Investment.pdf

Chapter 1

The Investment

Setting

After you read this chapter, you should be able to answer the following questions:

➤

Why do individuals invest?

➤

What is an investment?

➤

How do investors measure the rate of return on an investment?

➤

How do investors measure the risk related to alternative investments?

➤

What factors contribute to the rates of return that investors require on alternative

investments?

➤

What macroeconomic and microeconomic factors contribute to changes in the required

rates of return for individual investments and investments in general?

This initial chapter discusses several topics basic to the subsequent chapters. We begin by

defining the term investment and discussing the returns and risks related to investments. This

leads to a presentation of how to measure the expected and historical rates of returns for an indi-

vidual asset or a portfolio of assets. In addition, we consider how to measure risk not only for an

individual investment but also for an investment that is part of a portfolio.

The third section of the chapter discusses the factors that determine the required rate of return

for an individual investment. The factors discussed are those that contribute to an asset’s total

risk. Because most investors have a portfolio of investments, it is necessary to consider how to

measure the risk of an asset when it is a part of a large portfolio of assets. The risk that prevails

when an asset is part of a diversified portfolio is referred to as its systematic risk.

The final section deals with what causes changes in an asset’s required rate of return over

time. Changes occur because of both macroeconomic events that affect all investment assets and

microeconomic events that affect the specific asset.

W HAT I SAN I NVESTMENT ?

For most of your life, you will be earning and spending money. Rarely, though, will your current

money income exactly balance with your consumption desires. Sometimes, you may have more

money than you want to spend; at other times, you may want to purchase more than you can

afford. These imbalances will lead you either to borrow or to save to maximize the long-run ben-

efits from your income.

When current income exceeds current consumption desires, people tend to save the excess.

They can do any of several things with these savings. One possibility is to put the money under

a mattress or bury it in the backyard until some future time when consumption desires exceed

current income. When they retrieve their savings from the mattress or backyard, they have the

same amount they saved.

Another possibility is that they can give up the immediate possession of these savings for

a future larger amount of money that will be available for future consumption. This tradeoff of

W HAT I SAN I NVESTMENT ? 5

present consumption for a higher level of future consumption is the reason for saving. What you

do with the savings to make them increase over time is investment. 1

Those who give up immediate possession of savings (that is, defer consumption) expect to

receive in the future a greater amount than they gave up. Conversely, those who consume more

than their current income (that is, borrow) must be willing to pay back in the future more than

they borrowed.

The rate of exchange between future consumption (future dollars) and current consumption

(current dollars) is the pure rate of interest. Both people’s willingness to pay this difference for

borrowed funds and their desire to receive a surplus on their savings give rise to an interest rate

referred to as the pure time value of money. This interest rate is established in the capital market

by a comparison of the supply of excess income available (savings) to be invested and the

demand for excess consumption (borrowing) at a given time. If you can exchange $100 of cer-

tain income today for $104 of certain income one year from today, then the pure rate of exchange

on a risk-free investment (that is, the time value of money) is said to be 4 percent (104/100 – 1).

The investor who gives up $100 today expects to consume $104 of goods and services in the

future. This assumes that the general price level in the economy stays the same. This price sta-

bility has rarely been the case during the past several decades when inflation rates have varied

from 1.1 percent in 1986 to 13.3 percent in 1979, with an average of about 5.4 percent a year

from 1970 to 2001. If investors expect a change in prices, they will require a higher rate of return

to compensate for it. For example, if an investor expects a rise in prices (that is, he or she expects

inflation) at the rate of 2 percent during the period of investment, he or she will increase the

required interest rate by 2 percent. In our example, the investor would require $106 in the future

to defer the $100 of consumption during an inflationary period (a 6 percent nominal, risk-free

interest rate will be required instead of 4 percent).

Further, if the future payment from the investment is not certain, the investor will demand an

interest rate that exceeds the pure time value of money plus the inflation rate. The uncertainty of

the payments from an investment is the investment risk. The additional return added to the nom-

inal, risk-free interest rate is called a risk premium. In our previous example, the investor would

require more than $106 one year from today to compensate for the uncertainty. As an example,

if the required amount were $110, $4, or 4 percent, would be considered a risk premium.

Investment Defined

From our discussion, we can specify a formal definition of investment. Specifically, an investment

is the current commitment of dollars for a period of time in order to derive future payments that

will compensate the investor for (1) the time the funds are committed, (2) the expected rate of

inflation, and (3) the uncertainty of the future payments. The “investor” can be an individual, a

government, a pension fund, or a corporation. Similarly, this definition includes all types of

investments, including investments by corporations in plant and equipment and investments by

individuals in stocks, bonds, commodities, or real estate. This text emphasizes investments by

individual investors. In all cases, the investor is trading a known dollar amount today for some

expected future stream of payments that will be greater than the current outlay.

At this point, we have answered the questions about why people invest and what they want

from their investments. They invest to earn a return from savings due to their deferred con-

sumption. They want a rate of return that compensates them for the time, the expected rate of

inflation, and the uncertainty of the return. This return, the investor’s required rate of return ,

is discussed throughout this book. A central question of this book is how investors select invest-

ments that will give them their required rates of return.

1 In contrast, when current income is less than current consumption desires, people borrow to make up the difference.

Although we will discuss borrowing on several occasions, the major emphasis of this text is how to invest savings.

6 CHAPTER 1 T HE I NVESTMENT S ETTING

The next section of this chapter describes how to measure the expected or historical rate of

return on an investment and also how to quantify the uncertainty of expected returns. You need

to understand these techniques for measuring the rate of return and the uncertainty of these

returns to evaluate the suitability of a particular investment. Although our emphasis will be on

financial assets, such as bonds and stocks, we will refer to other assets, such as art and antiques.

Chapter 3 discusses the range of financial assets and also considers some nonfinancial assets.

M EASURES OF R ETURN AND R ISK

The purpose of this book is to help you understand how to choose among alternative investment

assets. This selection process requires that you estimate and evaluate the expected risk-return

trade-offs for the alternative investments available. Therefore, you must understand how to mea-

sure the rate of return and the risk involved in an investment accurately. To meet this need, in this

section we examine ways to quantify return and risk. The presentation will consider how to mea-

sure both historical and expected rates of return and risk.

We consider historical measures of return and risk because this book and other publications

provide numerous examples of historical average rates of return and risk measures for various

assets, and understanding these presentations is important. In addition, these historical results are

often used by investors when attempting to estimate the expected rates of return and risk for an

asset class.

The first measure is the historical rate of return on an individual investment over the time

period the investment is held (that is, its holding period). Next, we consider how to measure the

average historical rate of return for an individual investment over a number of time periods. The

third subsection considers the average rate of return for a portfolio of investments.

Given the measures of historical rates of return, we will present the traditional measures of

risk for a historical time series of returns (that is, the variance and standard deviation).

Following the presentation of measures of historical rates of return and risk, we turn to esti-

mating the expected rate of return for an investment. Obviously, such an estimate contains a great

deal of uncertainty, and we present measures of this uncertainty or risk.

Measures of

Historical Rates

of Return

When you are evaluating alternative investments for inclusion in your portfolio, you will often be

comparing investments with widely different prices or lives. As an example, you might want to

compare a $10 stock that pays no dividends to a stock selling for $150 that pays dividends of

$5 a year. To properly evaluate these two investments, you must accurately compare their histor-

ical rates of returns. A proper measurement of the rates of return is the purpose of this section.

When we invest, we defer current consumption in order to add to our wealth so that we can

consume more in the future. Therefore, when we talk about a return on an investment, we are

concerned with the change in wealth resulting from this investment. This change in wealth can

be either due to cash inflows, such as interest or dividends, or caused by a change in the price of

the asset (positive or negative).

If you commit $200 to an investment at the beginning of the year and you get back $220 at

the end of the year, what is your return for the period? The period during which you own an

investment is called its holding period, and the return for that period is the holding period

return (HPR) . In this example, the HPR is 1.10, calculated as follows:

➤

1.1

HPR

Ending Value of Investment

Beginning Value of Investment

220

200

110

M EASURES OF R ETURN AND R ISK 7

This value will always be zero or greater—that is, it can never be a negative value. A value greater than

1.0 reflects an increase in your wealth, which means that you received a positive rate of return during

the period. A value less than 1.0 means that you suffered a decline in wealth, which indicates that you

had a negative return during the period. An HPR of zero indicates that you lost all your money.

Although HPR helps us express the change in value of an investment, investors generally eval-

uate returns in percentage terms on an annual basis. This conversion to annual percentage rates

makes it easier to directly compare alternative investments that have markedly different character-

istics. The first step in converting an HPR to an annual percentage rate is to derive a percentage

return, referred to as the holding period yield (HPY) . The HPY is equal to the HPR minus 1.

➤

1.2

HPY = HPR – 1

In our example:

HPY = 1.10 – 1 = 0.10

= 10%

To derive an annual HPY, you compute an annual HPR and subtract 1. Annual HPR is found by:

➤

1.3

Annual HPR = HPR 1/ n

where:

n = number of years the investment is held

Consider an investment that cost $250 and is worth $350 after being held for two years:

HPR

Ending Value of Investment

Beginning Value of Investment

350

250

Annual HPR

140

1 1832

1 1832 1 0 1832

18 32

Annual HPY

–

If you experience a decline in your wealth value, the computation is as follows:

HPR

Ending Value

Beginning Value

400

500

080

HPY

080 100

– .

020 20

– %

A multiple year loss over two years would be computed as follows:

HPR

Ending Value

Beginning Value

750

1 000

075

Annual HPR

(. )

075

1 2

Annual HPY

0 866

0 866 1 00

–.

0 134

–. %

. – .

075

13 4

8 CHAPTER 1 T HE I NVESTMENT S ETTING

In contrast, consider an investment of $100 held for only six months that earned a return of $12:

HPR

112

100

112

. ( . )

Annual HPR

112

1 2544

1 2544 1 0 2544

25 44

Annual HPY

–

Note that we made some implicit assumptions when converting the HPY to an annual basis. This

annualized holding period yield computation assumes a constant annual yield for each year. In the

two-year investment, we assumed an 18.32 percent rate of return each year, compounded. In the par-

tial year HPR that was annualized, we assumed that the return is compounded for the whole year.

That is, we assumed that the rate of return earned during the first part of the year is likewise earned

on the value at the end of the first six months. The 12 percent rate of return for the initial six months

compounds to 25.44 percent for the full year. 2 Because of the uncertainty of being able to earn the

same return in the future six months, institutions will typically not compound partial year results.

Remember one final point: The ending value of the investment can be the result of a positive

or negative change in price for the investment alone (for example, a stock going from $20 a share

to $22 a share), income from the investment alone, or a combination of price change and income.

Ending value includes the value of everything related to the investment.

Computing Mean

Historical Returns

Now that we have calculated the HPY for a single investment for a single year, we want to con-

sider mean rates of return for a single investment and for a portfolio of investments. Over a

number of years, a single investment will likely give high rates of return during some years and

low rates of return, or possibly negative rates of return, during others. Your analysis should con-

sider each of these returns, but you also want a summary figure that indicates this investment’s

typical experience, or the rate of return you should expect to receive if you owned this invest-

ment over an extended period of time. You can derive such a summary figure by computing the

mean annual rate of return for this investment over some period of time.

Alternatively, you might want to evaluate a portfolio of investments that might include simi-

lar investments (for example, all stocks or all bonds) or a combination of investments (for exam-

ple, stocks, bonds, and real estate). In this instance, you would calculate the mean rate of return

for this portfolio of investments for an individual year or for a number of years.

Single Investment Given a set of annual rates of return (HPYs) for an individual invest-

ment, there are two summary measures of return performance. The first is the arithmetic mean

return, the second the geometric mean return. To find the arithmetic mean (AM) , the sum (

∑

)

of annual HPYs is divided by the number of years ( n ) as follows:

➤

1.4

AM =∑HPY/ n

where:

¬HPY = the sum of annual holding period yields

2 To check that you understand the calculations, determine the annual HPY for a three-year HPR of 1.50. (Answer:

14.47 percent.) Compute the annual HPY for a three-month HPR of 1.06. (Answer: 26.25 percent.)

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