2. Chapter 10 Chapter 11 Chapter 12
Some Lessons
from Capital
Markets
History
Risk and
Return
Cost of Capital
10-2
3. Learn how to calculate the return on an
investment
Understand the historical returns on various types
of investments
Introduction to the risk and return relationship
Overall concept
Understand the historical risks on various types of
investments
10-3
5. Total Dollar
Return
The return on an
investment
measured in $
$ Return = Dividends + Capital Gains
Capital Gains = Price Received - Price Paid
10-5
6. You invest in a stock with a share price of $25
After one year, the stock price per share is $35
Each share paid a $2 dividend
What was your dollar return after one year?
A. $2
B. $10
C. $12
D. $35
E. $37
10-6
7. You invest in a stock with a share price of $25
After one year, the stock price per share is $35
Each share paid a $2 dividend
What was your dollar return after one year?
$ Return = Dividends + Capital Gains
= $2 + ($35-$25)
= $2 + $10
= $12
10-7
8. Total % Return
The return on an
investment measured
as a percentage of the
original investment
% Return =
$ Return
$ Invested
10-8
9. You invest in a stock with a share price of $25
After one year, the stock price per share is $35
Each share paid a $2 dividend
What was your % return after one year?
A. 8%
B. 40%
C. 48%
D. 34.3%
E. 5.7%
10-9
10. Dividend Yield
Capital Gains
Yield
Dt+1 Pt
Pt+1 - Pt
Pt
D = Dividend
P = Price of Stock
t = time 0
% Return = Dividend Yield +
Capital Gains
Yield
=
Dt+1 + Pt+1 - Pt
Pt 10-10
11. You invest in a stock with a share price of $25
After one year, the stock price per share is $35
Each share paid a $2 dividend
What was your % return after one year?
% Return = Dividend Yield +
Capital Gains
Yield
=
Dt+1
Pt
+
Pt+1 - Pt
Pt =
$2
$25 +
($35-$25)
$25
= 8% + 40% = 48%
10-11
14. Historical Average
Return
=
Sum of Yearly Returns
# of Years
Historical Average
Return
=
10.77
89 Years
Sum of the 89
years of returns
per Table 10-1
(for Large Stocks)
= 12.1% per year
10-14
15. Investment Average Return
Large Stocks 12.1%
Small Stocks 16.7%
Long-Term Corporate Bonds 6.4%
Long-Term Government Bonds 6.1%
U.S. Treasury Bills 3.5%
Inflation 3.0%
10-15
19. Why did you classify the investments
in this manner from a risk standpoint?
Startup vs. established company
Dividend paying vs. not paying dividends
Volatility of returns
Historical track record
Level of certainty on the returns
10-19
20. Is there an
investment that
has no risk?
Yes!
U.S. Treasury Bills
Note: While there is a remote possibility there could
be risk with U.S. Treasury Bills, it is considered to be so
small we consider it risk-free.
10-20
21. Why are U.S. government Treasury
bills considered risk-free?
Short time to maturity
Taxes can be raised to pay all of the
government bills
Government can “print” money
10-21
22. Risk Premium
The excess return
required from an
investment in a risky
asset over that required
from a risk-free
investment
The risk premium can also be considered
as the reward for bearing risk.
10-22
23. If the US Treasury bills have an average return of
3.5% and large stocks have an average return of
12.1%, what is the risk premium for large stocks?
A. 12.1%
B. 15.6%
C. 8.6%
D. Need more information
10-23
24. All investments, other than a risk-
free investment, will have a risk
premium
10-24
25. Lesson #1
Risky assets, on
average, earn a risk
premium
This is the reward
for bearing risk
10-25
26. What determines the relative sizes of
the risk premium for the different
assets?
This question is the heart of modern
finance and the focus of next chapter
Part of the answer can be found by
looking at the historical variability of the
returns of different investments
10-26
27. Risk is measured by the dispersion,
spread, or volatility of returns
10-27
28. Both Investment A and Investment B deliver
an average of 5% return over 4 years.
Which one is more risky? Why?
Investment A
Annual Returns
Investment B
Annual Returns
Year 1 6% 15%
Year 2 4% -10%
Year 3 3% 20%
Year 4 7% -5%
Average Annual
Return
5% 5%
10-28
29. To understanding risk, it is critical to
understand both of the following
when it comes to returns on
investments:
Average
Returns
Volatility of
Returns
10-29
30. Risk is measured by the dispersion,
spread, or volatility of returns
10-30
31. Since volatility of returns is a key risk
driver, we can better quantify risk by
calculating volatility. There are statistical
tools to do just this:
Variance
Standard
Deviation
•
•
•
Common measure of
return dispersion
Also called variability
VAR(R) or σ2
•
•
•
•
Square root of the variance
Sometimes called volatility
Same “units” as the average
SD(R) or σ
10-31
32. The statistical tools for historical
returns:
Return variance: (“T" =number of
returns)
T
2
R R
i
VAR(R) = σ2 = i=1
T 1
Standard deviation
SD(R) = σ = VAR(R)
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McGraw-Hill Education. 10-32
( )
33. Average: 11.48 Variance: 859.19
VAR(R) = σ
2
=
T
i=1
(R
T
R
i
1
2
Standard Deviation: 29.31
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McGraw-Hill Education.
10-33
(1) (2) (3) (4) (5)
Year
Average
Return Return:
Difference:
(2) - (3)
Squared:
(4) x (4)
1926
1927
1928
1929
1930
11.14 11.48
37.13 11.48
43.31 11.48
-8.91 11.48
-25.26 11.48
-0.34
25.65
31.83
-20.39
-36.74
0.12
657.82
1013.02
415.83
1349.97
Sum: 57.41 Sum: 3436.77
)
36. Normal distribution:
A symmetric frequency distribution
The “bell-shaped curve”
Completely described by the mean and
variance
Historical returns on securities
roughly approximate a normal
distribution
10-36
37. An observation on a normally distributed
random variable has a:
• 68% chance of being with +/- one
standard deviation of the mean
• 95% chance of being within +/- two
standard deviations of the mean
• >99% chance of being within +/- three
standard deviations of the mean
Illustrated returns are based on the historical return and
standard deviation for a portfolio of large common stocks.
Average return = 12.1%; Standard Deviation = 20.1%
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McGraw-Hill Education. 10-37
38. From 1926 to 2014, long-term corporate bonds
had an average return of 6.4% with a standard
deviation of 8.4%. What range of returns would you
expect to see 68% of the time?
A. -14.8% to +14.8%
B. -10.4% to +23.2%
C. -2.0% to 14.8%
D. -8.4% to 8.4%
10-38
39. From 1926 to 2014, long-term corporate bonds had
an average return of 6.4% with a standard deviation of
8.4%. What range of returns would you expect to see
68% of the time?
Range of returns = Mean +/- 1 Standard Deviation
= 6.4% +/- 8.4%
= -2.0% to 14.8%
Answer is C
10-39
40. Lesson #2
The greater the
potential reward, the
greater the risk
On average, bearing
risk is rewarded
But, in a given year,
there is a significant
chance of a large
change in value
10-40
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McGraw-Hill Education. 10-41
42. Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education. 10-42
43. Your 75 year-old grandparents ask you for advice on how
they should invest their assets. What do you think is the
best recommendation of the following choices?
A. 100% Treasury bonds
B. 100% corporate bonds
C. 100% stocks
D. 50% stocks and 50% corporate bonds
E. 1/3 stocks; 1/3 corporate bonds; 1/3 Treasury bonds
10-43
44. You are committed to contributing the maximum allowed
to your 401(k) plan once you begin work upon
graduation. What do you think is the best way to invest
these funds of the following choices?
A. 100% Treasury bonds
B. 100% corporate bonds
C. 100% stocks
D. 50% stocks and 50% corporate bonds
E. 1/3 stocks; 1/3 corporate bonds; 1/3 Treasury bonds
10-44
45. You want to save for a down payment on a house
purchase to be made in the next 3-5 years. What do you
think is the best way to invest these funds of the
following choices?
A. 100% Treasury bonds
B. 100% corporate bonds
C. 100% stocks
D. 50% stocks and 50% corporate bonds
E. 1/3 stocks; 1/3 corporate bonds; 1/3 Treasury bonds
10-45
47. What was the average annual return
for this investment over 2 years?
A. 75%
B. 25%
C. 0%
D. None of the above
10-47
48. Year 1
Year 2
Cumulative
$ Return
-$50
+$50
% Return
-50%
+100%
Average =
=
-50%+100%
2
25%
Geometric
Average
Arithmetic
Average
10-48
$0 0%
49. Arithmetic
Average
Return earned in an average
period over multiple periods
Answers the question, “What were
your returns in an average year
over a particular period?”
Geometric
Average
Average compound return per
period over multiple periods
Answers the question, “What has
been your average compound
return per year over a particular
period?”
Geometric Average < Arithmetic Average
(unless all returns are equal)
10-49
50. GAR = [(1 + R
1
) (1 + R2 ) ... (1 + RN)
1/T
1 /T 1
Where:
Ri = return in each period
T = number of periods
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McGraw-Hill Education. 10-50
]
51. Arithmetic
Average Return
= 11.48%
(1.4870)^(1/5):
Geometric Average Return:
1.0826
8.26%
10-51
Year
Percent
Return
One Plus Compounded
Return Return:
1926
1927
1928
1929
1930
11.14
37.13
43.31
-8.91
-25.26
1.1114
1.3713
1.4331
0.9109
0.7474
1.1114
1.5241
2.1841
1.9895
1.4870
52. Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education. 10-52
53. If you invested $1.00 (one dollar) 89 years ago and
thought you were going to earn a return of 16.7%,
but only earned a return of 12.2%, about how much
less money did you earn compared to what you
thought you would have earned?
A. $900
B. $9,000
C. $90,000
D. $900,000
E. $9,000,000
10-53
55. Real rate of interest
= Change in purchasing power
Nominal rate of interest
= Quoted rate of interest
= Change in purchasing power and inflation
The nominal rate of interest includes our
desired real rate of return plus an
adjustment for expected inflation
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McGraw-Hill Education. 10-55
56. The Fisher Effect defines the relationship
between real rates, nominal rates and
inflation
( 1 + R ) = ( 1 + r)(1 + h )
R= nominal rate (Quoted rate)
r= real rate
h= expectedinflation rate
Approximation: R= r+ h
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Hill Education. 10-56
57. If we require a 10% real return and we
expect inflation to be 8%, what is the
nominal rate?
( 1 + R ) = ( 1 + r)(1 + h )
R = (1.1)(1.08) – 1 = .188 = 18.8%
Approximation: R = 10% + 8% = 18%
10-57
58. On a particular risky investment, investors require an
excess return of 7 percent in addition to the risk-
free rate of 4 percent. What is this excess return
called?
A. Inflation premium
B. Required return
C. Real return
D. Average return
E. Risk premium
10-58
59. One year ago, you purchased 600 shares of a stock.
This morning you sold those shares and realized a total
return of 3.1 percent. Given this information, you know
for sure the:
A. Stock price increased by 3.1 percent over the last year.
B. Stock increased in value over the past year.
C. Stock paid a dividend.
D. Dividend yield is greater than zero.
E. Sum of the dividend yield and the capital gains yield is
3.1 percent.
10-59
60. Assuming a normal distribution of a data set,
what percentage of all data observations will
be captured +/- one standard deviation from
the mean?
Same question but +/- two standard deviations
from the mean?
Same question but +/- three standard deviations
from the mean?
What is the difference between the arithmetic
and geometric average?
10-60
