3. MAJOR FINANCIAL STATEMENTS AND OTHER INFORMATION SOURCES

In order to perform an equity or credit analysis of a company, an analyst collects a great deal of information. The nature of the information collected will vary on the basis of the individual decision to be made (or the specific purpose of the analysis) but will typically include information about the economy, industry, and company as well as information about comparable peer companies. Much of the information will likely come from outside the company, such as economic statistics, industry reports, trade publications, and databases containing information on competitors. The company itself provides some of the core information for analysis in its financial reports, press releases, investor conference calls, and webcasts.

Companies prepare financial reports at regular intervals (annually, semiannually, and/or quarterly depending on the applicable regulatory requirements). Financial reports include financial statements along with supplemental disclosures necessary to assess the company’s financial position and periodic performance. Financial statements are the result of an accounting recordkeeping process that records economic activities of a company, following the applicable accounting standards and principles. These statements summarize the accounting information, mainly for users outside the company (such as investors, creditors, analysts, and others) because users of financial information inside a company have direct access to the underlying financial data that are summarized in the financial statements and to other information that is collected but not included in the financial reporting process. Financial statements are almost always audited by independent accountants who provide an opinion on whether the financial statements present fairly the company’s performance and financial position in accordance with a specified, applicable set of accounting standards and principles.

In order to perform an equity or credit analysis of a company, an analyst collects a great deal of information. The nature of the information collected will vary on the basis of the individual decision to be made (or the specific purpose of the analysis) but will typically include information about the economy, industry, and company as well as information about comparable peer companies. Much of the information will likely come from outside the company, such as economic statistics, industry reports, trade publications, and databases containing information on competitors.

Financial Statements and Supplementary Information

A complete set of financial statements include a statement of financial position (i.e., a balance sheet), a statement of comprehensive income (i.e., a single statement of comprehensive income or an income statement and a statement of comprehensive income), a statement of changes in equity, and a statement of cash flows.2 The balance sheet portrays the company’s financial position at a given point in time. The statement of comprehensive income and statement of cash flows present different aspects of a company’s performance over a period of time. The statement of changes in equity provides additional information regarding the changes in a company’s financial position. In addition, the accompanying notes or footnotes to the financial statements are required and considered an integral part of a complete set of financial statements.

Along with the required financial statements, a company typically provides additional information in its financial reports. In many jurisdictions, some or all of this additional information is mandated by regulators or accounting standards boards. The additional information provided may include a letter from the chairman of the company, a report from management discussing the results (typically called management discussion and analysis [MD&A] or management commentary), an external auditor’s report providing assurances, a governance report describing the structure of the company’s board of directors, and a corporate responsibility report. As part of his or her analysis, the financial analyst should read and assess this additional information along with the financial statements. The following sections describe and illustrate each financial statement and some of the additional information.

The balance sheet (also called the statement of financial position or statement of financial condition)

Volkswagen, a German-based automobile manufacturer, prepares its financial statements in accordance with International Financial Reporting Standards (IFRS). IFRS require companies to present classified balance sheets that show current and non-current assets and current and non-current liabilities as separate classifications.However, IFRS do not prescribe a particular ordering or format, and the order in which companies present their balance sheet items is largely a function of tradition. As shown, Volkswagen presents non-current assets before current assets, owners’ equity before liabilities, and within liabilities, non-current liabilities before current liabilities. This method generally reflects a presentation from least liquid to most liquid. In other countries, the typical order of presentation may differ. For example, in the United States, Australia, and Canada, companies usually present their assets and liabilities from most liquid to least liquid. Cash is typically the first asset shown, and equity is presented after liabilities.

3.1.2. Statement of Comprehensive Income

The statement of comprehensive income, under IFRS, can be presented as a single statement of comprehensive income or as two statements, an income statement and a statement of comprehensive income that begins with profit or loss from the income statement.

The income statement presents information on the financial results of a company’s business activities over a period of time. The income statement communicates how much revenue and other income the company generated during a period and the expenses it incurred to generate that revenue and other income. Revenue typically refers to amounts charged for the delivery of goods or services in the ordinary activities of a business. Other income includes gains, which may or may not arise in the ordinary activities of the business. Expensesreflect outflows, depletions of assets, and incurrences of liabilities that decrease equity. Expenses typically include such items as cost of sales (cost of goods sold), administrative expenses, and income tax expenses and may be defined to include losses. Net income (revenue plus other income minus expenses) on the income statement is often referred to as the “bottom line” because of its proximity to the bottom of the income statement. Net income may also be referred to as “net earnings,” “net profit,” and “profit or loss.” In the event that expenses exceed revenues and other income, the result is referred to as “net loss.”

Income statements are reported on a consolidated basis, meaning that they include the income and expenses of subsidiary companies under the control of the parent (reporting) company. The income statement is sometimes referred to as a statement of operations or profit and loss (P&L) statement. The basic equation underlying the income statement is Revenue + Other income – Expenses = Income – Expenses = Net income.

In general terms, when one company (the parent) controls another company (the subsidiary), the parent presents its own financial statement information consolidated with that of the subsidiary. (When a parent company owns more than 50 percent of the voting shares of a subsidiary company, it is presumed to control the subsidiary and thus presents consolidated financial statements.) Each line item of the consolidated income statement includes the entire amount from the relevant line item on the subsidiary’s income statement (after removing any intercompany transactions); however, if the parent does not own 100 percent of the subsidiary, it is necessary for the parent to present an allocation of net income to the minority interests. Minority interests, also called non-controlling interests, refer to owners of the remaining shares of the subsidiary that are not owned by the parent. The share of consolidated net income attributable to minority interests is shown at the bottom of the income statement along with the net income attributable to shareholders of the parent company.

Exhibit 5 presents the income statement of the Volkswagen Group from its Annual Report 2009.

Exhibit 5. Income Statement of the Volkswagen Group for the Period 1 January to 31 December*

€ million	Note		2009		2008
Sales revenue	1		105,187		113,808
Cost of sales	2		–91,608		–96,612
Gross profit			13,579		17,196
Distribution expenses	3		–10,537		–10,552
Administrative expenses	4		–2,739		–2,742
Other operating income	5		7,904		8,770
Other operating expenses	6		–6,352		–6,339
Operating profit			1,855		6,333
Share of profits and losses of equity-accounted investments	7		701		910
Finance costs	8		–2,268		–1,815
Other financial result	9		972		1,180
Financial result			–595		275
Profit before tax			1,261		6,608
Income tax income/expense	10		–349		–1,920
Current			–1,145		–2,338
Deferred			796		418
Profit after tax			911		4,688
Minority interests			–49		–65
Profit attributable to shareholders of Volkswagen AG			960		4,753
Basic earnings per ordinary share in €	11		2.38		11.92
Basic earnings per preferred share in €	11		2.44		11.98
Diluted earnings per ordinary share in €	11		2.38		11.88
Diluted earnings per preferred share in €	11		2.44		11.94

*The numbers are as shown in the annual report and may not add because of rounding.

Exhibit 5 shows that Volkswagen’s sales revenue for the fiscal year ended 31 December 2009 was €105,187 million. Subtracting cost of sales from revenue gives gross profit of €13,579 million. After subtracting operating costs and expenses and adding other operating income, the company’s operating profit totals €1,855 million. Operating profit represents the results of the company’s usual business activities before deducting interest expense or taxes. Operating profit (also called operating income) is thus often referred to as earnings before interest and taxes (EBIT). Next, operating profit is increased by Volkswagen’s share of the profits generated by certain of its investments (€701 million) and by profits from its other financial

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3.1.2.2. Other Comprehensive Income

Comprehensive income includes all items that impact owners’ equity but are not the result of transactions with shareowners. Some of these items are included in the calculation of net income, and some are included in other comprehensive income (OCI). Under IFRS, when comprehensive income is presented in two statements, the statement of comprehensive income begins with the profit or loss from the income statement and then presents the components of other comprehensive income. Although US generally accepted accounting principles (US GAAP) indicate a preference for this type of presentation when a single statement of comprehensive income is not presented, they permit companies to present the components of other comprehensive income in the statement of changes in equity.5

Exhibit 6 presents the statement of comprehensive income of the Volkswagen Group from its Annual Report 2009.

Exhibit 6. Statement of Comprehensive Income of the Volkswagen Group for the Period 1 January to 31 December

€ million	2009		2008
Profit after tax	911		4,688
Exchange differences on translating foreign operations:
Fair value changes recognized in other comprehensive income	917		–1,445
Transferred to profit or loss	57
Actuarial gains/losses	–860		190
Cash flow hedges:
Fair value changes recognized in other comprehensive income	683		1,054
Transferred to profit or loss	–908		–1,427
Available-for-sale financial assets (marketable securities):
Fair value changes recognized in other comprehensive income	200		–330
Transferred to profit or loss	71		100
Deferred taxes	216		145
Share of profits and losses of equity-accounted investments recognized directly in equity, after tax	30		–188
Other comprehensive income	406		–1,901
Total comprehensive income	1,317		2,787
Of which attributable to
Shareholders of Volkswagen AG	1,138		3,310
Minority interests	179		–523

Exhibit 6 shows that other comprehensive income, although smaller in absolute terms than profit after tax (net income), had a significant effect on total comprehensive income. In 2009, other comprehensive income represented approximately 31 percent of total comprehensive income and was approximately 45 percent of the size of profit after tax (net income). In 2008, other comprehensive income was negative (a loss) and was approximately 41 percent of the size of profit after tax (net income) in absolute terms. The statement

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3.1.3. Statement of Changes in Equity

The statement of changes in equity, variously called the “statement of changes in owners’ equity” or “statement of changes in shareholders’ equity,” primarily serves to report changes in the owners’ investment in the business over time. The basic components of owners’ equity are paid-in capital and retained earnings. Retained earnings include the cumulative amount of the company’s profits that have been retained in the company. In addition, non-controlling or minority interests and reserves that represent accumulated other comprehensive income items are included in equity. The latter items may be shown separately or included in retained earnings. Volkswagen includes reserves as components of retained earnings.

The statement of changes in equity is organized to present, for each component of equity, the beginning balance, any increases during the period, any decreases during the period, and the ending balance. For paid-in capital, an example of an increase is a new issuance of equity and an example of a decrease is a repurchase of previously issued stock. For retained earnings, income (both net income as reported on the income statement and other comprehensive income) is the most common increase and a dividend payment is the most common decrease.

Volkswagen’s balance sheet in Exhibit 3 shows that equity at the end of 2009 totaled €37,430 million, compared with €37,388 million at the end of 2008. The company’s statement of changes in equity presents additional detail on the change in each line item. Exhibit 7 presents an excerpt of the statement of changes in equity of the Volkswagen Group from its Annual Report 2009.

Exhibit 7. Excerpt from Statement of Changes in Equity of the Volkswagen Group for the Period 1 January to 31 December 2009*

	Sub-scribed capital	Capital reserves	RETAINED EARNINGS						Equity attributable to shareholders of VW AG	Minority interests	Total equity
€ millions			Accumu-lated profit	Currency translation reserve	Reserve for actuarial gains/losses	Cash flow hedge reserve	Fair value reserve for securities	Equity- accounted investments
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
Balance at 1 Jan. 2009	1,024	5,351	31,522	–2,721	–672	1,138	–192	–439	35,011	2,377	37,388
Capital increase	0	4							4		4
Dividend payment			–779						–779	–95	–874
Capital transactions involving change in ownership			–76						–76	–316	–392
Total comprehensive income			960	839	–851	–361	271	30	888	214	1,102
Deferred taxes					247	83	–80		250	–34	216
Other

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3.1.4. Cash Flow Statement

Although the income statement and balance sheet provide measures of a company’s success in terms of performance and financial position, cash flow is also vital to a company’s long-term success. Disclosing the sources and uses of cash helps creditors, investors, and other statement users evaluate the company’s liquidity, solvency, and financial flexibility. Financial flexibility is the ability of the company to react and adapt to financial adversities and opportunities. The cash flow statement classifies all cash flows of the company into three categories: operating, investing, and financing. Cash flows from operating activities are those cash flows not classified as investing or financing and generally involve the cash effects of transactions that enter into the determination of net income and, hence, comprise the day-to-day operations of the company. Cash flows frominvesting activities are those cash flows from activities associated with the acquisition and disposal of long-term assets, such as property and equipment. Cash flows from financing activities are those cash flows from activities related to obtaining or repaying capital to be used in the business. IFRS permit more flexibility than US GAAP in classifying dividend and interest receipts and payments within these categories.

Exhibit 8 presents Volkswagen’s statement of cash flows for the fiscal years ended 31 December 2009 and 2008.

Exhibit 8. Cash Flow Statement of the Volkswagen Group: 1 January to 31 December

€ million	2009		2008
Cash and cash equivalents at beginning of period (excluding time deposit investments)	9,443		9,914
Profit before tax	1,261		6,608
Income taxes paid	–529		–2,075
Depreciation and amortization of property, plant and equipment, intangible assets and investment property	5,028		5,198
Amortization of capitalized development costs	1,586		1,392
Impairment losses on equity investments	16		32
Depreciation of leasing and rental assets	2,247		1,816
Gain/loss on disposal of noncurrent assets	–547		37
Share of profit or loss of equity-accounted investments	–298		–219
Other noncash expense/income	727		765
Change in inventories	4,155		–3,056
Change in receivables (excluding financial services)	465		–1,333
Change in liabilities (excluding financial liabilities)	260		815
Change in provisions	1,660		509
Change in leasing and rental assets	–2,571		–2,734
Change in financial services receivables	–719		–5,053
Cash

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A trial balance is a list of all open accounts in the general ledger and their balances.

• For every amount debited, an equal amount must be credited.
• The total of debits and credits for all the T-accounts must be equal.
• A trial balance is prepared to test this. It proves whether or not the ledger is in balance.
• It is usually prepared at the end of a month or accounting period.

Since certain accounts may not be accurately stated, adjusting entries may be required to prepare an adjusted trial balance.

Liquidity refers to the "nearness to cash" of assets and liabilities, or having enough cash available to pay debts when they are due.

The tenor is the time remaining until the bond’s maturity date. The tenor is an important consideration in the analysis of a bond. It indicates the period over which the bondholder can expect to receive the interest payments and the length of time until the principal is repaid in full.

Maturities typically range from overnight to 30 years or longer. Fixed-income securities with maturities at issuance (original maturity) of one year or less are known as money market securities . Issuers of money market securities include governments and companies. Commercial paper and certificates of deposit are examples of money market securities.

Fixed-income securities with original maturities that are longer than one year are called capital market securities

Although very rare, perpetual bonds , such as the consols issued by the sovereign government in the United Kingdom, have no stated maturity date.

Bonds can be issued in any currency, although a large number of bond issues are made in either euros or US dollars.

The currency of issue may affect a bond’s attractiveness. If the currency is not liquid or freely traded, or if the currency is very volatile relative to major currencies, investments in that currency will not appeal to many investors.

Bond Issuers may choose to issue in a foreign currency if they are expecting cash flows in the foreign currency because the interest payments and principal repayments can act as a natural hedge, reducing currency risk.

If a bond is aimed solely at a country’s domestic investors, it is more likely that the borrower will issue in the local currency.

borrowers in developing countries often elect to issue bonds in a currency other than their local currency, such as in euros or US dollars, because doing so makes it easier to place the bond with international investors.

Generally, the source of repayment for bonds issued by supranational organizations is either the repayment of previous loans made by the organization or the paid-in capital from its members. National governments may also act as guarantors for certain bond issues. If additional sources of repayment are needed, the supranational organization can typically call on its members to provide funds.

Journalizing is the process of chronologically recording transactions.

• General journal is the simplest and most flexible.
• A separate journal entry records each transaction.
• Useful for obtaining detailed information regarding a particular transaction.

The five major items found in the current asset section are: cash, marketable securities, accounts receivables, inventories and prepaid expenses.

Intangible assets include patents, copyrights, franchises, goodwill, trademarks, trade names, secret processes, and organization costs.

LEARNING OUTCOMES

The candidate should be able to:

1. define a derivative and distinguish between exchange-traded and over-the-counter derivatives;

2. contrast forward commitments with contingent claims;

3. define forward contracts, futures contracts, options (calls and puts), swaps, and credit derivatives and compare their basic characteristics;

4. describe purposes of, and controversies related to, derivative markets;

5. explain arbitrage and the role it plays in determining prices and promoting market efficiency.

1. INTRODUCTION

Equity, fixed-income, currency, and commodity markets are facilities for trading the basic assets of an economy. Equity and fixed-income securities are claims on the assets of a company. Currencies are the monetary units issued by a government or central bank. Commodities are natural resources, such as oil or gold. These underlying assets are said to trade in cash markets or spot markets and their prices are sometimes referred to as cash prices or spot prices, though we usually just refer to them as stock prices, bond prices, exchange rates, and commodity prices. These markets exist around the world and receive much attention in the financial and mainstream media. Hence, they are relatively familiar not only to financial experts but also to the general population.

A derivative is a financial instrument that derives its performance from the performance of an underlying asset.

This definition, despite being so widely quoted, can nonetheless be a bit troublesome. For example, it can also describe mutual funds and exchange-traded funds, which would never be viewed as derivatives even though they derive their values from the values of the underlying securities they hold. Perhaps the distinction that best characterizes derivatives is that they usually transform the performance of the underlying asset before paying it out in the derivatives transaction. In contrast, with the exception of expense deductions, mutual funds and exchange-traded funds simply pass through the returns of their underlying securities. This transformation of performance is typically understood or implicit in references to derivatives but rarely makes its way into the formal definition. In keeping with customary industry practice, this characteristic will be retained as an implied, albeit critical, factor distinguishing derivatives from mutual funds and exchange-traded funds and some other straight pass-through instruments. Also, note that the idea that derivatives take their performance from an underlying asset encompasses the fact that derivatives take their value and certain other characteristics from the underlying asset. Derivatives strategies perform in ways that are derived from the underlying and the specific features of derivatives.

Derivatives are similar to insurance in that both allow for the transfer of risk from one party to another. As everyone knows, insurance is a financial contract that provides protection against loss. The party bearing the risk purchases an insurance policy, which transfers the risk to the other party, the insurer, for a specified period of time. The risk itself does not change, but the party bearing it does. Derivatives allow for this same type of transfer of risk. One type of derivative in particular, the put option, when combined with a position exposed to the risk, functions almost exactly like insurance, but all derivatives can be used to protect against loss. Of course, an insurance contract must specify the underlying risk, such as property, health, or life. Likewise, so do derivatives. As noted earlier, derivatives are associated with an underlying asset. As such, the so-called “underlying asset” is often simply referred to as theunderlying, whose value is the source of risk.1 In fact, the underlying need not even be an asset itself. Although common derivatives underlyings are equities, fixed-income securities, currencies, and commodities, other derivatives underlyings include interest rates, credit, energy, weather, and even other derivatives, all of which are not generally thought of as assets. Thus, like insurance, derivatives pay off on the basis of a source of risk, which is often, but not always, the value of an underlying asset. And like insurance, derivatives have a definite life span and expire on a specified date.

Derivatives are created in the form of legal contracts. They involve two parties—the buyer and the seller (sometimes known as the writer)—each of whom agrees to do something for the other, either now or later. The buyer, who purchases the derivative, is referred to as the long or the holder because he owns (holds) the derivative and holds a long position. The seller is referred to as the short because he holds a short position.2

A derivative contract always defines the rights and obligations of each party. These contracts are intended to be, and almost always are, recognized by the legal system as commercial contracts that each party expects to be upheld and supported in the legal system. Nonetheless, disputes sometimes arise, and lawyers, judges, and juries may be required to step in and resolve the matter.

There are two general classes of derivatives. Some provide the ability to lock in a price at which one might buy or sell the underlying. Because they force the two parties to transact in the future at a previously agreed-on price, these instruments are called forward commitments. The various types of forward commitments are called forward contracts, futures contracts, and swaps. Another class of derivatives provides the right but not the obligation to buy or sell the underlying at a pre-determined price. Because the choice of buying or selling versus doing nothing depends on a particular random outcome, these derivatives are called contingent claims. The primary contingent claim is called an option.

The existence of derivatives begs the obvious question of what purpose they serve. If one can participate in the success of a company by holding its equity, what reason can possibly explain why another instrument is required that takes its value from the performance of the equity? Although equity and other fundamental markets exist and usually perform reasonably well without derivative markets, it is possible that derivative markets can improve the performance of the markets for the underlyings.

Derivative markets create beneficial opportunities that do not exist in their absence. Derivatives can be used to create strategies that cannot be implemented with the underlyings alone. For example, derivatives make it easier to go short, thereby benefiting from a decline in the value of the underlying. In addition, derivatives, in and of themselves, are characterized by a relatively high degree of leverage, meaning that participants in derivatives transactions usually have to invest only a small amount of their own capital relative to the value of the underlying. As such, small movements in the underlying can lead to fairly large movements in the amount of money made or lost on the derivative. Derivatives generally trade at lower transaction costs than comparable spot market transactions, are often more liquid than their underlyings, and offer a simple, effective, and low-cost way to transfer risk. For example, a shareholder of a company can reduce or even completely eliminate the market exposure by trading a derivative on the equity. Holders of fixed-income securities can use derivatives to reduce or completely eliminate interest rate risk, allowing them to focus on the credit risk. Alternatively, holders of fixed-income securities can reduce or eliminate the credit risk, focusing more on the interest rate risk. Derivatives permit such adjustments easily and quickly.

The practice of risk management has taken a prominent role in financial markets. Indeed, whenever companies announce large losses from trading, lending, or operations, stories abound about how poorly these companies managed risk. Such stories are great attention grabbers and a real boon for the media, but they often miss the point that risk management does not guarantee that large losses will not occur. Rather, risk management is the process by which an organization or individual defines the level of risk it wishes to take, measures the level of risk it is taking, and adjusts the latter to equal the former. Risk management never offers a guarantee that large losses will not occur, and it does not eliminate the possibility of total failure. To do so would typically require that the amount of risk taken be so small that the organization would be effectively constrained from pursuing its primary objectives. Risk taking is inherent in all forms of economic activity and life in general. The possibility of failure is never eliminated.

THE STRUCTURE OF DERIVATIVE MARKETS

Having an understanding of equity, fixed-income, and currency markets is extremely beneficial—indeed, quite necessary—in understanding derivatives. One could hardly consider the wisdom of using derivatives on a share of stock if one did not understand the equity markets reasonably well. As you likely know, equities trade on organized exchanges as well as in over-the-counter (OTC) markets. These exchange-traded equity markets—such as the Deutsche Börse, the Tokyo Stock Exchange, and the New York Stock Exchange and its Eurex affiliate—are formal organizational structures that bring buyers and sellers together through market makers, or dealers, to facilitate transactions. Exchanges have formal rule structures and are required to comply with all securities laws.

OTC securities markets operate in much the same manner, with similar rules, regulations, and organizational structures. At one time, the major difference between OTC and exchange markets for securities was that the latter brought buyers and sellers together in a physical location, whereas the former facilitated trading strictly in an electronic manner. Today, these distinctions are blurred because many organized securities exchanges have gone completely to electronic systems. Moreover, OTC securities markets can be formally organized structures, such as NASDAQ, or can merely refer to informal networks of parties who buy and sell with each other, such as the corporate and government bond markets in the United States.

The derivatives world also comprises organized exchanges and OTC markets. Although the derivatives world is also moving toward less distinction between these markets, there are clear differences that are important to understand.

Derivative instruments are created and traded either on an exchange or on the OTC market. Exchange-traded derivatives are standardized, whereas OTC derivatives are customized. To standardize a derivative contract means that its terms and conditions are precisely specified by the exchange and there is very limited ability to alter those terms. For example, an exchange might offer trading in certain types of derivatives that expire only on the third Friday of March, June, September, and December. If a party wanted the derivative to expire on any other day, it would not be able to trade such a derivative on that exchange, nor would it be able to persuade the exchange to create it, at least not in the short run. If a party wanted a derivative on a particular entity, such as a specific stock, that party could trade it on that exchange only if the exchange had specified that such a derivative could trade. Even the magnitudes of the contracts are specified. If a party wanted a derivative to cover €150,000 and the exchange specified that contracts could trade only in increments of €100,000, the party could do nothing about it if it wanted to trade that derivative on that exchange.

This standardization of contract terms facilitates the creation of a more liquid market for derivatives. If all market participants know that derivatives on the euro trade in 100,000-unit lots and that they all expire only on certain days, the market functions more effectively than it would if there were derivatives with many different unit sizes and expiration days competing in the same market at the same time. This standardization makes it easier to provide liquidity. Through designated market makers, derivatives exchanges guarantee that derivatives can be bought and sold.3

The cornerstones of the exchange-traded derivatives market are the market makers (or dealers) and the speculators, both of whom typically own memberships on the exchange.4 The market makers stand ready to buy at one price and sell at a higher price. With standardization of terms and an active market, market makers are often able to buy and sell almost simultaneously at different prices, locking in small, short-term profits—a process commonly known as scalping. In some cases, however, they are unable to do so, thereby forcing them to either hold exposed positions or find other parties with whom they can trade and thus lay off (get rid of) the risk. This is when speculators come in. Although speculators are market participants who are willing to take risks, it is important to understand that being a speculator does not mean the reckless assumption of risk. Although speculators will take large losses at times, good speculators manage those risks by watching their exposures, absorbing market information, and observing the flow of orders in such a manner that they are able to survive and profit. Often, speculators will hedge their risks when they become uncomfortable.

Standardization also facilitates the creation of a clearing and settlement operation. Clearing refers to the process by which the exchange verifies the execution of a transaction and records the participants’ identities. Settlement refers to the related process in which the exchange transfers money from one participant to the other or from a participant to the exchange or vice versa. This flow of money is a critical element of derivatives trading. Clearly, there would be no confidence in markets in which money is not efficiently collected and disbursed. Derivatives exchanges have done an excellent job of clearing and settlement, especially in comparison to securities exchanges. Derivatives exchanges clear and settle all contracts overnight, whereas most securities exchanges require two business days.

The clearing and settlement process of derivative transactions also provides a credit guarantee. If two parties engage in a derivative contract on an exchange, one party will ultimately make money and the other will lose money. Derivatives exchanges use their clearinghouses to provide a guarantee to the winning party that if the loser does not pay, the clearinghouse will pay the winning party. The clearinghouse is able to provide this credit guarantee by requiring a cash deposit, usually called the margin bond or performance bond, from the participants to the contract. Derivatives clearinghouses manage these deposits, occasionally requiring additional deposits, so effectively that they have never failed to pay in the nearly 100 years they have existed. We will say more about this process later and illustrate how it works.

Exchange markets are said to have transparency, which means that full information on all transactions is disclosed to exchanges and regulatory bodies. All transactions are centrally reported within the exchanges and their clearinghouses, and specific laws require that these markets be overseen by national regulators. Although this would seem a strong feature of exchange markets, there is a definite cost. Transparency means a loss of privacy: National regulators can see what transactions have been done. Standardization means a loss of flexibility: A participant can do only the transactions that are permitted on the exchange. Regulation means a loss of both privacy and flexibility. It is not that transparency or regulation is good and the other is bad. It is simply a trade-off.

Derivatives exchanges exist in virtually every developed (and some emerging market) countries around the world. Some exchanges specialize in derivatives and others are integrated with securities exchanges.

Although there have been attempts to create somewhat non-standardized derivatives for trading on an exchange, such attempts have not been particularly successful. Standardization is a critical element by which derivatives exchanges are able to provide their services. We will look at this point again when discussing the alternative to standardization: customized OTC derivatives.

Over-the-Counter Derivatives Markets

The OTC derivatives markets comprise an informal network of market participants that are willing to create and trade virtually any type of derivative that can legally exist. The backbone of these markets is the set of dealers, which are typically banks. Most of these banks are members of a group called the International Swaps and Derivatives Association (ISDA), a worldwide organization of financial institutions that engage in derivative transactions, primarily as dealers. As such, these markets are sometimes called dealer markets. Acting as principals, these dealers informally agree to buy and sell various derivatives. It is informal because the dealers are not obligated to do so. Their participation is based on a desire to profit, which they do by purchasing at one price and selling at a higher price. Although it might seem that a dealer who can “buy low, sell high” could make money easily, the process in practice is not that simple. Because OTC instruments are not standardized, a dealer cannot expect to buy a derivative at one price and simultaneously sell it to a different party who happens to want to buy the same derivative at the same time and at a higher price.

To manage the risk they assume by buying and selling customized derivatives, OTC derivatives dealers typically hedge their risks by engaging in alternative but similar transactions that pass the risk on to other parties. For example, if a company comes to a dealer to buy a derivative on the euro, the company would effectively be transferring the risk of the euro to the dealer. The dealer would then attempt to lay off (get rid of) that risk by engaging in an alternative but similar transaction that would transfer the risk to another party. This hedge might involve another derivative on the euro or it might simply be a transaction in the euro itself. Of course, that begs the question of why the company could not have laid off the risk itself and avoided the dealer. Indeed, some can and do, but laying off risk is not simple. Unable to find identical offsetting transactions, dealers usually have to find similar transactions with which they can lay off the risk. Hedging one derivative with a different kind of derivative on the same underlying is a similar but not identical transaction. It takes specialized knowledge and complex models to be able to do such transactions effectively, and dealers are more capable of doing so than are ordinary companies. Thus, one might think of a dealer as a middleman, a sort of financial wholesaler using its specialized knowledge and resources to facilitate the transfer of risk. In the same manner that one could theoretically purchase a consumer product from a manufacturer, a network of specialized middlemen and retailers is often a more effective method.

Because of the customization of OTC derivatives, there is a tendency to think that the OTC market is less liquid than the exchange market. That is not necessarily true. Many OTC instruments can easily be created and then essentially offset by doing the exact opposite transaction, often with the same party. For example, suppose Corporation A buys an OTC derivative from Dealer B. Before the expiration date, Corporation A wants to terminate the position. It can return to Dealer B and ask to sell a derivative with identical terms. Market conditions will have changed, of course, and the value of the derivative will not be the same, but the transaction can be conducted quite easily with either Corporation A or Dealer B netting a gain at the expense of the other. Alternatively, Corporation A could do this transaction with a different dealer, the result of which would remove exposure to the underlying risk but would leave two transactions open and some risk that one party would default to the other. In contrast to this type of OTC liquidity, some exchange-traded derivatives have very little trading interest and thus relatively low liquidity. Liquidity is always driven by trading interest, which can be strong or weak in both types of markets.

OTC derivative markets operate at a lower degree of regulation and oversight than do exchange-traded derivative markets. In fact, until around 2010, it could largely be said that the OTC market was essentially unregulated. OTC transactions could be executed with only the minimal oversight provided through laws that regulated the parties themselves, not the specific instruments. Following the financial crisis that began in 2007, new regulations began to blur the distinction between OTC and exchange-listed markets. In both the United States (the Wall Street Reform and Consumer Protection Act of 2010, commonly known as the Dodd–Frank Act) and Europe (the Regulation of the European Parliament and of the Council on OTC Derivatives, Central Counterparties, and Trade Repositories), regulations are changing the characteristics of OTC markets.

When the full implementation of these new laws takes place, a number of OTC transactions will have to be cleared through central clearing agencies, information on most OTC transactions will need to be reported to regulators, and entities that operate in the OTC market will be more closely monitored. There are, however, quite a few exemptions that cover a significant percentage of derivative transactions. Clearly, the degree of OTC regulation, although increasing in recent years, is still lighter than that of exchange-listed market regulation. Many transactions in OTC markets will retain a degree of privacy with lower transparency, and most importantly, the OTC markets will remain considerably more flexible than the exchange-listed markets.

Forward Commitments

Forward commitments are contracts entered into at one point in time that require both parties to engage in a transaction at a later point in time (the expiration) on terms agreed upon at the start. The parties establish the identity and quantity of the underlying, the manner in which the contract will be executed or settled when it expires, and the fixed price at which the underlying will be exchanged. This fixed price is called the forward price.

A forward contract is an over-the-counter derivative contract in which two parties agree that one party, the buyer, will purchase an underlying asset from the other party, the seller, at a later date at a fixed price they agree on when the contract is signed

a forward contract is a commitment. Each party agrees that it will fulfill its responsibility at the designated future date. Failure to do so constitutes a default and the non-defaulting party can institute legal proceedings to enforce performance. It is important to recognize that although either party could default to the other, only one party at a time can default. The party owing the greater amount could default to the other, but the party owing the lesser amount cannot default because its claim on the other party is greater. The amount owed is always based on the net owed by one party to the other.

To gain a better understanding of forward contracts, it is necessary to examine their payoffs. As noted, forward contracts—and indeed all derivatives—take (derive) their payoffs from the performance of the underlying asset. To illustrate the payoff of a forward contract, start with the assumption that we are at time t = 0 and that the forward contract expires at a later date, time t = T.5 The spot price of the underlying asset at time 0 is S₀ and at time T is S_T. Of course, when we initiate the contract at time 0, we do not know what S_T will ultimately be. Remember that the two parties, the buyer and the seller, are going long and short, respectively.

At time t = 0, the long and the short agree that the short will deliver the asset to the long at time T for a price of F₀(T). The notation F₀(T) denotes that this value is established at time 0 and applies to a contract expiring at time T. F₀(T) is the forward price. Later, you will learn how the forward price is determined. It turns out that it is quite easy to do, but we do not need to know right now.6

So, let us assume that the buyer enters into the forward contract with the seller for a price of F₀(T), with delivery of one unit of the underlying asset to occur at time T. Now, let us roll forward to time T, when the price of the underlying is S_T. The long is obligated to pay F₀(T), for which he receives an asset worth S_T. If S_T > F₀(T), it is clear that the transaction has worked out well for the long. He paid F₀(T) and receives something of greater value. Thus, the contract effectively pays off S_T – F₀(T) to the long, which is the value of the contract at expiration. The short has the mirror image of the long. He is required to deliver the asset worth S_T and accept a smaller amount, F₀(T). The contract has a payoff for him of F₀(T) – S_T, which is negative. Even if the asset’s value, S_T, is less than the forward price, F₀(T), the payoffs are still S_T – F₀(T) for the long and F₀(T) – S_T for the short. We can consolidate these results by writing the short’s payoff as the negative of the long’s, –[S_T – F₀(T)], which serves as a useful reminder that the long and the short are engaged in a zero-sum game, which is a type of competition in which one participant’s gains are the other’s losses. Although both lose a modest amount in the sense of both having some costs to engage in the transaction, these costs are relatively small and worth ignoring for our purposes at this time. In addition, it is worthwhile to note how derivatives transform the performance of the underlying. The gain from owning the underlying would be S_T – S₀, whereas the gain from owning the forward contract would be S_T – F₀(T). Both figures are driven by S_T, the price of the underlying at expiration, but they are not the same.

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An important element of forward contracts is that no money changes hands between parties when the contract is initiated. Unlike in the purchase and sale of an asset, there is no value exchanged at the start. The buyer does not pay the seller some money and obtain something. In fact, forward contracts have zero value at the start. They are neither assets nor liabilities. As you will learn in later readings, their values will deviate from zero later as prices move. Forward contracts will almost always have non-zero values at expiration.

As noted previously, the primary purpose of derivatives is for risk management. Although the uses of forward contracts are covered in depth later in the curriculum, there are a few things to note here about the purposes of forward contracts. It should be apparent that locking in the future buying or selling price of an underlying asset can be extremely attractive for some parties. For example, an airline anticipating the purchase of jet fuel at a later date can enter into a forward contract to buy the fuel at a price agreed upon when the contract is initiated. In so doing, the airline has hedged its cost of fuel. Thus, forward contracts can be structured to create a perfect hedge, providing an assurance that the underlying asset can be bought or sold at a price known when the contract is initiated. Likewise, speculators, who ultimately assume the risk laid off by hedgers, can make bets on the direction of the underlying asset without having to invest the money to purchase the asset itself.

Finally, forward contracts need not specifically settle by delivery of the underlying asset. They can settle by an exchange of cash. These contracts—called non-deliverable forwards(NDFs), cash-settled forwards, or contracts for differences—have the same economic effect as do their delivery-based counterparts. For example, for a physical delivery contract, if the long pays F₀(T) and receives an asset worth S_T, the contract is worth S_T – F₀(T) to the long at expiration. A non-deliverable forward contract would have the short simply pay cash to the long in the amount of S_T – F₀(T). The long would not take possession of the underlying asset, but if he wanted the asset, he could purchase it in the market for its current price of S_T. Because he received a cash settlement in the amount of S_T – F₀(T), in buying the asset the long would have to pay out only S_T – [S_T – F₀(T)], which equals F₀(T). Thus, the long could acquire the asset, effectively paying F₀(T), exactly as the contract promised. Transaction costs do make cash settlement different from physical delivery, but this point is relatively minor and can be disregarded for our purposes here.

As previously mentioned, forward contracts are OTC contracts. There is no formal forward contract exchange. Nonetheless, there are exchange-traded variants of forward contracts, which are called futures contracts or just futures.

Formally, a futures contract is defined as follows:

A futures contract is a standardized derivative contract created and traded on a futures exchange in which two parties agree that one party, the buyer, will purchase an underlying asset from the other party, the seller, at a later date and at a price agreed on by the two parties when the contract is initiated and in which there is a daily settling of gains and losses and a credit guarantee by the futures exchange through its clearinghouse.

Probably the most important distinctive characteristic of futures contracts is the daily settlement of gains and losses and the associated credit guarantee provided by the exchange through its clearinghouse. When a party buys a futures contract, it commits to purchase the underlying asset at a later date and at a price agreed upon when the contract is initiated. The counterparty (the seller) makes the opposite commitment, an agreement to sell the underlying asset at a later date and at a price agreed upon when the contract is initiated. The agreed-upon price is called the futures price. Identical contracts trade on an ongoing basis at different prices, reflecting the passage of time and the arrival of new information to the market. Thus, as the futures price changes, the parties make and lose money. Rising (falling) prices, of course, benefit (hurt) the long and hurt (benefit) the short. At the end of each day, the clearinghouse engages in a practice called mark to market, also known as the daily settlement. The clearinghouse determines an average of the final futures trades of the day and designates that price as the settlement price. All contracts are then said to be marked to the settlement price. For example, if the long purchases the contract during the day at a futures price of £120 and the settlement price at the end of the day is £122, the long’s account would be marked for a gain of £2. In other words, the long has made a profit of £2 and that amount is credited to his account, with the money coming from the account of the short, who has lost £2. Naturally, if the futures price decreases, the long loses money and is charged with that loss, and the money is transferred to the account of the short.7

The account is specifically referred to as a margin account. Of course, in equity markets, margin accounts are commonly used, but there are significant differences between futures margin accounts and equity margin accounts. Equity margin accounts involve the extension of credit. An investor deposits part of the cost of the stock and borrows the remainder at a rate of interest. With futures margin accounts, both parties deposit a required minimum sum of money, but the remainder of the price is not borrowed. This required margin is typically less than 10% of the futures price, which is considerably less than in equity margin trading. In the example above, let us assume that the required margin is £10, which is referred to as the initial margin. Both the long and the short put that amount into their respective margin accounts. This money is deposited there to support the trade, not as a form of equity, with the remaining amount borrowed. There is no formal loan created as in equity markets. A futures margin is more of a performance bond or good faith deposit, terms that were previously mentioned. It is simply an amount of money put into an account that covers possible fu...

The clearinghouse moves money between the participants, crediting gains to the winners and charging losses to the losers. By doing this on a daily basis, the gains and losses are typically quite small, and the margin balances help ensure that the clearinghouse will collect from the party losing money. As an extra precaution, in fast-moving markets, the clearinghouse can make margin calls during the day, not just at the end of the day. Yet there still remains the possibility that a party could default. A large loss could occur quickly and consume the entire margin balance, with additional money owed.8 If the losing party cannot pay, the clearinghouse provides a guarantee that it will make up the loss, which it does by maintaining an insurance fund. If that fund were depleted, the clearinghouse could levy a tax on the other market participants, though that has never happened.

Some futures contracts contain a provision limiting price changes. These rules, called price limits, establish a band relative to the previous day’s settlement price, within which all trades must occur. If market participants wish to trade at a price above the upper band, trading stops, which is called limit up, until two parties agree on a trade at a price lower than the upper limit. Likewise, if market participants wish to trade at a price below the lower band, which is called limit down, no trade can take place until two parties agree to trade at a price above the lower limit. When the market hits these limits and trading stops, it is called locked limit. Typically, the exchange rules provide for an expansion of the limits the next day. These price limits, which may be somewhat objectionable to proponents of free markets, are important in helping the clearinghouse manage its credit exposure. Just because two parties wish to trade a futures contract at a price beyond the limits does not mean they should be allowed to do so. The clearinghouse is a third participant in the contract, guaranteeing to each party that it ensures against the other party defaulting. Therefore, the clearinghouse has a vested interest in the price and considerable exposure. Sharply moving prices make it more difficult for the clearinghouse to collect from the parties losing money.

Most participants in futures markets buy and sell contracts, collecting their profits and incurring their losses, with no ultimate intent to make or take delivery of the underlying asset. For example, the long may ultimately sell her position before expiration. When a party re-enters the market at a later date but before expiration and engages in the opposite transaction—a long selling her previously opened contract or a short buying her previously opened contract—the transaction is referred to as an offset. The clearinghouse marks the contract to the current price relative to the previous settlement price and closes out the participant’s position.

At any given time, the number of outstanding contracts is called the open interest. Each contract counted in the open interest has a l

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a. calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment;

b. contrast the NPV rule to the IRR rule, and identify problems associated with the IRR rule;


A company should choose those capital investment processes that maximize shareholder wealth.

The net present value (NPV) of an investment is the present value of its cash inflows minus the present value of its cash outflows. The internal rate of return (IRR) is the discount rate that makes net present value equal to 0.

According to the NPV rule, a company should accept projects where the NPV is positive and reject those in which the NPV is negative. A positive NPV suggests that cash inflows outweigh cash outflows on a present value basis. That is, the positive cash flows are sufficient to repay the initial investment along with the capital costs (opportunity cost) associated with the project. If the company must choose between two, mutually-exclusive projects, the one with the higher NPV should be chosen.

• According to the IRR Rule, a company should accept projects where the IRR is greater than the discount rate used (WACC) and reject those in which the IRR is less than the discount rate. An IRR greater than the WACC suggests that the project will more than repay the capital costs (opportunity costs) incurred.
  
  There are three problems associated with IRR as a decision rule.

• Reinvestment
  The IRR is intended to provide a single number that represents the rate of return generated by a capital investment. As such, it is an easy number to interpret and understand. However, calculation of the IRR assumes that all project cash flows can be reinvested to earn a rate of return exactly equal to the IRR itself. In other words, a project with an IRR of 6% assumes that all cash flows can be reinvested to earn exactly 6%. If the cash flows are invested at a rate lower than 6%, the realized return will be less than the IRR. If the cash flows are invested at a rate higher than 6%, the realized return will be greater than the IRR.

• Scale
  In most cases, NPV and IRR rules provide the same recommendation as to whether to accept or reject a given capital investment project. However, when choosing between two mutually-exclusive projects (ranking), NPV and IRR rules may provide conflicting recommendations. In such cases, the NPV rule's recommendation should take precedence.
  One of the situations in which IRR is likely to contradict NPV is when there are two mutually-exclusive projects of greatly differing scale: one that requires a relatively small investment and returns relatively small cash flows, and another that requires a much larger investment and returns much larger cash flows.

• Timing
  The other situation in which IRR is likely to contradict NPV is when there are two mutually-exclusive projects whose cash flows are timed very differently: one that receives its largest cash flows early in the project and another that receives its largest cash flows late in the project.

The net present value (NPV) of an investment is the present value of its cash inflows minus the present value of its cash outflows. The internal rate of return (IRR) is the discount rate that makes net present value equal to 0.

Holding Period Return

When analyzing rates of return, our starting point is the total return, or holding period return (HPR). HPR measures the total return for holding an investment over a certain period of time, and can be calculated using the following formula:

• P_t = price per share at the end of time period t
• P_(t-1) = price per share at the end of time period t-1, the time period immediately preceding time period t
• P_t - P_t-1 = price appreciation of the investment
• D_t = cash distributions received during time period t: for common stock, cash distribution is the dividend; for bonds, cash distribution is the coupon payment.

It has two important characteristics:

• It has an element of time attached to it: monthly, quarterly or annual returns. HPR can be computed for any time period.
• It has no currency unit attached to it; the result holds regardless of the currency in which prices are denominated.

Example

A stock is currently worth $60. If you purchased the stock exactly one year ago for $50 and received a $2 dividend over the course of the year, what is your holding period return?

R_t = ($60 - $50 + $2)/$50 = 0.24 or 24%

The return for time period t is the capital gain (or loss) plus distributions divided by the beginning-of-period price (dividend yield). Note that for common stocks the distribution is the dividend; for bonds, the distribution is the coupon payment.

The holding period return for any asset can be calculated for any time period (day, week, month, or year) simply by changing the interpretation of the time interval.

Return can be expressed in decimals (0.05), fractions (5/100), or as a percent (5%). These are all equivalent.

Learning Outcome Statements

c. calculate and interpret a holding period return (total return);

Dollar-weighted and Time-weighted Rates of Return

The dollar-weighted rate of return is essentially the internal rate of return (IRR) on a portfolio. This approach considers the timing and amount of cash flows. It is affected by the timing of cash flows. If funds are added to a portfolio when the portfolio is performing well (poorly), the dollar-weighted rate of return will be inflated (depressed).

The time-weighted rate of return measures the compound growth rate of $1 initial investment over the measurement period. Time-weighted means that returns are averaged over time. This approach is not affected by the timing of cash flows; therefore, it is the preferred method of performance measurement.

Example

Jayson bought a share of IBM stock for $100 on December 31, 2000. On December 31, 2001, he bought another share for $150. On December 31, 2002, he sold both shares for $140 each. The stock paid a dividend of $10 per share at the end of each year.

To calculate the dollar-weighted rate of return, you need to determine the timing and amount of cash flows for each year, and then set the present value of net cash flows to be 0: - 100 - 140/(1 + r) + 300/(1 + r)² = 0. You can use the IRR function on a financial calculator to solve for r to get the dollar-weighted rate of return: r = 17%.

To calculate the time-weighted rate of return:

• Split the overall measurement period into equal sub-periods on the dates of cash flows. For the first year:
  • beginning price: $100
  • dividends: $10
  • ending price: $150
  For the second year:
  • beginning price: $300 (150 x 2)
  • dividends: $20 (10 x 2)
  • ending price: $280 (140 x 2)

• Calculate the holding period return (HPR) on the portfolio for each sub-period: HPR = (Dividends + Ending Price)/Beginning Price - 1. For the first year, HPR₁: (150 + 10)/100 - 1 = 0.60. For the second year, HPR₂: (280 + 20)/300 - 1 = 0.

• Calculate the time-weighted rate of return:
  • If the measurement period < 1 year, compound holding period returns to get an annualized rate of return for the year.
  • If the measurement period > 1 year, take the geometric mean of the annual returns.
    
    

    Learning Outcome Statements

    d. calculate and compare the money-weighted and time-weighted rates of return of a portfolio and evaluate the performance of portfolios based on these measures;

Money market instruments are low-risk, highly liquid debt instruments with a maturity of one year or less. There are two types of money market instruments: interest-bearing instruments (e.g., bank certificates of deposit), and pure discount instruments (e.g., U.S. Treasury bills).

Pure discount instruments such as T-bills are quoted differently than U.S. government bonds. They are quoted on abank discount basis rather than on a price basis:

• r_BD = the annualized yield on a bank discount basis
• D = the dollar discount, which is equal to the difference between the face value of the bill, F, and its purchase price, P
• t = the number of days remaining to maturity
• 360 = the bank convention of the number of days in a year.

Bank discount yield is not a meaningful measure of the return on investment because:

• It is based on the face value, not on the purchase price. Instead, return on investment should be measured based on cost of investment.
• It is annualized using a 360-day year, not a 365-day year.
• It annualizes with simple interest and ignores the effect of interest on interest (compound interest).

Holding period yield (HPY) is the return earned by an investor if the money market instrument is held until maturity:

• P₀ = the initial price of the instrument
• P₁ = the price received for the instrument at its maturity
• D₁ = the cash distribution paid by the instrument at its maturity (that is, interest).

Since a pure discount instrument (e.g., a T-bill) makes no interest payment, its HPY is (P₁ - P₀)/P₀.

Note that HPY is computed on the basis of purchase price, not face value. It is not an annualized yield.

The effective annual yield is the annualized HPY on the basis of a 365-day year. It incorporates the effect of compounding interest.

Money market yield (also known as CD equivalent yield) is the annualized HPY on the basis of a 360-day year using simple interest.

Example

An investor buys a $1,000 face-value T-bill due in 60 days at a price of $990.

• Bank discount yield: (1000 - 990)/1000 x 360/60 = 6%
• Holding period yield: (1000 - 990)/990 = 1.0101%
• Effective annual yield: (1 + 1.0101%)^365/60 - 1 = 6.3047%
• Money market yield: (360 x 6%)/(360 - 60 x 6%) = 6.0606%

If we know HPY, then:

• EAY = (1 + HPY)^365/t - 1
• r_MM = HPY x 360/t

If we know EAY, then:

• HPY = ( 1 + EAY)^t/365 - 1
• r_MM = [(1 + EAY)^t/365 - 1] x (360/t)

If we know r_MM, then:

• HPY = r_MM x (t/360)
• EAY = (1 + r_MM x t/360)^365/t - 1
  
  

  Learning Outcome Statements

  e. calculate and interpret the bank discount yield, ho

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Statistics can refer to numerical data (e.g., a company's average revenue for the past 20 years). It can also refer to methods of collecting, classifying, analyzing, and interpreting numerical data. Statistical methods provide a powerful set of tools for making decisions in business and other fields.

Statistics involves two different processes:

• Describing sets of data. Descriptive statistical methods can be used to describe the important aspects of data sets that have been collected. This reading will focus on the use of descriptive statistics to consolidate a mass of numerical data into useful information.
• Drawing conclusions (making estimates, judgments, predictions, etc.). Inferential statistical methods can be used to draw conclusions about a large group from a smaller group actually observed.

We use statistical methods to analyze the results of data. Since the amount of information available may be vast, it may be extremely time-consuming and expensive to collect all the necessary data. For instance, suppose we are interested in the durability of tennis balls. Theoretically, in order to carry out an accurate assessment, we would need to collect large quantities of all different makes of tennis balls from all over the world. Clearly, this is not practical; aside from taking up lots of time, it would be cost-prohibitive to purchase all the balls we would need for our study. A more practical solution would be to use a sample.

A population consists of an entire set of objects, observations, or scores that have something in common. It comprises every possible member of the specified group. In our example above, the population of tennis balls consists of every tennis ball that has ever been manufactured anywhere in the world. This is a huge number of tennis balls. Another example of a population would be all males between the ages of 15 and 18.

A sample is a subset of a population. The sample is comprised of some of the members of the population. Since it is usually impractical (or too expensive or time-consuming) to test every member of a population, using data gathered from a sample of the population is typically the best approach available for describing that population.

In our example above, a sample might be a selection of 1,000 tennis balls of various makes collected from different sources. It would be a virtually impossible task to collect every possible tennis ball in the world; this same size provides a manageable number to work with as well as a substantial amount of possible data.

Before we move on, there are several points worth noting:

• Don't be fooled by the word "population." This does not necessarily refer to people. As with the example above, we can have a population of tennis balls. A population can consist of anything, living or not.
• Although populations are often vast, they can also be of manageable size. For example, the population of even numbers between 1 and 9 would comprise the numbers 2, 4, 6 and 8. In this case, it is possible to sample the entire population and get accurate results. This is rare, however, and for your purposes, populations can generally be considered to be vast.
• In general, the bigger the sample, the better your results will be (because you are using data from more of the population for analysis). However, this point can present difficulties, as you will see when we study variance and standard deviation later.
• The ideal process would be to select a sample that is "representative" of the population (a sample that takes into account extreme values on both sides but contains many "average" values). In this way, the results that we get will be more meaningful. Because we frequently don't know about the exact values of a population (which is why we sample in the first place), we will never really know if our sample is truly representative or not. It's a

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