### Chapter 7

```Chapter 7
An Introduction to
Risk and Return:
History of Financial
Market Returns
Slide Contents
• Learning Objectives
• Principles Used in This Chapter
1. Calculate Realized and Expected Rates of Return
and Risk.
2. Describe the Historical Pattern of Financial Market
Returns.
3. Compute Geometric and Arithmetic Average Rates
of Return.
7-2
Slide Contents (cont.)
4. Explain Efficient Market Hypothesis and
Why it is Important to Stock Prices.
• Key Terms
7-3
Principles Used in This Chapter
• Principle 2: There is a Risk-Return
– We will expect to receive higher returns for
assuming more risk.
• Principle 4: Market Prices Reflect
Information.
– Depending on the degree of efficiency of the
market, security prices may or may not fully
reflect all information.
7-4
7.1 Realized and
Expected Rates of
Return and Risk
Calculating the Realized Return from
an Investment
• Realized return or cash return measures
the gain or loss on an investment.
7-6
Calculating the Realized Return from
an Investment (cont.)
• Example 1: You invested in 1 share of
Apple (AAPL) for \$95 and sold a year later
for \$200. The company did not pay any
dividend during that period. What will be
the cash return on this investment?
7-7
Calculating the Realized Return from
an Investment (cont.)
• Cash Return
= \$200 + 0 - \$95
= \$105
7-8
Calculating the Realized Return from
an Investment (cont.)
• We can also calculate the rate of return as
a percentage. It is simply the cash return
divided by the beginning stock price.
7-9
Calculating the Realized Return from
an Investment (cont.)
• Example 2: You invested in 1 share of
share Apple (AAPL) for \$95 and sold a year
later for \$200. The company did not pay
any dividend during that period. What will
be the rate of return on this investment?
7-10
Calculating the Realized Return from
an Investment (cont.)
• Rate of Return = (\$200 + 0 - \$95) ÷ 95
= 110.53%
• Table 7-1 has additional examples on measuring an
investor’s realized rate of return from investing in
common stock.
7-11
7-12
Calculating the Realized Return from
an Investment (cont.)
• Table 7-1 indicates that the returns from
investing in common stocks can be
positive or negative.
• Furthermore, past performance is not an
indicator of future performance.
• However, in general, we expect to receive
higher returns for assuming more risk.
7-13
Calculating the Expected Return
from an Investment
• Expected return is what you expect to
earn from an investment in the future.
• It is estimated as the average of the
possible returns, where each possible
return is weighted by the probability that it
occurs.
7-14
Calculating the Expected Return
from an Investment (cont.)
7-15
7-16
Calculating the Expected Return
from an Investment (cont.)
• Expected Return
= (-10%×0.2) + (12%×0.3) + (22%×0.5)
= 12.6%
7-17
Measuring Risk
• In the example on Table 7-2, the expected
return is 12.6%; however, the return could
range from -10% to +22%.
• This variability in returns can be quantified
by computing the Variance or Standard
Deviation in investment returns.
7-18
Measuring Risk (cont.)
• Standard deviation is given by square root
of the variance and is more commonly
used.
7-19
Calculating the Variance and Standard Deviation
of the Rate of Return on an Investment
• Let us compare two possible investment
alternatives:
– (1) U.S. Treasury Bill – Treasury bill is a shortterm debt obligation of the U.S. Government.
Assume this particular Treasury bill matures in
one year and promises to pay an annual return
of 5%. U.S. Treasury bill is considered riskfree as there is no risk of default on the
promised payments.
7-20
Calculating the Variance and Standard Deviation
of the Rate of Return on an Investment (cont.)
– (2) Common stock of the Ace Publishing
Company – an investment in common stock
will be a risky investment.
7-21
Calculating the Variance and Standard Deviation
of the Rate of Return on an Investment (cont.)
• The probability distribution of an
investment’s return contains all possible
rates of return from the investment along
with the associated probabilities for each
outcome.
• Figure 7-1 contains a probability
distribution for U.S. Treasury bill and Ace
Publishing Company common stock.
7-22
7-23
Calculating the Variance and Standard Deviation
of the Rate of Return on an Investment (cont.)
• The probability distribution for Treasury bill
is a single spike at 5% rate of return
indicating that there is 100% probability
that you will earn 5% rate of return.
• The probability distribution for Ace
Publishing company stock includes returns
ranging from -10% to 40% suggesting the
stock is a risky investment.
7-24
Calculating the Variance and Standard Deviation
of the Rate of Return on an Investment (cont.)
• Using equation 7-3, we can calculate the
expected return on the stock to be 15%
while the expected return on Treasury bill
is always 5%.
• Does the higher return of stock make it a
better investment? Not necessarily, we
also need to know the risk in both the
investments.
7-25
Calculating the Variance and Standard Deviation
of the Rate of Return on an Investment (cont.)
• We can measure the risk of an investment
by computing the variance as follows:
7-26
7-27
Calculating the Variance and Standard Deviation
of the Rate of Return on an Investment (cont.)
Investment
Expected
Return
Standard
Deviation
Treasury Bill
5%
0%
15%
12.85%
Common Stock
• So we observe that the publishing company stock
offers a higher expected return but also entails
more risk as measured by standard deviation. An
investor’s choice of a specific investment will be
determined by their attitude toward risk.
7-28
Checkpoint 7.1
Evaluating an Investment’s Return and Risk
Clarion Investment Advisors is evaluating the distribution of returns for a new
stock investment and has come up with five possible rates of return for the
coming year. Their associated probabilities are as follows:
a. What expected rate of return might they expect to realize from the
investment?
b. What is the risk of the investment as measured using the standard deviation
of possible future rates of return?
7-29
Checkpoint 7.1
7-30
Checkpoint 7.1
7-31
Checkpoint 7.1
7-32
Checkpoint 7.1: Check Yourself
Compute the expected return and standard
deviation for an investment with the five following
possible probabilities for the coming year:
.2, .2,.3,.2 and .1
7-33
Step 1: Picture the Problem
7-34
Step 2: Decide on a Solution
Strategy
• We can use Equation 7-3 to measure its
expected return and Equation 7-5 to
measure its standard deviation.
7-35
Step 3: Solve
• Calculating Expected Return
• E(r) = (-20%×.20) + (0%×.2) + (15%×.3)
+ (30%×.2) + (50%×.1)
= 11.5%
7-36
Step 3: Solve (cont.)
• Calculating Standard Deviation
= √([-.20-.115]2.2) + ([0-.115]2.2) +
([.15-.115]2.3) + ([.30-.115]2.2) + ([.50.115]2.1)
= .2111 or 21.11%
7-37
Step 4:Analyze
• The expected return for this investments is
11.5%.
• However, it is a risky investment as the
returns can range from a low of -20% to a
high of 50%. Standard deviation captures
this risk and is equal to 21.11%. Standard
deviation is a measure of the average
dispersion of the investment returns.
7-38
7.2 A Brief
History of the
Financial Markets
A Brief History of the Financial
Markets
• We can use the tools that we have
learned to determine the risk-return
7-40
A Brief History of the Financial
Markets (cont.)
• Investors have historically earned higher
rates of return on riskier investments.
• However, having a higher expected rate of
return simply means that investors
“expect” to realize a higher return. Higher
return is not guaranteed.
7-41
U.S. Financial Markets — Domestic
Investment Returns
• Figure 7-2 shows the historical returns
earned on four types of investments (small
stocks, large stocks, government bonds,
treasury bills) over the period 1926-2008.
• The graph shows the value of \$1
investment made in each of these asset
categories in 1926 and held until the end
of 2008.
7-42
U.S. Financial Markets — Domestic
Investment Returns (cont.)
7-43
U.S. Financial Markets — Domestic
Investment Returns (cont.)
• We observe a clear relationship between
risk and return. Small stocks have the
highest annual return but higher returns
are associated with much greater risk.
Annual
Small
Stocks
Large
Stocks
Governme
nt Bonds
Treasur
y Bills
Return
11.7%
9.6%
5.7%
3.7%
S.D.
34.1%
21.4%
8.5%
0.9%
7-44
Lessons Learned from Historical
Returns in the Financial Market
Lesson #1: The riskier investments have
historically realized higher returns.
–
The difference between the return on riskier
stock investments and government securities
is called the equity risk premium. For
example, the equity risk premium is 6% for
small stocks over government bonds.
7-45
Lessons Learned from Historical Returns
in the Financial Market (cont.)
Lesson #2: The historical returns of the
higher-risk investment classes have
higher standard deviations.
For example, small stocks had a standard
deviation of 34.1% while the standard
deviation of treasury bill was only 0.9%.
7-46
U.S. Stocks versus Other Categories
of Investments
• Figure 7-3 illustrates the growth in the
value of \$1 invested in 1980 until the end
of 2008 for five different asset classes:
–
–
–
–
–
U.S. stocks
Real estate
International stocks
Commodities
Gold
7-47
7-48
U.S. Stocks versus Other Categories
of Investments (cont.)
• We can observe from Figure 7-3 that U.S.
stocks had the highest annual return of
10.7% while gold had the lowest return of
1.8%.
7-49
Global Financial Markets –
International Investing
• Figure 7-4 compares the historical returns
from investing in U.S. stocks and bonds to
returns on international stocks and bonds.
• The fluctuation in rates of return over a
period of time is called the investment’s
volatility, which is measured by standard
deviation.
7-50
Global Financial
Markets –
International
Investing
(cont.)
7-51
Global Financial Markets –
International Investing (cont.)
• We observe that Pacific stocks had the
highest volatility with returns ranging from
a high of 107.5% to a low of -36.2%.
• In contrast, the US stocks had the least
volatility with returns ranging from a high
of 37.6% and a low of -37.0%.
7-52
Global Financial Markets –
International Investing (cont.)
• Figure 7-5 compares the average rate of
return earned from investing in developed
countries, such as the US and Europe and
some parts of Asia, to the returns from
investing in equities of companies located
in emerging markets.
7-53
Global Financial Markets –
International Investing (cont.)
• An emerging market is one located in
country with low-to-middle per capita
income (such as China, India). These
countries represent about 80% of the
world’s population and about 20% of the
world’s economies.
• A developed country is sometimes
referred to as an industrialized country
that have highly sophisticated and well
developed economies.
7-54
7-55
Global Financial Markets –
International Investing (cont.)
• We observe from figure 7-5 that the
average rates of return from investing in
emerging markets were generally higher
than those earned in developed countries
group. However, emerging market also had
much more volatile returns over the period
1988-2008.
7-56
7.3 Geometric
vs. Arithmetic
Average Rates
of Return
Geometric vs. Arithmetic Average
Rates of Return
• Arithmetic average may not always
capture the true rate of return realized on
an investment. In some cases, geometric
or compound average may be a more
appropriate measure of return.
7-58
Geometric vs. Arithmetic Average
Rates of Return (cont.)
• For example, suppose you bought a stock
for \$25. After one year, the stock rises to
\$30 and in the second year, it falls to \$15.
What was the average return on this
investment?
7-59
Geometric vs. Arithmetic Average
Rates of Return (cont.)
• The stock earned +20% in the first year
and -50% in the second year.
• Simple average = (20%-50%) ÷ 2 = -15%
7-60
Geometric vs. Arithmetic Average
Rates of Return (cont.)
• However, over the 2 years, the \$25 stock
lost the equivalent of 22.54%
({(\$15/\$25)1/2} - 1 = 22.54%).
• Here, -15% is the simple arithmetic
average while -22.54% is the geometric or
compound average rate.
• Which one is the correct indicator of
return? It depends on the question being
7-61
Geometric vs. Arithmetic Average
Rates of Return (cont.)
• The geometric average rate of return
answers the question, “What was the
• The arithmetic average rate of return
answers the question, “what was the
average of the yearly rates of return?
7-62
Computing Geometric Average
Rate of Return
7-63
Computing Geometric Average Rate
of Return (cont.)
Compute the arithmetic and geometric
average for the following stock.
Year
Annual Rate of
Return
0
Value of the
stock
\$25
1
40%
\$35
2
-50%
\$17.50
7-64
Computing Geometric Average Rate
of Return (cont.)
• Arithmetic Average = (40-50) ÷ 2 = -5%
• Geometric Average
= [(1+Ryear1) × (1+Ryear 2)]1/2 - 1
= [(1.4) × (.5)] 1/2 - 1
= -16.33%
7-65
Choosing the Right “Average”
• Both arithmetic average geometric average are important
and correct. The following grid provides some guidance as
to which average is appropriate and when:
Question being
Appropriate Average
Calculation:
What annual rate of
The arithmetic average
return can we expect for calculated using annual
next year?
rates of return.
What annual rate of
return can we expect
over a multi-year
horizon?
The geometric average
calculated over a similar
past period.
7-66
Checkpoint 7.2
Computing the Arithmetic and Geometric Average Rates of Return
Five years ago Mary’s grandmother gave her \$10,000 worth of stock in the
shares of a publicly traded company founded by Mary’s grandfather. Mary is now
considering whether she should continue to hold the shares, or perhaps sell
some of them. Her first step in analyzing the investment is to evaluate the rate
of return she has earned over the past five years.
The following table contains the beginning value of Mary’s stock five years ago
as well as the values at the end of each year up until today (the end of year 5):
What rate of return did Mary earn on her investment in the stock given to her
by her grandmother?
7-67
Checkpoint 7.2
7-68
Checkpoint 7.2
7-69
Checkpoint 7.2
7-70
Checkpoint 7.2: Check Yourself
• Mary has decided to keep the stock given
to her by her grandmother. However, now
she wants to consider the prospect of
ago by her grandmother. What are the
arithmetic and geometric average rates of
return for the following investment?
• See table on the next slide.
7-71
Problem (cont.)
Year
Annual Rate of
Return
0
Value of the Stock
\$10,000.00
1
-15.0%
\$8,500.00
2
15.0%
\$9,775.00
3
25.0%
\$12,218.75
4
30.0%
\$15,884.38
5
-10.0%
\$14,295.94
7-72
Step 1: Picture the Problem
Value of Stock
\$18,000.00
\$16,000.00
\$14,000.00
\$12,000.00
\$10,000.00
\$8,000.00
\$6,000.00
\$4,000.00
\$2,000.00
\$0.00
0
1
2
3
Year
4
5
6
7-73
Step 2: Decide on a Solution
Strategy
• We need to calculate the arithmetic and
geometric average.
• The arithmetic average fails to capture the
effect of compound interest, which can be
measured by geometric average.
7-74
Step 3: Solve
• Calculate the Arithmetic Average
• Arithmetic Average
= Sum of the annual rates of return ÷ Number of
years
= 45% ÷ 5 = 9%
• Based on past performance of the stock,
Mary should expect that it would earn 9%
next year.
7-75
Step 3: Solve (cont.)
• Calculate the Geometric Average
• Geometric Average = [(1+Ryear1) × (1+Ryear 2 ) ×
(1+Ryear3) × (1+Ryear4) × (1+Ryear5) ]1/5 - 1
= [(.85) × (1.15) × (1.25) × (1.30) × (.90)] 1/5 - 1
= 7.41%
7-76
Step 4: Analyze
• The arithmetic average is 9% while the
geometric average is 7.41%. The
geometric average is lower as it
incorporates compounding of interest.
• Both of these averages are useful and
meaningful but in answering two very
different questions.
7-77
Step 4: Analyze (cont.)
• The arithmetic average answers the
question, what rate of return Mary can
expect from her investment next year
assuming all else remains the same as in
the past?
• The geometric average answers the
question, what rate of return Mary can
expect over a five-year period?
7-78
7.4 What
Determines
Stock Prices?
What Determines Stock Prices?
• In short, stock prices tend to go up when
there is good news about future profits,
and they go down when there is bad news
• Since US businesses have generally done
well over the past 80 years, the stock
returns have also been favorable.
7-80
The Efficient Market Hypothesis
• The efficient market hypothesis (EMH) states
that securities prices accurately reflect future
expected cash flows and are based on information
available to investors.
• An efficient market is a market in which all the
available information is fully incorporated into the
prices of the securities and the returns the
investors earn on their investments cannot be
predicted.
7-81
The Efficient Market Hypothesis
(cont.)
• We can distinguish among three types of
efficient market, depending on the degree
of efficiency:
1. The Weak-Form Efficient Market Hypothesis
2. The Semi-Strong Form Efficient Market
Hypothesis
3. The Strong Form Efficient Market Hypothesis
7-82
The Efficient Market Hypothesis
(cont.)
(1) The Weak-Form Efficient Market
Hypothesis asserts that all past security
market information is fully reflected in
security prices. This means that all price
reflected in a security’s price.
7-83
The Efficient Market Hypothesis
(cont.)
(2) The Semi-Strong-Form Efficient
Market Hypothesis asserts that all
publicly available information is fully
reflected in security prices. This is a
stronger statement as it includes all public
information (such as firm’s financial
statements, analysts’ estimates,
industry, or company.)
7-84
The Efficient Market Hypothesis
(cont.)
(3) The Strong-Form Efficient Market
Hypothesis asserts that all information,
regardless of whether this information is
public or private, is fully reflected in
securities prices. It asserts that there isn’t
embedded into the prices of all securities.
7-85
Do We Expect Financial Markets To
Be Perfectly Efficient?
• In general, markets are expected to be at
least weak form and semi-strong form
efficient.
• If there did exist simple profitable
strategies, then the strategies would
attract the attention of investors, who by
implementing their strategies would
compete away the profits.
7-86
Do We Expect Financial Markets To
Be Perfectly Efficient? (cont.)
• We would not expect financial markets to be
strong-form efficient. We expect the markets to
partially, but not perfectly, reflect information that
is privately collected.
• The markets will be inefficient enough to provide
some investors with an opportunity to recoup their
costs of obtaining information, but not so
inefficient that there is easy money to be made in
the stock market.
7-87
The Behavioral View
• Efficient market hypothesis is based on
the assumption that investors, as a
group, are pretty rational. This view has
been challenged.
• What if investors are not rational?
7-88
The Behavioral View (cont.)
• If investors do not rationally process
information, then markets may not
accurately reflect even public information.
7-89
The Behavioral View (cont.)
• For example, overconfident investors may under
react when management announces earnings as
they have too much confidence in their own views
of the company’s true value and tend to place too
little weight on new information provided by
management.
• As a result, this new information, even though it
is publicly and freely available, is not completely
reflected in stock prices.
7-90
Market Efficiency – What does the
Evidence Show?
• The degree of efficiency of financial
markets is an important question and has
generated extensive research.
• Historically, there has been some evidence
of inefficiencies in the financial markets.
This is summarized by three observations
in Table 7-4.
7-91
7-92
Market Efficiency – What does the
Evidence Show? (cont.)
• If equity markets are inefficient it means
that investors can earn returns that are
greater than the risk of their investment
by taking advantage of mispricing in the
market.
• More recent evidence suggests that these
patterns (as noted in Table 7-4) have
largely disappeared after 2000.
7-93
Market Efficiency – What does the
Evidence Show? (cont.)
• Why is the more recent time period
different?
• Following the publication of academic
research on market inefficiencies,
institutional investors set up quantitative
hedge funds to exploit these return
patterns. By trading aggressively on these
patterns, the hedge funds have largely
eliminated the inefficiencies.
7-94
Market Efficiency – What does the
Evidence Show? (cont.)
• Looking forward, we can probably assume
that the financial markets are pretty
efficient, at least in the semi-strong form.
• In other words, market prices will reflect
public information fairly accurately.
7-95
Key Terms
•
•
•
•
•
•
•
Arithmetic average returns
Cash return
Developed country
Efficient market hypothesis
Emerging market
Expected rate of return
7-96
Key Terms (cont.)
•
•
•
•
•
•
•
Expected rate of return
Geometric or compound average returns
Holding period return
Probability distribution
Realized rate of return
Risk-free rate of return
Semi-strong form efficient markets
7-97
Key Terms (cont.)
•
•
•
•
•
Standard deviation
Strong-form efficient markets
Variance in investment return
Volatility
Weak form efficient market