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Chapter
A Brief History of Risk and Return
Fundamentals
of Investments
Valuation & Management
second edition
Charles J. Corrado Bradford D.Jordan
McGraw Hill / Irwin
Slides by Yee-Tien (Ted) Fu
@2002 by the McGraw- Hill Companies Inc.All rights reserved.
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Who Wants To Be A Millionaire?
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A Brief History of Risk and Return
Goal
Our goal in this chapter is to see
what financial market history can tell
us about risk and return.
 Two key observations emerge.
 There
is a reward for bearing risk, and at least on
average, that reward has been substantial.
 Greater rewards are accompanied by
greater risks.
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Returns
Total dollar return
The return on an investment measured in
dollars that accounts for all cash flows and
capital gains or losses.
Example
Total dollar return = Dividend + Capital gain
on stock
income
(or loss)
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Returns
Total percent return
The return on an investment measured as a
% of the originally invested sum that
accounts for all cash flows and capital gains
or losses.
It is the return for each dollar invested.
Example
Percent return = Dividend + Capital gains
on stock
yield
yield
or Total dollar return
Beginning stock price
.
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Returns
Example: Calculating Returns
 Suppose you invested $1,000 in a stock at $25 per
share. After one year, the price increases to $35. For
each share, you also received $2 in dividends.
 Dividend yield = $2 / $25 = 8%
 Capital gains yield = ($35 – $25) / $25 = 40%
 Total percentage return = 8% + 40% = 48%
 Total dollar return = 48% of $1,000 = $480
 At the end of the year, the value of your $1,000
investment is $1,480.
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The Historical Record:
A First Look
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The Historical Record:
A Longer Range Look
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Returns
A company total market capitalization ( or
market cap. For short ) is equal to its stock
price multiplied by the number of shares of
stocks . In other words , it’s the total value of
the company stock .
Large companies are called “large cap” stocks
and small companies are called “small cap
“stocks .
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The Historical Record: A Closer Look
Figure 1.3
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The Historical Record: A Closer Look
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The Historical Record: A Closer Look
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The Historical Record: A Closer Look
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The Historical Record: A Closer Look
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Average Returns: The First Lesson
 Average annual =  yearly returns
return
number of years
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Average Returns: The First Lesson
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Average Returns: The First Lesson
Risk-free rate
The rate of return on a riskless investment.
Risk premium
The extra return on a risky asset over the
risk-free rate; the reward for bearing risk.
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Average Returns: The First Lesson
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Average Returns: The First Lesson
The First Lesson
 There is a reward, on average, for bearing risk.
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Return Variability: The Second Lesson
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Return Variability: The Second Lesson
Variance
A common measure of volatility.
Standard deviation
The square root of the variance.
Normal distribution
A symmetric, bell-shaped frequency
distribution that is completely defined by its
average and standard deviation.
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Return Variability: The Second Lesson
Variance of return
 R  R 
N
Var R   σ 
2
i 1
2
i
N 1
where N is the number of returns
Standard deviation of return
SDR  σ  VarR
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Return Variability: The Second Lesson
Example about variance :
Suppose a particular investment had returns of 10% - 12% - 3%(-9%)
Over the last four years
The average return is :
(10% + 12%+ 3%+ (-9%))/4 = 4 %
The deviation from the average is :
(10-4 )²=36
(12-4) ²=64
(3-4) ²=1
(-9-4) ²=169
_________________ variance= 270 /3 = 90
S. D. =90 = 9.487%
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Return Variability: The Second Lesson
Example about variance :
variance= 270 /3 = 90
S. D. =90 = 9.487%
From these two numbers we can say that :
 with a normal distribution the probability that we
end up with one standard deviation from the
average is about 68% .
 with a normal distribution the probability that we
end up with two standard deviation from the
average is about 95% .
 with a normal distribution the probability that we
end up with three standard deviation from the
average is about 1% .
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Return Variability: The Second Lesson
To let you know :
If you know that the standard deviation of returns in
the previous ex. Are 7% , and the average return
that calculated before are 4%,
The probability that the return in a given year is in
the range of ( (4+7) to (4-7) )= ( 11% to -3% )
within one standard deviation is about 68%.
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Return Variability: The Second Lesson
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Return Variability: The Second Lesson
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Return Variability: The Second Lesson
The Second Lesson
 The greater the potential reward, the greater
the risk.
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Return Variability: The Second Lesson
Top 12 One-Day Percentage Changes in the
Dow Jones Industrial Average
October 19, 1987
October 28, 1929
October 29, 1929
November 6, 1929
December 18, 1899
August 12, 1932
McGraw
Hill /Dow
IrwinJones
Source:
- 22.6 %
- 12.8
- 11.7
- 9.9
- 8.7
- 8.4
March 14, 1907
October 26, 1987
July 21, 1933
October 18, 1937
February 1, 1917
October 27, 1997
- 8.3 %
- 8.0
- 7.8
- 7.7
- 7.2
- 7.2
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Companies Inc.All
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Risk and Return
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Risk and Return trade off
 The risk-free rate represents compensation for
just waiting. So, it is often called the time
value of money.
 If we are willing to bear risk, then we can
expect to earn a risk premium, at least on
average.
 Further, the more risk we are willing to bear,
the greater is that risk premium.
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Risk and Return trade off
 The time value of money is the value of money
figuring in a given amount of interest earned over a
given amount of time.
 For example, 100 dollars of today's money invested
for one year and earning 5 percent interest will be
worth 105 dollars after one year. Therefore, 100
dollars paid now or 105 dollars paid exactly one year
from now both have the same value to the recipient
who assumes 5 percent interest; using time value of
money terminology, 100 dollars invested for one
year at 5 percent interest has a future value of 105
dollars.
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Risk and Return trade off
 Investment advisers like to say that an investment has a ”wait “
component and a “worry” component .
 The time value of money is the compensation for waiting , and
the risk premium is the compensation for worrying .
 Risky investment do not always pay more than risk free
investment , this mean that there are a risk premium on
average ,but over any particular time interval , there is no
guarantee .
 Note that not all risk are compensated , as there are some risks
which are cheaply and easily avoidable , and there are no
expected reward for bearing them .
 Those risks that can not be easily avoided that are
compensated (on average ).
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A Look Ahead
This text focuses exclusively on
financial assets: stocks, bonds, options,
and futures.
 We will learn how to value different assets and
make informed, intelligent decisions about the
associated risks.
 We will also discuss different trading
mechanisms and the way different markets
function.
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Chapter Review
 Returns
Dollar Returns
 Percentage Returns

 The Historical Record
A First Look
 A Longer Range Look
 A Closer Look

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Chapter Review
 Average Returns: The First Lesson
Calculating Average Returns
 Average Returns: The Historical Record
 Risk Premiums
 The First Lesson

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Chapter Review
 Return Variability: The Second Lesson
Frequency Distributions and Variability
 The Historical Variance and Standard Deviation
 The Historical Record
 Normal Distribution
 The Second Lesson

 Risk and Return
The Risk-Return Trade-Off
 A Look Ahead

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