Investments by Ravi Shukla

Investments
Ravi Shukla
Finance Department
School of Management
Syracuse University

c 1995, Ravi Shukla.
Typeset in LATEX2ε.

Contents
Preface ii
Introduction 1
1 Securities Markets 3
1.1 The Securities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Money Market Securities . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Capital Market Securities . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.3 Mutual Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.4 Options and Futures . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Security Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Investment Proﬁts and Returns . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Investors and their Motives . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 The Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5.1 Primary Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5.2 Secondary Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 The Trading Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.7 Long and Short Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.8 Cash and Margin Accounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.8.1 Long Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.8.2 Short Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.8.3 Mixed Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.8.4 Account Closing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.9 Investment Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.10 Market Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Return and Risk 30
2.1 Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Conversion of Units of Return . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.1 Subperiod and Continuous Compounding . . . . . . . . . . . . . . . . 34
i

Contents ii
2.3 Leverage and Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4 Return as a Random Variable . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 Investment Decision Making under Risk . . . . . . . . . . . . . . . . . . . . 38
2.6 Estimating Return Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.6.1 Using the Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.7 Sources of Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.8 Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.8.1 Investor’s Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.8.2 Risk Aversion and Dominance . . . . . . . . . . . . . . . . . . . . . . 48
2.8.3 Risk and Return: Historical Evidence . . . . . . . . . . . . . . . . . . 49
2.9 Other Determinants of Rates of Return . . . . . . . . . . . . . . . . . . . . . 50
2.9.1 Basic Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.9.2 Expected Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.9.3 Time to Maturity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.9.4 Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 Portfolio Analysis 58
3.1 Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Portfolio Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3 Diversification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3.1 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3.2 Diversification Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 An Overview of the Portfolio Selection Process . . . . . . . . . . . . . . . . . 66
3.5 Calculating Portfolio Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.6 Identifying the Optimal Portfolio . . . . . . . . . . . . . . . . . . . . . . . . 71
3.7 Optimal Portfolio with Risky and Risk-free Securities . . . . . . . . . . . . . 75
3.7.1 Efficient Frontier and Tangency Line . . . . . . . . . . . . . . . . . . 79
3.7.2 Constrained Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.7.3 Portfolio Revision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.8 Analysis of Diversification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.8.1 The Effect of Correlation . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.8.2 The Effect of the Number of Securities . . . . . . . . . . . . . . . . . 85
3.9 Mutual Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.10 Portfolio Selection in a Perfect Market . . . . . . . . . . . . . . . . . . . . . 90
3.11 Systematic and Unsystematic Risks . . . . . . . . . . . . . . . . . . . . . . . 91
3.12 Capital Asset Pricing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.12.1 CAPM and Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.12.2 Using the CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.12.3 Problems with the CAPM . . . . . . . . . . . . . . . . . . . . . . . . 97
3.13 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Contents iii
4 Security Selection and Performance Evaluation 104
4.1 Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2 Calculating Present Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.2.1 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.2 Some Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3 Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.1 Security Selection using Rates of Return . . . . . . . . . . . . . . . . 115
4.4 Market Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.4.1 Efficient Market Hypothesis . . . . . . . . . . . . . . . . . . . . . . . 118
4.4.2 Are Securities Markets Efficient? . . . . . . . . . . . . . . . . . . . . 120
4.4.3 Investing in an Efficient Securities Market . . . . . . . . . . . . . . . 121
4.5 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.5.1 Do Mutual Funds Exhibit Superior Performance? . . . . . . . . . . . 127
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5 Common Stocks 133
5.1 Stockholder Rights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2 Issue and Repurchase of Shares . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.3 Cash Dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.4 Reading Stock Quotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.5 Common Stock Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.5.1 Mature Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.5.2 Growth Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.5.3 Finite Holding Period . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.6 Obtaining Information for Valuation Decisions . . . . . . . . . . . . . . . . . 143
5.7 Factors Affecting Stock Prices . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6 Fixed Income Securities 149
6.1 Basic Terminology and Valuation . . . . . . . . . . . . . . . . . . . . . . . . 149
6.2 Bond Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.3 Risks of Fixed Income Securities . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.4 Bond Issuers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.5 Reading Bond Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.5.1 Corporate Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.5.2 Treasury Securities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
6.6 Bond Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Contents iv
6AInterest Rate Risk and Duration 164
6A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
6A.2 Interest Rate Changes and Realized Return . . . . . . . . . . . . . . . . . . 165
6A.2.1 Case 1: Interest Rates Remain Unchanged . . . . . . . . . . . . . . . 165
6A.2.2 Case 2: Interest Rates Go Up . . . . . . . . . . . . . . . . . . . . . . 166
6A.2.3 Case 3: Interest Rates Go Down . . . . . . . . . . . . . . . . . . . . . 167
6A.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6A.3 Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6A.3.1 Sensitivity of Duration . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6A.3.2 Duration for a Zero Coupon Bond . . . . . . . . . . . . . . . . . . . . 170
6A.4 Applications of Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
7 Options 171
7.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.2 Option as Risk Transferring Contracts . . . . . . . . . . . . . . . . . . . . . 175
7.3 Option vs. Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.4 Option Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.5 Option Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
7.5.1 American Options vs. European Options . . . . . . . . . . . . . . . . 182
7.5.2 Payoﬀ Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.5.3 Put-Call Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7.5.4 Call Valuation—Binomial Formulation . . . . . . . . . . . . . . . . . 187
7.5.5 Call Valuation—Black-Scholes Formulation . . . . . . . . . . . . . . . 189
7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
7AFutures 193
Normal Distribution Table 195
Data 197

Preface
These notes are intended to be used in a one semester course in investments. The students
are expected to have knowledge of algebra, statistics, and basic finance.
The objective of these notes is to present a concise introduction to the fundamentals
of investments. The notes take a risk-return valuation approach in an efficient markets
framework and do not delve into technical and fundamental analyses. To keep the notes
to reasonable length so that they can be covered in a one semester course, some secondary
topics have been presented briefly or omitted entirely. Also, many ideas have been brought
out only through the end-of-the-chapter exercises. It is extremely important for students to
try out these exercises for a better understanding of the subject.
I would like to express my gratitude to my teachers: Professors Donald Bosshardt, Sris
Chatterjee, Robert Hagerman, Philip Perry, and Charles Trzcinka, who taught me finance
and encouraged me to learn more about this exciting field of study. I would also like to
acknowledge the influence of seminal textbooks in finance and investments by authors such
as Brealey and Myers, Copeland and Weston, Sharpe, and Francis, that may be evident in
my presentation.
I have used these notes as a basis for my lectures during the past few semesters at SUNY
Brockport and Syracuse University. Feedback from students has significantly improved the
quality of these notes. I am obliged to James Cordeiro, Roberta Klein, Joan Norton and
Mike Tomas who read the notes patiently and provided detailed comments.
August 16, 1995 Ravi Shukla
v

Introduction
Welcome to the exciting world of investments. When you think of investment, you probably
imagine men and women in dark pinstripe suits, talking about millions of dollars as if it were
pocket change; or maybe you think of the traders in stock or futures exchanges (as seen in
movies such as Wall Street, Trading Places, Blue Steel, etc.); or maybe you think of the ticker
tape running at the bottom of the screen in CNN Headline News with those seemingly endless
symbols and numbers. Those are the glamorous, the chaotic, and the mysterious sides of
investments. In this course, we will take some of the mystery out of the world of investments.
When you finish this course, you may not become a smooth talking investment banker or a
frenzied trader, but you will have an understanding of the investment fundamentals that are
used by the investment bankers and traders. You will learn the language of investments and
the process of investment analysis and decision making. You may apply this knowledge to
your personal investments or become an investment professional and manage other people’s
money.
This course is about stocks, bonds, mutual funds, options, and futures. More importantly,
it is about risk and reward; about portfolios and diversification; about value and price. These
are the fundamental tools of investment decision making. Once you know these fundamentals,
you will have the background to make proper investment decisions. I have no doubt that
sooner or later you will be faced with an investment decision making situation, if you haven’t
done so already. Someday, you may want to set some money aside either with a definite
motive of using it as a down payment for a house or a car, or with a general motive of having
it for emergencies. You will examine alternative places to put this money: a savings account,
a money market mutual fund, a stock mutual fund, or maybe stock or bond of your favorite
company. To make an intelligent decision you should be able to evaluate these alternatives.
This course gives you the background to make that evaluation.
Let us begin by defining investment. When we make an investment, we are using the
money that could otherwise have been consumed. We could have used it to buy groceries, buy
a car, take a vacation, or build a house. By making the investment, we are sacrificing these
pleasures. There ought to be some reward for this sacrifice. The reward is that we expect to
get back more than what we put in. We can then consume the amount that we get back. In
economic terms, when we invest, we trade current consumption for future consumption. For
an investment to be acceptable, the trade-off should be favorable, i.e., we must expect that
1

Introduction 2
the pleasure derived from the future consumption will be more than the pleasure foregone.
Since the economic term for pleasure is utility, we can define investment as the act of
giving up current consumption and using it so that the resulting future consumption may
provide an improvement in utility. For an investment to be acceptable it is not enough that
the amount received in the future be more than what we invested. It should be more by
such an amount that it compensates for the inconvenience caused by the postponement of
consumption.
Investments are classified into two categories: real and financial. Real investments are
made in tangible assets. If you invest $100,000 in a factory or a restaurant, you are making
a real investment. Real investments are made by people who have technical knowledge or
insight that can lead to a valuable product or service. Often, these people do not have enough
capital to make the investment and therefore they look elsewhere for financial support.
Financial investors invest in the companies formed for the sake of real investment, and thus,
support real investment activity in the economy.
Financial markets bring the real and financial investors together. When you make a
financial investment, you receive a piece of paper known as a security that outlines the
terms and conditions of the investment. This course deals with financial investments and
therefore concentrates on securities such as stocks and bonds. Securities may be marketable
or privately placed. A marketable security is one that can be bought and sold in an open
market. Most corporations and governments issue marketable securities. Privately placed
securities are issued by companies to family, friends, relatives and acquaintances, and are not
traded publicly. Our focus will be on the marketable securities issued by the governments
(federal, state, and local) and corporations.
These notes are organized as follows: Chapter 1 describes the different kind of securities,
how the securities are issued and traded, and where one can get information about the
securities. Chapter 2 explores the concepts of return and risk. Chapter 3 shows how investors
can reduce risk by investing in portfolios of several securities. Chapter 4 discusses the process
of security selection and performance evaluation. Chapters 5, 6, and 7 are devoted to the
individual securities: stocks, bonds, and options and futures, respectively.

Chapter 1
Securities Markets
In this Chapter you will learn about the different kind of securities, how the securities are
issued and traded in the market, how investors buy and sell securities, and where one can get
investment information. The description focuses on the important aspects of these topics.
For detailed information you should consult the additional readings listed at the end of the
Chapter.
1.1 The Securities
Securities, also called financial instruments, are the medium of financial investments.
Common stock, preferred stock, bonds, mutual funds, and options and futures contracts are
examples of securities. Common and preferred stock, and bonds are issued by corporations
or governments to raise capital. Mutual funds are created by financial companies using
existing securities. Options and futures contracts are created by the investors and involve
other securities. Brief descriptions of these securities are provided later in this section.
1.1.1 Money Market Securities
Short term securities issued by corporations and governments to borrow money are known
as money market securities and are traded in the money market. Securities are classified
as short term if they have a life of one year or less, i.e., all the obligations associated with
the security are paid off within a year. Commercial paper (issued by corporations) and
Treasury bills (issued by the U.S. Treasury for the federal government) are examples of
short term securities. Money market securities do not pay any interim interest. They are
sold at a discount, the discount being the interest. Consider an investor who buys GMAC
commercial paper for $98,000. On maturity, three months later, GMAC pays back $100,000
to the investor. The $2,000 difference is the interest amount.
3

Securities Markets 4
1.1.2 Capital Market Securities
Long term securities issued by corporations and governments are known as capital market
securities and are traded in the capital market. Bonds, preferred stocks, and common
stocks are capital market securities.
Bonds and preferred stocks are debt securities.1
By buying these securities, investors
lend money to the issuer. In return, the issuer promises to pay interest periodically till the
maturity date and to pay the face value on the maturity date. The interest and face value
payments to be made by the issuer are usually fixed and known at the time the security
is issued. For this reason, bonds and preferred stock are also known as fixed income
securities.
Common stocks are issued by corporations. By buying shares of common stock, investors
become part owners of the issuing corporation. Common stockholders are entitled to certain
ownership privileges, most important of which is a claim to the corporation’s assets and
earnings net of the payments to the bondholders and other lenders. Since common stock-
holders receive what is left over after paying the bondholders and lenders, common stock is
also known as a residual income security. Even though common stock gives the investor
the privileges of ownership, the liability from the ownership is limited to the amount invested
in the common stock. For example, if you bought 100 shares of Kodak at $50, and Kodak
were to go bankrupt (because of a lawsuit, for example), the maximum you could lose is
the $5,000 you already invested. For this reason, common stock is known to have a limited
liability.
Corporations pass their earnings to the common stockholders in form of dividend pay-
ments. A corporation, however, is not obligated to pay dividends. It may retain the earnings
for reinvestment purposes. Retained earnings increase the value of the corporation’s assets
and therefore the market price of the stock.
Common stock is the most popular form of investment among individuals. Therefore,
majority of the financial news is concentrated on common stock. Keeping with this spirit,
common stock will be used to illustrate the concepts in Chapters 1 through 4 of these notes,
although many of the concepts apply to other securities also.
1.1.3 Mutual Funds
Investors like to diversify by distributing their money over several different securities so that
the losses on some securities may be compensated by the gains on the others. Forming such
portfolios, however, is time consuming and expensive for individual investors. Financial
companies such as Fidelity Investments and Vanguard create and manage portfolios known
as mutual funds. Investors buy shares in these mutual funds and receive the benefits of
1
While preferred stock is treated in the same manner as common stock for accounting purposes, it shares
more investment characteristics with bonds than with common stocks. Therefore, it is treated as a bond
here.

diversiﬁcation. Mutual fund companies aggregate the shareholders wealth and invest it
in securities. Investing in mutual funds is considered an indirect investment because
individuals are investing in funds which in turn are investing in securities. If individual
investors buy securities directly, it is known as a direct investment.
There are many kind of mutual funds: funds that invest in stocks, funds that invest
in short term bonds (money market funds), funds that invest in municipal bonds, etc.
Investors can choose the funds that meet their objectives and preferences. Mutual funds
have become immensely popular during the last twenty years. The number of mutual funds
available has grown from 477 in 1977 to 5,375 at the end of 1994. The total assets invested in
mutual funds amount to $2,164.5 billion. About 31% of the US households invest in mutual
funds.
1.1.4 Options and Futures
Options and futures are contracts between investors. An option or a futures contract is
created if there are two investors who want to enter the contract: one wants to buy it and
the other wants to sell it.
A futures contract involves the sale of an asset on a future date at a price agreed upon
now. For example, we may enter a futures contract which states that you will sell me 5,000
bushels of corn 3 months from now at $2.40 per bushel. Why would we enter this contract?
Suppose the current price of corn is $2.36 per bushel. I know that I will need 5,000 bushels
of corn three months later but I don’t want to face the risk of the price going up too much.
You, on the other hand, are willing to take that risk. So you oﬀer to sell me the corn for
$2.40. Three months later, if the corn price goes up to $2.50, I will save $0.10 per bushel. If
the price goes down to $2.30, you will make $0.10 per bushel.
An option contract involves one person giving the other a right for a transaction in
the future. For example, we may enter the following option contract. For a small fee (say
$1) that I pay you now, you give me the right to buy from you a share of Kodak for $45
any time during the next 2 months. Why would we enter this contract? I may do it because
I believe that the price of Kodak will go up during the next two months and will be more
than $45. You may enter the contract because you believe that the share price will not go
above $45. If the price goes above $45, I will exercise the right you gave me and buy a share
of Kodak for $45 while it is worth a lot more. On the other hand, if the price does not go
above $45, I will not exercise the right you gave me and you will make $1.
Options and futures allow security risk to be transferred from one person to another. In
the corn futures example, I transferred the risk of corn price going up to you for a small fee
($0.04 per bushel). Similarly, in the Kodak option example, I transferred the risk of share
price going up to you for $1. In popular literature, options and futures are viewed as risky
investments and investing in these securities is considered similar to gambling. However,
judicious use of options and futures with other securities such as stocks and bonds can be
extremely useful to investors.

1.2 Security Prices
Security prices are determined by the process of supply and demand. Under ideal con-
ditions, the market price of a security should be equal to the intrinsic value of the security.
The intrinsic value of a security comes from the cashflows expected from the security in the
future. Investors estimate the value of a security using the information available to them.
Since investors differ from each other in information, age, attitudes, tax brackets, and needs,
they arrive at different estimates for the same security. These differential estimates create
supply and demand for securities.
If the market price is below the estimated value, investors want to buy the security, and if
the price is above the estimated value, they want to sell it. The market price of the security
responds to demand and supply: it goes up if the demand exceeds supply, and it goes down
if the supply exceeds demand. The condition when supply equals demand, i.e., the market
clears, is known as equilibrium. The securities markets are very dynamic. New information
and interpretations arrive in the market constantly which causes the demand and supply to
fluctuate continuously. As a result, market equilibrium does not last very long. The market
moves from one equilibrium to another. For our discussion we will often freeze the market
at a particular point. Otherwise, by the time we finish our discussion the market would be
at a different point!
1.3 Investment Profits and Returns
Buying and selling securities creates profits or losses for investors. If an investor buys a
security at a low price and sells at a high price, he makes a profit. On the other hand, if
he buys high and sells low, he realizes a negative profit, i.e., a loss. Any cash distributions
(dividends or interest) that the investor receives from the security add to the profits. To
be able to compare the profits from one security with another, the profits are scaled by
dividing by the investment amount. The resulting number is known as the rate of return on
investment, or simply return. Other things being the same, investments with higher returns
are more desirable.
Suppose you bought 100 shares of a stock at $60 a share, held them for one year, received
a dividend of $2 per share, and sold the shares at $70 a share after receiving the dividend,
then your profit per share was ($70 − $60) + $2 = $12. The profit of $12 was made up of
two parts: a capital gain of ($70 − $60) = $10 from the increase in price and an income
of $2 in form of the dividend. Since you made $12 on your investment of $60, your return
was 12/60 = 0.20 or 20%. It is important to associate a time unit with the rate of return.
Since you made this profit over a one year period, your return was 20% per year.
To generalize the above example, suppose at the beginning of a period, you make an
investment of w0 and at the end of the period the securities are worth w1, then the profit

from the investment is w1 − w0 and the return r is:
r =
w1 − w0
w0
(1.1)
For a security, let us express the initial price by p0, the final price by p1, and the interest or
dividend by d, then the total profit is p1 − p0 + d and the return is:
r =
p1 − p0 + d
p0
(1.2)
1.4 Investors and their Motives
The investment marketplace is filled with many different kind of investors:
• Individual investors like you and me who mostly use investments as a vehicle for
savings. About 51 million Americans owned shares in 1994, either directly or indirectly
through mutual funds, etc.
• Corporations who purchase securities when they have excess funds. Sometimes they
may do it to gain ownership and control of other companies.
• Institutional investors such as insurance companies, pension funds, college endow-
ment funds, and mutual funds whose professional function is to invest.
Individual investors usually make relatively small trades. For example, an individual
investor may buy 100 shares of AT&T, or sell 200 shares of Kodak. Institutional investors
deal with large amounts of money and therefore often trade shares in large quantities. If a
trade involves 10,000 shares or more, it is known as a block trade. Block trades usually
cause the market prices to fluctuate significantly. In this way, institutional investors exercise
great influence on the market. In 1994, 55.5% of the shares traded in the New York Stock
Exchange were through block trades. Block trades, however, accounted for only 5.8% of all
trades conducted on the NYSE. 78.8% of the trades involved 2,000 or fewer shares.
Different investors have different motives for trading in securities. The motives can be
classified as follows:
• Need for liquidity: Liquidity motivated investors buy securities when they have
excess funds and sell them when they need funds. Most trades by individual investors
are liquidity motivated.
• Speculation: An investor who speculates is betting on the movement of the price of
a security. Speculators believe that they can predict the movement of security prices.
Therefore, they invest in specific securities at specific times. If you were to buy 100
shares of Microsoft Corporation because of a hot tip, you would be speculating. While
liquidity motivated investors use their own money, speculators may even borrow money
for investment.

• Hedging: An investment that is made to reduce risk is called hedging. Hedging is
similar to buying insurance to protect against loss. Options and futures contracts are
used for hedging purposes. Options, for example, allow investors to recover some or
all the losses from unfavorable price movements.
1.5 The Markets
Investors buy and sell securities in securities markets. The securities markets can be classified
as primary and secondary.
1.5.1 Primary Market
Corporations and governments that need capital sell securities in the primary market. Rather
than being an actual place, primary market refers to the process through which securities are
exchanged for money between investors and the issuer. The process of issuing securities is
managed by investment banking firms. Merrill Lynch, Salomon Brothers, Smith Barney, and
CS First Boston are some of the well known investment banking firms. Investment banking
firms advise the issuing corporations on the following matters related to the security issue:
• The kind of security to issue: “Stock or bond?” “Common or preferred stock?” “Serial
or term bonds?”
• The proper time to issue the securities: “Should we issue the securities now or will the
market respond better in three months?”
• The price at which to sell the securities: “The market price of the existing common
stock is $8.50. Should we try to sell the issue at $8.00? Will a discount of $0.50
guarantee the sale of all the shares the corporation wants to sell?”
• Fulfilling the legal requirements: Designing the prospectus. Filing necessary papers
with the Securities and Exchange Commission (SEC). Making necessary announce-
ments.
• Actual selling of the securities: In addition to the basic salesmanship, the investment
bankers may also act as risk takers or underwriters for the issue. The two major
types of agreements between the issuing corporation and the investment banking firms
for selling the securities are firm commitment and best efforts.
◦ Under a firm commitment agreement, the corporation sells the securities to
investment banker(s) at a price below the issue price. The difference being the
commission. For example, if the offering price is $8.00 a share, the corporation

Figure 1.1: A security offerings announcement.
This announcement is not an offer of securities for sale or a solicitation of an offer to buy securities.
June 17, 1991
1,650,000 Shares
Ecogen Inc.
Common Stock
Price $8 per share
Copies of the prospectus may be obtained from such of the undersigned (who are
among the underwriters named in the prospectus) as may legally
offer these securities under applicable securities laws.
Dillon, Read & Co. Inc.
Prudential Securities Incorporated
Piper, Jaffray & Hopwood
Incorporated
Bear, Stearns & Co. Inc. The First Boston Corporation Alex. Brown & Sons
Incorporated
Donaldson, Lufkin & Jenrette Hambrecht & Quist Kidder, Peabody & Co.
Securities Corporation Incorporated Incorporated
Lazard Frères & Co. Merrill Lynch & Co. Montgomery Securities
PaineWebber Incorporated Robertson, Stephens & Company
Smith Barney, Harris Upham & Co. Wertheim Schroder & Co.
Incorporated Incorporated
Deutsche Bank Capital Advest. Inc. Arnhold and S. Bleichroeder, Inc.
Corporation
Interstate/Johnson Lane Janney Montgomery Scott Inc.
Corporation
Jessup, Josephthal & Co., Inc Ladenburg, Thalmann & Co. Inc.
Legg Mason Wood Walker Neuberger & Berman Raymond James & Associates, Inc.
Incorporated
Wheat First Butcher & Singer W. H. Newbold’s Son & Co., Inc.
Capital Markets
Nordberg Capital Inc. Pennsylvania Merchant Group Ltd
Source: The Wall Street Journal, June 17, 1991.

may sell the securities to the investment banker for $7.25 a share. Thus, if one
million shares are to be issued, the potential income to the investment bankers
is $0.75 million. Of course, the realized income will depend on how many shares
are sold. The issuing corporation is not concerned with the number of shares sold
because it will get the money from the investment bankers. Firm commitment is
the common method of issue for large corporations.
◦ In the best efforts arrangement, investment banking firms do not take any risk.
Their commission is either fixed regardless of how many shares are sold, or is
a combination of a fixed fee plus a commission on each share sold. Any unsold
shares are returned to the issuing corporation. Best efforts arrangements are used
for smaller, lesser known firms.
Investors are informed about security issues through announcements in The Wall Street
Journal and other business publications. An announcement that appeared in the Journal on
June 17, 1991 is shown in Figure 1.1. Note that the advertisement refers to a prospectus.
The prospectus outlines the history of the company, its current financial situation, and its
plans. If investors find the prospectus appealing, they may purchase the shares from the
investment bankers. Usually, many investment bankers are involved in selling the securities
even though they do not act as advisors. In the announcement in Figure 1.1, Dillon, Read &
Co. Inc., Prudential Securities Incorporated, and Piper, Jaffray & Hopwood, Incorporated
are the primary investment bankers, i.e., they advised Ecogen Inc. throughout the issue. The
remaining investment bankers only acted as sellers.
The securities issue process is a very time consuming activity. From start to finish, it
may take as long as four to six months. It is also very expensive. The commissions to the
sellers and underwriters and other expenses may amount to as much as 10% of the size of
the issue.
1.5.2 Secondary Market
Once the securities have been issued, investors who bought the securities may want to sell
them and others may want to buy them. These trades occur in the secondary market. The
New York Stock Exchange (NYSE) is a major secondary market. Other secondary mar-
kets include the American Stock Exchange (AMEX or ASE) and many regional exchanges
located in various parts of the country.2
The trading in these stock exchanges takes place
through face-to-face contact between the brokers who act as agents for the investors. The
brokers make offers for the securities by shouting and using hand signals, much like in an
auction. This trading method is known as the open outcry system. With the advances in
2
Sometimes, in popular financial reporting, the term secondary markets is used for smaller exchanges
such as American Stock Exchange or the over-the-counter markets only. That use of the term is technically
imprecise.

computers and communications, the over-the-counter (OTC) has become a very prominent
secondary market. The OTC market is a network of communications between the securities
dealers. The securities that are traded over-the-counter are listed on the NASDAQ (National
Association of Securities Dealers Automated Quotation) system. The communication net-
work makes the most recent prices available on computer terminals and trades are completed
through communication lines without the two parties ever meeting each other.
There are organized exchanges for other securities and financial contracts also. Bonds
are traded in a separate area in the New York and other stock exchanges. Option contracts
are traded in Chicago Board Options Exchange (CBOE), American Stock Exchange, and
regional exchanges. Futures contracts are traded in Chicago Board of Trade (CBT), New
York Futures Exchange (NYFE), New York Mercantile Exchange, etc. There are organized
exchanges for trading securities in other countries as well. Some of the world’s largest stock
exchanges are located in Tokyo, London, Toronto, Milan, Paris, Amsterdam, Stockholm,
Brussels, Frankfurt, Montreal, Hong Kong, Singapore, and Sydney.
The New York Stock Exchange, founded in 1792, is the largest stock exchange in the
United States. It is located in a large building at 18 Broad Street. The stocks are traded on
a floor about the size of a football field which is divided into several chambers. There are
several booths, known as trading posts, on the trading floor, each trading a few securities.
There are electronic bulletin boards and TV monitors throughout the exchange floor that
constantly display security prices and news from around the world. Along the boundary of
the trading areas, there are offices for the brokers. These offices are managed by clerical staff
and runners who convey orders received on the phone to the brokers. During the trading
hours, the exchange floor appears to be a crowded mad house with paper all over the place
and people screaming and gesturing endlessly with their hands.
Trading in the exchange is done by the members, who have to buy seats in the exchange.
At present there are 1,366 seats in the NYSE. Fifty eight non-seat owning members have
access to the exchange by paying an annual fee. The seats are owned by individuals and
companies, and are traded in the open market. The price of a big board seat during 1994
fluctuated between $760,000 and $830,000. Members of the exchange can be classified as
follows:
• Traders buy and sell on their personal account.
• Commission brokers execute orders for their customers.
• Floor brokers engage in miscellaneous trading. One of their functions is to trade for
a commission broker who may be temporarily busy.
• Specialists are traders who specialize in trading some particular securities. They
manage the trading posts and facilitate in trading among brokers and dealers by keeping
track of their orders and matching the buy and sell orders as feasible. Specialists also
have the responsibility of being the market makers. In other words, they have an

obligation to keep the market going by buying and selling shares as needed. For
example, if many investors want to sell their shares of IBM during an afternoon, the
market will shut down if there are no buyers. The IBM specialist has the responsibility
to buy the shares in this situation. Similarly, if there is a sudden demand for the shares
of IBM, the specialist has to sell the shares. For such contingencies, the specialist must
carry a large inventory of shares. However, only 17.3% of the trades in 1994 involved
specialists. In rest of the cases, brokers traded among themselves.
The NYSE is open for trading between 9:30 am and 4:00 pm. Two after-hours sessions
(known as crossing sessions I and II) allow trading between 4:15 pm and 5:00 pm, and
4:00 pm and 5:15 pm, respectively, at that day’s closing prices. The average daily trading
volume (number of shares traded) during 1994 was 291.4 million shares. The annual trading
volume was 73.4 billion shares, accounting for $2.45 trillion in value. The rate at which the
shares change hands on the NYSE works out to over 10,000 shares per second. Clearly, face
to face trading among brokers and dealers would not be able to accomplish this rate. A
computerized order matching system known as SuperDot3
was responsible for 44.4 billion,
or 60.5% of all shares traded in 1994.
For a stock to be traded on the NYSE, it has to be listed on the exchange. Firms have
to meet strict requirements and pay a fee to be listed and traded on the NYSE. These
requirements are designed to make sure that only the nationally prominent securities are
traded in the NYSE. Despite the strict listing requirements, corporations like their stock to
be listed on the big board—a nickname for the NYSE—because it gives them visibility and
prominence which is useful when issuing new securities. At the end of 1994, the NYSE had
2,570 firms listed which made up 3,060 stock issues, with over 142 billion shares having a
total market value of $4.45 trillion. The price of an average share in the NYSE in 1994 was
$31.26.
1.6 The Trading Process
Investors who want to buy and sell securities have to contact a brokerage house, open an
investment account, and be assigned an account executive (AE). There are two kind of
brokerage houses: discount and full service. Discount brokerage houses just trade for their
customers while full service brokerage houses provide recommendations and advice as well.
Some well known brokerage houses are Merrill Lynch, Dean Witter, and Charles Schwab.
To buy or sell some securities, the investor places an order with the account executive. The
order can be a day order or a good till cancelled order. Day orders must be executed
during the specified day, while good till cancelled orders are valid from the time the order
is placed till the order is filled or cancelled. With respect to price, there are three kinds of
orders:
3
The Dot stands for Designated Order Turnaround.

• Market order is an order to buy or sell securities at the best price available. A market
order is placed when an investor wants to leave the judgement about the price to the
broker.
• Limit order is an order to buy at a specified price (called the limit price) or less, or
sell at a specified price or more. Limit orders are placed to make sure that securities
are bought at a low enough price or sold at a high enough price.
• Stop loss order is an order to sell if the price falls to a particular level (stop level)
or to buy if the price rises to a particular level. Stop loss orders are placed when an
investor wants to cut losses.
The order is transmitted to the exchange floor office of the commission broker associated
with the brokerage house. The order is taken by the runner to the commission broker. The
commission broker goes to the booth where the security is traded. There may be other
brokers at the booth waiting to buy or sell. The specialist who deals in the stock quotes
two prices: a price at which he will sell the shares—the ask price—and another at which
he will buy the shares—the bid price. As you may expect, the ask price is higher than
the bid price. The difference is known as the bid-ask spread and provides a commission
to the specialist. If the bid and ask prices4
on the stock of XYZ are 241/4 and 241/2 then
an investor’s buy order for the shares will be executed at 241/2 and sell order at 241/4. The
order may be executed at an intermediate price, say 243/8, if there are two brokers: one who
wants to sell and another who wants to buy, and they decide to bypass the specialist. Upon
completion of the trade, the broker notifies the account executive through the runner who
in turn notifies the investor that the order has been executed. The investor usually makes
the payment (for a buy transaction) or receives the payment (for a sell transaction) within
three business days of the transaction.
In addition to the security price, the investor has to pay commissions and trading costs.
These transaction costs are always incurred by the investor whether he is buying or selling the
securities. The amount of transaction costs depends on the kind of account, the brokerage
house, the size of the order, etc. The transaction costs are not fixed and different brokerage
houses may charge different amounts for the same transaction. The commissions are higher
if an investor wants to trade in odd lots (not multiples of 100 shares). A good estimate
for transaction costs for a round lot (multiples of 100 shares) is 2% of the security price.
For example, if the shares were purchased for $100 each, the investor will have to pay
approximately $102. If they were sold for $100 the investor will get approximately $98. A
popular term used in the market is round trip transaction costs. Round trip refers to
buying and then selling a security. If an investor paid $30 in commissions when buying the
securities and $35 while selling them then the round trip transaction cost is $65.
4
The securities are traded at price intervals of 1/8, 1/16, or 1/32 depending on the exchange and the type of
security. 1/8, 1/16, or 1/32 is known as a tick. A tick is the smallest price movement allowed by the exchange.
A proposal for making the smallest price movement a penny is being studied by the SEC.

1.7 Long and Short Positions
Suppose the common stock of ABC is selling at $10 today. Based on your information you
expect the price to go up to $15 in 6 months. To make a profit one must buy low and sell
high. So, you may buy 100 shares of ABC for a total of $1,000 today. This is a positive
investment of $1,000 in ABC on your part. You will be 100 shares long on ABC, i.e., you
will own the shares of ABC. In six months, when the price does go up to $15, you may sell
the shares and make a profit of $500 on your investment. Of course, you will have a loss
if the price goes down. When you go long, your dollar loss is limited to the amount you
invested because the market price of a common stock can never be negative. However, there
is no limit to your profits because the stock price can keep rising without any limit.
Another stock, XYZ, is also selling at $10 today. Based on your information about this
stock, you expect the price to go down to $5 in 6 months. Since the stock price is high,
you should sell the shares now and buy them when the price is low. If you do not own any
shares to sell, you may borrow 100 shares from a friend, sell them, and pocket the proceeds
($1,000). This represents a negative investment of $1,000 because money has come into your
pocket, not gone out. You will be 100 shares short in XYZ. You do not own the shares but
you owe them; they are a liability. Six months later, when the price does go down to $5,
you may buy 100 shares of XYZ in the market (for $500), return them to your friend and
keep $500 as your profit. When you go short, there is a limit on your dollar gain because
the lowest the price can go is zero, but there is no limit on your losses because the price can
keep going up without any limit.
Short selling is risky not only because of unlimited losses but also because for each short
seller, there are two investors—the lender and the buyer—who have a positive outlook about
the stock. The lender must feel optimistic about the stock otherwise he would have sold the
shares himself. The buyer must also feel positively about the shares otherwise he would not
buy them. Therefore, one must be very sure of one’s information before short selling.
Going short is not as simple as described above. Even your best friends may not trust
you so much as to lend you the shares without any guarantee. In actual investing situations,
you borrow the shares from your broker. The broker requires you to maintain a collateral
for the market value of the borrowed shares ($1,000 in the example above) till the shares are
returned. The deposit must always be equal to the market value of the securities. Therefore,
if the share price in the example above were to go up to $13 in a week, you will have to add
$300 to the deposit. On the other hand, if it were to go down to $7, you could withdraw
$300 from the account. The collateral is maintained in an interest free account with the
broker. Therefore, the investor does not receive any interest on these funds. The investor
may substitute the collateral cash by other securities whose market values equal the required
collateral.
The short seller is required to pay dividends to the lender if the stock pays a dividend. Let
us understand the reason for this by following the mechanism of short selling carefully using
Figure 1.2. When you short sell 100 shares of XYZ, your broker borrows them on your behalf

Figure 1.2: Transactions in short selling.
Lender
Short
Seller Buyer
Deposit
......................................................................................................................................................................
.....................
......................................................................................................................................................................
.....................
......................................................................................................................................................................
....................................................................................................
.....................
1. Shares 2. Shares
3. Cash
4. Cash
Initial Transaction
......................................................................................................................................................................
.....................
......................................................................................................................................................................
.....................
......................................................................................................................................................................
.....................
...............................................................................
.....................
Lender
Short
Seller Seller
Deposit
4. Shares 3. Shares
2. Cash
1. Cash
Final Transaction
from another investor’s account, say Ms. L. You sell the shares to Mr. B. Now, suppose the
stock declares the dividend. Since Mr. B owns the shares, he will get the dividends directly
from the corporation. Ms. L, on the other hand, has only lent the shares.5
She still owns
them. Therefore, she expects the dividends that the stock paid. Since you borrowed the
shares, you are expected to pay those dividends.
Trading restrictions do not allow short selling if the last movement in the security price
has been downward. This is called the up-tick rule and is designed to keep the market free
of any psychological pressures. Regulators believe that if the market is on a downward trend
due to selling, short selling could put additional artiﬁcial downward pressure on the prices.
A large amount of short selling in the market indicates that investors are bearish about
the market, i.e., they expect the prices to go down. Does this mean that other investors
should also sell? Maybe. However, remember that the shares that have been sold short
will be bought back. This assures a demand for the shares in the future. Therefore, some
investors should be willing to buy the shares and sell them later when short sellers go to the
market to buy the shares back to replace them. However, short sellers may not need to buy
back all the shares if they are shorting against the box, i.e., short selling the shares they
already own. Shorting against the box is used by investors because it allows them to lock in
the proﬁts they have made (see problems 1.8 and 1.15). In that case, only those shares that
have not been shorted against the box will need to be replaced. This information is conveyed
by short interest. Short interest is the net short position of an investor. For example, if
5
As a matter of fact, she may not even know that her shares have been lent.

I sell 300 shares of XYZ short while I am long 200 shares of XYZ, my net short position or
short interest is only 100 shares of XYZ because, to replace the borrowed shares, I will need
to buy only 100 shares of XYZ, not 300 shares. The Wall Street Journal publishes a short
interest report every month around the end of the third week. It contains a lot of useful
information about short selling and short interest trends in the market.
An important lesson from the idea of short selling is that you never have to stay out of
the market. If you find a security that is a good buy, i.e., you expect its price to go up, you
should go long on it. If you find a security that is not a good buy, i.e., you expect its price
to go down, you should not ignore that security. If you hold that security, sell it. If you do
not own that security, you may make a profit by selling it short.
1.8 Cash and Margin Accounts
When you open an investment account with a brokerage house, you can make it either a cash
account or a margin account. In a cash account all the transactions are financed by 100% of
your funds. You do not borrow any money from the broker. A margin account allows you
to take loans from the brokerage house to finance your investments.
When you purchase securities using a cash account, you may take possession of the
securities, i.e., take them home, or you may leave them with the broker. Securities left with
the broker are said to be held in street name. When the securities are held in street name,
your account statement reflects the fact that you own the securities. This arrangement is
preferred by the brokerage houses because selling and buying transactions are quite easy to
perform—they become mere book-keeping exercises. The arrangement is also preferred by
the investors because they do not have to guard the securities from theft and accidents.
In a margin account the securities must be kept in the street name because they are used
as collateral against the loan made by the brokerage house. The broker, however, does not
advance full value of the securities as a loan. The investor has to put up some cash to make
the purchase. This cash is required to cover the losses that may result from adverse price
movements.
The size of the loan that an investor is allowed in a margin account is governed by many
factors. The two important ones are the risk of the investment and the status of the investor
and the account. Accounts are allowed bigger loans if the investment is less risky. Also,
the amount of loan that an account may be forwarded depends on the investor’s other asset
holdings and reputation. The interest rate on the margin loans are quite low because these
loans are secured by marketable securities.
The Federal Reserve Bank and the securities exchanges provide guidelines which are
followed by the brokerage houses in maintaining the margin accounts. The brokerage houses
usually impose stricter requirements. The guidelines are defined in terms of the margin ratio
or simply the margin. The margin ratio measures the amount of equity in the account as

a fraction of the market value of securities:
Margin =
Equity
Market Value of Securities
. (1.3)
The higher the margin, the higher the equity and the less the debt in the account. A 100%
margin account is fully equity financed—it is a cash account—while a 40% margin account
is financed by 40% equity and 60% loan.
Each account has two margin requirements: initial margin and maintenance margin.
When the account is opened, the margin in the account must at least be equal to the
initial margin specified for that account. Once the account is well established and in good
standing, the margin may drop, but it should not go below the maintenance level. Initial
and maintenance margins specify the minimum equity that the investor must have in the
account.
The margin in an account fluctuates with the market price of the securities held in the
account. If the margin falls below the maintenance level, the investor receives a margin
call from the brokerage house to bring the account up to the initial margin. If the investor
does not respond to the margin call, the brokerage house may sell some of the securities to
make the account current. If the margin in the account is above the maintenance level, the
investor can use the excess equity to make more investments or even withdraw cash from the
account. In the following subsections we will look at some common calculations in margin
accounts.
1.8.1 Long Position
Let us take the example of Mr. Garner, who has a margin account with Lean Hitter. The
initial and maintenance margin requirements for his account are 60% and 25%. Mr. Garner
wants to buy 100 shares of QVC. The shares are priced at $31 each. Since the initial margin
requirement is 60%, Mr. Garner must have equity worth at least 0.6 × $3,100 = $1,860. He
may take a loan for the remaining amount.6
Let us say Mr. Garner takes the maximum loan
permitted to him. The balance sheet of Mr. Garner’s account after the transaction is:
Assets ($) Liabilities and Equity ($)
Mkt. Val. of QVC 3,100 Loan 1,240
Equity 1,860
Total 3,100 Total 3,100
Now we will examine Mr. Garner’s account under different scenarios.
6
An investor is not required to borrow anything from the broker. He may choose to borrow all or part of
what he can. In our examples we will assume that investors borrow as much as they can.

$ Let us say that the market price goes up to $40. The account position is:
Equity 2,760
Note that the equity value increased as the market value of shares went up while the
loan amount did not change. The margin ratio now is 2,760/4,000 = 69%. Mr. Garner
is not required to maintain such a high margin. He can reduce his margin either by
selling some shares and withdrawing the cash resulting from this transaction, or by
making additional investment. Let us examine each of these alternatives.
(a) If Mr. Garner decides to sell some shares and withdraw the proceeds, he has to be
careful that margin does not fall below the maintenance level of 25%. Let us say
Mr. Garner wants to sell enough shares to bring the margin down to 40%, keeping
some cushion for himself. We want to ﬁnd out how many shares he can sell. If
the number of shares he can sell is n then the remaining shares is (100 − n). The
equity is $40(100 − n) − 1,240. The position of the account is:
Mkt. Val. of QVC 40(100 − n) Loan 1,240
Equity 40(100 − n) − 1,240
Total 40(100 − n) Total 40(100 − n)
The margin ratio that Mr. Garner wants to keep gives us:
0.40 =
40(100 − n) − 1,240
40(100 − n)
.
Solving this equation gives n = 48.33. To keep the margin above 0.40, he should
sell 48 shares and withdraw the resulting $1,920,7
leaving behind 52 shares with
a total value of $2,080. The value of equity becomes $840. The balance is:
Equity 840
7
We are not rounding to the nearest integer here. Even if n were 48.7, we will sell 48 shares because
selling 49 shares will bring the margin below the target.

Rather than withdrawing the cash from the account, Mr. Garner may use it to
reduce the loan in the account.
(b) Suppose Mr. Garner decides to buy shares of another stock, TBC, selling for $20
each. The cash needed for this purchase will be loaned by the broker. We want
to ﬁnd out how many shares Mr. Garner can buy. Let us denote the number of
shares by n. Again, let us assume that Mr. Garner does not want the margin to
fall below 40%. The balance sheet is now made up of $4,000 + $20n in market
value of shares, $1,240 + $20n in loan, and $2,760 in equity. From the margin
requirement we get:
0.40 =
2,760
4,000 + 20n
,
which results in n = 145. Mr. Garner can buy 145 shares of TBC. The balance
sheet now is:
Mkt. Val. of TBC 2,900 Equity 2,760
& The previous set of examples assumed that the share price went up from the initial
price of $31. What happens if the price goes down? Let us calculate the price P at
which Mr. Garner will receive a margin call. The market value of shares at that price
will be 100P which will make the equity equal to 100P − 1,240. The margin call will
go out when the margin ratio falls to 0.25. Therefore,
0.25 =
100P − 1,240
100P
,
which gives us P = 16.53. Let us say that the price actually falls to $15 before
Mr. Garner can respond. At this price the balance sheet looks like:
Equity 260
To increase the margin to the initial level, Mr. Garner may either increase equity by
adding cash or reduce the market value of shares by selling some shares and leaving
the cash in the account. Let us examine these choices.

(a) If he adds cash, on the assets side we will have a new entry for cash and there will
be an increase in equity. A simple calculation will show that the required amount
of cash is $640. The balance sheet of the restored account is:
Cash 640 Equity 900
(b) He may sell some shares and create cash in the account. In fact, if Mr. Garner
does not respond in a reasonable amount of time (usually 5 business days), the
broker will do it for him. You can check that the required number of shares to be
sold is 72. The balance sheet after selling the shares is:
Mkt. Val. of QVC 420 Loan 1,240
Cash 1,080 Equity 260
1.8.2 Short Position
Let us take the case of Ms. Stanford. Her account with Lean Hitter has an initial margin
of 50% and a maintenance margin of 40%. Ms. Stanford begins by short selling 100 shares
of QVC at $31 each. This generates $3,100 which is deposited with the broker. To protect
himself against price increases, the broker asks Ms. Stanford to deposit cash. To understand
the need for this cash, imagine what will happen if there were no cash in the account and the
share price went up to $32. The broker will have to contact Ms. Stanford for an additional
$100. If he cannot ﬁnd Ms. Stanford, he will have to absorb the loss.8
The initial margin
requirement is 50% so Ms. Stanford must put in $1,550. The balance sheet of the account
is:
Cash 1,550 Mkt. Val. of QVC 3,100
Deposit 3,100 Equity 1,550
Note that the market value of the securities is a liability because the securities are a loan
and have to be returned.
8
To return the securities, the broker will have to buy them back for $3,200 and there are only $3,100 in
the account.

Suppose the price goes up to $33—bad news for Ms. Stanford. This will require a total
deposit of $3,300 with the broker. The additional amount required will be taken out of the
cash and added to the collateral deposit. The account position will be:
Cash 1,350 Mkt. Val. of QVC 3,300
Deposit 3,300 Equity 1,350
The margin on the account now is 40.9% which is slightly above the maintenance margin
of 40%. You can check to see that Ms. Stanford will get a margin call at the price of $33.21.
1.8.3 Mixed Position
Let us consider the account of Mr. and Mrs. Murphy. The initial and maintenance margins
for their account are 70% and 40%, respectively. The Murphys began by buying 2,500 shares
of XLC at $40. The balance sheet at that point was:
Mkt. Val. of XLC 100,000 Loan 30,000
Equity 70,000
Total 100,000 Total 100,000
Once their account was in good standing, they went short 500 shares of PCM selling at
$80. The account balance sheet was:
Mkt. Val. of XLC 100,000 Mkt. Val. of PCM 40,000
Deposit 40,000 Loan 30,000
Equity 70,000
Total 140,000 Total 140,000
This is where the account stands now. The margin ratio is:
Margin =
Equity
Market Value of Securities
=
70, 000
100, 000 + 40, 000
= 50%
which is above the maintenance margin. Note that the two market values are added even
though one is on the asset side and the other is on the liabilities side.

The broker will make additional loans to the account as long as the margin stays above
the maintenance level of 40%. Suppose the share price of PCM becomes $86, the additional
deposit of $3,000 will be loaned by the broker and the account position will be:
Equity 67,000
Total 143,000 Total 143,000
The margin in the account will be 46.8%, which is above the maintenance margin. Now,
if the market price of XLC drops to $32, the account balance sheet will be:
Equity 47,000
Total 123,000 Total 123,000
The margin now is 38% which is below the maintenance level. The margin call will go
out to the Murphys. They may restore their account by either adding cash, or selling some
shares of XLC, or buying some shares of PCM. If they choose to add cash, they will have to
add $39,100. The balance sheet, after adding cash, will be:
Cash 39,100 Equity 86,100
Total 152,100 Total 152,100
1.8.4 Account Closing
An investor may close the whole account or some of the positions in the account at any
time by selling the long securities, and buying back the short securities and returning them.
The proceeds from selling the long holdings will create cash. The cash needed to close the
short position will come from the collateral deposit. Neither of these actions will aﬀect the
equity position. The investor may reduce the equity by taking out cash from the account or
completely close the account by reducing the equity to zero.

In our discussion of margin accounts, we did not consider the effect of interest and
commissions on the transactions. In reality these costs are incorporated as they are incurred.
For example, if an investor buys 100 shares at the price of $31 per share and the transaction
costs are $100 for this round lot, the investor will have to pay $3,200 to purchase $3,100
worth of shares. Similar costs will be incurred at the time of selling. Interest on loan
outstanding will be deducted from the equity periodically (monthly or quarterly). While
doing the exercises, you may let such costs accrue and assume they are paid in the end while
closing the account.
1.9 Investment Information
All investment decisions depend on information. Without proper information and the ability
to interpret and use it, investors will not be able to make proper decisions. The most popular
sources of investment information are financial and business publications such as The Wall
Street Journal, Financial Times, Barron’s, Business Week, Forbes, Money Magazine, and
Fortune. Several TV programs are also good sources of information. Nightly Business
Report and Wall Street Week on PBS, and various business related programs on CNN are
some of them. CNBC is a cable channel dedicated to financial programming. TV news
services such as CNN Headline News and CNBC display a ticker tape at the bottom of the
screen during the trading hours. This ticker tape shows the trades as they happen. The
company names in these trades are indicated using special symbols known as ticker symbols.
You can find the list of ticker symbols in The Wall Street Journal stock tables. The ticker
tape shows the most recent trade and the price at which the trade took place. For example,
IBM 3s58 on the tape means that 300 shares of IBM were traded at $58 per share.
If you really get serious about investing, you may want to subscribe to a computerized
news services such as Dow Jones News Retrieval (DJNR). DJNR lets you access the breaking
business and political stories from around the world. You may also be connected to a broker
through your computer and a modem, and be able to place your order instantly after reading
a news item from DJNR.
Like any specialized subject, investment markets have their own jargon. To a novice the
financial news may sound like a foreign language. You will have to follow these news sources
for a few weeks before you become comfortable with the terminology. You should make it a
habit to watch at least one hour of financial news a week. Also, go through the Money &
Investing section of The Wall Street Journal at least once a week.
Probably the single most popular investment term is Dow Jones Industrial Average
(DJIA). The DJIA is an index of the prices in the stock market. The index is created by
summing the prices of 30 carefully selected stocks of industrial companies in the NYSE and
dividing the sum by a constant. DJIA is intended to be a measure of the prices of the stocks
in the market. There are other broader indices, e.g., the Standard and Poor’s 500 (S&P
500), and the NYSE and NASDAQ composites. While following these indices you should

keep in mind that it is the relative change in the index value, and not the index value itself,
that is important. For example, the news that Dow closed at at 3,721.50 today is not of
much use without knowing that yesterday it was 3,710. Over the period of one day the index
value increased by 11.50. This represents an increase of 0.31% in one day. The change in the
index is useful to the investors in assessing the change in the value of their own investment
portfolios. For example, if you hold a portfolio of securities which are very much like those
included in the DJIA then by knowing that the DJIA went up by 0.31%, you know that your
portfolio value also went up by about 0.31%.
Other economic data items to watch for are the number of issues traded, share volume,
odd lot trading, short interest, etc. Most of this information is contained in the Money &
Investing section of The Wall Street Journal. General information about the economy as a
whole e.g., interest rates, money supply, GNP, and dollar exchange rates are also important
because they have a bearing on the value of the securities.
1.10 Market Regulation
Securities markets are mostly self regulated. Self regulation works quite efficiently most of
the time. Nevertheless, sometimes special events require intervention of outside agencies.
An important external agency that watches over the securities issue and trading is the
Securities and Exchange Commission (SEC). The SEC sets the reporting requirements
for corporations and brokerage houses. It also keeps a watch on the trading to make sure
that there are no irregularities or fraud. Some areas of trading fraud being examined by the
securities regulators are insider trading and market manipulation. An insider trade is
a trade driven by information that should be available to corporate insiders only. Market
manipulation refers to fixing the market price by a brokerage house or by an institutional
investor using false information or tricks such as block trades. Insider trading and market
manipulation are considered damaging to the market because they deter other investors from
the market, and if investors stay away from the market, it may be difficult for corporations
to raise capital, which in turn hurts the economy as a whole.
1.11 Conclusion
A wide range of information about the securities markets was presented in this Chapter.
This Chapter was intended to only introduce the basics of the securities markets. You
should consult the additional readings listed below for detailed information. The investment
environment is changing constantly and therefore the best source of information is current
literature and news. Therefore, you should make it a practice to read and watch business
news regularly. You may also want to call up some brokerage houses and ask for free literature
on various investment alternatives.

Additional Reading
• Educational Service Bureau. The Dow Jones Averages: A Non-Professional’s Guide. Dow Jones &
Co. Inc., 1986. A good description of the Dow Jones Averages.
• Sonny Kleinfield. The Traders. New York: Holt, Rinehart and Winston, 1983. An entertaining look
at the lives of the traders in various securities markets.
• Matthew Lesko. The Investor’s Information Sourcebook. New York: Harper Row, 1987. A good
desktop reference for where to find investment related information.
• New York Stock Exchange. Fact Book. Detailed information about the NYSE.
• New York Stock Exchange. Margin Trading Guide. Good practical information about margin trading.
• U. S. Securities and Exchange Commission. “The SEC: Organization and Functions.” The Investments
Reader, Jay Wilbanks (ed.), Homewood, Ill: Richard D. Irwin, 1989. pp. 11–39. A summary of what
the SEC is all about.
• Richard Saul Wurman, Alan Siegel, and Kenneth Morris. The Wall Street Journal Guide to Under-
standing Money & Markets. New York: Access Press, 1989. An excellent reference for the general
information on the securities.
• Kenneth M. Morris and Alan M. Siegel. The Wall Street Journal Guide to Understanding Personal Fi-
nance. New York: Lightbulb Press, 1992. An excellent reference for personal finance and information
on the securities.
Exercises
1.1 Return
On January 1, 1990 Rebecca Wong bought a commercial paper issued by GMAC for $98,000. Three
months later the commercial paper matured and she received a check for $100,000 from GMAC. What was
the rate of return on Rebecca’s investment?
1.2 Return
On March 15, 1988, John bought 100 shares of Federal Express at 241/2. John sold the shares a year
later for 273/4. There were no other payments or costs involved. What was the rate of return on John’s
investment?
1.3 Round and Odd Lots
Mr. Williams owns 375 shares of D/A Devices, Inc. The bid and ask prices for the stock are $2.75 and
$3.00. The commission charges on a round lot are $12. On odd lot trades the commission is $0.15 per share.
How much money will Mr. Williams receive if he were to sell all his shares?
1.4 Transaction Costs and Return
Alvin Lee got a tip from his brother Ric that the stock of Ten Years After (TYA) should be in big demand
soon because of their new product called A Space In Time. Alvin immediately called his account executive,
Leo Lyons, and issued a market order to buy 200 shares of TYA. The floor broker for Leo’s company filled
the order when the bid and ask prices for TYA were 131/8 and 131/4. One month later, when the price had
indeed climbed, Alvin called his AE again and issued a market order to sell the shares. The shares were sold
when the bid and ask prices were 151/2 and 157/8. The commission charges for the transactions were 2% of
the value of the transaction.

(a) What was the initial outflow from Alvin’s pocket for the shares?
(b) What was the inflow to Alvin from the shares?
(c) What was the rate of return?
1.5 Round Trip Transaction Cost
Alice Jenkins placed an order to buy 100 shares of Kodak. The order was executed when the bid and
ask prices were 471/4 and 471/2. How much money did she send in for this transaction? Assume that there
were no commission expenses.
Two weeks later, Alice realized that she should not have made this investment. She called her AE and
asked him to sell the shares. The shares were sold when the bid and ask prices were exactly the same as
when the shares were bought, i.e., 471/4 and 471/2. How much money did she receive from this transaction?
What was the round trip transaction cost? Who received the money paid by Alice?
What would the round trip cost have been if the brokerage commissions were 2% of the trading value?
1.6 Long and Short
(a) You bought 100 shares of AT&T on January 1, 1991 at $30 per share. What is the maximum profit you
can make? What is your maximum possible loss? What are the corresponding maximum and minimum
returns?
(b) Your friend went short 100 shares of AT&T on January 1, 1991 at $30 per share. What is the maximum
profit she can make? What is her maximum possible loss? What are the corresponding maximum and
minimum returns?
1.7 Short Interest
What are the short interests in the following cases?
(a) Ramone Fernandes is long 500 shares of IBM.
(b) Sheila Stewart is long 300 shares of Kodak and short 200 shares of Kodak.
(c) Andrew Johnson is long 200 shares of AT&T and short 200 shares of AT&T.
(d) Brenda Myers is long 200 shares of Sears and short 500 shares of Sears.
(e) Glen Watkins is short 300 shares of McDonald’s.
(f) Susan Love is long 200 shares of IBM and short 500 shares of McDonald’s.
1.8 Shorting Against the Box
Gorba the Zeek bought 500 shares of Purex, Inc. at $19 on March 15, 1988. On August 30, the price
had gone to $35. While Gorba was pleased with the performance of his investments, he was worried that his
profits would vanish if the price took a downswing. For tax reasons Gorba did not want to sell his shares in
1988. So, he borrowed 500 shares from a friend and sold them short. He closed all his positions on January
1, 1989 when the price was $50. What was Gorba’s profit from the investment? What would Gorba’s profit
had been if the price on January 1 were $15?
1.9 Margin Accounts
Ms. Miller’s brokerage account requires a 60% initial margin and 40% maintenance margin. Ms. Miller’s
first transaction was to purchase 500 shares of a stock at $40 using full initial margin.
(a) What were the initial equity and loan balances in her account?
(b) At what stock price will she receive a margin call?

(c) Today the stock price fell to $20. How much cash will Ms. Miller be asked to add to her account to
bring the account to the initial margin level?
(d) The account executive (AE) tried to get hold of Ms. Miller. Ms. Miller, however, was not available. How
many shares must the AE sell to restore the account to the initial margin level?
1.10 Margin Accounts
Jack Bruce has a margin account with the brokerage ﬁrm of Smith & Wesson. The initial and mainte-
nance margins on his account are 60% and 40%, respectively. The interest rate on margin loans is 11% per
year. On October 11, 1988, Jack purchased 500 shares of Toledo Bakeries at $18. He took the maximum
loan possible to make his purchase. The stock did not pay dividends during the year and today (October
11, 1989) Jack is selling his shares for $20 each.
(a) Show the position of Jack’s account after the initial transaction on October 11, 1988, and today before
the sale of the shares.
(b) Calculate the return on Jack’s investment during the year.
(c) Jack was lucky that the stock price went up. If the price had started going down, Jack would have
received a margin call sooner or later. Determine the stock price at which Jack would have received the
margin call.
Kate Bush opened a new investment account at Yoshida and Barenbom. Her account executive, Kenji
Yoshida, explained that she had a margin account with initial margin of 75% and maintenance margin of
50%. Margin loans will be made to Kate at 9.2% per year. Kate started by asking Kenji to buy 100 shares
of CMA for her at market using full margin. CMA is traded on the OTC. Kenji executed the trade when
the bid and ask prices for the stock were 231/4 and 241/2, respectively. Yoshida and Barenbom charge a 3%
commission for the OTC transactions.
(a) How much money did Kate have to pay upon completion of the transaction?
(b) A year later, Kate issued a sell order which was executed when the bid and ask prices were 27 and 271/2.
How much money did Kate receive?
(c) What was the rate of return on Kate’s investment?
Dr. Hannibal Lecter opened an account with the brokerage company of Duran, Duran, Duran, and
Duran. The initial and maintenance margin on his account are 75% and 40%, respectively. The opening
transaction of Dr. Lecter was to purchase 500 shares of Classic Automobiles. The transaction was executed
when the bid and the ask prices of the stock were 121/8 and 123/8, respectively. Dr. Lecter paid 90% of the
value of the shares and borrowed the rest at 8% per year. He wrote a separate check to cover the commission
expenses.
(a) What was the position of Dr. Lecter’s account after the opening transaction?
(b) At what stock price will Dr. Lecter receive a margin call?
(c) Six months after the initial transaction, the bid and ask prices for the stock were 141/4 and 143/8. What
was the margin of Dr. Lecter’s account?

1.13 Short Selling and Margin
Freddie, on a tip from his acquaintance Bertie, sold short 100 shares of Diet Purina at $12. Initial margin
requirement on Freddie’s account is 70%.
(a) What did the balance sheet of the account look like after this initial transaction?
(b) The maintenance margin on Freddie’s account is 40%. At what price will Freddie get a margin call?
(c) What are the two choices available to Freddie to make his account current if he gets the margin call?
(d) Show the account positions after these choices have been executed.
1.14 Long, Short, and Margin
On January 1, 1991, Earl Conway opened a margin account with a discount broker with initial and
maintenance margins of 60% and 35%.
(a) On January 1, he purchased 200 shares of AT&T at $30. How much cash did he send in if he took the
maximum loan possible? What was the position of his account after this transaction?
(b) On February 1, the price of AT&T was $32. Earl placed an order to short sell 100 shares of IBM selling at
$104 per share. His account was considered to be in good standing on February 1. Calculate the margin
in his account after the short sale is completed. Did he have to send any cash for this transaction? If
yes, how much? What was be the position of the account after adding the cash?
(c) On April 1, the price of AT&T was $34 and IBM was selling at $101. What was the margin in the
account?
(d) If Earl decided to liquidate his investments on April 1, what steps would he have taken? What would be
the net proceeds to Earl assuming that there were no transaction costs or interest? What would be the
net proceeds if the transaction costs were 1.5% of the trade value and the interest rate on the margin
loan was 2.1% per quarter?
1.15 Shorting Against the Box and Margin
On August 1, 1987 Ms. Agatha Forsythe bought 1,000 shares of UBM for $21.50 per share. Ms. Forsythe
used her initial margin of 50% to purchase these securities. The broker provides loans at a simple interest
of 1% per month. The interest is not payable till the account is closed. The broker does not charge any
commission. Show the status of her account after this purchase.
By October 1, 1987 things had vastly improved for Ms. Forsythe because the price of UBM had climbed
to $45.75. What did the account look like on October 1, 1987?
During late evening of October 1, 1987 Ms. Forsythe received a phone call from a close friend who
predicted that a major stock market crash was imminent. Convinced after a long talk, Ms. Forsythe decided
to sell her securities and get out of the market. What would be the profit to Ms. Forsythe at this point if
she closed her account?
When she told her broker about closing the account, the broker almost chuckled, “No way, Agatha, the
market is much too strong to go down during the next year or two. I am a professional, you should listen to
me. Crash. Huh!” Ms. Forsythe, however, had more faith in her friend. She insisted,“What if the market
does go down and I lose all my profits? I want to sell my shares now.” “But,” the broker said, “if you
sell your shares now you will have to pay taxes on your gains in 1988. If you wait till January 1, you will
defer your taxes till 1989.” This made sense to Ms. Forsythe. After all, why pay taxes now if they could be
delayed. She asked the broker if he knew of a way by which she could lock in her profits but not have to
pay taxes till later. The broker suggested to Ms. Forsythe to short sell 1,000 shares of UBM—not the ones
that she owned but a different 1,000 shares that she would borrow from the broker. How much cash did
Ms. Forsythe have to add to her account to accomplish this transaction to stay above maintenance margin
of 25%?

Verify the broker’s claim by looking ahead to January 1, 1988. Create the statement of Ms. Forsythe’s
account first assuming that the price of UBM went up to $50 and then assuming that it went down to
$20. Calculate the profits on January 1, 1988 under each scenario. Summarize your findings about shorting
against the box by comparing the numbers for January 1, 1988 with the corresponding numbers from October
1, 1987.

Chapter 2
Return and Risk
Return and risk are the basis of all investment decisions. In this chapter you will learn how
to define and measure return and risk. You will also learn about investors’ attitudes towards
risk and the resulting relationship between return and risk.
2.1 Return
Return—rate of return on investment to be precise—arises from the profit on an investment.
Return is also known as interest rate and yield. Suppose you bought 100 shares of DEC
at $55 for a total of $5,500, and sold them a year later at $62 for a total of $6,200. You made
a profit of $7 per share, or a total of $700. For analysis and decision making we would like to
be able to compare alternative investments. It may not be possible to compare alternative
investments using profits because profits depend on the amount invested: the higher the
investment, the higher the profit. To get around this problem, profits are divided by the
amount invested to calculate return. Return is comparable across securities regardless of the
amount invested. The return on your investment in DEC, for example, was 700/5,500 =
0.127 or 12.7 percent. The same answer is obtained if we use per share values rather than
total values: 7/55 = 0.127. In most of the illustrations and exercises, we will use per share
values rather than total values.
Let us take another example. Suppose you bought 200 shares of IBM at $107. Three
months later, you received a dividend of $1 per share and then you sold the shares at $110.
Your profit was: $1 (from dividend) + $3 (from change in price) = $4. The return on your
investment, therefore, was 4/107 = 0.037 or 3.7%.
Suppose we want to compare returns from investments in DEC and IBM. The return on
DEC was 12.7% while that on IBM was 3.7%. It seems, therefore, that DEC was a better
investment. However, by comparing the DEC return of 12.7% with the IBM return of 3.7%,
we are essentially comparing apples and oranges. The two returns were earned over different
periods: DEC’s return was earned over a year while IBM’s over only three months. We
30

Return and Risk 31
made the mistake of comparing the returns earned over different periods because we did not
include the time unit when stating the returns. The proper way to state the returns would
be 12.7% per year for DEC and 3.7% per quarter for IBM. Now, we would be less likely to
make the mistake of comparing 12.7% with 3.7%. If we do want to compare them, we will
have to convert them to identical time units. We will see how to do that in the next section.
Let us take one final example. Suppose you bought 100 shares of General Motors at
$47, held them for three months, received a dividend of $0.40 per share, and sold them at
$45.50. The return on your investment was −1.10/47 = −0.023 or −2.3% per quarter. This
example shows that it is possible for return to be negative. The return can take values
between −100% and +∞. The return cannot be less than −100% because the maximum
you can lose is your initial investment. There is no limit to how high your profits can go
because the stock price can keep rising without limit. These observations about maximum
and minimum returns assume positive initial investment, i.e., a long position. With short
selling, the highest possible return is +100% while the lowest possible return is −∞.
Let us write the definition of return in algebraic notation. Suppose a person invests w0
in some securities and the value of the securities some time later becomes w1, then the rate
of return r can be calculated as:
r =
w1 − w0
w0
. (2.1)
The numerator in equation (2.1), w1 −w0, represents profits from the investment. The profit
may come from one of the two sources:
Capital gain: It results from an increase in the value of the securities. A negative capital
gain is a capital loss.
Income: Commonly known examples of income are dividends and interest.
Separating the profit into capital gain and income components, we can write equation
(2.1) as:
r =
p1 − p0 + d
p0
(2.2a)
or,
r =
p1 − p0
p0
+
d
p0
, (2.2b)
where p0 is the initial purchase price, p1 is the final selling price, and d is the income. The
first part of the right hand side in equation (2.2b) is the return from the price change alone.
It is also known as capital gains yield. The second part is the return from the income. It
is known as current yield in the case of bonds and dividend yield in the case of stocks.
A high dividend yield is important to those investors who seek regular income from their
investments. Those investors who seek growth of their capital look for investments with low
dividend yields.

Return and Risk 32
In these equations, we ignored the taxes and transaction costs incurred by the investor.
This is customary in the investment literature. The reason is that different investors have
different taxes and transaction costs. Ignoring taxes and transaction costs puts all securities
on a common footing and often provides a meaningful basis for comparison across securities.
To determine the return from an investment in a real life situation, one should use the actual
cashflows which take taxes and transaction costs into account.
The equations and the examples given above are necessarily simplistic. They involve only
two transactions: the initial investment (cash outflow) and the final redemption (the cash
inflow). We also assume that the income from the investment is received at the same time
as the investment is redeemed. The situation described by the examples above is known as
a single period situation. Most real life situations are multiperiod because they involve
multiple cash flows. For example, you may buy some shares, receive quarterly dividends for
several years and then sell them. We will see how to calculate the rate of return in such
situations in Chapter 4.
Rate of return can be viewed as growth rate also. For example, if you invest $100, and
earn a return of 10% in a year, your profit will be $10, and the total value of your investment
will be $110. Going from $100 to $110, your money will grow by 10% during the year, which
is the same as the rate of return.
2.2 Conversion of Units of Return
As we saw in section 2.1, to compare returns between two securities, we have to make sure
that they are expressed in the same time unit. Therefore, we need to know how to convert
returns from one time unit to another. Before going to the topic of conversion of units of
return, read a short story:
A lady left her house at 4:00 and was pulled over by a cop at 4:15 for driving too fast. When
the cop told her that she was going at 90 miles per hour, the lady lost her temper. She said,
“It can’t be. I have been driving for only 15 minutes. How do you know I would have done 90
miles in the hour?” “But Ma’am, you were doing 90 when I caught you.” said the cop, “Here
is your ticket. Have a nice day.”
The moral of the story is that you don’t have to be driving an hour for your speed to be
measured at the hourly rate. The cop’s radar gun probably clocked the lady at 0.025 miles
per second. The rest was easy. The radar gun just converted the speed from per second to
per hour by multiplying 0.025 by 3600 because there are 3600 seconds in an hour. Actually,
the conversion was necessary only because the cop would have looked pretty silly telling the
lady that she was going 0.025 miles per second.
The conversion of units of returns is necessary for similar reasons. It is customary to
express the returns on an annual basis. However, you don’t have to invest for a year for your
return to be measured on an annual basis. Returns may be converted from one time unit

Return and Risk 33
Table 2.1: Compounded growth of $1.00 at 3.7% per quarter for four quarters.
Quarter Beginning Balance Profit Ending Balance
1 1.000 1.000 × 0.037 = 0.037 1.000 + 0.037 = 1.037
2 1.037 1.037 × 0.037 = 0.038 1.037 + 0.038 = 1.075
3 1.075 1.075 × 0.037 = 0.040 1.075 + 0.040 = 1.115
4 1.115 1.115 × 0.037 = 0.041 1.115 + 0.041 = 1.156
to another quite easily. The assumption in such conversions is that the rate at which return
was earned in a period will continue through other periods.1
Let us take the IBM example
from section 2.1. The quarterly return there was 3.7%. What would be the corresponding
annual return? Since there are 4 quarters in a year, based on the speeding example, you may
be tempted to say 3.7% × 4 = 14.8%. This is quick and easy but not correct. Conversion of
units become a little complicated when we are dealing with percentages because the same
percentage is being applied to different amounts in different intervals. Let us see this by
following the progress of a dollar invested at the beginning of the first quarter.
Since the dollar earned a return of 3.7%, the profit at the end of the quarter would be
0.037 × $1.00 = $0.037, making the accumulated sum to be $1.037. In the second quarter,
3.7% would be earned again (this is the assumption behind the conversion of units), but this
return would now be earned on the amount at the beginning of the quarter, i.e., $1.037. The
profit during the second quarter, therefore, would be 0.037×$1.037 = $0.038. The extra 1/10
of a cent comes from the interest earned during the second quarter on the interest from the
first quarter. This process of earning interest on interest is known as compounding.
The compounding process for all four quarters is shown in Table 2.1. The Table shows
that continuing at the rate of return IBM earned during the first quarter, a dollar would
have grown to $1.156 at the end of the year. The profit on a dollar, therefore, would have
been $0.156. Therefore, the annual return on IBM was 15.6%.
The conversion process can be summarized using the following formula:
(1 + rq)4
= (1 + ra), (2.3)
where rq is the quarterly rate of return and ra is the annual rate of return. In using this
formula, the rate of returns should be expressed as fractions rather than percentages. To
use the formula for the IBM example, we substitute rq = 0.037 and calculate ra as:
ra = (1 + 0.037)4
− 1 = 1.156 − 1 = 0.156.
So the annual rate is 15.6%, which is the same as the result of the long calculation.
1
The same kind of assumption was made by the radar gun in the speeding example.

Return and Risk 34
Let us explore equation (2.3) a little bit. It gives the relationship between a quarterly
rate and an annual rate. So, this equation can be used to convert from an annual rate to a
quarterly rate also. For example, take the case of DEC in section 2.1. The annual return
there was 12.7%. To express this rate on a quarterly basis, use equation (2.3), substitute
ra = 0.127 and solve for rq:
rq = (1 + 0.127)(1/4)
− 1 = 0.03034.
The quarterly rate, therefore, is 3.034%.
Equations similar to (2.3) can be written for other time units. The general form of those
equations can be understood by carefully examining equation (2.3). In equation (2.3), to
relate quarterly rate rq to the annual rate ra, we raise (1 + rq) to power 4 because there are
4 quarters in one year. Using this logic, while relating a monthly rate rm and an annual rate
ra, we would raise (1 + rm) to the power 12 because there are 12 months in one year. So we
can write:
(1 + rm)12
= (1 + ra). (2.4)
Similarly, we can write some other relationships as:
(1 + rs)2
= (1 + ra), (2.5a)
(1 + rq)2
= (1 + rs), (2.5b)
(1 + rm)3
= (1 + rq), (2.5c)
(1 + rm)6
= (1 + rs), (2.5d)
(1 + rd)365
= (1 + ra) (2.5e)
where rs is the semiannual rate and rd is the daily rate. Using these formulae, you can
convert a rate given in any time unit into another. More importantly, you should see the
general pattern of these relationships so that you can write the formula for conversion from
any unit to another.
2.2.1 Subperiod and Continuous Compounding
Rates of return or interest rates are often stated as follows: 12% per year compounded
quarterly. This statement is just another way of saying that the rate of return is 3% per
quarter. 3% per quarter is the subperiod rate. Similarly, 15% per year compounded monthly
means that the subperiod rate is 15/12 or 1.25% per month. The full period (annual) rates
can be calculated using equations (2.3) and (2.4). The 12% in 12% per year compounded
quarterly and 15% in 15% per year compounded monthly are known as stated rates that are
being compounded during subperiods. The corresponding numbers used in and calculated
using equations (2.3) and (2.4), respectively, are known as the eﬀective rates. For example,
for the stated rate of 12% per year compounded quarterly, the eﬀective rates are 3% per

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