Thomas D. Le

Financial Mathematics

Part I - Financial System





Part I










The United States Financial System






Risk and Return




Overview of the Financial Sector




Financial Markets



Financial Sources and Intermediaries



Financial Assets



Money Markets and Capital Markets



Money Markets



Capital Markets



The Federal Reserve System (the Fed)



The Securities and Exchange Commission (SEC)



Part II



The Time Value of Money




The Compound Value (CV) or Future Value (FV)



The Present Value (PV)



The Net Present Value (NPV)









Loan Amortization




Practical Problems




The Compound Value (CV) or Future Value (FV)



The Present Value (PV)



The Net Present Value (NPV)



The Compound Value of an Annuity



The Present Value of an Annuity



Loan Amortization









Internet Resources



This work is an effort to summarize in a compact format the essentials of financial mathematics that underlie computations in finance with a view to practical utility.

In a complex market economy like ours finance plays a vital role that permeates every aspect of life, whether we realize it or not. In fact, the financial sector is at the heart of the market economy, providing needed money for firms, ventures, entrepreneurs, and households to conduct their business.

My guiding principle throughout has been pragmatism, an attempt at making this manual a useful tool for individuals and households. I have tried to demystify one aspect of the world of finance without being too technical or too superficial, which is admittedly a real challenge.

Within the confines I have set for myself, I tried to be as concise yet as comprehensible as possible. Examples are geared toward everyday life of households and individuals, although the concepts are applicable to business as well. A mortgage loan is a mortgage loan regardless of who the mortgagor is.

If you can find in the following pages answers to some of your questions on finance matters as they impinge on your daily life, this work will have achieved its purpose. If you learn how to compare two investment vehicles, how to calculate the outstanding balance of your loan, or how to save up for some future purpose in a systematic manner using the formulas given, then you will have helped yourself to a better understanding of finance and its relevance in the modern world.

My friend Giang N. Trinh, D.Ph., played a tacit but central role in the existence of this work. I therefore dedicate it to her. Her quiet yet powerful inspiration and encouragement had the effect of a tidal wave, without a ripple.

Thomas D. Le
22 July 2003

To Financial Mathematics - Part II

Chapter 1


1.1    Overview

Why would anyone want or need financial mathematics? The simple answer is that they are of practical use for everyone living in a market economy like, or patterned after, that of the United States.

Have you borrowed money to buy a car or a home, purchased a certificate of deposit or opened a savings account at a commercial bank, purchased stocks or bonds at a brokerage firm, or invested in mutual funds? You may want to save up for the education of your child or for a trip abroad, or plan for retirement. You want to maximize the return of your investments. And most of us pay income tax. In short, if you have to deal with money over time (even for short periods), you cannot avoid the concepts and formulas of financial mathematics.

Many of us trust the financial institution, the broker, the tax accountant, the financial planner, the estate advisor, and a host of other financial experts to do the calculations for us, at a fee, of course.

Many of us also use “financial calculators” on the Internet to get the desired results without bothering to understand how these results were calculated. Or we may have friends who are financially trained and provide us with answers without going into the trouble of explanation.

Now you can learn financial mathematics here, in the privacy of your own home.

This article is not intended to be exhaustive, nor is it intended to replace your investment or financial advisor and planner.

It introduces you to financial concepts, formulas that you can use, problems for practice, and some practical tips.

The mathematics in the presentation requires nothing more than a working knowledge of elementary algebra to grasp and use. Furthermore, I have translated the mathematical formulas into Excel spreadsheet formulas so you don’t have to. You can still use your own calculator, or the Excel financial functions, if you so desire.

Chapter 2 lays the foundation by explaining the essential financial terminology and fundamental concepts. In the process, you will gain a clearer understanding of the financial system and the relevance of the mathematics to be discussed in Chapter 3. This chapter deals with the mathematics of finance with a practical purpose. If you are already familiar with financial concepts, you can skip right to Chapter 3 without loss of continuity. Chapter 4 provides ample opportunities to put your grasp of financial mathematics to a test with practical problems. Appendixes contain tables of interest factors that underpin a vast array of calculations, and loan amortization schedules. Finally, the references and Web resources point to further sources of information.

1.2    The United States Financial System

The United States has one of the most, if not the most, complex and advanced financial systems of any country in the world. This financial system is being mimicked in varying degrees by other countries, and serves as a model as well as a framework for international financial transactions.

While it is the most complex, its complexity continues to grow as innovations and demands from the market and investment world continue to appear in the financial arena. Like everything else in the market economy, financial products change with time and economic conditions. Any study of the historical development of the stock market in this country quickly reveals the changes that have taken place since its early days, and particularly since the Depression of 1929, which became the Great Depression of 1933, during which the stock market crash sent millions into economic hardship. Bankruptcies, widespread unemployment, corporate failures, bank failures, deflation, and stagnation demanded forceful and decisive governmental intervention into an economy that was prostrated and unable to right itself up from market forces alone.

Today, new laws, statutes, and federal agencies, such as the Federal Deposit Insurance Corporation (FDIC), and the Securities and Exchange Commission (SEC), have been put in place to insure that the catastrophic depression of the twentieth century does not recur, and to enhance the stability of the economy’s financial sector, without which the market economy cannot function.

The governmental measures taken since the Depression, far from being guarantees against economic collapse, or even recession, are just necessary safeguards. As times go by, and more is learned about the market economy on the global scale, there will undoubtedly be more actions, legislative, political, and economic, instituted to inject a degree of stabilization necessary for economic growth and prosperity for a greater proportion of the population at home and abroad.

But even financial and accounting innovations will make use of the fundamental concepts herein discussed, and can be understood with extrapolation from these concepts.

As an example, a new financial product called Collateralized Debt Obligation (CDO) within the broad category known as Structured Finance has existed for probably no more than twenty years. Yet the vast majority of calculations require nothing really esoteric at all. The novel financial instrument is at bottom a structure that uses debt as collateral to issue another form of debt through the intermediary of a legal entity known as special purpose entity (SPE) or special purpose vehicle (SPV), a bankruptcy-remote organization designed to spread risk and enhance financing sources. To be sure some new financial structures require sophisticated statistical studies, modeling and simulation that are done primarily by credit rating agencies such as Standard and Poor’s. These studies necessarily lie outside the scope of the present work. This is a topic that deserves book-length treatment of its own.

In 2002 the United States experienced a serious crisis of confidence in the integrity of its financial system with corporate scandals of unparalleled proportions popping up all across the private sector. Enron, WorldCom, Adelphia Communications, Global Crossing, to name a few, went bankrupt amid accounting irregularities and other violations of the law. Arthur Anderson, the accounting firm that audited Enron, among other major corporations, had signed off on faulty reports. Allegations of conflict of interest abounded. Firm after firm suddenly found itself having to admit overstating its earnings over the past two or three years. Corporate malfeasance, mismanagement, lack of internal controls, and accounting and other fraud combined to sap investors’ confidence in the financial system. As firms revised their earnings downward, it became clear they were not as financially viable as their books had made them out to be. As a result, the stock market stumbled, further compounded by the collapse of the technology sector. The economy nose-dived into one of the worst recessions since the Great Depression. We are still struggling through the lingering effects of this recession.

However, it is hoped that the systemic flaw in the financial system will eventually be addressed, as recent legislative and regulatory actions indicate, and the economy will get back on its feet. None of these unfortunate events had any effect on our discussion of financial mathematics.

1.3    Money

Any economy that functions above subsistence level needs a means of exchange backed by the full faith and credit of the issuing sovereign country. Money, composed of currency, i.e. notes and coins, is such a medium of exchange. It is also a store of value, i.e., it maintains value over time, and can be tendered at a future date for the purchase of goods and services.Money is a unit of account because all prices are quoted and accounts kept in terms of these units. Finally, money is a standard of deferred payments. Units of money, such as dollars and cents, are used as legal tender to discharge debt obligations in long-term transactions, such as loans.

The money stock in the economy has three major components, or money aggregates , depending on its role as a medium of exchange. The first is the basic component of the money supply, and fulfills the role of means of exchange because it is liquid. It comprises: (1) M1-A money supply, which includes cash and demand deposits (checkable deposits) in commercial banks, but excludes certain interest-bearing checking accounts, and (2) M1-B, which is a broadened M1-A supply. It consists of cash, interest-bearing checking accounts and non-interest-bearing checking accounts in commercial banks as well as in thrift institutions, such as savings and loan associations, mutual savings banks, and credit unions. The second component, called M2, includes M1, and time and savings deposits as well as money market funds, certificates of deposit, eurodollars, and Treasury bills. Even though some money market funds allow check withdrawals, they are not part of M-1B. M2 includes near-money, assets that are highly liquid, and can be easily exchanged for money, but cannot be used directly to purchase goods. The best examples are savings accounts, certificates of deposit, and similar bank accounts. These savings near monies are added to M1 to derive M2.The third basic monetary aggregate is called M3, comprised of everything in M2 plus investment types of near monies, including large denomination certificates of deposit, institutional money market deposits, and longer term repurchase agreements and eurodollars (cf. Chapter 2, Section 2.2.1). M3 is typically 25 percent higher than M2 and five times as large as M1.

1.4     Risk and Return

All investments are exposed to risk. In the financial world risk is incurred every time we invest money for an intended return. Risk is the contingency that results in a different return outcome than the one expected. Economists measure security risk, called beta, in terms of the standard deviation in a frequency distribution of values. Because the standard deviation of a well-diversified investment portfolio remains fairly stable over time, it is used as a risk measure of portfolios.

Statistically the standard deviation is the measure of dispersion of values around a mean (arithmetic average) value. Applied to an investment, the standard deviation measures the extent to which the actual return or price varies below and above the expected value. In other words, it measures variability. The larger is the standard deviation, the riskier is the security

As an illustration of the standard deviation, take the example of the share price of XYZ Corporation stock trading on the New York Stock Exchange. The market price of a share of the XYZ Corporation’s stock fluctuates daily. There is no way to predict this fluctuation from day to day: it varies more or less at random. Plot all the daily prices of a given year, or 365 days, called n, on graph paper with the Y-axis representing probability of occurrences or frequency, and the X-axis representing the daily prices. First, we divide the number of price values into groups or classes by using the rule of the power of 2. The first power of 2 that equals or exceeds n gives the number of classes to use. In this example, 28 = 256 and 29 = 512. Since 365 falls below 29 the number of classes is 9. Now group all prices into 9 groups. Since these data are historical, the standard deviation is known as ex-post standard deviation. If expected prices are used, as in mapping out an investment strategy, the result is referred to as ex-antstandard deviation.

Range of                 Class marks                 Number of observations fj                   Percentage of observations
share prices (Xj)

15-19                         17                                                              4                                              1.1                                        
20-24                         22                                                              4                                              1.1
25-29                         27                                                            43                                            11.8
30-34                         32                                                            42                                            11.5
35-39                         37                                                            58                                            15.9
40-44                         42                                                            98                                            26.9
45-49                         47                                                            65                                            17.8
50-54                         52                                                            41                                            11.2
55-60                         57                                                            10                                              2.7
                                                                                                365                                           100.0

For simplicity, let us posit the average share price in each group as the mean price of the group: 17, 22, 27, 32, 37, 42, 47, 52, 57. These are the class marks, i.e., the mean value of the class. Thus, the weighted mean μ, or the average price for the entire year, called population of share prices, weighted by frequency of occurrence is:

    μ = ((17*4) + (22*4) + (27*43) + (32*42) +(37*58) + (42*98) + (47*65) + (52*41) + (57*10)) / 365

     = 40.21

The median price, i.e., the price at which half the price points are below it, and half are above it, is 42. The distribution of the price values, called frequency distribution, can be graphed as a histogram consisting of nine vertical bars, each representing a group. When these bars are joined by a line running along their tops, they form a curve. Some curves tend to bell-shaped curves where the extreme values have the lowest frequencies while the values with the highest frequency make up the mode.In our example the mode is 42.

The squared value of the standard deviation is the variance, which is calculated first. The result of extracting the square root of the variance is the standard deviation. Here we deal with grouped data and the population standard deviation, which is calculated as follows:

                              σ = √­­ (1/N * ∑ (Xj – μ)2 * fj) = 8.479
                                                  j = 1

where σ is the population standard deviation, N the total number of occurrences (365), Xj the average share price, μ the weighted mean of share prices, and fj the frequency (number of occurrences) of each price.

An empirical rule for standard deviations states that ninety percent of the values lies within plus or minus three standard deviations from the mean. This means that in our example, 90% of the stock price of an XYZ Corp.’s share fall between $40.21 ± (3*8.479), or between 14.78 and 66.66. On the other hand, in bell-shaped data, in which data values are distributed in a configuration that can be delineated by a bell-shape curve, about two-thirds or 67 percent of the values lie within one standard deviation, μ ± σ, of the mean; 95% lies within μ ±2σ; and virtually all values lie within μ ± 3σ.

Obviously a different set of data results in a different standard deviation. If ABC Corporation has a smaller standard deviation than XYZ Corp.’s, it is deemed less risky than XYZ Corporation, all other things being equal.

Each investor has his or her own risk preferences. In general, a larger return on investment (ROI) is associated with a larger risk of exposure to loss. Thus the risk-averse investor would prefer a smaller standard deviation in return for greater stability of income. The risk-seeking investor is willing to risk a larger standard deviation in a security in hopes in reaping greater profits. And the risk-neutral investor seeks the middle ground in the risk- return trade-off spectrum.

To minimize unsystematic, or diversifiable, risk, investors need to broadly diversify their portfolio. As the old adage says, “Don’t put all your eggs in one basket.” Diversification entails spreading investments among different types of securities, different issuing entities, different industries, different maturity structures, even different regions or countries. The idea is to include securities with no correlation with one another in the portfolio so that one bad security does not adversely affect the others in the portfolio. Risks are systematic when they are inherent in the nature of the security or the industry, and cannot be diversified away.

Risks come from different directions, and include but are not limited to:

Credit Risk. Credit risk refers to the changes in the credit quality of a security issuer. Weak firms generally must pay higher interest to finance their operations than stronger firms. They are required to maintain certain levels of capital in proportion to the perceived credit risk of their asset mix. The higher the credit risk, the more capital is required to hold these assets. Closely related to credit risk is default risk, which is the measure of the firm’s probability of defaulting on their obligations, such as non-payment of interest and principal when due.

Prepayment Risk.  Any payment of mortgage debt before it is due is called prepayment. Prepayment risk is the chance that borrowers prepay their mortgages or other loans faster than expected. This reduces the investment's life and yield. Most mortgages may be prepaid at any time by the borrower without penalty; but borrowers are more likely to prepay when interest rates drop. Prepayments of mortgages may be made piecemeal or in one lump sum. Extra monthly principal payments made near the beginning of the mortgage term significantly reduce the total interest amount paid. Lower interest rates spur borrowers to refinance the entire mortgage loan, thereby getting rid of the original higher interest rate. If the inflation rate is expected to be high, the borrower may prefer the tax deduction of interest payment to making prepayments.

Market Risk. Market risk is the chance that the price of the security may change over time. For example, the price of a mortgage security is sensitive to prevailing interest rates, the liquidity of the issue, and the length of time the security is expected to be outstanding.

While the interest payment, known as the coupon rate, cannot be changed during the life of a fixed-rate bond, its market price changes as market conditions change. Municipal bonds sold prior to maturity will receive the current market price, which may be more or less than their original price. As with other fixed-income securities, municipal bond prices fluctuate in response to changing interest rates. Prices increase when interest rates decline, and decrease when interest rates rise. The non-mathematical reasons may be summarized as follows. When interest rates fall, new issues come to market with lower yields than older securities, making the older securities paying a fixed and higher coupon worth more; hence the increase in price. Conversely, when interest rates rise, new issues come to market with higher yields than older securities (paying lower fixed coupons), making the older ones worth less; hence the decline in price. You will see the precise mathematical mechanism responsible for the relationship between bond prices and interest rates in Section 3.2 on the present value.

Inflation Risk.  Among all risks, inflation risk is impossible to diversify away. It is a fact of economic life, and the most insidious since it creeps up on everyone, and affects prices at all levels, yet remains out of the control of investors. The worst part is that inflation is cumulative, i.e., it adds to the already-inflated price of the previous year. In financial terms, this fact is known as compounding. We will study the effect of compounding in Chapter 3. The Federal Reserve is the one governmental agency that takes an active part in dealing with inflation through monetary policy.

Chapter 2

Overview of the Financial Sector

This chapter provides an overview of the financial sector of the United States. Readers who are already familiar with the structure and organization of the US financial sector can skip this chapter and move right into Chapter 3, which deals with the mathematics of finance.

2. 1    Financial Markets

When a consumer borrows money to purchase a car, this transaction results in a two-sided event. For the borrower the transaction represents a financial liability, that is, a legal obligation to repay the principal amount borrowed plus the interest as specified in the loan contract. For the financing company, the transaction is booked as a financial asset, the positive side of its balance sheet that it can use to finance its operations. The creation and transfer of financial assets and liabilities constitute the financial markets.. Just as other markets, such as the housing market or the automobile market, the financial market exists to satisfy the supply and demand functions, i.e., the trade function, of the economy.

Trades of securities, i.e., stocks and bonds, take place in many locations. These trades occur in regulated stock exchanges such as the New York Stock Exchange and regional stock exchanges, and in the over-the-counter (OTC) market consisting of a network of thousands of brokers and dealers scattered across the country (such as the NASDAQ, National Association of Securities Dealers Quotation system displayed on computer terminals).  Individual transactions in retail stores, commercial and savings banks, and other financial institutions also create financial assets and liabilities.

The financial markets are further categorized into money markets, in which financial obligations have a maturity of less than one year, and the capital markets where securities with maturity of one year or longer are traded.

Financial markets are important in many ways: they are the mechanism by which firms raise funds necessary for their operations, consumers find funds to enhance the level of their living, and firms and individuals store their wealth.

2.1.1 Financing Sources and Financial Intermediaries

All the complex financial transactions that take place daily must be carried out in some sort of institutions that specialize in handling these transactions in a way that is conducive to orderly, systematic, trustworthy, and predictable behavior of the financial system. We briefly examine the agencies of this system here. Funds come from financing sources and flow through the economy by financial intermediation.

Commercial banks are financial institutions that accept money deposited in demand deposit (checking) accounts by firms and individuals. They can loan these funds, but must keep a reserve, called federal reserve requirement, as required by the Federal Reserve Board, to satisfy immediate fund withdrawal demands by depositors. Commercial banks also accept savings deposits, sell securities and insurance policies, hold in trust individual retirement accounts (IRAs), provide retirement planning and investment counseling, trade foreign currencies, and more.

Savings and loan associations (S&L) traditionally accept savings deposits and invest them in residential mortgages. The collapse of the S&L industry in 1980’s due to imprudent bad loans and other abuses led to reforms with the abolition in 1989 of the Federal Home Loan Bank Board (FHLBB) and the Federal Savings and Loan Insurance Corporation (FSLIC). The Office of Thrift Supervision (OTS) and the Federal Deposit Insurance Corporation (FDIC) took over all the former functions of the FHLBB and the FSLIC.

Mutual savings banks are a cross between the commercial bank and the savings and loan, evolving in the late nineteenth century in New England, and now operate only in New England and New York. They obtain funds from time and savings deposits, make mortgage and some consumer loans, and invest in corporate bonds.

Credit unions are very similar to mutual savings banks, with the exception that members of credit unions share some common bond. Most credit unions are organized to serve people in a particular community, group or groups of employees, or members of an organization or association. Credit unions are nonprofit, cooperative financial institutions owned and run by its members. They accept shares as savings deposits, from which checks may be drawn, hold Treasury bills, and make all sorts consumer loans and mortgage loans to members. Federal credit unions are regulated by the National Credit Union Administration (NCUA), an independent federal agency. The National Credit Union Share Insurance Fund (NCUSIF), operated by the NCUA and backed by the full faith and credit of the US government, insures over 80 million account holders in federal credit unions. Some state-chartered credit unions do not have the insurance coverage of the NCUSIF. There are currently fewer than 500 non-federally insured state-chartered credit unions. Credit unions operate not for profit, not for charity, but for service to their members.

Finance companies provide loans to other business firms and individuals. Some finance companies are tied to amanufacturer or retailer, such as automobile manufacturers. General Motors Acceptance Corporation (GMAC) and Toyota Automobile Credit Company are examples of auto finance companies. Others were tied to commercial banks to circumvent regulations against bank branching. The third type of finance companies accepts consumer deposits and bank loans to fund consumer loans, and business loans and leases. Finance companies are the second most important source of consumer installment credit behind commercial banks. Whereas other most financial institutions are federally regulated, finance companies are essentially unregulated.

Life insurance companies sell protection to individuals against loss of income due to disability or death and obtain funds from premiums charged. Regulated by states, life insurance companies are a major player in the capital markets. They are the single largest purchaser of corporate bonds, and among the largest buyers of commercial mortgages. Property and casualty insurance companies invest heavily in municipal bonds due to their tax exposure.

Pension funds collect retirement contributions from employees and employers to make periodic payments upon the employees’ retirement. Four characteristics of pension funds are: vesting, funding, insurance, and commitment. Since the Employee Retirement Income Security Act (ERISA) of 1974, firms can use any of the three options of vesting: (a) ten-year vesting, requiring ten years of service, (b) graded vesting, a gradual phase-in of vesting depending on the number of years of service, and (c) rule of 45, whereby a participant’s age and years of service add up to 45. Funding rules require that pension benefits must be funded the same year they are earned. The Department of Labor provides pension funds an insurance program administered by the Pension Benefit Guarantee Corporation (PBGC), which currently protects the retirement incomes of about 44 million American workers in about 32,500 private defined benefit pension plans. Firms commit themselves to pay beneficiaries a fixed monthly amount for life. The Employee Benefits Security Administration (EBSA) formerly known as the Pension and Welfare Benefits Administration (PWBA), in the Department of Labor, protects the integrity of pensions, health plans, and other employee benefits for more than 150 million people.  EBSA’s mission statement includes: assist workers in getting the information they need to protect their benefit rights; assist plan officials to understand the requirements of the relevant statutes in order to meet their legal responsibilities; develop policies and laws that encourage the growth of employment-based benefits; and deter and correct violations of the relevant statutes.

Recently pension funds have been a major investor in equity securities. They also invest heavily in corporate bonds.

Investment companies or mutual funds are portfolios of stocks, bonds, and/or cash managed by an investment company on behalf of a large number of investors. The latter typically purchase shares in a fund and become part owners of the fund. The fund manager invests the investors’ money in equity securities (stocks) and debt securities (bonds). The return to the investor consists of dividend distributions, generally every six months, and capital gains distributions at the end of the year. There are tax consequences depending on whether income consists of dividends or capital gains. Since purchases may be made by all investors at any time these funds are also called open-end funds. Most mutual funds are open-ended.

Investment banks are financial firms that underwrite, i.e., guarantee or buy, new issues of stock by companies seeking equity financing, and resell them to investors, thus bearing the risk of holding the new issue until it is sold. The issuing firm may invite bids from investment banking firms, which form temporary syndicates to compete with other syndicates. Or the issuing company may choose a particular investment banking firm with which it maintains a long-term relationship to handle its offerings.

Other sources of funds are government at all levels, other business firms, households and individuals. These agencies are both lenders and borrowers. By implementing fiscal policy (taxes and purchases), and monetary policy (buying or selling U.S. Treasuries, changing the money supply, setting federal reserve requirements, and setting federal funds interest rate by the Fed), government is a vital and decisive sector. All business firms finance their operations by issuing shares of stock and debt. And households contribute by spending disposable income and incurring debt.

Almost all the above sources of funds invest in the stock and bond markets.

All the financial institutions above, except government and households, are also financial intermediaries since they create financial assets and financial liabilities by reallocating savings surplus from other sources to spur the profitability and growth of business firms, which are savings deficit units. By thus reallocating surplus funds throughout the economy to where they are needed, these financial intermediaries make it more productive and efficient.

2.1.2 Financial Assets

Firms and households use three major types of financial assets: money, stock, and debt.

Money (cf. Section 1.3 above) consists of paper currency and coins issued by the United States Treasury. The Federal Reserve System, which is the central bank, in conjunction with the commercial banking system creates demand deposit (checking) accounts by which 90 percent of commercial transitions are conducted. As seen earlier, one category of money, M-1, in its components M-1A and M-1B, is liquid, i.e., ready to use for settlement of transactions.

Stock, generally understood as common stock, represents ownership in a firm. Shares of common stock are frequently referred to as equity securities or equities as they are “residual” claims on the income stream of the firm. Stockholders, therefore, have claims on the firm’s assets only after suppliers, creditors, and taxing authorities have had their claims satisfied first. But they have the right to vote at stockholders’ meetings, and the right to excess profits as well as to assets. Their income stream consists of periodic dividend distributions, and the profit (or loss) from sale of shares of stock. Dividends are not guaranteed, and do not accumulate, that is, do not accrue if they are not declared.

Holders of preferred stock, however, give up the right to vote and to excess profits in exchange for guaranteed dividends, which are stated on the certificate and are cumulative. If the firm skips periodic dividend payments, these payments have to be paid before common stockholders are paid their share of dividends, once the firm resumes paying them. All stockholders have no preference over the prior claims of suppliers, creditors and government taxation. Some preferred stock may be, at the holder’s option, convertible to common stock at a future date and at a predefined conversion ratio. Convertibility is a feature that enhances the attractiveness of preferred stock to investors.

Debt is a promise to pay the money borrowed and the interest it generates to the creditor at a specified future date. It is a claim on a specified portion of an income stream accruing to an asset. Debt generally has a maturity date, at which the amount of the debt has to be completely paid off, and an interest rate, which represents the cost of the money borrowed. Short-term debt usually consists of a promissory note, such as a car loan or a consumer loan at retail stores, which has a maturity of up to five years.

Long-term debt, called a bond, matures in ten years or more. The United States Treasury issues 30-year bonds, which are being phased out.Municipalities may issue general obligation bonds, and business firms also issue corporate bonds of various maturities and interest rates known as coupons.

A mortgage is a long-term loan secured by real property, such as a house, a building or a plant. A debenture is a long-term bond that is not secured by a pledge of any property. Prepayment is an option that allows a debtor to pay off the debt before its maturity. A mortgage borrower prepays a loan when he refinances at a more favorable interest rate than the rate of the original loan.

A call provision allows the issuing firm to call in the bond for redemption before its term. The extra amount (difference between call price and face value, i.e., the amount of the security at issuance) paid to redeem the security being called is referred to a call premium. From the investor’s point of view, when a bond is called the stream of income stops. A sinking fund is a provision that calls for a gradual retirement of the debt either by periodically calling in a fixed percentage of the bonds or buying the bonds on the open market. Debt is categorized by priority of claims, or order of precedence of claims in case of liquidation. A senior secured mortgage (first mortgage) has prior claims on the firm’s assets and earnings; a junior mortgage (second or third mortgage) has a subordinate lien to the senior mortgage. Debentures are subordinated. Debt of a lower priority cannot be paid at liquidation until the prior claims of senior debt holders have been satisfied. Bondholders, being creditors, have priority over stockholders, who are owners of the firm.

2.2    Money Markets And Capital Markets

Securities are bought and sold in money markets and capital markets. Securities with maturity of one year or less are traded in the money markets. Because of their short maturities money market instruments are relatively less exposed to default risk, and are highly marketable. Securities with maturity of more than one year are traded in the capital markets. They are generally exposed to greater default risk and varying degrees of marketability.

2.2.1 Money Markets

Money market instruments are “sold” by businesses with a temporary need for funding to those with surplus cash. These securities, generally issued in large denominations ($100 million is not uncommon), are purchased by institutions. Individuals participate mainly though the agency of money market funds, which are financial intermediaries who pool investments from shareholders to buy and manage the money market securities.

Money market instruments include:

United States Treasury bills (T-bills) are sold, mainly at auction, by the US Treasury to finance government spending. Bills with three-month and six-month maturities are sold every week; and bills with one-year maturity every four weeks. T-bills are pure discount bonds as they do not pay a coupon (i.e., interest). The return on investment consists solely of bond price appreciation. T-bills are considered risk-free instruments. Issues by the US Treasury, whether bills, notes, or bonds, are commonly known as Treasuries.

Other US Government Obligations include obligations (securities) sold by various Federal government agencies. In spite of their short terms, high marketability and low risk, they are commonly regarded as capital market instruments. In general, they are offered at a higher yield than T-bills.

Short-Term Municipal Obligations are offered with maturity ranging from one month to 30 years by municipal entities, which are defined as non-federal government: state, county, city, school districts, port and turnpike authorities. They fall in four types: (1) tax anticipation notes, also known as general obligations, which are short-term instruments to finance current government operations and to be repaid with near-term anticipated tax revenues; (2) revenue anticipation notes or revenue obligations, which are to be repaid from non-tax sources such as a municipal electric system; (3) bond anticipation notes to temporarily finance a project, which is soon to be refinanced with a long-term bond issue; and (4) project notes, issued by the US Department of Housing and Urban Development (HUD) to finance federally-sponsored local neighborhood development, urban renewal, and low-cost housing projects.

Commercial paper is a short-term (270 days or less) unsecured promissory note in denominations of $100,000 and up, issued by financially strong manufacturing firms and finance companies, and backed by a bank line of credit. Firms issue commercial paper as an alternative to borrowing from banks or other institutions to finance current transactions. The paper is usually sold to other companies which invest in short-term money market instruments. According to the Federal Reserve Bank of New York, currently more than 1,700 companies in the United States issue commercial paper. Financial companies comprise the largest group of commercial paper issuers, accounting for nearly 75 percent of the commercial paper outstanding at mid-year 1990. Financial-company paper is issued by firms in commercial, savings and mortgage banking; sales, personal and mortgage financing; factoring; finance leasing and other business lending; insurance underwriting; and other investment activities. The remaining 25 percent of commercial paper outstanding at mid-year 1990 was issued by non-financial firms such as manufacturers, public utilities, industrial concerns and service industries.

Negotiable certificates of deposits (CD’s) are issued with short-term maturity by banks in denominations of $100,000 and more, at a stated interest rate. Due to their low risk they are bought and sold on the open market, and command a higher yield than T-bills.

Banker’s acceptances are short-term promissory notes, known as time drafts, drawn on a bank, with a stipulated amount to be paid and the date of payment. They are issued by a bank to a foreign exporter at the request of a US importer in the form of a letter of credit that guarantees payment up to the approved line of credit. Upon shipping of goods the foreign exporter presents the letter of credit to its foreign bank for payment. The foreign bank sends the letter of credit and supporting documentation to the US bank that accepts it (in the form of a pre-issued banker’s acceptance), and approves it for payment. The US importer makes final payment. Due to low risk banker’s acceptances are actively traded on the open market, generally at a discount. The investor’s return consists of the difference between the price paid and the acceptance’s face value, i.e., the amount of the acceptance.

Eurodollars originally are deposits in US dollar denominations in a European bank. Today the term extends to US dollar-denominated short-term (6 months or less) deposits in any foreign bank or US branch bank in foreign countries. They pay a stated interest rate. The foreign bank uses eurodollars in deposit to make loans at rates closely pegged to US Federal Funds rates. The rate at which banks in London offer eurodollars in the placement market (the other eurodollar market being the loan market) is referred to as the London interbank offered rate, or LIBOR with rollover every 3 or 6 months, plus a spread, or an additional percentage. Depositors of eurodollars include large corporations (domestic, foreign, multinational), central banks and other government bodies, supranational institutions such as the Bank for International Settlements (headquartered in Switzerland, acting as a forum for financial cooperation among several world banks), and wealthy individuals.  Most of the funds come in the form of time deposits with fixed maturities. 

Today the eurodollar market is the international capital market of the world, as is reflected in the mix of borrowers.  It includes US corporations funding foreign operations, foreign corporations funding foreign or domestic operations, and foreign governments funding investment projects or general balance-of-payment deficits. Regardless of where they are deposited, places such as the Bahamas, Bahrain, Canada, the Cayman Islands, Hong Kong, Japan, the Netherlands Antilles, Panama, or Singapore, and regardless of who owns them, eurodollars never leave the US.

Federal funds  (Fed funds) are short-term funds available to commercial banks in the Federal Reserve System to maintain federally mandated reserve requirements. Commercial banks find themselves either in excess of reserves (in vault cash and in deposits with a Federal Reserve bank), which earn no interest, or in deficit. Thus a market develops in which banks with a deficit borrow from banks with a surplus to maintain their reserve requirements, usually for one day (overnight) and pay an interest rate called Fed funds rate. Because of this active trading traders in the Fed funds consider the Fed funds rate a base rate on which other money market rates are based.

Repurchase agreements (RP’s or Repo’s) essentially short-term agreements to buy back the issued securities, generally Government securities, at a given future date. Interest rates on repo’s are generally lower than the current prevailing rates. Investors are willing to accept the low rates simply for lack of other better investment opportunities. Overnight buying and selling of Fed funds are nothing but repo’s, i.e., short-term loans.

2.2.2 Capital Markets

Capital market securities differ from money market securities in three ways: (1) maturity exceeding one year, (2) higher risk of default, and (3) poorer marketability. This is a more artificial distinction than a real one. Capital market securities near maturity are just as less risky and as marketable as money market securities. The following are capital market securities that promise to pay a fixed income.

US Treasury Issues offer two types of securities with maturity greater than one year: (1) Treasury notes, and (2) Treasury bonds (T-bonds). Notes have maturity of 10 years or less, and bonds maturity greater than 10 years. They pay coupons semiannually, and are sold in competitive auctions where bidders submit the desired yields to maturity, rather than “discounts” as with T-bills. Flower bonds are US Treasury bonds that are accepted at face value usually to pay estate tax. Flower bonds, which trade at a discount because they already have a relatively low interest rate, are rapidly disappearing. Treasury notes and bonds are traded by large Government security dealers. Buyers pay the dealer an asked price, and sellers receive the bid price. Some US Treasuries also have a call provision. All Treasury securities are part of the public debt. The Bureau of the Public Debt in the US Treasury Department is responsible for the accounting for and reporting of the debt in accordance with statutory direction. The Bureau does not have any public policy decision-making authority. The public debt is all Federal debt held by individuals, corporations, federal reserve banks, state and local governments, foreign governments, and other entities outside of the United States Government less Federal Financing Bank securities.The Federal Financing Bank (FFB) is a government corporation, created by Congress in 1973, under the general supervision of the Secretary of the US Treasury, established to centralize and reduce the cost of federal and federally-assisted borrowing from the public. When you buy a US Treasury, you are in effect lending money to Uncle Sam, and become a creditor. You are part owner of the public debt, and stand to benefit from it to the extent that you lend money.

US Agency Issues come from various agencies of the Federal government, not from the US Treasury.

The Federal National Mortgage Association (FNMA, “Fannie Mae”) is a Government-sponsored corporation owned by private investors to provide mortgage financing. Their issues ranging from short-term discount notes (for the money market) to 25-year debentures are not guaranteed by the US Government. Proceeds from their bonds go to purchase mortgages from savings and loans, mortgage companies, and insurance companies.

The Federal Home Loan Bank (FHLBank), one of 12 regional shareholder-owned FHLBanks that comprise the FHLBank System, a government sponsored organization, has the mission to enhance the availability of residential mortgage credit by providing a readily available, low cost source of funds to its member institutions.  Eligible institutions include financial institutions with at least 10 percent of their assets in residential mortgage loans, or any FDIC-insured institution with average total assets over the preceding three- year period of less than $500 million adjusted annually.  Their goal is to fund housing, small business, small agribusiness and economic and community development loans in their communities.  FHLB issues, not insured by the US Government, range from one to 20 years.

The Federal Land Bank (FLB), one of 12 regional institutions, part of the Federal Land Bank Association (FLBA) or the Federal Farm Credit System (FLCA), a financial service provider specializing in long-term loans to farmers and ranchers only for various agricultural purposes, including farms, ranches, recreational property, agribusiness, timberland, agricultural equipment, livestock, agricultural operating capital, and rural homes. FLBs are cooperatively owned and locally operated. The FLB bonds range in maturities from 18 months to 25 years.

On May 20, 1988, the FLB of Jackson was placed in receivership and liquidated. On July 6, 1988, the 11 remaining FLBs merged with the Federal Intermediate Credit Bank (see next paragraph) in their respective districts to form Farm Credit Banks (see below). The mergers were required by the Agricultural Credit Act of 1987.

The Federal Intermediate Credit Bank (FICB) one of 12 regional banks formed to discount farmers' short-term (9 months) and intermediate-term (2-4 years) notes made by commercial banks, livestock loan companies, thrift institutions and, beginning in 1933, production credit associations.

On July 6, 1988, 11 of the 12 then existing FICBs merged with the Federal Land Bank in their respective districts to form Farm Credit Banks in implementation of the Agricultural Credit Act of 1987. The last remaining FICB, the FICB of Jackson, merged with the FCB of Columbia on October 1, 1993.

Farm Credit Banks (FCBs) were created on July 6, 1988, in 11 of the 12 then existing Farm Credit districts when the Federal Land Bank and Federal Intermediate Credit Bank in each district merged. The mergers were required by the Agricultural Credit Act of 1987. FCBs provide services and funds to local Associations that, in turn, lend those funds to farmers, ranchers, producers and harvesters of aquatic products, rural residents for housing, and certain farm-related businesses. Since 1988, mergers between FCBs have reduced their number to six.

Banks for Cooperatives (BC), of which there were 13 that provided lending and other financial services to farmer-owned cooperatives, rural utilities (electric and telephone), and rural sewer and water systems. A BC is also authorized to finance U.S. agricultural exports and provide international banking services for farmer-owned cooperatives. The last existing BC in the Farm Credit System, the St. Paul Bank for Cooperatives, merged into CoBank Agricultural Credit Bank, on July 1, 1999. An Agricultural Credit Bank (ACB) is the result of the merger of a Farm Credit Bank and a Bank for Cooperatives and has the combined authorities of those two institutions.

Government National Mortgage Association (GNMA, “Ginnie Mae”), a wholly owned corporation within HUD, operates the Mortgage-Backed Securities (MBS) program. Ginnie Mae helps to ensure mortgage funds are available throughout the United States including rural and urban areas in which it has been harder to borrow money to buy a home. These Mortgage-Backed Securities are issued by Ginnie Mae-approved private institutions: commercial banks, mortgage companies, and savings and loans. The mortgages are insured by the Federal Housing Administration (FHA), or by the Rural Housing Service (RHS), or they are guaranteed by the Department of Veterans Affairs (VA). The Ginnie Mae guaranty is backed by the full faith and credit of the United States. Ginnie Mae MBS are created when mortgage loans are pooled by eligible issuers. Commonly referred to as "pass-through" certificates, these MBS entitle an investor to an undivided interest in the underlying mortgage loan pool, including pass-through securities, modified pass-through securities, mortgage-backed bonds, and mortgage pay-through securities. Ginnie Mae I MBS are modified pass-through mortgage-backed securities on which registered holders receive separate principal and interest payments on each of their certificates. Their maximum maturity is 30 years for single-family, 40 years for multifamily. The minimum pool size is $1,000,000 with the minimum certificate size of $25,000. Ginnie Mae II MBS are modified pass-through mortgage-backed securities on which registered holders receive an aggregate principal and interest payment from a central paying agent on all of their Ginnie Mae II MBS. Their maximum maturity is 30 years. The minimum pool size is $250,000 to $1,000,000 with a minimum certificate size of $25,000. Payment of principal and interest to investors is made every month.

Municipal Issues. Municipal bonds are debt obligations issued by states, cities, counties, and other governmental entities to raise money to build schools, highways, hospitals, and sewer systems, as well as many other projects for the public good. Interest income from these bonds is generally exempt from federal income tax, and income tax of the state of issuance.

Municipal securities consist of long-term bonds with maturity of more than a year, and short-term notes, which typically mature in a year or less. Short-term notes are used by an issuer to raise money in anticipation of future revenues such as taxes, state or federal aid payments and bond proceeds, and to cover irregular cash flows, meet unanticipated deficits and raise immediate capital for projects until long-term financing can be arranged. Bonds are usually sold to finance capital projects over the longer term. The two basic types of municipal securities are: (1) General obligation bonds, which >are voter-approved. Principal and interest are secured by the full faith and credit of the issuer and usually supported by either the issuer's unlimited or limited taxing power.  (2) Revenue bonds. Principal and interest are secured by revenues derived from tolls, charges or rents paid by users of the facility built with the proceeds of the bond issue. Public projects financed by revenue bonds include toll roads, bridges, airports, water and sewage treatment facilities, hospitals and housing for the poor. Many of these bonds are issued by special authorities created for the purpose.

Taxable municipal bonds exist because the federal government will not subsidize the financing of certain activities, which do not provide a significant benefit to the public at large. Investor-led housing, local sports facilities, refunding of a refunded issue and borrowing to replenish a municipality's underfunded pension plan are just four types of bond issues that are federally taxable. Taxable municipals offer yields more comparable to those of other taxable sectors, such as corporations or agencies, than to those of other municipals. Forty billion dollars of the roughly $60 billion of outstanding taxable municipal issues has been issued since 1990, the most phenomenal growth of the taxable municipal market in recent years.

Corporate Issues. Corporate bonds are usually long-term bonds with a maturity of 5 years or more. An indenture (i.e., agreement) spells out financial obligations of the corporate issuer. They include call provisions, which allow the issuer to redeem the bonds at a specified price with the call premium being the difference between the call price and the face value. Sinking funds are periodic payments made to a trustee as guarantee of future repayment of the bonds, either held in trust till maturity, or used to immediately retire a portion of the bonds by purchasing it in the open market. Collateral provisions require the issuer to pledge specific assets as collateral or security for the issue. Bonds with such a pledge are secured bonds. Mortgage bonds are secured by real assets such as buildings and plants. Holders of unsecured bonds, known as debentures, are general creditors, who in case of liquidation are paid only after the mortgage bondholders have their prior claims to the pledged assets satisfied.

As inducements to purchasers of bonds, firms sweeten them with convertibility and warrants. Convertible bonds allow bondholders to convert them to shares of common stock. Bonds with attached warrants allow holders to buy a given number of shares of stock at a favorable exercise price at some future time before the exercise date.

Income bonds pay interest and principal only if the issuer earns income from assets. There are no contractual obligations for the issuer to pay interest or principal. Municipal revenue bonds are income bonds.

2.3    The Federal Reserve System (the Fed)

Founded by Congress in 1913 the Federal Reserve System, also known as the Fed, is the central bank of the United States created to provide the nation with a safer, more flexible, and more stable monetary and financial system. Though “independent within the government,” having its own income derived from its Treasury bond holdings and from services provided to commercial banks, and its own budget, the Federal Reserve generally orients its monetary policy toward the economic policy of the government.

The Federal Reserve System consists of a central government agency (the Board of Governors in Washington, D.C.), and twelve regional Federal Reserve Banks located in Boston, New York, Philadelphia, Cleveland, Richmond, Atlanta, Chicago, St. Louis, Minneapolis, Kansas City, Dallas and San Francisco.

The Federal Reserve's responsibilities cover four general areas: (1) conducting monetary policy; (2) supervising and regulating banking institutions and protecting the credit rights of consumers; (3) maintaining the stability of the financial system; and (4) providing certain financial services to the US government, the public, financial institutions, and foreign official institutions.

The Fed implements monetary policy by (1) changing the money supply through the operations of the Federal Open Market Committee (FOMC), (2) changing the reserve requirements (the percentage of deposits that must be kept in reserve as vault cash and deposits with the Federal Reserve banks), and (3) changing the discount rate, i.e., the interest rate it charges in loans to commercial banks.

The Federal Open Market Committee purchases and sells Treasury bonds and other Federal agency securities to influence the money stock. When the Fed buys Treasuries, it takes part of the money out of circulation, thus tightening credit. The Fed embarks on an expansionary course when it sells Treasuries.

2.4 The Securities and Exchange Commission (SEC)

The information in this section may be found at the SEC website. The US Securities and Exchange Commission (SEC) was created in the aftermath of the Great Crash of October 1929, when the stock market lost half of its value, and countless investors were ruined financially. Banks, being big investors in the stock market, lost great sums of money. When people feared their banks might not be able to pay back the money that depositors had in their accounts, a "run" on the banking system caused many bank failures.

The primary mission of the SEC is to protect investors and maintain the integrity of the securities markets. As more and more investors turn to the markets to help secure their financial futures, buy homes, and finance their children’s college education, these goals are more compelling than ever.

The world of investing is complex, risky, but can be very fruitful. Unlike deposits in commercial banks, which are protected by the federal government (the Federal Deposit Insurance Corporation or FDIC), stocks, bonds and other securities can lose value. There are no guarantees. Investors must protect their investments in the securities markets by doing thorough research and asking questions.

The key for all investors is access to certain basic facts about an investment prior to buying it. To this end, the SEC requires public companies to disclose meaningful financial and other information to the public, which serves as a common pool of knowledge on which investors depend to make sound investment decisions.

The SEC oversees participants in the securities industry, including stock exchanges, broker-dealers, investment advisors, mutual funds, and public utility holding companies. The SEC is concerned primarily with promoting disclosure of important information, enforcing the securities laws, and protecting investors who interact with these various organizations and individuals.

Crucial to the SEC's effectiveness is its enforcement authority. Each year the SEC brings between 400-500 civil enforcement actions against individuals and companies that break the securities laws. Typical infractions include insider trading, accounting fraud, and providing false or misleading information about securities and the companies that issue them.

Fighting securities fraud requires teamwork. At the heart of effective investor protection is an educated and careful investor. The SEC offers the public a wealth of educational information on its Internet website at

Though it is the primary overseer and regulator of the U.S. securities markets, the SEC works closely with many other institutions, including Congress, other federal departments and agencies, the self-regulatory organizations (e.g., the stock exchanges), state securities regulators, and various private sector organizations.

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