© 2009 McGraw-Hill Ryerson Limited 1-1 Chapter 1 A Brief History of Risk and Return Prepared by Ayşe Yüce Ryerson University

© 2009 McGraw-Hill Ryerson © 2009 McGraw-Hill Ryerson LimitedLimited

1-1-11

Chapter 1Chapter 1

A Brief History A Brief History of Risk and of Risk and

ReturnReturn

Prepared byPrepared by

AyAyşşe Ye Yüücece

Ryerson UniversityRyerson University

© 2009 McGraw-Hill Ryerson © 2009 McGraw-Hill Ryerson LimitedLimited 1-1-22

Chapter 1 OutlineChapter 1 Outline

ReturnsReturns The Historical RecordThe Historical Record Average ReturnsAverage Returns Return VariabilityReturn Variability Arithmetic versus Geometric ReturnsArithmetic versus Geometric Returns Risk and Return Risk and Return Tulipmania and Stock Market CrashesTulipmania and Stock Market Crashes


A Brief History of Risk and ReturnA Brief History of Risk and Return We will find out in this chapter what We will find out in this chapter what

financial market history can tell us about financial market history can tell us about risk and return.risk and return.

Two key observations emerge.Two key observations emerge. First, there is a substantial reward, on First, there is a substantial reward, on

average, for bearing risk.average, for bearing risk. Second, greater risks accompany greater Second, greater risks accompany greater

returns.returns.


Dollar ReturnsDollar Returns

Total dollar return Total dollar return is the return on an is the return on an investment measured in dollars, accounting for investment measured in dollars, accounting for all interim cash flows and capital gains or losses.all interim cash flows and capital gains or losses.

Loss)(or Gain Capital Income Dividend Stock aon Return Total


Percent ReturnsPercent Returns

Total percent return Total percent return is the return on an investment is the return on an investment measured as a percentage of the original investment. measured as a percentage of the original investment. The total percent return is the return for The total percent return is the return for each dollareach dollar invested.invested. Example, you buy a share of stock:Example, you buy a share of stock:

)Investment Beginning (i.e., PriceStock Beginning

Stock aon Return Dollar Total Return Percent

or

PriceStock Beginning

Loss)(or Gain Capital Income DividendStock aon Return Percent


Total Dollar and Total Percent ReturnsTotal Dollar and Total Percent Returns

Suppose you invest $1,000 in a stock with a share price of $25 Suppose you invest $1,000 in a stock with a share price of $25 After one year, the stock price per share is $35. After one year, the stock price per share is $35. Also, for each share, you received a $2 dividend.Also, for each share, you received a $2 dividend.

What was your total dollar return?What was your total dollar return? $1,000 / $25 = 40 shares$1,000 / $25 = 40 shares Capital gain: 40 shares times $10 = $400Capital gain: 40 shares times $10 = $400 Dividends: 40 shares times $2 = $80Dividends: 40 shares times $2 = $80 Total Dollar Return is $400 + $80 = $480Total Dollar Return is $400 + $80 = $480

What was your total percent return?What was your total percent return? Dividend yield = $2 / $25 = 8%Dividend yield = $2 / $25 = 8% Capital gain yield = ($35 Capital gain yield = ($35 –– $25) / $25 = 40% $25) / $25 = 40% Total percentage return = 8% + 40% = 48%Total percentage return = 8% + 40% = 48%Notice: $480 divided by $1000 is 48%Notice: $480 divided by $1000 is 48%


A $1 Investment in Different Portfolios,1983-2007A $1 Investment in Different Portfolios,1983-2007

A $1 Investment in Different Types of Portfolios

0

2

4

6

8

10

12

Year

Dol

lar

Inflation

SP/TSX

T-Bill


Large Company Returns 1983-2007Large Company Returns 1983-2007Year-to-Year Total Return on Large Company Stocks: 1983-2007

-40

-20

0

20

40

60

80

Year

Tota

l Ret

urn(

%)

S&P/TSX 60


Treasury Bill Returns 1983-2007Treasury Bill Returns 1983-2007T-bill

0

2

4

6

8

10

12

14

Year

To

tal R

etu

rn(%

)

T-bill


Inflation, 1983-2007Inflation, 1983-2007Canadian Inflation

0

1

2

3

4

5

6

7

Year

Tota

l ReT

urn

(%)

Canadian Inflation


Historical Average ReturnsHistorical Average Returns A useful number to help us summarize historical financial data A useful number to help us summarize historical financial data

is the simple, or arithmetic average. is the simple, or arithmetic average. Using the data in Table 1.1, if you add up the returns for large-Using the data in Table 1.1, if you add up the returns for large-

company stocks from 1983 through 2007, you get 302.25 company stocks from 1983 through 2007, you get 302.25 percent.percent.

Because there are 25 returns, the average return is about Because there are 25 returns, the average return is about 12.09%. How do you use this number?12.09%. How do you use this number?

If you are making a guess about the size of the return for a year If you are making a guess about the size of the return for a year selected at random, your best guess is 12.09%.selected at random, your best guess is 12.09%.

The formula for the historical average return is:The formula for the historical average return is:

n

returnyearly Return Average Historical

n

1i


S&P/TSX Historical returnsS&P/TSX Historical returns1990 -9.06

1991 2.06

1992 0.21

1993 11.23

1994 7.26

1995 11.05

1996 11.27

1997 40.81

1998 5.67

1999 2.98

2000 54.69

Average 12.56091

Std Deviation 18.6447


Average Returns: The First LessonAverage Returns: The First Lesson

Risk-free rateRisk-free rate:: The rate of return on a riskless, i.e., certain The rate of return on a riskless, i.e., certain investment.investment.

Risk premiumRisk premium:: The extra return on a risky asset over the The extra return on a risky asset over the risk-free rate; i.e., the reward for bearing risk.risk-free rate; i.e., the reward for bearing risk.

The First LessonThe First Lesson:: There is a reward, on average, for There is a reward, on average, for bearing risk.bearing risk.

By looking at Table 1.3, we can see the risk premium By looking at Table 1.3, we can see the risk premium earned by large-company stocks was 5.74%!earned by large-company stocks was 5.74%!

Average Annual Risk PremiumsAverage Annual Risk PremiumsInvestment Average Risk Premium

Large Stocks 12.09 5.74 Treasury Bills 6.35 0.00 Inflation 2.88 0.00


Why Does a Risk Premium Exist?Why Does a Risk Premium Exist?

Modern investment theory centers on this question.Modern investment theory centers on this question. Therefore, we will examine this question many times in Therefore, we will examine this question many times in

the chapters ahead.the chapters ahead. However, we can examine part of this question by However, we can examine part of this question by

looking at the dispersion, or spread, of historical returns.looking at the dispersion, or spread, of historical returns. We use two statistical concepts to study this dispersion, We use two statistical concepts to study this dispersion,

or variability: variance and standard deviation.or variability: variance and standard deviation.The Second LessonThe Second Lesson:: The greater the potential reward, The greater the potential reward, the greater the risk.the greater the risk.


Return Variability: The Statistical ToolsReturn Variability: The Statistical Tools The formula for return variance is ("n" is the number of The formula for return variance is ("n" is the number of

returns):returns):

Sometimes, it is useful to use the standard deviation, Sometimes, it is useful to use the standard deviation, which is related to variance like this:which is related to variance like this:

1N

RR σ VAR(R)

N

1i

2

i2

VAR(R) σ SD(R)


Return Variability Review and ConceptsReturn Variability Review and Concepts VarianceVariance is a common measure of return dispersion. is a common measure of return dispersion.

Sometimes, return dispersion is also call variability.Sometimes, return dispersion is also call variability. Standard deviationStandard deviation is the square root of the is the square root of the

variance.variance. Sometimes the square root is called volatility. Sometimes the square root is called volatility. Standard Deviation is handy because it is in the Standard Deviation is handy because it is in the

same "units" as the average.same "units" as the average. Normal distributionNormal distribution:: A symmetric, bell-shaped A symmetric, bell-shaped

frequency distribution that can be described with only frequency distribution that can be described with only an average and a standard deviation.an average and a standard deviation.

Does a normal distribution describe asset returns?Does a normal distribution describe asset returns?


Frequency Distribution of Stock Returns,Frequency Distribution of Stock Returns, 1983-2007 1983-2007

2007

2006

1999 2004

1998 2003

1990 1994 1996 2005

2002 1986 1992 1995 1989 1997

2001 1988 1984 1991 1993 1985 1987 2000 1983

-30 -20 -10 0 10 20 30 40 50 60


Calculating Historical Variance andCalculating Historical Variance and Standard Deviation Standard Deviation

Let’s use data from Table 1.1 for large-company stocks, Let’s use data from Table 1.1 for large-company stocks, from 1983 to 1987. The spreadsheet below shows us how to from 1983 to 1987. The spreadsheet below shows us how to calculate the average, the variance, and the standard calculate the average, the variance, and the standard deviation.deviation.

Year Return Average Return Difference Squared

1983 69.33 25.27 44.06 1941.46

1984 -5.51 25.27 -30.78 947.29

1985 21.5 25.27 -3.77 14.20

1986 -1.64 25.27 -26.91 724.04

1987 42.66 25.27 17.39 302.48

Sum 126.34 Sum 3929.47

Average 25.27 Variance 982.37

Std. Dev 31.34


The Normal Distribution and Large The Normal Distribution and Large Company StocksCompany Stocks

Figure 1.7Figure 1.7


Return Variability: “Non-Normal” DaysReturn Variability: “Non-Normal” DaysTop 12 One-Day Percentage Declines in the Top 12 One-Day Percentage Declines in the

Dow Jones Industrial AverageDow Jones Industrial Average

Source: Dow JonesSource: Dow Jones

December 12, 1914December 12, 1914 -24.4%-24.4% August 12, 1932August 12, 1932 -8.4%-8.4%

October 19, 1987October 19, 1987 -22.6-22.6 March 14, 1907March 14, 1907 -8.3-8.3

October 28, 1929October 28, 1929 -12.8-12.8 October 26, 1987October 26, 1987 -8.0-8.0

October 29, 1929October 29, 1929 -11.7-11.7 July 21, 1933July 21, 1933 -7.8-7.8

November 6, 1929November 6, 1929 -9.9-9.9 October 18, 1937October 18, 1937 -7.7-7.7

December 18, 1899December 18, 1899 -8.7-8.7 February 1, 1917February 1, 1917 -7.2-7.2


Arithmetic Averages versusArithmetic Averages versusGeometric AveragesGeometric Averages

The arithmetic average return answers the question: The arithmetic average return answers the question: “What was your return in an average year over a “What was your return in an average year over a particular period?”particular period?”

The geometric average return answers the question: The geometric average return answers the question: “What was your average “What was your average compound return per yearcompound return per year over a particular period?”over a particular period?”

When should you use the arithmetic average and When should you use the arithmetic average and when should you use the geometric average?when should you use the geometric average?

First, we need to learn how to calculate a geometric First, we need to learn how to calculate a geometric average. average.


Example :Calculating a Example :Calculating a Geometric Average ReturnGeometric Average Return

Again, let’s use the data from Table 1.1 for large-Again, let’s use the data from Table 1.1 for large-company stocks, from 1983 to 1987. company stocks, from 1983 to 1987.

Year Return One Plus Return Compounded Return

1983 69.33 1.6933 1.6933

1984 -5.51 0.9449 1.599999

1985 21.5 1.215 1.148054

1986 -1.64 0.9836 1.195074

1987 42.66 1.4266 1.403204

(2.7278)^(1/5)-1= 1.2223-1

Geometric Average Return =22.23%


Arithmetic Averages versus Geometric AveragesArithmetic Averages versus Geometric Averages The arithmetic average tells you what you earned in a typical The arithmetic average tells you what you earned in a typical

year.year.The geometric average tells you what you actually earned per The geometric average tells you what you actually earned per year on average, compounded annually.year on average, compounded annually.

When we talk about average returns, we generally are talking When we talk about average returns, we generally are talking about arithmetic average returns.about arithmetic average returns.For the purpose of forecasting future returns:For the purpose of forecasting future returns: The arithmetic average is probably "too high" for long The arithmetic average is probably "too high" for long

forecasts.forecasts. The geometric average is probably "too low" for short The geometric average is probably "too low" for short

forecasts.forecasts.


Geometric versus Arithmetic AveragesGeometric versus Arithmetic Averages

Table 1.4


Risk and ReturnRisk and Return

The risk-free rate represents compensation for just waiting. The risk-free rate represents compensation for just waiting. Therefore, this is often called the Therefore, this is often called the time value of moneytime value of money..

First LessonFirst Lesson:: If we are willing to bear risk, then we can If we are willing to bear risk, then we can expect to earn a risk premium, at least on average.expect to earn a risk premium, at least on average.

Second LessonSecond Lesson:: Further, the more risk we are willing to Further, the more risk we are willing to bear, the greater the expected risk premium.bear, the greater the expected risk premium.


Historical Risk and ReturnHistorical Risk and Return

Figure 1.8


A Look AheadA Look Ahead This text focuses exclusively on financial assets: This text focuses exclusively on financial assets:

stocks, bonds, options, and futures.stocks, bonds, options, and futures.

You will learn how to value different assets and You will learn how to value different assets and make informed, intelligent decisions about the make informed, intelligent decisions about the associated risks.associated risks.

You will also learn about different trading You will also learn about different trading mechanisms, and the way that different markets mechanisms, and the way that different markets function.function.


Useful Internet SitesUseful Internet Sites finance.yahoo.com (reference for a terrific financial web site)(reference for a terrific financial web site) www.globalfindata.com (reference for free historical financial market (reference for free historical financial market

data)data) www.tsx.com (reference for the Toronto Stock Exchange) (reference for the Toronto Stock Exchange) www.osc.gov.on.ca (reference for the Ontario Securities Commission) (reference for the Ontario Securities Commission) www.nyse.com (reference for the New York Stock Exchange)(reference for the New York Stock Exchange) www.sec.gov (reference for the Securities and Exchange Commission)(reference for the Securities and Exchange Commission) www.robertniles.com/stats (reference for easy to read statistics review)(reference for easy to read statistics review)

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© 2009 McGraw-Hill Ryerson Limited 1-1 Chapter 1 A Brief History of Risk and Return Prepared by Ayşe Yüce Ryerson University