and to investors at the margin. Few existing stockholders would think favorably of a project that promised its first return in 100 years. We must take into account the time pattern of returns in our analysis.

Another shortcoming of the objective of maximizing earnings per share is that it does not consider the risk or uncertainty of the prospective earnings stream. Some investment projects are far more risky than others. As a result, the prospective stream of earnings per share would be more uncertain if these projects were undertaken. In addition, a company will be more or less risky depending upon the amount of debt in relation to equity in its capital structure. This risk is known as financial risk; and it, too, contributes to the uncertainty of the prospective stream of earnings per share. Two companies may have the same expected future earnings per share, but if the earnings stream of one is subject to considerably more uncertainty than the earnings stream of the other, the market price per share of its stock may be less.

For the reasons above, an objective of maximizing earnings per share may not be the same as maximizing market price per share. The market price of a firm’s stock represents the focal judgment of all market participants as to what the value is of the particular firm. It takes into account present and prospective future earnings per share, the timing, duration, and risk of these earnings, and any other factors that bear upon the market price of stock. The market price serves as a performance index or report card of the firm’s progress; it indicates how well management is doing in behalf of its stockholders.

Management vs. StockholdersIn certain situations the objectives of management may differ from those of the firm's stockholders. In a large corporation whose stock is widely held, stockholders exert very little control or influence over the operations of the company. When the control of a company is separate from its ownership, management may not always act in the best interests of the stockholders [Agency Theory]. [Managers] sometimes are said to be "satisficers" rather than "maximizers"; they may be content to "play it safe" and seek an acceptable level of growth, being more concerned with perpetuating their own existence than with maximizing the value of the firm to its shareholders. The most important goal to a management [team]of this sort may be its own survival. As a result, it may be unwilling to take reasonable risks for fear of making a mistake, thereby becoming conspicuous to the outside suppliers of capital. In turn, these suppliers may pose a threat to management’s survival.

It is true that in order to survive over the long run, management may have to behave in a manner that is reasonably consistent with maximizing shareholder wealth. Nevertheless, the goals of the two parties do not necessarily have to be the same. Maximization of shareholder wealth, then, is an appropriate guide for how a firm should act. When management does not act in a manner consistent with this objective, we must recognize this as a constraint and determine the opportunity cost. This cost is measurable only if we determine what the outcome would have been had the firm attempted to maximize shareholder wealth.

A Normative GoalBecause the principal of maximization of shareholder wealth provides a rational guide for running a business and for the efficient allocation of resources in society, we use it as our assumed objective in considering how financial decisions should be made. The purpose of capital markets is to efficiently allocate savings in an economy from ultimate savers to ultimate users of funds who invest in real assets. If savings are to be channeled to the most promising investment opportunities, a rational economic criteria must exist that governs their flow. By and large, the allocation of savings in an economy occurs on the basis of expected return and risk. The market value of a firm’s stock embodies both of these factors. It therefore reflects the market’s tradeoff between risk and return. If decisions are made in keeping with the likely effect upon the market value of its stock, a firm will attract capital only when its investment opportunities justify the use of that capital in the overall economy.

Put another way, the equilibration process by which savings are allocated in an economy occurs on the basis of expected return and risk. Holding risk constant, those economic units (business firms, households, financial institutions, or governments) willing to pay the highest yield are the ones entitled to the use of funds. If rationality prevails, the economic units bidding the highest yields will be the ones with the most promising investment opportunities. As a result, savings will tend to be allocated to the most efficient users. Maximization of shareholder wealth then embodies the risk-return tradeoff of the market and is the focal point by which funds should be allocated within and among business firms. Any other objective is likely to result in the suboptimal allocation of funds and therefore lead to less than optimal level of economic want satisfaction.

This is not to say that management should ignore the question of social responsibility. As related to business firms, social responsibility concerns such things as protecting the consumer, paying fair wages to employees, maintaining fair hiring practices, supporting education, and becoming actively involved in environmental issues like clean air and water. Many people feel that a firm has no choice but to act in socially responsible ways; they argue that shareholder wealth and, perhaps, the corporations vary existence depends upon its being socially responsible. However, the criteria for social responsibility are not clearly defined, making formulation of a consistent objective function difficult.

Moreover, social responsibility creates certain problems for the firm. One is that it falls unevenly on different corporations. Another is that it sometimes conflicts with the objective of wealth maximization. Certain social actions, from a long-range point of view, unmistakably are in the best interests of stockholders, and there is little question that they should be undertaken. Other actions are less clear, and to engage in them may result in a decline of profits and in shareholder wealth in the long run. From the standpoint of society, this decline may produce a conflict. What is gained in having a socially desirable goal achieved may be offset in whole or part by an accompanying less efficient allocation of resources in society. The latter will result in a less than optimal growth of the economy and a lower total level of economic want satisfaction. In an era of unfilled wants and scarcity, the allocation process is extremely important.

Many people feel that management should not be called upon to resolve the conflict posed above. Rather, society, with its broad general perspective, should make the decisions necessary in this area. Only society, acting through Congress and other representative governmental bodies, can judge the relative tradeoff between the achievement of a social goal and the sacrifice in the efficiency of apportioning resources that may accompany realization of the goal. With these decisions made, corporations can engage in wealth maximization and thereby efficiently allocate resources, subject, of course, to certain governmental constraints. Under such a system, corporations can be viewed as producing both private and social goods, and the maximization of shareholder wealth remains a viable corporate objective.

FUNCTIONS:As the primary objective of the firm is to maximize stockholders wealth as reflected in the stock price, then the primary function of management is also to address that objective. Management accomplishes this through convincing investors that the "quality of future earnings" is strong – that is, that future earnings are both "likely" (have a high probability of coming to pass) and robust (exhibiting healthy growth through time). If management is effectively convincing, then a demand for a share of ownership in the firm will apply the upward pressure on the price, and management will have succeeded in fulfilling their objective - for the time being.

1. The function of a financial manager is to support the primary objective through simultaneous actions in four major areas. The first area is in the "capitalization of the firm", or the issue of sources of funding. The two major sources are stocks (selling equity) and bonds (issuing debt), with a third, and not inconsequential, source being the internally generated capitalization from earnings. This area is also referred to as "the capital structure" decision, in which the financial manager tries to anticipate the optimum mix of debt and equity (proportion of bonds to stock) to achieve the primary objective of maximizing stock price. While there are many models addressing the capital structure decision, the study by Miller [see also: Blackboard/Readings/Varian] raises doubts as to those models' efficacy.2. The next major decision is in the use of the capitalization that was raised as a result of the capital structure decision. The "uses" of capital in the corporate environment is generally called "capital budgeting", and the objective of this area is, again, the maximization of stock price. In cruder terms, the firm just raised a lot of money. Now, what should they to do with it? They should invest it into projects that have the greatest positive impact on the stock price. The terminology of capital budgeting refers to "capital projects", or those activities that require some up-front investment in hopes of reaping longer-term rewards. Capital projects may take the form of buying another company, building a new manufacturing plant, developing a new product, or some other activity (there's a wide range). 3. The third major functional area in financial management is determining how much of the earnings (generated by capital projects) should be distributed to shareholders in the form of dividends. This determination may be based on the firm's "dividend policy" that is established by the board of directors. A rough perspective of this decision is that 1) all the profits [earnings available to common stockholders (EAC)] of the company belong to the stockholders, 2) but those earnings may be plowed back into the firm or sent to the shareholders. The question is how much should go to each of the two destinations.

4) The first three functions (raising the funding, investing the capital, distributing the harvest) all require a careful oversight of the flow of actual cash. It is this "cash flow management" function that is cited as

the fourth major function of the financial manager. Cash flow management requires planning and oversight with diligent accounting skills. The traditional functions of the financial manager of the firm include the four major areas described above. In addition, the financial manager often has oversight responsibility for the non-financial areas of accounting and information technology. Accountants are the first to gather the monetary transactions of the firm and to put those transactions into some sort of order for the raw material for the financial departments. Therefore the financial manager has vested interest in the integrity of the work of the accountants. And information technology made its corporate debut in the accounting department (for the processing of those same transactions) and likewise fell under the management umbrella of the financial manager. But as for the clearly financial functions, the four functions above are the most often mentioned.

CAPITAL STRUCTURE:

In finance, capital structure refers to the way a corporation finances its assets through some combination of equity, debt, or hybrid securities. A firm's capital structure is, then, the composition or 'structure' of its liabilities. For example, a firm that sells $20 billion in equity and $80 billion in debt is said to be 20% equity-financed and 80% debt-financed. The firm's ratio of debt to total financing, 80% in this example, is sometimes referred to as the firm's leverage. In reality, capital structure may be highly complex and include multiple sources. Gearing Ratio is the proportion of the capital employed by the firm that comes from outside of the business finance, e.g. by taking a long term loan.The Modigliani-Miller theorem, proposed by Franco Modigliani and Merton Miller, forms the basis for modern thinking on capital structure, though it is generally viewed as a purely theoretical result since it assumes away many important factors in the capital structure decision. The theorem states that, in a perfect market, how a firm is financed is irrelevant to its value. This result provides the base with which to examine real world reasons why capital structure is relevant, that is, a company's value is affected by the capital structure it employs. These other reasons include bankruptcy costs, agency costs, taxes, information asymmetry, to name some. This analysis can then be extended to look at whether there is in fact an optimal capital structure: the one which maximizes the value of the firm.[Adapted from: Wikipedia "capital structure"]

CAPITAL BUDGETING:Capital budgeting (or investment appraisal) is the planning process used to determine a firm's long term investments into projects such as new and replacement equipment, new plants, new products, and research development. The word "projects" is commonly used as a "catch-all" term for these capital investments, but the range of project is wide and might include buying a whole company, entering the global market or other huge investments. Recall the accounting distinction between capital spending and expense spending: capitalized items become assets on the balance sheet and are depreciated over time and expense items are shown as costs for the current time period on the income statement.

The capital budgeting process involves 1) identifying potential projects, 2) estimating the incremental cash flows related to the respective projects, 3) identifying and quantifying risk associated with each project, 4) application of various financial models to quantify the projects value to the firm, prioritize the

project relative to other potential projects, and to make the final decision as to whether to pursue the project.

The financial models, or methods, used in capital budgeting, include the following techniques:

Net present value (NPV) or Discounted cash flow (DCF)Profitability indexInternal rate of return (IRR)Modified Internal Rate of Return (IRR*)Ascending Discount RatesEquivalent Annual annuity (EAA)Payback period (using cash flow)Payback period (using discounted cash flow)

NET PRESENT VALUE (NPV)DISCOUNTED CASH FLOW (DCF)

The net present value method and the discounted cash flow method are two names for the same thing. It is a technique used to take an estimated cash flow and to discount it to yield a net present value.

1) To discount a cash flow (CF), one must first determine the discount rate. For academic purposes, this is often given as a constant, although sometimes it is a variable increasing through time. In the following models, we use "k" as the variable for discount rate. For corporate purpose, there are various theoretical approaches to determine the rate's intrinsic value. For example, one approach suggests using the weighted average cost of capital of the firm and then adding a risk premium for the particular project to yield a discount rate.

DISCOUNT RATE:(Not to be confused with the Fed's Discount Rate)Adapted from Wikipedia

The rate used to discount future cash flows to their present values is a key variable of the capital budgeting process. A firm's weighted average cost of capital (after tax) is often used, but many people believe that it is appropriate to use higher discount rates to adjust for risk for riskier projects or other factors. A variable discount rate with higher rates applied to cash flows occurring further along the time span might be used to reflect the yield curve premium for long-term debt. Also called "ascending discount rates".

Another approach to choosing the discount rate factor is to decide the rate which the capital needed for the project could return if invested in an alternative venture. If, for example, the capital required for Project A can earn five percent elsewhere, use this discount rate in the NPV calculation to allow a direct comparison to be made between Project A and the alternative. Related to this concept is to use the firm's Reinvestment Rate. Reinvestment rate can be defined as the rate of return for the firm's investments on average. When analyzing projects in a capital constrained environment, it may be appropriate to use the reinvestment rate rather than the firm's weighted average cost of capital as the discount factor. It reflects opportunity cost of investment, rather than the possibly lower cost of capital.

A NPV amount obtained using variable discount rates (if they are known for the duration of the investment) better reflects the real situation than that calculated from a constant discount rate for the entire investment duration. Refer to the tutorial article written by Samuel Baker [2] for more detailed relationship between the NPV value and the discount rate.

To some extent, the selection of the discount rate is dependent on the use to which it will be put. If the intent is simply to determine whether a project will add value to the company, using the firm's weighted average cost of capital may be appropriate. If trying to decide between alternative investments in order to maximize the value of the firm, the corporate reinvestment rate would probably be a better choice.

Using variable rates over time, or discounting "guaranteed" cash flows differently from "at risk" cash flows may be a superior methodology, but is seldom used in practice. Using the discount rate to adjust for risk is often difficult to do in practice (especially internationally), and is really difficult to do well. An alternative to using discount factor to adjust for risk is to explicitly correct the cash flows for the risk elements using rNPV or a similar method, then discount at the firm's rate.

For some professional investors, their investment funds are committed to target a specified rate of return. In such cases, that rate of return should be selected as the discount rate for the NPV calculation. In this way, a direct comparison can be made between the profitability of the project and the desired rate of return.

2) Once the discount rates have been determined, the discount factors can be calculated using:discount factor = (1+k)-n , where "k" is the rate and "n" is the number of years hence.You'll recognize this from PV=FV(1+k)-n, where "FV" is the future value, or the future cash flow.The spreadsheet format for the discount factor is: =(1+k)^(-n), where actual cell locations may be substituted for k and n.

3) Using the PV formula above, each year's cash flow is multiplied by its respective discount factor to get its present value. This step is applied to every year including "year 0".

4) The present values for all the years (including year 0) are added together to get the "net present value(NPV)", or in other words, the "discounted cash flow (DCF)".

The NPV is the current value of all the cash flows, current and future. A firm's net value increases by the NPV of a project when the firm commits to that project. Sometimes this is counter-intuitive: a firm writes a check for $100K, committing itself to a new project, and suddenly the value of the firm goes up by $120K? Sure, the value of the project is $120K and the firm is doing it.

This notion is carried a little further. If the value of the firm goes up, then so, too, goes the stock price. They are, after all, directly proportional. The value of firm divided by number of shares equals stock price. Hence, the theoretical change in stock price for taking on a project will be the NPV of the project divided by the number of shares.

The NPV relates to the rate of return of the project in the following way: If the discount rate (think "cost of money") is less than the return of the project, then the project will "make money". More technically, if the discount rate is less than the internal rate of return, then the NPV will be positive. And, conversely, if the discount rate is more than the internal rate of return, then the NPV will be negative. Note also, that the discount rate is externally determined (by credit markets, and risk factors), whereas the project's rate of return is internally determined by the project's cash flows and discount rate. Finally, if the discount rate and the projects rate of return are equal, then the project isn't worth doing. This will be reflected in a NPV=0 and is intuitively illustrated with the scenario of borrowing money at 20% and putting the money in a 20% project.

Twisting the preceding paragraph around a bit, we could say that the internal rate of return (IRR)on a project is that rate that when applied to the cash flow yields a net present value of zero. And that is the definition of IRR.

MODIFIED INTERNAL RATE OF RETURN (IRR*)

Application: The IRR* model is applied to the projected cash flows of a proposed capital budget. The result, the IRR*, is used as a measure of the expected return of the investment.

Assumptions and Methodology: The model assumes that the positive cash flows generated by a project are reinvested at the firm's discount rate to the end of the last year of the cash flow. This assumption differs from the reinvestment assumption of the ordinary IRR model, which assumes implicitly that reinvestment of the cash flows are made at the derived IRR. In IRR*, the sum of the reinvested cash flows are an estimate of the future terminal value (TV) of the project (not counting the original investment). The terminal value is subsequently reevaluated to reflect its net present value, using a rate (the IRR*) that will discount the TV to an amount exactly equal to the original investment. By definition, the hypothetical discount rate which yields a net present value (NPV) of zero is the project's internal rate of return.

See also the spreadsheet with the formulas required to calculate IRR*

DIVIDEND POLICY:

A major function of the financial manager is to implement a dividend policy. Dividend policy is discretionary, that is, the amount of the quarterly dividends is determined by the board of directors. The criteria for determining a dividend policy should be "what policy will maximize the stock price?" The accounting is straightforward: Net Profits (EAC) is split into dividends and retained earnings. There is no third bucket where profits end up. Here are some abstracts of various theoretical dividend policy models:

1. Modigliani & Miller (MM) say that dividends don't matter, "dividends are irrelevant", that stock price is determined by "basic earning power [ROA] of firm", not by dividend policy. MM acknowledge a "signaling effect" and offer a "clientele theory".

2. Gordon & Lintner says dividends are everything, that investors have a preference for liquidity. MM call this the "Bird in the hand theory". P0=D1/(ke-g) .

3. Harkavy did empirical test to find a slight positive correlation between payout ratios and stock price. Both MM and Gordon/Lintner claim that Hakavey's study lends credibility to their respective theories.

4. Walter's theory of Residuals: Walters posited that firms should use EAC to fund projects whose IRR* are expected to be greater than the stockholders required rate of return. Dollars not expended on these projects should be paid out to stockholders in the form of dividends.

Here are some “real-world” models. That is, many actual companies follow the following models:

5. Constant dollars: Pay out same amount of dollars per share every quarter.6. Constant dollars with a kicker: Add a bonus every now and then.7. Constant increases: Increase dollar amount every quarter.8. Constant payout ratio: Hold the proportion of payout (div/EAC) constant each quarter.9. Tie changes in dividends to changes in CPI: Increase div by cost of living.

---------- end of corporate finance section ------------------------

2. Portfolio Theory: This topic goes beyond the firm to regard "modern portfolio theory" (MPT), attributed to Markowitz, and introduces the management of portfolios. The related exercise (port.xls) simulates the portfolio analysis implied by MPT.

2. PORTFOLIO MANAGEMENT

The practice of finance is not limited to the financial management of the firm. Considerable wealth is held by unincorporated entities such as individuals, trusts, non-profit organizations, municipalities and a wide range of other institutions. And financial institutions, while often technically incorporated, manage their financial assets with portfolio management models more than with "corporate" revenue-to-profit models. The wealth held in portfolios, or collections of the financial instruments, and the management of these portfolios requires financial professionals with portfolio management skills.

Modern Portfolio Theory (MPT): The discipline of portfolio management had a major incarnation with the introduction of Modern Portfolio Theory (MPT). See also the first section of the Varian article on Markowitz. Prior to MPT, portfolio management focused on active stock picking – that is, speculating and selecting those stocks with the highest expected returns. This is an intuitive and still popular focus of many investors. However, with MPT, Markowitz quantified the notion of minimizing risk through diversification, and lowering the probability of losing principal. This is not to say that "maximizing returns" is wrong-headed or undesirable, but it suggests that "minimizing risk" is a worthwhile and simultaneous endeavor. His model identifies a set of portfolios that have the lowest risk for a given return - or said another way, a set of portfolios with the highest return for a given level of risk. This set is the “efficient frontier”.

1) The development of the MPT model can be illustrated with a series of charts. [Note: Ctrl + click on a chart to see larger version]. This first chart shows daily stock prices, or price per share (pps), through time. In this example the time span is one year and shows pps at the close of each trading day. The blue dash line is a projection of the original value at the start of the measured year. The short red vertical line represents the change (Δ) in pps over the course of the year.

2) The second chart shows returns (K) for each of those same trading days using the classic “K = Δ/orig” model, or “returns equal the change in price divided by the original price”. “K” is a percentage, and is expressed either as a percent (i.e. 25%) or as a decimal (i.e. .25). Although dividends are ignored in this return calculation example, total stock returns are more correctly calculated with dividends, taxes and transaction costs factored in.

3) The third chart illustrates the calculation of the variability, (the "bounciness" of the data, or volatility) of the returns. The statistic that reflects this volatility is the standard deviation (σ) of the returns, and is, by definition, the risk of the stock. There is a natural attraction to think of risk as the volatility of the price, and indeed, a bouncy price will cause bouncy returns, however, the volatility of the returns is the accepted measure. Note that data in this third chart is the same as the second chart, but a line has been added representing the mean and a normal distribution of returns based on the mean and standard deviation.

4) MPT suggests that the standard deviation of the returns, the risk, can be mitigated by the introduction of a second security whose return pattern is significantly different than the original security. In the adjacent chart the original security (from the previous charts) is shown as "A" in blue, and the second security is shown as "B" in red. Their respective distributions, based on their respective means and standard deviations, are shown on the right side of the chart. The two distributions might be similar, but probably won't be identical.

5) As the two securities are combined into a single portfolio, the resulting composite return (the return of the portfolio) is shown in blue in this chart. A correlation coefficient is used to compare return patterns, with a low correlation indicating greater differences in patterns, and results in a portfolio with less volatility (less risk) than either of the original securities. [This is a good chart to click on to better see the low risk portfolio].

6) Chart 6 illustrates this same (as 5) phenomenon from a different perspective. Again, consider the same securities, A and B. A has some historical risk/return profile, and let's assume that B has a somewhat higher risk and higher return (consistent with the CAPM, as shown here). A portfolio with 100% of the dollar invested in A and 0% in B, would have a risk/return profile ( σ vs. K%) at point A on

the chart. As B is incrementally added to the portfolio, the return of the portfolio will rise and the risk will be reduced, the risk/return profile starts moving toward the upper left in the chart, beginning to trace a hyperbola. Around the apex of the hyperbola, there is a 50/50 dollar mix of A and B in the portfolio, and at this mix, the portfolio of A &B has lower risk than either A or B. Magic. The returns of the portfolio will always be a weighted average of the returns of the components.

7) A set of portfolios composed of six securities will trace five hyperbolas (A to B, B to C, etc.), but will also define an area representing every possible weight-combination of A,B,C,D,E,F. The upper left boundary of this set of portfolios is a line that represents those portfolios with the lowest risk for a given return (or the highest return for a given level of risk.) This boundary is the "efficient frontier".

8) Tobin posited that a line emanating from the risk-free rate (Krf)and laying on the efficient frontier will have a point of contact at the risk/return point of market portfolio (e.g. an S&P 500 index fund). The line between the risk-free rate and the market portfolio represents a set of portfolios comprised of varying weights of risk-free assets and market funds. The line extending beyond the market represents a set of portfolios, all fully invested in the market funds, but with ever increasing amounts of borrowing at the risk-free rate.

9) The last chart shows that as more firms are added to a portfolio, the risk of the portfolio tends to decline to the level of the market's risk (systematic risk). The first point on the left on the red line represents a portfolio with one security. The risk of the portfolio is thus the same as the risk of that single security. The next point shows how the addition of a second security to the portfolio reduces the risk of that portfolio. With the addition of each additional security, the portfolio tends to diminish until it reaches the market risk. Note that the market risk is the same as the risk of a portfolio with every publically traded security included.

Further References: VarianMathematical finance

Concepts:1. modern portfolio theory2. price per share (pps)3. returns4. standard deviation5. Normal distribution6. risk7. hyperbolas8. efficient frontier 9. Tobin's line

3. Strategies: This topic explores several different financial strategies that are used by firms, individuals, and institutions. Strategies include: hedging, speculation, arbitrage, active vs. passive, Efficient Market Hypothesis (EMH), behavioral finance, fundamental and technical analysis, and the infamous Ponzi scheme.

3. STRATEGIES

This topic explores different financial strategies that are used by firms, individuals, and institutions. Items in this list are not necessarily mutually exclusive (an investor might use a combination of several strategies), but they are representative of currently popular approaches. Excluded from the list are some well-known and commonly practiced approaches that are rational methods for saving and investing (e.g. 401Ks, dollar-cost-averaging, buy-and-hold, buy low-sell high) but whose underlying assumptions are too obvious to warrant further academic discussion in this context.

1) Speculation: This strategy assumes that the investor has some special insight into what might happen in the future. As the investor believes that the price of a security will go up, he/she will "buy low" and wait for the security to go up and "sell high". This special insight may be due to the recognition of an historical pattern that other investors either do not perceive or perhaps other investors believe the pattern does not apply to this particular environment. The notion of "alpha", excess returns above market returns, are tied to this strategy. Speculators believe they have a good chance of generating alpha.

2) Hedging: This strategy requires Investing in multiple instruments that are likely to perform differently from each other, such that if one investment under-performs, the other is likely to over-perform. A passive investor whose entire portfolio is comprised of market index funds has essentially hedged all the firm-specific risk and is guaranteed, by definition, not to generate any alpha, but to achieve the market return. Hedge funds derive their name from this strategy, as they originally invested in instruments that were negatively correlated with existing portfolios, however, through the years, many hedge funds have tended to follow more speculative strategies 3) Arbitrage: This strategy requires highly sophisticated computer systems to identify relatively small dis-equilibriums in a market and trading with very large sums of cash. For these two reasons, arbitrage is engaged in by institutions rather than individuals. A simple example of an arbitrage would entail noticing a small price difference in the price of gold in two markets, buying at the low price in one market and immediately selling in the other market at the higher price. Large differentials in prices tend not to occur, and small differentials tend to disappear quickly. But imbalances do happen in the normal course of changing prices and it is in the process of arbitrage that prices tend to seek equilibrium.

4) Active Management: [a term used in the context "active versus passive"] An active investment management strategy implies an underlying belief that through rigorous analysis, quality information and rational decision making, an investor can, on average, beat the market. A disparaging phrase for this approach is "chasing alpha". Stock brokers and professional portfolio managers tend to fall into the category of "active" managers, as they sell their clients on the concept that their active management adds value to the portfolio and justifies their management fees. Traditional portfolio management fees are about 1% of the portfolio's value per year. Carried to extremes, an overly active manager who continually re-balances a client's portfolio, presumably for the additional commissions related to the trades, might be accused of "churning", not for higher returns, but for excessive fees. 5) Passive Management: [in contrast to "active" above] A passive investment strategy implies an underlying belief in the efficiency of markets and the futility of chasing alpha. This strategy manifests itself in the investment in market index funds, such that the returns of the investor will invariably approximate the market, except for the minimal management expense fees (typically .25%)charged by index funds. Professional portfolio managers may use this strategy with clients who have little interest in the details of the allocation of assets. The value added in passive management is in the knowing which index funds to invest in, how to mechanically implement the investments, and in being able to justify the reduced activity in the portfolio.

6) Efficient Market Hypothesis (EMH): Eugene Fama of the University of Chicago is credited for having brought EMH into focus. His premise is that financial markets (and equity markets in particular) are efficient in the sense that prices in the markets respond instantaneously to new information, and as a consequence, prices are always reflective of the fair market value. These assumptions imply that an investor cannot consistently beat the market - with the following caveat: Given the great number of investors in the world, there exists the very real probability that a few investors will consistently beat the market simply through blind dumb luck. And the fact that these lucky investors may also be intelligent, honest, hard working, and convinced (as well as being convincing) of their special prowess does not negate the randomness of their golden touch. The Mann interview [unavailable at the time of this writing] with Eugene Fama elaborates on this theory.

7) Behavioral Finance: This branch of finance is not so much a strategy itself, but is the study of financial strategies from a psychological perspective. Given that most financial transactions are the result of a human being making a decision, then understanding the process of human decision making becomes an essential component of understanding financial markets. Amos Tversky and Daniel Kahneman are credited with extensive studies of decision making, and Richard Thaler has juxtaposed their work against the efficient market hypothesis to expose some significant conflicts between these two widely accepted theories. Perhaps the significance of behavioral finance to students is that this field reveals how little we really know about the hows and whys of human financial decision making, and this may help mitigate the intimidation of the vast amount of technical knowledge that appears to have accumulated over the years. The Kolbert article and Wikipedia's behavioral economics, lend substance to this discussion. The Hilsenrath article gives a summary of the Fama/Thaler dispute.

8) Fundamental Analysis: In the taxonomy of financial analysis, there is often a distinction made between fundament analysis and technical analysis. These two approaches are perhaps not so much strategies, per se, as they are techniques or methods used in the pursuit of a speculation strategy. There exist certain empirical dimensions of a firm that are called the "fundamentals" of the firm, similar in concept to a broader view of the "fundamentals" of the economy. The fundamentals of the firm include, for example, market share, revenue growth, earnings, and leverage. And fundamental analysis is the process of regarding the trends (historical long term and short term) of these variables, plus their relative and absolute levels, and ultimately makes a subjective judgment about the health of the firm based on the fundamentals.

9) Technical Analysis: A technical analysis takes a different approach by regarding stock price data and the patterns imbedded therein and further using these patterns to forecast price trends. An implicit assumption is that past patterns will tend to repeat in the future, so the critical step is to discover and recognize the patterns. And if an analyst can find a new, previously undiscovered pattern, then acting on that new pattern will give the analyst (now, the investor) a competitive edge over the rest of the market. Related to technical analysis are "event studies" in which the analyst tries to identify a previously undiscovered relationship between some variable, or variables, and stock prices. An example that has become a historical cliché is the relationship between sun spots and stock prices, in which there was for many years a tight correlation between the two data sets and the resulting predictive model enjoyed surprising success. That there was no rational causal relationship between the two variables did not negate the strong statistical significance of this finding.

10) Black Swans and Fat Tails: For hundreds of years "black swans" have been a symbol of completely unanticipated events. In recent years, Nissam Taleb has popularized the symbol in the context of finance, using as examples the collapse of Long Term Capital Management (LTCM) and 9/11 and the effects of these events on financial markets. The impact of black swans on financial strategies is that non-believers will tend to bet on probable outcomes, where probabilities are estimated from past occurrences. Believers, on the other side of the bet, will assume that the tails of the probability distributions, while historically "thin", contain unpredictable and calamitous outcomes. Hence, the tails are fat.

11) Ponzi Schemes: Named for Charles Ponzi of Boston, this illegal strategy involves soliciting assets from investors on the grounds that the "investment manager" has created a unique combination of trades that can yield extraordinary returns for the investor. The hoax attains credibility as the manager pays extraordinary returns to the original investors using assets from new investors and may be further reinforced by issuing fictitious statements that reflect those extraordinary returns. The fraud may

continue for years, continually harvesting new money, avoiding regulatory scrutiny, until enough investors try to withdraw their non-existent funds. When the pyramid scheme collapses, it falls quickly. But given the frailties of human nature, new Ponzi schemes will probably continue to emerge.

CONCEPTS:1. alpha2. speculation3. hedging4. arbitrage5. active vs. passive6. Efficient Market Hypothesis (EMH), 7. behavioral finance, 8. fundamental and technical analysis9. Black Swans & fat tails 10. Ponzi/Madoff

4. Valuation: The techniques of determining the inherent value of financial instruments are reviewed with present value concepts (PV, FV, PVa, FVa) for lump sums, annuities, loans, bonds , stocks (PE, Gordon's Model)

4. VALUATION

The process of valuation in finance is consistent with the more general meaning of valuation – that is, assigning a value to, assessing, or appraising some asset. And, not surprisingly, the assets commonly valued in finance are stocks and bonds. Consider that a share of stock (or a bond, too, in this case) is simply a contract (a written legal agreement) between two parties that entitles one party to certain rights in consideration of an agreed upon purchase price. The valuation issue is: how much is that contract (the stock/the bond) worth? What is its value? How much should the buyer pay for the contract?

The answer is: The buyer should pay the current value of the future cash flows related to that contract. Let's embellish our terms and instead of referring to the "contract", let's refer to "financial instruments", or a "share of stock", or a "bond" and switch from "purchase price" to "price per share" (pps) or the price of a bond. And while we're at it, let's change "current value" to "present value", as that is more consistent with the common name of the models used in this valuation process.

1) Value of Stock:Myron Gordon offered a model for the valuation of stock based on the premise as that shown above. That is, the value of a share of stock is the present value of the future cash flows associated with that particular security. Gordon suggested that the only real cash flow associated with a share of stock is the dividends. Further, he assumed that dividends can be expected to grow at a constant growth rate (often tied to expected growth in earnings) and that these cash flows should be discounted at the required rate of return of the stockholder. For more on Gordon's model, see gordon.html and Gordon-model.

Several inherent problems with stock valuation models in general can be illustrated using Gordon's model as a straw man. First, some input data is historical, or empirical, in nature. The data itself is true enough, but there are no guarantees that the data will hold true in the future. Second, some input data is speculative, and looking into the future is a foggy view at best. And third, even if the historical data holds true for the future AND the speculative data is luckily "dead-on", the resulting perfect answer of what the intrinsic value of the stock should be, as often as not, is not likely to be the same as the actual current market price. This leads to an investor's valuation dilemma.

The dilemma is that regardless of the integrity of a valuation, there is little assurance that the market will tend towards that valuation. For example, if an analyst determines that a particular stock is worth $60, and the spot price (current market price) is $50, the rational investor would buy the stock (at $50) and wait for the rest of the market to wise up and drive the stock to $60. But the nature of the market is that stocks do not consistently trend toward their valuations.

2) Valuation of a Bond:The following illustrates how the value of a bond is determined. The sample bond, issued by Sample, Inc. promises to pay the bondholder a fixed 5 1/4 % (annual) coupon rate. That is, 5.25% each year of the face value (denomination). By convention, the actual payments are paid every six months in amounts equal to half of the amount due annually. The denomination of corporate bonds is typically $1000. And for this example, let's assume that the bond matures (that is, the firm returns the principal to the bondholder) in the year 2017 [Note: This valuation was done in 2009 when there was 8 years to maturity. Through time, the date of maturity does not change, but the years to maturity changes every year.] This bond would be listed as:SMPL 5.25% 2017 (or some variation of company_name , coupon_rate, date_of_maturity) These three properties of the bond are fixed – they do not change over the life of the bond. If this sounds like an I.O.U. that's because it is an I.O.U.. Further, assume that current market rate for comparable (same risk category) bonds is only 4%. [See also: bond risk] How much should this investor pay for the Simple, Inc. bond? What is its value? The "future cash flow" will be 1) the interest payments of $26.25 every 6-months for 8years, plus 2) the face value of the bond, $1000, at maturity. The firm, Sample, Inc. will eventually pay $26.25x16=$420 in coupon payments, plus $1000 back to the investor, for a total of $1420. But the $1420 isn't all paid today. The present value of that future cash flow can be calculated using "time value of money" concepts. Use the "Present Value of an Annuity" model [see also:……], where the 6-month discount rate is .04/2=.02, the number of 6-month compounding periods is 16, and the annuity payment amount is $26.25. See the spreadsheet bonds.xls for the calculations. The answer is $1084.86.

3) Continuous Compounding: The classic FV=PV(1+k)n model illustrates how more frequent compounding yields greater future values than less frequent compounding over the same period with the same rate. For example: Given PV=$1000, annual rate = 5%, for 2 years yields $1102.50 when compounded annually (twice over the period), but yields $1105.16 when compounded daily. In this example, the frequency of compounding went from 2 to 730 over the two years. Imagine the frequency going to a million, or to a gazillion, or to infinity. That's continuous compounding. In the model FV=PV(1+k)n , k would be equal to the annual rate divided by infinity, and n would equal two times infinity. One needs a little Calculus to handle infinity in an equation, but it can be done, and the

resulting model looks like FV=PV erT, where r=annual rate, T = time, and e is the natural log. To execute this in a spreadsheet, try FV=PV*(EXP(r*T)). You should get an extra penny for all your work, $1105.17.This model is commonly used in valuation of derivatives, for example BSOPM.

4) Loans: Typical “vanilla” loans (so called, recently, to differentiate traditional loans from exotic adjustable rate, up-front points, etc.) have payments equal to the sum of the interest due on the outstanding balance plus a payment that contributes to paying off the principal. The actual formula is PMTS= (PVa x k) / [1-(1+k)^-n] where PVa=present value of the annuity, or the amount that the bank is willing to give to you if you sign a contract promising to pay them a fixed amount (the annuity) every month (the timing of the payments doesn’t HAVE to be monthly, but that’s the traditional timing). K= the rate for the period of compounding (usually the annual/quoted rate divided by 12 months of the year). And n= the number of periods of compounding.

The amortization of the loan can be expressed in a table in which every period (or month) the interest is calculated on the outstanding loan balance using the following logic:Interest $ = (annual rate/12 months of the year) X outstanding balance of the loan.The interest$ are subtracted from the fixed monthly payments to yield the "reduction in the balance of the loan" (Red'n Bal). And when the Red'n Bal is subtracted from the "Beginning Balance" the result is the ending balance for that period. The ending balance of one period is the beginning balance of the next period.

5) Expected Value:Beyond present value/future value concepts, the notion of expected value is often seen in the valuation process. Expected value is the product of the anticipated cash flow multiplied by the probability the cash flow actually materializing. For example, if I roll a die (that's singular for dice) and will pay you $100 if I roll "6", then the value of that game to you equals $100 x .166666…. = $16.67

5. Derivatives: This class of financial contracts has grown to economic significance as a result of financial engineering conducted by hedge funds, banks, and other institutions. The mechanics of mutual funds, index funds, and stock options are regarded in some detail.

5. DERIVATIVES

Derivatives are a general class of financial contracts that have grown to huge economic significance as measured in dollars of positions held and transactions conducted. They are currently highlighted in the financial news as being at least partially responsible for the larger economic meltdown. Yet, for all their detractors, there are many who defend the existence of derivatives as being essential for the flow of cash in a free market system. Regardless of whether derivatives are good or evil, some derivatives will likely survive the character assassination and thus they are entitled to a close regard.

1) Mutual Funds:Mutual funds are incorporated entities created by a parent company. Two dominant examples of parent companies are Vanguard and Fidelity. As the parent company creates a new mutual fund, the contributors (investors) in the fund become the stockholders. With capitalization from the investors, the fund manger re-invests in financial instruments with characteristics that were decided upon a priori into a portfolio that is owned mutually [hence the name] by the stockholders/investors. As a

hypothetical example, if Fidelity decided to start a "Green Energy Fund", they would incorporate the fund, sell shares in the fund, and buy shares of companies serving the environmentally-friendly energy market. As the share prices of the companies fluctuated, so too would the value of the portfolio fluctuate. The net asset value (NAV) of the portfolio and the value of the mutual fund company (not the parent, but the individual fund) are the same, so the share price of the mutual fund changes proportionally also. Hence the term "derivative" – the value of a share of the mutual fund is derived from the underlying assets, the green companies.

1.1) Index Funds:Index funds are a sub-group of mutual funds. Their unique characteristic is that their portfolios are constructed to mirror the performance of a particular market index, for example the Dow Jones Industrial Average (DJIA) or the Standard & Poor's 500 index. Index funds are popular vehicles for passive investors because capital put into index funds are likely to have the same yield as the entire market – with the following exception: fund managers need to be compensated. Typical management expense fees for index funds average about .25% of invested assets per year, so net yields to the fund investor will tend to be lower than the market yield by that fractional percent.

1.1.1) S&P 500 Index Funds:The S&P 500 Index is constructed by S&P (the firm) selecting the top 500 firms according to level of market capitalization. And because each firms influence on the index is weighted by that firm's market cap, then a portfolio (an S&P 500 index fund) that endeavors to match the performance of the index must hold positions in each firm according to the firm's weighting in the index. As a firm's stock price fluctuates continually, the firm's weighting in the index will also fluctuate. But, conveniently, the weighting in the index fund will also fluctuate by the same proportions, as they are based on the same dynamic market value.

1.1.2) DJIA Index Funds:The DJIA is constructed differently than the S&P500. In the DJIA, the firms' influences on the index are weighted according to price per share. Those firms with the higher stock prices have the higher influence. Thus, a DJIA Index fund would be constructed with the same number of shares for each firm in order to match the performance of the index.

2. Options: Options are derivative financial instruments whose values are a function of the price of the underlying asset. The more common underlying assets are stocks, but options may be written on other financial asset classes such as commodities and currencies. The two variations of stock options include calls and puts. Calls give the purchaser the option to buy shares at a pre-determined fixed price (the strike price) from the seller of the option. Puts are options to sell at the strike price. Further, investors may take either side of an option trade – they may buy or sell a call, or buy or sell a put. An option has an expiration date, as a specification of the contract, that is either 1) the one future date at which the option must be exercised or allowed to expire (a so called "European" option), versus 2) the last date of a period during which the option may be exercised (the "American" option). The mechanics of options are relatively straight-forward [See mechanics]. The valuation of options is more complex [See BSOPM]

3. Hedge Funds: Hedge funds are "derivatives" in the sense that the value of a share of a hedge fund is derived from the value of the underlying assets held by the fund , similar to the value of a share of a mutual fund. Hedge funds differ from mutual funds on several dimensions, for instance 1) minimum initial investment in a hedge fund tends to be higher than in a mutual fund by a factor of perhaps a 100. 2) hedge funds are sold privately versus public offering of mutual funds 3) consequently, hedge funds are subject to less scrutiny and less regulation 4) management expense fees for hedge funds tend to be much higher than mutual funds. 5) Hedge funds provide an environment for financial engineering, or the construction and design of new derivatives. (See also: the article "Hedge Clipping" by Cassidy)

4. Credit Default Swaps (CDS): A swap is contractual arrangement between two parties whereby a trade is conducted, no cash is exchanged, and the items traded are similar entities, for example, and in this case, credit default contracts. No cash is exchanged initially because both parties are swapping cash flows of equal net present value. A credit default contract is similar to an insurance policy against the defaulting on a loan obligation, such that if the loan goes into default, the insurer would then be obligated to cover the loan payments. In a credit default swap, the two counterparties exchange their risk (and coverage obligation) of their respective third party defaults.

5. Collateralized Debt Obligations (CDO): Large collections of loans, most of which are typically backed by (collateralized) real estate are called CDOs. After the loans are aggregated, shares of the whole are sold much like shares of stock. The ability to measure the probability of default on an individual loan is challenging enough, let alone measuring the probability of default on a bundle of hundreds, perhaps thousands of loans. Many CDOs received excellent (but totally baseless) default risk ratings from reputable rating agencies, and paid higher yields than instruments of comparable ratings and were popular with large investors. When the individual loans start defaulting, the values of these CDOs become impossible to measure. See Patterson "Math Wizards".

6. FinModels: Here is a sampling of financial models that appear frequently in the literature and the real world, including Pi, Monte Carlo, Brownian Motion, MATLAB, Volatility (VIX,), Black Swans & Fat Tails, LIBOR, and some other indices (DJIA,S&P)

6. FINANCIAL MODELS

Here is a sampling, in alphabetical order, of some other financial models that appear frequently in the academic literature, in the real world and in this course.

1. Alpha: Alpha is the excess return over a benchmark return. For US stocks in general, the benchmark return is the S&P500, or similarly, an S&P500 index fund. The concept is used to measure performance, often of a fund manager, such that a manager who consistently "generates" alpha is "beating the market".

2. Beta: Beta is a measure of risk of a stock relative to the risk of the market. Technically, it is the slope of the regression line y=mx + b derived from the least-squares method where the dependent variable (y) is the return of the stock being measured, versus the independent variable (x), the return of the market. When market returns are regressed against market returns, the slope will equal 1.000 by definition, in other words, the beta of the market is 1.000. Stocks with greater volatility than the market have betas greater than one [ > 1.00], and stocks with volatility less than the market have betas less than one.

3. Black Swans & fat tails: A black swan is an unusual, unanticipated, statistically unlikely, and particularly ugly market event. A fat tail refers to the tails of the probability distribution of returns (or sometimes prices). A fat tail refers to the likelihood of the unlikely happening. See also blackswan.

4. Brownian Motion:Brownian motion was originally observed and defined as a physical phenomenon, specifically, the motion of dust particles in suspension in water. The motion was later associated with bond price movements (See also: Bachelier), mathematically defined by Weiner and Einstein, and is now regarded as the classic model of random movement in stock prices.

5. Dow Jones Industrial Average (DJIA): The DJIA is the standard measure of US stock prices, not so much for its accuracy in reflecting changes in market value, but more for its longevity and exposure in the popular media. It is somewhat narrow in scope, using price information on a stable set of 30 large cap firms. A major flaw in its logical integrity is in its price weighted property – the stocks with the higher nominal price-per-share have greater impact on the index than those of more modest pps.

6. LIBOR:The "London Inter Bank Offer Rate" is a composite index of rates charged by large banks to other banks.

7. MATLAB:The name "MATLAB" is short for "matrix laboratory", where a matrix is a table of rows and columns and the basis of a branch of mathematics – matrix algebra. MATLAB is a proprietary software package owned by Mathworks, Inc. and licensed to PSU for educational use. Within MATLAB there are financial modules that can plot efficient frontiers of portfolios and perform many of the calculations related to the valuation of derivatives.

8. Monte Carlo Simulation:"Monte Carlo" refers to the city in Monaco with the grand casino, and Monte Carlo simulation models use random variables, not unlike the randomness on the roulette wheels at the casino. While there are several variations of the model, they all have the property of being able to integrate probabilities into the outcomes, thus distinguishing them from deterministic models. They are used in financial forecasting because the outcomes expressed as a distribution of results (with related probabilities) can be more useful than outcomes expressed without their related probabilities.

9. Pi ():

One of the most recognized mathematical relationships, pi's connection to finance in its use with the Normal distribution model. Specifically, it is used in computing the area under the curve, or the cumulative distribution function (cdf). While practitioners of finance rarely have the need to actually calculate pi's value, they will see that it is an essential piece in some financial models, for example BSOPM. Students should be comfortable pi's definition and memorize pi to at least a few places past the decimal point. See also Pi.

7. International: The scope of finance is broadened to include a global perspective. The relationship among various world currencies has direct financial implications, illustrated through the mechanics of cross rates, arbitrage, forward, futures, swaps, and international commercial transactions. Also noted are the rationale for global investing, direct foreign investment, EAFE, and MSCI.

7. INTERNATIONAL FINANCE

A variety of new financial issues arise when one broadens their perspective from concentrating on the internal domestic scene to regarding the financial interaction among the various other countries of the world. While many of the traditional financial models still hold true (e.g. portfolio management, time value of money, and corporate finance), these models are made increasing complex with the introduction of differences in currency exchange rates, national interest rates and foreign accounting conventions. With the increasing complexity there is also an expansion of opportunity for new variations of financial activity with foreign investment instruments. Here are some of the more significant financial instruments related to international finance.

1) Foreign Currency Exchange: Every country has an official currency for transactions. Each country's currency's value is stated in terms of every other country's currency. The relationship between the currencies is established by government policy and/or by world markets. For example, an exchange rate between one country's currency and another may be "fixed" by policy, whereby the value relationship doesn't change between it and some other currency (e.g. the Chinese yuan pegged to the US dollar). Or currencies may "float", whereby the value relationship is constantly changing as determined by supply and demand in the currency markets. At any point in time all exchange rates are more or less in equilibrium, and this can be expressed in a "cross rate table".

A student grappling with exchange rates might do well to start with the simple $/€ format. This fraction-like looking expression means "the number of US dollars required to buy one euro". It does NOT mean dollars divided by euros. Further, the exchange rate of $/€ = 1.35 means $1.35 = €1.00. It is true that, similar to a fraction, that the reciprocal of the exchange rate format equals the reciprocal of the value, that is, €/$ = .74074.

Another format for expressing exchange rates is the cross rate table. These tables used to be printed daily in The Wall Street Journal although the numbers are in a constant state of flux. Understanding how to read and how to construct a cross rate table is a useful exercise in understanding foreign exchange.

Cross rates are calculated using the following logic: If $/€ =1.35 and $/C$ = .80, then €/C$ = ($/C$)/($/€) or €/C$ = .80/1.35 = .592593

It should be noted that some countries also have "unofficial" currencies that are used in addition to their official currency. A common example can be found in developing countries in which transactions are conducted with both the official national currency and also with the US dollar. Transactions with unofficial currencies are often illegal (but not always) in the countries where the practice is common.

2. Arbitrage: Currency arbitrage is conducted by professional traders who take advantage of the small dis-equilibrium that occurs among currencies as a result of the floating valuations between the many different currencies. The profits generated by arbitrage trading are small as a percent of the amounts traded, but the amounts traded are huge, transaction costs are small and thus actual dollar profits can be significant. The process of arbitraging currencies has the effect of restoring equilibrium to the currency markets. Arbitrage opportunities are recognized by computers and trades are executed within fractions of a second. There is fierce ongoing competition for faster and faster trading systems among trading houses, because being second best means losing the trade.

Two way currency arbitrage is conducted by professional traders who use super-fast computer systems to scan bank quotes looking for even the slightest imbalance in exchange rates. When banks quote their exchange rates, they list both the bid and ask prices. See also the example below. That is,

€/C$ @ .71076-78 means that Deutsche Bank is offering to buy Canadian dollars at € .71076 per C$ and is willing to sell Canadian dollars at €.71078 per C$. The two-way arbitrage opportunity is created when a second bank, in this case, Royal Bank of Canada, quotes bid/ask prices outside the range, either above or below, the first bank, as in the example below. Over-lapping ranges do not create an arbitrage opportunity.

In the example, a trader could buy Canadian dollars from Royal Bank of Canada at €.71074 and sell to Deutsche Bank at €.71076. The profits are small (.00002/.71074), working out to the equivalent of $28.14 for every $1 million traded, or .002814%. However, if a bank trades in quantities of several million dollars per trade, and trades several times per day, the profits are enough to buy lunch. Note also that the first trade will signal both banks that their pricing structures are out of balance, and they will react quickly to closing the gap and ending the arbitrage opportunity. On the other hand, trades are not guaranteed by law or by circumstances to be immediately transparent to all parties, and thus arbitrage opportunities continue to emerge.

Example: At 13:45 hrs GMT on 9 November 2010 Deutsche Bank quotes €/C$ @ .71076-78 and Royal Bank of Canada quotes €/C$ @.71072-74a) Is there an arbitrage opportunity? Y/N? _yes___b) If so, one would buy from _RBoC___ and sell to _Deutsche Bank_? c) Calculate the return (i.e. the profit as a %) _.002814__%

Three way currency arbitrage is similar to the two way arbitrage, in that it is conducted by professional traders who use computer systems to watch multiple exchange rates simultaneously. When the opportunity arises, the system conducts the trade quickly. In the following example it suggests that a human is doing the trading, whereas the reality is that systems are actually executing the trades.

The mechanics: The trader starts with some amount of currency A. Trader uses A to buy currency B, then, uses B to buy currency C. And finally, uses C to buy currency A. Or, A to B, B to C, C to A. If the currencies were in perfect equilibrium, then the trader would end up with the same amount of currency A as when he/she started. However, when the currencies are in disequilibrium, there is a potential to make a profit through the three-way trade.

There is also the opportunity to lose money after the three trades. If A to B , B to C, and C to A generates a profit, then it is certain that trading in the other direction (A to C, C to B, B to A) will generate a loss. One should not assume that even an experienced trader can identify disequilibrium in currency rates by merely glancing at the various data. So, as an academic exercise, if A to B, B to C, and C to A generates a loss, then a student should recalculate in the reverse order (A to C, C to B, B to A). In the real world, the system does these calculations.

Example: Assume that $/Ps=.092 in Mexico City, and Ps/€ = 16.06 in Zürich and €/$=.675 in NYC. Start with $1M and show the trades (a,b,c) that would yield an arbitrage profit. Note: in sell& buy answers, show both currency and amount. The "trial" is for you to see if your path will make a profit. If it does, then that is your answer. If it doesn't, then reverse direction and put the results in "final".

Trial:a) city__NYC_____ sell_$1,000,000_ buy___________b) city___________ sell__________ buy____________c) city___________ sell__________ buy____________

Final:a) city___________ sell__________ buy____________b) city___________ sell__________ buy____________c) city___________ sell__________ buy____________

Calculate the arbitrage profit as a percent of original investment.__________%

3. Forward Contracts: Forward currency contracts are a popular investment vehicle used for hedging against future changes in exchange rates. An investor with a known obligation to provide funds in a foreign currency at a future date (for example, to pay for imported goods scheduled to be delivered in several weeks) may be motivated to buy forward contracts to lock in the cost of obligation. Forwards are sold for only a few currencies and are sold at a premium or discount relative the current spot price.

The currencies that have forward contracts available are the Canadian dollar (C$), Japanese yen (¥), Swiss franc (SF), and the UK pound (£). Within each of these currencies, there are 1 month, 3 month, and 6 month forwards available. That is, the currency delivery date is one month (or 3 or 6 months) from the date of purchase.

For a given currency, for example the Swiss franc, the forwards may be selling at premium or discount to the recent market or spot price. The forward prices are set by supply and demand and change based on currency traders' aggregate assumptions regarding future exchange rates between, in this case, the US dollar and the Swiss franc. A clipping from the 8 July 2009 issue of The Wall Street Journal from their table called "Currencies July 7, 2009 U.S. –dollar foreign-exchange rates in late New York trading" shows in part the following:

Switzerland franc .91771-mos forward .91803-mos forward .91886-mos forward .9203

The first quote is the spot price of the SF (from the day before) and is in US$ , or number of US$ to buy one Swiss franc, ($/SF). The 6-mos forward is selling at a premium over the spot, and this is generally expressed as a percentage. (.9203 - .9177) / .9177 = 0.00283317 or "the 6-mos forward is selling at a .28% premium". Forwards selling at a premium reflect the widely held assumption that the value of the currency (the SF in this case) is more likely to rise than to fall in relation to the US dollar over the next few months.

4. Futures: Futures are similar to forward contracts in that they represent advance sales of currencies at an agreed upon price. However, only a few specific currencies are traded, they are only traded in a few physical markets (e.g. IMM and CME), and they are only sold in the following fixed denominations:GBP 62,500 Great Britian poundCAD 100,000 Canadian dollarJPY 12,5000,000 Japanese yenCHF 125,000 Swiss francMXP 500,000 Mexican pesoEUR 125,000 euro

5. Options : Options on currency are mechanically similar to options on stocks, indices, and commodities. There are calls and puts, strike prices and expiration dates as with a stock option. Straddle and strangle strategies can be created as with stock options and individual investors as well as institutions engage in this popular market for speculating and hedging.

8. Statistics : Several statistical concepts are essential elements of financial models, these concepts include correlation coefficients, regression analysis, the option Greeks, Logs, ln, e, Normal distribution, and Standard Deviation.

8. STATISTICS(and other scary math concepts)

1. Correlation Coefficients: A "coefficient" is a fancy word for an "index", or a "measurement", and "correlation" might be thought of as "co-relation" – or the relation between two streams (or series) of data. In finance, correlation coefficients are used to measure how closely (or how differently) two data sets follow each other. A common example is the measurement of the returns, through time, of two equities; for instance, how closely do the daily returns of Ford match the daily returns of GM?

The variable "r" is used for the correlation coefficient and the range of possible values goes from r = 1.00 to r = -1.00, where 1.00 indicates "perfect positive correlation", -1.00 shows "perfect negative correlation", and r = 0.00 indicates that there is no positive or negative correlation at all. Perfect positive correlation occurs when the percent change in one series is matched by the same exact percent change in the second series. Perfect negative correlation is when the changes in the two series are the same in magnitude, but opposite in sign.

Using the Ford/GM example above, assume that the two data series consisted of daily returns for 250 consecutive trading days (about one calendar year). Further, assume that on most days Ford and GM's stock prices move in the same direction as the market (sometimes up, sometimes down), but that their

respective "percent change from the previous day" are usually slightly different from one another. And further assume that on some days the percentage changes are in the opposite direction from each other. The correlation coefficient of Ford and GM's daily returns is likely to be "mildly positive", for example r = .342 Note: Correlating Ford with GM

In MS Excel, the correlation coefficient function is "CORREL". Assume Ford's daily returns are in column A, and GM's returns are in B. The correlation coefficient expression would be: =CORREL(A1:A250,B1:B250) See also: Wikipedia "Correlation Coefficient"

2. Regression Analysis: Regression analysis also regards two series of data as does the calculation of correlation coefficients, however, regression analysis treats the two series differently by designating one data series a dependent variable, and the other an independent variable. The regression analysis seeks to measure how much of the change in the dependent variable can be explained by changes in the independent variable.

In finance, the daily returns of the market are often considered the independent variable and the individual security (e.g. Ford) considered the dependent variable. Hence, the question becomes "how much of the daily change in Ford's stock price can be explained by the daily change in the market"

3. Z-Scores: In the Normal distribution, the number of standard deviations away from the mean is called the z-score. The z-score is used to find the percent of the total area under the curve, which in turn, represents the probability of occurrence of some condition (or event) – in this case, the probability of a stock being over (or under or between) some finite price. The area is more technically called the cumulative standard normal distribution. To convert z-score to area/probability, one may use a z-score table.xls, a z-score table.doc, the Excel function "=NORMSDIST(…)", or on a TI-83 there is a fairly easy routine to generate the area/probability (2nd function /DIST. Select #2 on menu. NORMCDF(lower limit, upperlimit) [where lower limit = -1E99 and upper limit=0] and E="EE" on the TI-83 keypad.

9. People: This is a separate area for a collection of significant contributors in the realm of finance, concentrating less on biographical data and more on their particular influence on the discipline.

11. Bibliography : A listing of reference material for this course, the bibliography includes listings of both the on-line readings as well as several reference texts.

LESSONS:

Each lesson module below corresponds to an academic week of this semester. Click on the numbered "lesson" links for detailed instructions.

Lesson 1: Topic: Corporate Finance Readings: VanHorne; Varian (Miller) Text: through pg.32 Exercise: Ratio Analysis

Lesson 2: Topic: Corporate Finance (capital budgeting)Reading: Markowitz; SurowieckiText: through pg.64 Exercise: NPV & MIRR

Lesson 3: Topic: Portfolio Theory IReading: Varian(Markowitz); BogleText: through pg.96 Exercise: port.xls Tiers 1,2,3

Lesson 4: Topic: Portfolio Theory IIReading: Mann; HilsenrathText: through pg.128 Exercise: hyperbola

Lesson 5: Topic: StrategiesReading: Gladwell; Gladding; Text: through pg.160Exercise: CAPM (port.xls)

Lesson 6: Topic: Valuation Reading: Varian(Sharpe); LewellenText: through pg.192 Exercise: Gordon, Vb, loan, Cont. Comp.

Lesson 7: Topic: DeriviativesReading: Mollencamp; CassidyText: through pg.224Exercise: BSOPM

Lesson 8: Topic: Financial ModelsReading: Lanchester; PattersonText: through pg.256Exercise: No. of Firms

Lesson 9: Topic: InternationalReading: Malkiel; KolbertText: through pg.288Exercise: cross rates

Lesson 10: Topic: Final ExamReading: Chernow; SorosText: through pg.320Exercise: Final Exam

LESSON 1:

Topic: Corporate Finance I Reading: 1) Start by reading the corporate finance notes. This will give you an idea of the scope of the topic for the week. Actually, we'll spend two weeks on corporate finance. Many other finance courses spend the entire semester on the topic, but we have lots of other stuff to do.

2) There are two outside (copyright material used by permission) readings for this week. The first reading regards the "objective of the firm", which is about as close as one gets to "the meaning of life" in a finance course. It addresses the question of why corporations exist, what their function is, and it implies that all management decisions in a firm should be made with this objective in mind. The reading is from the textbook by James C. Van Horne that I was assigned to read in MY first finance course years ago, but the message is still completely valid, hasn't changed in the last 35 years and probably won't change in the next 35 years. 3) The second reading for the week, by Hal Varian, is accessed through Moodle. It’s in the "Readings" page in the top block of the main page for the course as well as having a link in the first week’s block. This article has three major sections, and for this first week, you should concentrate on the last section of Varian (on "Miller") because it's Miller's work that relates most closely to corporate finance in general, and to capital structure specifically. As you read about Miller's work, note the connection between the Van Horne work (see above) and Miller's work. Hint: The connection is between “firm value” and “objective of the firm”.

4) Start reading the Justin Fox text, The Myth of the Rational Market. Dividing the 321 pages into 10 equal chunks means that you should read about 32 pages per week in order to finish the book by the end of the term. But these numbers are just suggested “benchmarks” so that you won’t get too far behind. For this week, read through page 32.

Exercise: [See also exer1.doc] This exercise involves using some classic financial ratios to perform an analysis of the firm. The point of the exercise is to experience how some fairly simple calculations can reveal a whole lot about the health of a firm. It is also the first opportunity to have you build a spreadsheet and send it to me. Future quant exercises will be more challenging.

LESSON 2:

Topic: Corporate Finance (continued). There are no new notes on Corporate Finance – just the ones from last week. But this week the concentration is on the capital budgeting function of corporate financial management.

Reading: 1) There are some brief course notes on capital budgeting within the corporate finance notes that you read last week and these could be reviewed as background for the capital budgeting exercise for this week.

2) Also, there is a small reference to NPV and IRR in the beginning of the Varian article (see the indented paragraph on the first page of Varian). You already opened Varian last week when you read about Miller and his work on capital structure. Now note what Varian says about NPV and IRR.

3) With the dearth of lively capital budgeting readings, this might be a good time to read a couple of non-capital budgeting articles. The first is by Harry Markowitz, with some comments about corporate morality [See: Markowitz – Markets and Morality listed in Moodle in “week2” and in the “Readings” page].

4) Another reading [See: Readings/Surowiecki – Performance Pay]. In this article, the author touches on an ever-controversial issue in corporate governance – and it has significant financial implications for both corporate insiders and corporate shareholders. 5) Another source of learning about capital budgeting is The Wall Street Journal. Often around this time of the year there are short articles regarding the aggregate level of capital spending that companies are planning. If companies, in aggregate, are planning to do a lot of spending, that's a sign of growth for the entire economy.

6) Continue reading the Fox text through page 64.

Exercise: The quant exercise is to re-build a spreadsheet, replacing ”value only" cells with "formulas" that you will create. See exer2 for details. It is a capital budgeting project for which you need to calculate some values.

LESSON 3

Topic: Portfolio Management / Modern Portfolio Theory (MPT).

Reading: 1) There are course notes on portfolio management at porttheory.doc. While not lengthy, these notes describe the essence of MPT and provide the logical basis for several of the exercises that you will be submitting over the next few weeks. Therefore, your graded exercises will be easier for you to complete if you can truly understand the content in these few pages.

2) Go back to the Varian article to read the first section on Markowitz. This reading gives some anecdotal history on the development of MPT. Every graduate student of finance studies MPT, but not every student has read about its origins.

3) Also, read the article by John Bogle and Burton Malkiel (one article, co-authors). In reading the Bogle & Malkiel article you may not immediately understand how it relates to what we're doing in this course. You may also be wondering what you should be learning from any of the articles. To this I say: Relax. Just read the stuff. It does relate. Over time it will make more and more sense as the vocabulary and the people become more familiar. The more finance you read, the more you'll realize how little you know. And perhaps you'll be internally conflicted by being both overwhelmed with the quantity of information and interested enough to want to figure it all out.

4) Continue Fox through about page 96.

Exercises: See exer3.doc. This exercise is the first of several that we’ll be doing based on an actual portfolio.

LESSON 4

Topic: Portfolio Theory (continued).

Reading: 1) The course notes on portfolio theory should be re-read for this week, especially the paragraphs about hyperbolas [proper Latin: plural form of hyperbola is “hyperbolae”], because this week's exercise deals with hyperbolas, and they are a topic that you should feel comfortable with.

2) There is an introduction to Eugene Fama’s Efficient Market Hypothesis (EMH) by Charles Mann. The topic is pretty conceptual, but the implications of the theory are far-reaching. And while not all investors believe in the market’s efficiency, most everyone understands what efficiency means in this context.

3) A reading by Jon E. Hilsenrath pits two highly respected academics against each other in "Fama versus Thaler". And while this is only a summary of their arguments, their respective points are well laid out.

4) Continue with Fox’s The Myth of the Rational Market. This week’s benchmark page is 128.

Exercise: In this exercise you will create a hyperbola in Excel [See also: exer4.doc] based on your data in port.xls, using Clorox (CLX) and Hershey (HSY)as firms A & B respectively. CLX and HSY were “cherry picked” from all the firms because 1) they have the classic relationship of low risk/low return for one (CLX) and higher risk/higher return for the other (HSY). In addition, 2) there was a relatively low correlation between the two firms’ daily return patterns. Both of these characteristics help exaggerate the shape of the hyperbola and thus make the results of the exercise conform most closely to the theory.

In exer4 you are asked to build five portfolios, plot each of them onto a single risk/return chart (risk on the horizontal axis, return of the vertical axis). The smoothed line connecting the points is the hyperbola. All the points of the line represent portfolios, each with a different DOLLAR mix of CLX and HSY, starting with 100% CLX and 0% HSY. The second plotted portfolio point will have a 75% CLX and 25% HSY dollar mix. [There is a nasty little step in calculating the number of shares required to have

given dollar mix. See normalized.doc.] The other points will have 50/50, 25/75, and finally 100% HSY dollar mixes respectively.

Submit your hyperbola spreadsheet via Moodle the same way you submitted previous exercises. It would be helpful (for me) if you 1) put your name in the upper left corner where I’ll see it when I open it. Some of your spreadsheets look pretty similar (that’s understandable) and sometimes I get confused as to whose spreadsheet I’m looking at. 2) Save it so that your data and graph appear when opened so I don’t have to scroll around looking for it.

LESSON 5

Topic: This week we look at investment strategies that institutions, individuals and other investing entities adopt to meet their financial objectives.

Exercise: This week’s exercise is based on the Capital Asset Pricing Model (CAPM). The model is reviewed in three readings. The first two readings got misplaced into week6 (next week), but might better be read this week.1) The second section of the Varian article discusses William Sharpe’s development of CAPM. 2) And Lewellen discusses some of the shortcomings in matching CAPM to reality. 3) A quick description of the mechanics of CAPM, recently inserted onto the week5 Moodle homepage.

The exercise itself is to calculate the risk (beta) and return for your portfolio and draw a Security Market Line (SML). See more at exer5.doc

Readings: 1) The course notes on strategies attempts to replace a textbook collection of descriptions of different strategies. The notes are more of a vocabulary lesson and less of a "how-to" manual.

2) You should be about half way through Fox by the end of this week (about page 160

CHANGE: the reading of the two articles below can be postponed until next week.

3) The article, "Blowing Up", by Malcolm Gladwell, is one of my all time favorites. Gladwell's books "Outlier", "Blink", and "Tipping Point" have been on the WSJ business best-sellers lists for several years now. His ability to pull references from such a wide array of subject matter makes even a short article like "Blowing Up" a mother-lode for further research. Here he talks about Nassim Nicholas Taleb and Victor Neiderhoffer (both well-known investors and authors in their own right) and how they came to believe in their own respective (and totally opposite) investment strategies. The story is also a cute little introduction to options trading, a practice that involves billions of dollars of trading every day. There is a greater dollar volume of options traded every day than stocks.

4) A short article by Kent Gladding on Active versus Passive management fits well into this week’s topic of various strategies.

LESSON 6

Topic: Valuation concepts.

Reading: 1) The course notes on valuation discuss the underlying concepts that investor use to determine the intrinsic value of different types of financial assets. Much of the content in these notes are the basis for the valuation exercises that you will be doing this week. 2) The first reading from the published articles include the William Sharpe section (the second section) of the Hal Varian article that relates to CAPM. You also will (or already have) read about CAPM in the Fox text.

3) … and another perspective on CAPM by Jonathan Lewellen ripped out of a college newsletter from my old alma mater.

4) Fox through page 192.

Exercise: The focus of this exercise is to build a spreadsheet that calculates theoretical values of stocks and bonds. In addition, there are two other common valuation models that are to be built – a continuous compounding model and the loan amortization table. See more at exer6.doc.

LESSON 7

Topic: Derivatives

Reading: 1) The course notes on derivatives discuss various general types of derivative instruments.

2) The article by Carrick Mollencamp and Charles Flemming, “El Karoui” [pronounced el CAR wee] describes finance education at a different level in a different country, but there are some amusing similarities to what we are doing in this course. I found the references to esoteric derivative vocabulary intriguing enough to pursue doing more research on several of them.

3) And the second article by John Cassidy gives some insight into the realities of hedge funds. Check out the fees that are paid by investors in “funds of funds” - “2 & 20” plus another “1 & 10” !

4) The benchmark page for Fox is page 224.

Exercise: Here is a chance to work with Black -Scholes Option Pricing Model (BSOPM) to calculate the value of a call option. See also exer7.doc . This exercise requires the use of some relatively sticky math and some not-frequently-used Excel functions. The exercise is do-able, but tears of frustration have been shed in the process.

LESSON 8

Topic: Miscellaneous Financial Models

Reading:

1) The notes on Financial Models regards several models that are well known in the industry and students should recognize their names and function, if not their actual mathematical underpinnings. There is only a tenuous connection among the models – the biggest similarity is that they are all used in finance in one way or another.

2) The readings include one by John Lanchester , Outsmarted has some poignant observations about human beings and markets,

3) . . . and a quickie by Scott Patterson.

4) . . . and don’t forget Fox through page 256.

Exercise: The "number of Firms" exercise is another model that we can run on our portfolio (port.xls). The challenge is to create a graph showing the relationship between 1) the number of different firms in a portfolio versus 2) the risk of the resulting portfolio. In theory, the more firms in the portfolio, the more diversity, and consequently, the less risk. See exer8.doc for some detailed mechanics.

LESSON 9

Topic: International Finance

Reading: 1) The class notes on International Finance include discussions of foreign exchange rates among currencies and descriptions about some financial contracts particular to global transactions.

2) The article by Burton Malkiel, "Keep Your Money in the Market" was published during a precipitous slide in stock prices. In retrospect, we can analyze how good this advice was, but perhaps more importantly, we can learn some strategy from one of the masters.

3) Four months after Malkiel’s article, Elizabeth Kolbert had her article "What was I Thinking" published in The New Yorker in which she makes some interesting connection with Richard Thaler, Daniel Kahneman and Tversky.

4) Fox through page 288. Exercise 9; This is a stand-alone exercise (i.e. does not use port.xls) that forces the utilization of some specifically "international" models including manipulating cross rates, building a cross rate table, expressing the mechanics of arbitrage (both 2way and3 way), and calculation of forward premiums. See more at exer9.

LESSON 10

Topic: Final Exam

Reading: 1) There are no new content notes for this last week, but you are invited to peruse the statistics module for a few handy models for your intellectual tool kit.

2) For this final week you may be inclined to skip a reading, but Ron Chernow has a cautionary tale about Ponzi schemes – an investment “instrument”, or perhaps a strategy, that has seriously damaged the financial health of many intelligent investors. This one article may save you from blowing up in the future.

3) And George Soros, an interesting (and financially successful) fellow, gives us some final words on credit default swaps. The article is not exactly a capstone, wrap-up piece, but the fact that you can now read it with greater understanding than you might have been able to do ten weeks ago may give you a small sense of confidence and satisfaction.

4) Fox: finish the book.

Exercise: Exercise10 is the last exercise of the course. It is also your final exam, so it's a little longer than usual, but it's all work that you've done before. It will count somewhat more than the previous exercises, so allow yourself enough time so that you can do it well. There are a collection of questions based on the previous nine weeks of exercises and the models that you've already built. Don't hesitate to email me if you are uncertain about a question or the proper approach to a solution. The details are in exer10

EXERCISES:

A listing of the quantitative exercises to be completed, one per week.

1) Ratio Analysis: This is a classic analysis of the financial viability of the firm. While there are many other ratios that one may use to gain insight into the financial well-being of the firm, the ratios of this exercise are common and a representative sampling. The point of the exercise is to practice measuring a firm's health. See also: exer1.doc

EXERCISE 1

Ratio Analysis:(See also the page on financial analysis)1) Open sample1.xls. Save it as "ratio.xls" to your local drive. 2) Regard IBM's income statement and balance sheet, copied from Yahoo, for the year ending 31Dec08 and prior years. The data from these IBM statements have been retyped into the tabs “income” and “balance” at the bottom of sample1.xls. The tab “ratios” shows the results of doing a ratio analysis on these data.3) Assume that you are a financial analyst updating this ratio analysis. Start by getting the latest data on IBM, either from “finance.yahoo.com”>get data for “IBM”>income statements & balance sheets. Or click on these saved pages: ibminc10 and ibmbal10. Update tabs “income” and “balance” in your file.4) Also regard IBM's current market data from Yahoo's finance page. [Here’s a recent sample, but yours should be even more current]. Take the PE ratio and pps directly from Yahoo and enter them into your ratio.xls file. Overwrite the date that you downloaded this data into the appropriate cells (see the old

dates?). For the "Market to Book" ratio, take "Mkt Cap" from Yahoo and divide it by shareholders equity from balance sheet.5) As you update the various ratios, use Excel formulas as much as possible, for example use “=B7/F5”, or “=49004/42435”rather than typing in the actual number. This allows the reviewer of your work to see where you got your answers – especially helpful if your answers aren’t exactly correct. Indeed, for the calculated cells, you MUST use formulas (and not actual values) as input in order to receive full credit for your work.6) Notice column E in the ratio tab. These are brief comments regarding the change in the ratios and whether they are going in a favorable direction. To say that a value is getting bigger or smaller is not saying whether the firm is getting better or worse in the particular area that the ratio measures. Change the comments to reflect the changes from 2009 to 2010. Your comments will be the real “analysis”.7) Put your name in cell A1 of the first tab, and ensure that A1 is selected when you make the final save of your file. This way, when I open it, the selected cell will show your name and I won’t get it confused with all the other “ratio.xls” files that I’ll be opening.8) Submit your "ratio.xls" to me via Moodle. When you submit, see if you can find a block in which to leave a comment for the instructor – and please leave a comment. The comment may be as trite as “have a nice day” or more substantive e.g. “I hated this exercise”, but in aggregate, the comments give me vital feedback on the value of the exercises and assures me that the exercises are being submitted by real people and not some robot in an online mill.

2) Capital Budgeting: A typical capital budgeting project is evaluated for a period of five or ten years into the future. The standard metrics including NPV, estimated change in price per share (est Δpps), and modified internal rate of return (IRR*) are used. This exercise requires the student to make those calculations on a given cash flow. See also: exer2.doc

EXERCISE 2

NPV & IRR*

Regard the sample spreadsheet (sample2.xls) in which the net present value (NPV), estimated change in price per share (est Δpps) and modified internal rate of return (IRR*) for a project are calculated. The formulas for the cells have been intentionally suppressed in sample2.xls. The point of the exercise is for you to write your own formulas in your own spreadsheet so that new input data may be inserted and new results calculated. 1) Start by copying sample2.xls into a new worksheet that you will save as "npv.xls". 2) Save the file as an "Excel 97-2003 Workbook", not the default Vista format. 3) For every cell with black numbers, enter a formula overwriting the original data. Do NOT use the "NV" or "MIRR" functions available in Excel – show that you understand those models and can re-create them with basic +,-,*,/,^ operators. It's OK to use the "=sum( )" operator – I assume you could re-create that function . I will regard the formulas in your cells (there may be several correct variations) and will change a cell or two of input data to see if your spreadsheet works. Row 5: Use the same cash flows as in the sample spreadsheet,Row 6: Use the original discount rate for year 0, but increase it each year by the step amount shown in E20.

Row 7: Calculate discount factors based on (1+k)-n Hint: In Excel =(1+B6)^(-B4)Row 8: Calculate present value based on PV=FV(1+k)-n

Row 9: NPV=sum of the PVsRow 11: calculate the change using (NPV /No of shares). Remember: NPV is in thousands of dollars.Row 12: reinvestment rate equals original discount rate.Row 13 : reinvestment factors based on FV=PV(1+k)n Note: the exponent is positive.Row 14: calculate the future values (in year 5) for the reinvested cash flowsRow 15: Add up the future valuesRow 16: Original investmentRow 17: Divide TV by Original Investment. Raise to the 1/5th. Subtract 1. and using some changes in data as shown below in the "Note", re-calculate:1) the net present value (NPV) of the project, 2) the estimated change in price per share (pps) ,3) the modified internal rate of return (IRR*). Note: 1) For NPV, use the ascending discount rate model with an original "discount rate" of 15% for "year 0" and a 3/8% increase each year. 2) For "est change in pps" assume a half million shares outstanding,3) For IRR*, use a reinvestment rate of 15% for all 5yrs. 4) Submit your npv.xls to me via Moodle.

3) Port.xls: Stock price data is given representing a typical portfolio. The raw pps data is used to generate market values and daily returns. The daily returns data will be used in subsequent exercises to illustrate portfolio management concepts. See also: exer3.doc

EXERCISE 3

Creating port.xls:

In this exercise, you are given actual stock price data from an actual portfolio. You are to use the raw pps data (tier1) to generate market values (tier2) and daily returns (tier3). The daily returns data will be used in subsequent exercises to illustrate portfolio management concepts. A sample structure of port.xls can be seen at sample3. Your port.xls will be much larger than the sample. Note: Prices have been adjusted for stock splits. Dividends are ignored. Market data (last column) is the S&P500 Index (^SPX is the old ticker symbol, the new symbol is ^GSPC).

1. Open the Excel spreadsheet file called "portmaster.xls".

2. Save a copy to your local drive, name the file "port.xls" and save it as an "Excel 97-2003 Workbook".

3. Build a second block of data (tier2, market values) directly and immediately below tier1. Start by copying all the dates from tier1 into tier2 [this may already have been done for you]. Next, calculate the market value (pps x number of shares) for every day for every firm. Finally, calculate the market value of the portfolio (col. B) = the sum of all the stocks' market values. Note: The S&P500 data [^GSPC] should be copied from tier1 into tier2. This market data is being shown for comparison and is not part of the portfolio.

4. Build a third block of data (tier3, daily returns) directly and immediately below tier2. Calculate the daily returns for every stock for every day (except for the first day). Use the basic model of (new-old)/old. [What happens if you use new-old/old ?]. You cannot calculate a return for Day1 because you don't have the data for Day0. The first return is on Day2. Also, calculate these daily returns for the portfolio and for the S&P500 index (this needn't be an extra step – you can calculate daily returns for the portfolio, all the firms, and the market all in one copy- formula operation.

5) Calculate Standard Deviation using the Excel function =STDEVP on the daily returns for each stock, for the portfolio, and for the S&P 500. Place these data in a row under tier3.

6) Calculate total annual returns by using “(lastday marketvalue – firstday marketvalue)/firstday marketvalue” to calculate total annual returns for each stock, for the portfolio, and for the S&P 500. Place these data immediately under the standard deviation data.

7) Send your port.xls through Moodle’s "Assignments" link, the same way you've been sending previous assignments. Remember- accompanying comments are appreciated.

4) Hyperbola: Using two firms from port.xls, a hyperbola is created that results from plotting the risk/return profile of the set of all portfolios comprised of those two stocks as the dollar mix goes from 100% stock A with 0% stock B to 0% Stock A and 100% stock B. See also: exer4.doc

EXERCISE 4

Creating a hyperbola:

1) General: Given the data of two firms (stock A =Clorox; stock B = Hershey) from your port.xls use Excel to create the hyperbola that would result from plotting the risk/return profile of the set of portfolios comprised of the two stocks as the dollar mix goes from 100% of the dollars in stock A and 0% in stock B, to 0% in Stock A and 100% in stock B. For this exercise, you will generate data for five of

these portfolios. The data will be risk and return, where risk is the standard deviation of the daily returns of the portfolio and returns is the total annual (or 12 month) return. The first portfolio has a dollar mix of 100% Clorox and 0% Hershey, the second 75% CLX & 25% HSY, third 50/50, fourth 25/75, and the fifth 0% CLX and 100% HSY.

Note item 7 (below) that contains a couple of videos. It may be helpful to watch the videos first to get a general sense of what we are doing before trying to follow the step-by-step building of the hyperbola. Also, keep in mind that the data used in the video is from previous semester and will not match your data perfectly.

2) Setting Up: Open your port.xls. Copy the entire spreadsheet (currently and presumably on "Sheet1" tab at the bottom of the page) to "Sheet2" (in the same .xls file). Rename “Sheet2” to “Hyperbola”. While in "Hyperbola", enter zeros for "no. of shares" for all the firms. [This is called initializing the data]

Create five new rows of data immediately below the “total annual return” and “Std Dev” rows below Tier3.

Newrow1: Contains 5 labels in Col B through F: "port1","port2","port3","port4","port5"

Newrow2: Col. A= "stdevps" as a label for port1, port2, port3, port4, and port5.

Newrow3: Col. A= "Annual Returns" as a label for port1, port2, port3, port4, and port5 in Col B thru F.

Newrow4= Normalized no of shares for stockA for port1,port2,port3,port4,port5

Newrow5= Normalized no of shares for stockB for port1,port2,port3,port4,port5

Note: Use dollar mix of 100/0, 75/25, 50/50, 25/75, and 0/100 for port1, port2, port3, port4, port5. For Example: The Normalized no of shares for port2 are as follows: stockA = .75*original normalized amount, and stockB=.25*original normalized amount.

3) Run the numbers: For the 1st iteration: Cut’n”PasteSpecial/values” the 1st set of normalized no of shares to A. That is, go to Newrow4, col port1, grab [copy]the normalized no of shares for A and paste ("paste special"/"values") into "no of shares" for stockA at the top of the page. This is a good time to "split screen" so that the top and bottom of your spreadsheet shows at one time.

(You might cut'n paste StockB's no of shares, too, except they should already be at zero)

Your port1 data (stdevp and returns) should reflect the same as StockA’s because there is only one stock in the portfolio.

Cut'nPaste Special /values the portfolio's "Stdevp" and "Annual Returns" to Newrow2 and 3, colB “port1”. Save your work. It’s critical that you “cut ‘n paste special/ values” and NOT cut’n paste the formulas because after they are pasted, you’re going to change the master portfolio’s numbers but you want the port1 numbers to remain the same.

2nd iteration: Cut’nPaste the next set (port2) of normalized no of shares (Newrow4 & 5) to A & B "no of shares" at the top of your spreadsheet. This will reduce the no of shares in A, increase the no of shares in B, and change the composition of your portfolio and change the portfolio's return and stdevp data. Cut’nPaste the new Portfolio’s return & stdevp to col: port2, Newrow1&2.

3rd iteration: Similar to the 2nd iteration, i.e., use Newrow4&5 data for the next portfolio, cut'npaste the data into "no of shares" at the top of the page, scroll to the new portfolio return & stdevp data, and cut'npaste this new data into Newrow 2&3.

4th iteration: Do the same procedure for port4.

5th iteration: Do the same procedure for port5.

4) Draw the Hyperbola: Now you have the data required for the hyperbola in Newrow2 and Newrow3. Use the Excel charting routines to generate a graph [Insert/Charts (scatter)/Scatter with smooth lines and markers" or the older name: “scatter with data points connected by smooth lines”.]

5) Note: The instructions above are just a description of one approach to solving the problem. That approach might be described as: Build one portfolio. Copy the results (stdev & returns) to a table. Modify the portfolio. Copy the results. Modify & copy. Modify & copy. Modify & copy.

The steps will be difficult to follow unless there is a general understanding of what the outcome should look like. But this is the approach that I used in sample4.xls.

A totally different approach to the same problem would be to build 5 portfolios all on the same sheet. For the five portfolios, the columns could be:

1st col: 1st port = 100%clx

2nd col: 2nd port = 75% clx + 25% HSY

3rd col: 75% clx

4th col: 25% HSY

5th col: 3rd port = 50% clx + 50% HSY

6th col: 50% clx

7th col: 50% HSY

….etc

The advantage of this alternative approach would be that the sheet could be built once and remain static and unchanging.

6) Deliverable: Place your chart immediately below your data in “Hyperbola” sheet and leave your cursor near your chart at your last “save”. When I open your port.xls, your chart should come up on the screen so that I don’t have to look for it. Upload your port.xls to Moodle assignments – and don’t forget to add a comment about how much you enjoyed this exercise.

7) Videos: There are a couple of videos that show the process for building the hyperbolas at the following websites. There are two because the first video gets chopped at some “time-max” and the 2nd video is a continuation of the process.

http://screencast.com/t/MzAxZjdjMDIt Building a hyperbola

http://screencast.com/t/ZWU4ZGM0MTMt Building a hyperbola (continued)

5) Betas & CAPM: Betas are calculated for all the firms in the portfolio. They are then plotted against total annual returns to generate a scatter plot. Two lines are added to the graph – a theoretical Security Market Line (SML) and an empirical trend line. See also: exer5.doc

EXERCISE 5

CAPM & beta:

The goal of this exercise is to calculate risk and return data (a.k.a. "risk/return profile") for all the firms in the portfolio (as seen in port.xls) as well as risk/return profile for the entire portfolio and for the market. Having calculated the data, the secondary goal is to draw a Security Market Line (SML) that graphically represents the data. [Actually, below I’m asking you to draw TWO SMLs, a theoretical SML, and an empirical SML]. All the work is to done in your current port.xls.

1) Calculate the betas of all the firms in the portfolio (plus the portfolio and the market). Save them into a row below Tier3 on Sheet1 in port.xls. Use the Excel function SLOPE [Remember that the beta is the SLOPE of the regression line that is the result of regressing Ke against Kmkt] to make the calculations, as in =SLOPE(range of daily returns for the dependent variable, range of daily returns for the independent variable). Your first Excel cell format might look something like:

=SLOPE(B500:B750,AC500:AC750) Although actual rows and columns might be different for your spreadsheet. See also: sample5.xls

2) Calculate the total annual returns of each security (plus the portfolio and the market). This return calculation will be (last day mkt$-first day mkt$)/first day mkt$.

3) Create a scatter plot of risk/return profiles (of all the firms plus the portfolio plus the market) on a graph with risk on the horizontal axis, returns on the vertical axis.

4) Superimpose a line running from the current risk-free rate (use LIBOR=2.5%) to the risk/return point of the S&P500 (use Total Annual Returns of the market as the "expected market return". This line is the theoretical “security market line” (SML).

5) Superimpose a second line, a "trend line", or a regression line that best describes the actual points. This is the empirical SML.

6) Formatting the deliverable for presentation and submission: Create a new Excel file called “exer5.xls”. Copy from your original port.xls into the new file Tiers 1,2,& 3, plus the beta and return calculations, plus the graph. Move the cursor/selected cell to somewhere near the bottom of the sheet and do a final save so that when I open your exer5.xls I’ll see the graph and the relevant data. I don’t want to have to search around for your graph - not that I’m lazy (which may or may not be true) but I want to be sure that I can find it. Submit exer5 via Moodle.

6) Valuation Models: A spreadsheet is created with a variety of valuation models, including models for stocks, bonds, loans, continuous compounding, and annuities. See also: exer6.doc

EXERCISE 6

This exercise requires the building of a single spreadsheet with multiple modules. Each module will be a little valuation calculator for an assortment of financial instruments. See sample6.xls for an example of the format for your exer6.xls. Your task is to build formulas in the output cells so that when the inputs are changed, the outputs will change accordingly. Use the inputs and outputs in sample6.xls to check your formulas. Then replace the input with the new data (shown below in “New Inputs”) to get new outputs. Save the new results before submitting to Moodle.

1) The first module will have two parts. The first part will calculate the value (pps) of a share of stock using Gordon's model. The givens are: expected growth rate (g), last year's dividends (D0), and required rate of return (k). The second part will use the same model, except it will solve for required rate of return, given the current price per share.

2) The second module will calculate the value of bond (Vb). Inputs are: rates for comparable securities, interest payments on the bond, and years to maturity.

For the 2nd part of this module (on the right), use "trial and error" in "mkt rates" to find that rate that calculates the actual closing price.

Hint: Go to "Office Button/Excel Options/Advanced/Editing Options/ uncheck the "After pressing Enter, move selection". Then "OK".

Or for a more sophisticated approach, use the Excel routine that does the trial and error for you. Try the “Data” tab, “What-If-Analysis”, “Goal Seek”, where “Set cell”=G19, “To value”=1200, “by changing”=F16.

3) The third module will have two parts dealing with continuous compounding. The first part will calculate the future value (FV) of an asset given a present value (PV), a rate (k), and the length of time (T). The second part will calculate the present value (PV) given FV, k & T.

4) The fourth module will calculate monthly payments on a typical loan, given the amount of the loan, the annual rate, and the time of the loan. Then an Amortization Table is built, using the monthly payments (calculated above). You can read more about the construction of amortization tables in valuation.

New Inputs:

1) g=.06 Do=3.05 k=.12 solve for pps

g=.06 Do=3.05 pps=40.00 solve for k

2) coupon=.0688 mat_yrs=10 mkt rates=.0575 solve for value

Coupon=.075 mat_yrs=15 close= $1200 solve for mkt rates

3) pv= 2500 rate= .06 T=2.5 solve for FV

Rate=.075 T=1.25 Fv=37,000 solve for PV

4) PVa=23,750 no of yrs=5 Annual rate=.07 solve for PMTS and generate table

7) BSOPM: Black-Scholes Option Pricing Model (BSOPM) is representative of sophisticated approaches to complex derivatives. This exercise gives students the opportunity to translate the model from a verbal and mathematical description to their own spreadsheet. See also: exer7.doc

EXERCISE 7

Black - Scholes Option Pricing Model (BSOPM):

This exercise requires you to build a spreadsheet that will take the input variables S,K,r,T, and σ, to calculate C, the price of the call. See also: bsopm.doc , bsopm1.jpg , bsopm2.jpg and sample7.xls. The format of your spreadsheet should be the same as sample7.xls.

Note that there are two calls in the sample. The one on the left uses the same inputs as in the “bsopm2.jpg” file and was constructed as a check of the formulas. The other call, on the right, the so-called "dynamic" calculator allows you to input different variables and to see the results, without corrupting the original calculations on the left.

Here's what you should do:

1) Open my sample7.xls and save as your exer7.xls

2) Create formulas in the yellow highlighted cells. The results of your formulas in exer7.xls should generate the exact same data as in my sample7.xls

3) Enter this NEW input data into the right-hand “dynamic” calculator

S= $75.75, r= .0222 K= $74.00 T=.5 σ= .25

4) Save your results and submit your exer7.xls via Moodle.

Here are some supplemental comments to help you make the leap from the bsopm1.jpg & bsopm2.jpg files to your own exer7.xls worksheet:

a) The value of the option, C, is equal to…,

b) the current stock price(S) of the underlying stock, multiplied by…

c) a cumulative probability, N(d1), where the z-score= d1,

d) Subtract from the product calculated in "bxc shown above" the following:

e) the "discounted strike price" of the option, multiplied by…

f) the cumulative probability (Nd2), where the z-score=d2.

And here are some more hints applicable for when you are in Excel:

h) To calculate “e-rT “, use the Excel function "=exp(-r*T)", where r and T are replaced with cell locations. Or

i) use a rough equivalent of "e", where e=2.71828182845905

j) To calculate ln(S/K), use the Excel function "=ln(…)" where S and K are replaced with cell locations. Note: “ln” is lowercase LN, NOT uppercase “I” [pronounced “eye”] n.

k) To calculate N(d1) [read: "the N of D sub 1"] use the Excel function "=NORMSTDIST(z-score)", where z-score is replaced with the cell location of D1. D2 and N(D2) are handled similarly to D1 and N(D2).

8) No of Firms: Using the existing port.xls, students address the question of how many different securities it takes to be fully diversified. A graph is generated that implies an answer. See also: exer8.doc

EXERCISE 8: Number of Firms (NooF)

Updated: 27 Oct 2010

The Question: How many (randomly selected) firms does one need in his/her portfolio in order to be diversified enough to have the same risk as the market?

The Model: The adjacent chart shows that as more firms are added to a portfolio, the risk of the portfolio tends to decline to the level of the market's risk (systematic risk). The first point on the left on the red line represents a portfolio with one security. The risk of the portfolio is thus the same as the risk of that single security. The next point shows how the addition of a second security to the portfolio reduces the risk of that portfolio. With the addition of each additional security, the portfolio tends to diminish until it reaches the market risk. Note that the market risk is the same as the risk of a portfolio with every publically traded security included. [from: porttheory.doc]

The Assumptions:

1) Individual firms are riskier than the market as a whole;

2) As more firms are added to the portfolio, the overall volatility of the portfolio will decline.

3) At some point (i.e. at some number of firms having been added to the portfolio), the volatility of the portfolio will be [virtually] the same as the market.

Creating the Chart:

Create a chart in Excel showing the declining standard deviations of a portfolio (use your port.xls) as additional firms are added to the portfolio. The vertical axis is “std dev”, the horizontal axis is the “number of firms” in the portfolio (ranging from 1 to “no of firms in portfolio”). Also, show the standard deviation of the market as an extended horizontal line.

Recommended methodology:

Copy the first three tiers onto a new "sheet" (but still in "port.xls"). Rename the sheet “noof”.

Calculate standard deviations of the daily returns of the portfolio, every firm, and the market [you may have already done this]. This STDEVP row should probably be immediately under tier3.

Sort the firms (but NOT the portfolio or the market), from left to right, highest to lowest, by stdevp of the firms. Include firm labels, no of shares, daily prices (tier1), market values (tier2) and daily returns (tier3) in your sort. [Note: This step is cheating. Do you see why?]

Go back to top of Tier1.

Insert a new row above "No of shares". In this new row, calculate for all firms a NEW "no. of shares" to equal a normalized no. of shares for $10K. =$10000/average(share price)

Set all the ACTUAL no. of shares to zero ["initializing the data"]

The market value (Tier #2) should show all zeros.

Copy (and “paste special”/” values”) the first firm's “no of shares” to the initialized row.

Split your screen [drag down that tiny little bar above the scroll bar] Go to the bottom where you have the portfolio's stdevp

Cut 'n paste special/values the stdevp of the port (into the new blank next row down) in the col for the first firm.

Go back to top. cut 'n paste special/values the 2nd firms normalized no of shares to the initialized no of shares row.

Go back to bottom and cut 'n paste special/values the new stdevp of the port to the col for 2nd firm. Continue for all 30 odd firms. The stdevps of the portfolios are the data to plot on your graph.

Add the stdevp for the market as a horizontal line.

Put your name at the top of the sheet. Save the file. Send it to the instructor via Moodle.

9) Cross Rates and Arbitrage: This is an opportunity to practice working with exchange rates, building a cross rate table, working through two arbitrage scenarios (the two-way and three-way arbitrage) and calculating forward premiums and discounts. See also: exer9.doc

10) Final Exam: The final exercise will be a recap of all the prior exercises. Using a new spreadsheet and previously constructed ones, students work through problems that they have done before, except with new data. See also: exer10.doc

EXERCISE 10

Updated 8 May 2011

To START: Open sample10. Save as exer10.xls.

1) Ratio Analysis: Open finance.yahoo.com. Find most recent financials (income statement, balance sheet dated 26 Sept 2010), and current market data (8 May 2011 or later) for Apple, Inc. (AAPL). Save copies of those web pages as local files (your files).

In your file "exer10.xls", click on the "RATIO" tab at the bottom of the sheet. Fill in cells B3 thru B10 with data from Yahoo. Create formulas in cells B13 thru B18 to yield the appropriate output. Use space at right of inputs and outputs to do any intermediate steps. Outputs that you calculate in the RATIO sheet will automatically be read into the MAIN sheet. Hint: Refer to exer1.doc and sample1.xls for review of ratio concepts.

2) Capital Budgeting: Given a cash flow and a discount rate, calculate NPV and IRR*. Use "CAP BUD" sheet (See tab at the bottom of exer10.xls) to do the calculations for NPV and IRR*. Use cells B4 and B5 (in CAP BUD tab) for your answers. And similar to step 1, cells in the MAIN tab have already been set to equal B4 and B5 (in CAP BUD)

3) Portfolio Management: Tab PORT includes some price per share data. For this exercise we will only use a few days worth of data. Calculate the market values for the three firms (pps X no of shares) to fill in tier 2. Calculate the market value of the portfolio by adding the market values of the three firms. Calculate the daily returns of the portfolio, the three firms, and the market (S&P500) using (day2-day1)/day1. Calculate the standard deviation (=STDEVP) of the daily returns for the portfolio, the firms and the market. Calculate the total return (from 30Jun06 to 10Jul06) for portfolio, firms, and market.

4) Hyperbola: Continue working in the PORT tab to create a hyperbola using Clorox (CLX) and Nestlés (NSRGY.PK) stock. Their data can be found in columns M through P and rows 3 through 762. The data is laid out in the three tiers, similar to the previous problem 3 (above). Note: Tiers 2 & 3 were pasted “values only”. You’ll need to replace the values with formulas in order to see upated values in the “portfolio” column.

First, calculate the "normalized no of shares" (NNOS) for CLX and NSRGY.PK that would yield $10,000 worth of stock for each firm (=10000/Avg pps). There is a scratch box (G thru L in PORT tab) for you to work in. Then replace O3 & P3 with NNOS for CLX and ZERO shares for NSRGY. Calculate the “std dev” and “total K” for the Portfolio and put the numbers in I6 & I7. Next, change the no of shares of NSRGY to its NNOS and put the new “std dev” and “total K” in J6 & J7. Last, zero out the number of shares of CLX and put the resulting std dev and total K in K6 &K7. Note, the 50/50 portfolio will be twice as large as the 100/0 and the 0/100 portfolio, but that’s OK - the std dev and total K data will be the same as if we had held the total dollar value constant for all portfolios. Insert" a "scatter" plot (X-axis =std dev, Y-axis =total K, with smooth lines) representing the hyperbola plotted from a set of portfolios going from 100% CLX to 100% NSRGY.PK (with a 50/50 mix about half way between.) Save the chart somewhere in tab PORT. Also, try to copy the chart into the MAIN tab in the upper right corner within rows 1-12 and columns G through N. Do not change the formatting of the MAIN sheet in exer10.xls – that will mess up my viewing of your other data.

5) Betas: Continue working in PORT tab, but return to the left side to calculate the betas for the portfolio, the three firms (YHOO, GE, MMM) and the market. A space for the answers is on the lower left and is linked to the MAIN tab. There is no chart required in this step.

6) Valuations: Open the VALUATION tab and make the calculations for 1) expected stock price; 2) Bond valuation; 3) Continuous Compounding; 4) Payments on a loan; and 5) the first few periods of a loan amortization schedule (do only three periods for this exam). Use the "inputs" as the "givens" for all your calculations.

7) Black-Scholes Option Pricing Model: Open the BSOPM tab. Use the inputs as shown. Create (or copy from previous exercises) the formulas to yield the intermediate variables and the final price of the call option. Your answers from tab BSOPM should copy into the MAIN tab automatically.

8) International Currency: 1) Open the tab CURRENCY to find the beginning of a cross rate table based on current data. Complete the table. Hint: The first row will be the reciprocal of the first column. 2) Calculate the forward premiums (or discounts) related to the UK pound as of last week.

9) Comment on The Myth of the Rational Market: Write a sentence or two about the value (or lack thereof) of the Fox text to your understanding of the discipline of finance. Your comments will have NO influence on your course grade, but they may influence my continued use of this text.

10) Processing your final exam: Save your exer10.xls to your local files. Send a copy of exer10.xls via Moodle “assignments” as you have done in the previous exercises. Include a “note” with your exercise commenting on the final exam only (required). Reserve any ancillary comments about the course as a whole for the student course evaluations which should have been made available separately by the PSU grad office.

Do not hesitate to email me if you have questions regarding this final. Good luck.

* Bogle, John C. and Malkiel, Burton G. "Turn on a Paradigm?" WSJ 27 Jun 2006

http://library.plymouth.edu/r/http://proquest.umi.com/pqdweb?index=0&did=1066945591&SrchMode=1&sid=10&Fmt=3&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=12 48270016&clientId=15825

Alternate link:

http://oz.plymouth.edu/~harding/BU5120/bogle_malkiel.doc

Cassidy, John. "Hedge Clipping" The New Yorker 2 Jul 2007 p. 26-33

http://www.plymouth.edu/library/redirect.php?http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=25570438&site=ehost-live

Alternate link:

http://oz.plymouth.edu/~harding/BU5120/cassidy.htm

Chernow, Ron. "Madoff and his Models", The New Yorker, 23 Mar 2009 p. 28-33

http://www.plymouth.edu/library/redirect.php?http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=36966991&site=ehost-live

Gladding, Kent W. “Timely Topics: Active v. Passive”

http://oz.plymouth.edu/~harding/BU5120/gladding.jpg

link check: 4 jan 2011

Gladwell, Malcolm “Blowing Up”, The New Yorker 22 Apr 2002 p. 162-173

http://oz.plymouth.edu/~harding/BU5120/blowingup.htm

link check: 4 jan 2011

* Hilsenrath,J. "As Two Economist Debate Markets…” WSJ, 18 Oct 2004

http://library.plymouth.edu/r/http://proquest.umi.com/pqdweb?did=714793231&sid=2&Fmt=3&clientId=15825&RQT=309&VName=PQD

Kolbert, Elizabeth. "What was I Thinking" The New Yorker, 25 Feb 2008 p.77-79

http://www.plymouth.edu/library/redirect.php?http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=30033233&site=ehost-live

Lanchester, John. "Outsmarted" The New Yorker, 01 Jun 2009. p. 83-87

http://www.plymouth.edu/library/redirect.php?http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=40636862&site=ehost-live

Lewellen, Jonathan “"How the World Works. Sort of." Tuck Forum Winter 2007 p. 3

http://oz.plymouth.edu/~harding/BU5120/lewellen.jpg

* Malkiel, Burton G. "Keep Your Money in the Market" WSJ 13 Oct 08

http://library.plymouth.edu/r/http://proquest.umi.com/pqdweb?index=0&did=1573969541&SrchMode=1&sid=2&Fmt=3&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=124 8266264&clientId=15825

Alternative link:

http://oz.plymouth.edu/~harding/BU5120/malkiel.doc

Mann, Charles C. ”Fama’s Market” Investment Vision Oct/Nov 1991

http://oz.plymouth.edu/~harding/BU5120/mann1.jpg

http://oz.plymouth.edu/~harding/BU5120/mann2.jpg

http://oz.plymouth.edu/~harding/BU5120/mann3.jpg

* Markowitz, Harry. Markets and Morality, WSJ 14 may 1991

http://library.plymouth.edu/r/http://proquest.umi.com/pqdweb?index=0&did=27695649&SrchMode=1&sid=9&Fmt=3&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=12482 69798&clientId=15825

* Mollenkamp,C. & Flemming,C. “Why Students of Prof. El Karoui Are in Demand” WSJ 09Mar06 pg. A1

http://library.plymouth.edu/r/http://proquest.umi.com/pqdweb?index=0&did=999733071&SrchMode=1&sid=8&Fmt=3&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1248 269674&clientId=15825

* Patterson, Scott "Math Wizards Working On Spells to 'Cure'" WSJ 23 Feb09

http://library.plymouth.edu/r/http://proquest.umi.com/pqdweb?index=0&did=1649534951&SrchMode=1&sid=7&Fmt=3&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=124 8269497&clientId=15825

* Soros, George. "One Way to Stop Bear Raids" WSJ 24 Mar 09

http://library.plymouth.edu/r/http://proquest.umi.com/pqdweb?index=0&did=1665845251&SrchMode=1&sid=1&Fmt=3&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=124 8269150&clientId=15825

Surowiecki, James. "Performance Pay Perplexes" The New Yorker 12 Nov 2007 p.34

http://www.plymouth.edu/library/redirect.php?http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=27413047&site=ehost-live

Van Horne

Varian, Hal “A Portfolio of Nobel Laureates: Markowitz, Miller, and Sharpe” Journal of Economic Perspectives Winter 1993

http://oz.plymouth.edu/~harding/BU5120/varian.pdf