1. Ch 6: Risk and Rates of Return
 2002, Prentice Hall, Inc.

2. Chapter 6: Objectives Inflation and rates of return
How to measure risk
(variance, standard deviation, beta)
How to reduce risk
(diversification)
How to price risk
(security market line, CAPM)

3. Inflation, Rates of Return, and the Fisher Effect
Interest
Rates

4. Interest Rates
Conceptually:

5. Interest Rates
Conceptually:
Nominal
risk-free
Interest
Rate
krf

6. Interest Rates
Conceptually:
Nominal
risk-free
Interest
Rate
krf =

7. Interest Rates = krf k* Conceptually: Nominal Real risk-free Interest

8. Interest Rates = + krf k* Conceptually: Nominal Real risk-free

9. Interest Rates = + IRP krf k* Conceptually: Nominal Real Inflation-
risk-free
Interest
Rate
krf =
Real k* +
Inflation-
risk
premium
IRP

10. Interest Rates = + IRP krf k* Conceptually: Mathematically: Nominal
risk-free
Interest
Rate
krf =
Real k* +
Inflation-
risk
premium
IRP
Mathematically:

11. Interest Rates = + IRP krf k* (1 + krf) = (1 + k*) (1 + IRP)
Conceptually:
Nominal
risk-free
Interest
Rate
krf =
Real k* +
Inflation-
risk
premium
IRP
Mathematically:
(1 + krf) = (1 + k*) (1 + IRP)

12. Interest Rates = + IRP krf k* (1 + krf) = (1 + k*) (1 + IRP)
Conceptually:
Nominal
risk-free
Interest
Rate
krf =
Real k* +
Inflation-
risk
premium
IRP
Mathematically:
(1 + krf) = (1 + k*) (1 + IRP)
This is known as the “Fisher Effect”

13. (1 + krf) = (1 + k*) (1 + IRP) (1.08) = (1.03) (1 + IRP)
Interest Rates
Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium?
(1 + krf) = (1 + k*) (1 + IRP)
(1.08) = (1.03) (1 + IRP)
(1 + IRP) = (1.0485), so
IRP = 4.85%

14. Term Structure of Interest Rates
The pattern of rates of return for debt securities that differ only in the length of time to maturity.

15. Term Structure of Interest Rates
The pattern of rates of return for debt securities that differ only in the length of time to maturity.
yield to
maturity
time to maturity (years)

16. Term Structure of Interest Rates
The pattern of rates of return for debt securities that differ only in the length of time to maturity.
yield to
maturity
time to maturity (years)

17. Term Structure of Interest Rates
The yield curve may be downward sloping or “inverted” if rates are expected to fall.
yield to
maturity
time to maturity (years)

18. Term Structure of Interest Rates
The yield curve may be downward sloping or “inverted” if rates are expected to fall.
yield to
maturity
time to maturity (years)

19. For a Treasury security, what is the required rate of return?

20. For a Treasury security, what is the required rate of return?=

21. For a Treasury security, what is the required rate of return?=
Risk-free
Since Treasuries are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return.

22. For a corporate stock or bond, what is the required rate of return?

23. For a corporate stock or bond, what is the required rate of return?=

24. For a corporate stock or bond, what is the required rate of return?=
Risk-free

25. For a corporate stock or bond, what is the required rate of return?
= +
Risk-free
Risk
premium
How large of a risk premium should we require to buy a corporate security?

26. Returns
Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc.
Required Return - the return that an investor requires on an asset given its risk and market interest rates.

27. Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession % %
Normal % %
Boom % %
For each firm, the expected return on the stock is just a weighted average:

28. Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession % %
Normal % %
Boom % %
For each firm, the expected return on the stock is just a weighted average:
k = P(k1)*k1 + P(k2)*k P(kn)*kn

29. Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession % %
Normal % %
Boom % %
k = P(k1)*k1 + P(k2)*k P(kn)*kn
k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%

30. Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession % %
Normal % %
Boom % %
k = P(k1)*k1 + P(k2)*k P(kn)*kn
k (OI) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%

31. Based only on your expected return calculations, which stock would you prefer?

32. Have you considered
RISK?

33. What is Risk?
The possibility that an actual return will differ from our expected return.
Uncertainty in the distribution of possible outcomes.

34. What is Risk?
Uncertainty in the distribution of possible outcomes.

35. What is Risk? Uncertainty in the distribution of possible outcomes.
Company A
return

36. What is Risk? Uncertainty in the distribution of possible outcomes.
return
Company B
Company A

37. How do we Measure Risk?
To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year.
52 weeks Yld Vol Net
Hi Lo Sym Div % PE s Hi Lo Close Chg
IBM
MSFT …

38. How do we Measure Risk?
A more scientific approach is to examine the stock’s standard deviation of returns.
Standard deviation is a measure of the dispersion of possible outcomes.
The greater the standard deviation, the greater the uncertainty, and therefore , the greater the risk.

39. Standard Deviation s n
i=1 S
= (ki - k)2 P(ki)

40. = (ki - k)2 P(ki) s n
i=1 S
Orlando Utility, Inc.

41. s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 n
( 4% - 10%)2 (.2) = 7.2

42. s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0

43. s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8

44. s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
Variance =

45. s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
Variance =
Stand. dev. = =

46. s S = (ki - k)2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
Variance =
Stand. dev. = = %

47. = (ki - k)2 P(ki) s n
i=1 S
Orlando Technology, Inc.

48. s S = (ki - k)2 P(ki) Orlando Technology, Inc.
(-10% - 14%)2 (.2) =

49. s S = (ki - k)2 P(ki) Orlando Technology, Inc.
(-10% - 14%)2 (.2) =
(14% %)2 (.5) =

50. s S = (ki - k)2 P(ki) Orlando Technology, Inc.
(-10% - 14%)2 (.2) =
(14% %)2 (.5) =
(30% %)2 (.3) =

51. s S = (ki - k)2 P(ki) Orlando Technology, Inc.
(-10% - 14%)2 (.2) =
(14% %)2 (.5) =
(30% %)2 (.3) =
Variance =

52. s S = (ki - k)2 P(ki) Orlando Technology, Inc.
(-10% - 14%)2 (.2) =
(14% %)2 (.5) =
(30% %)2 (.3) =
Variance =
Stand. dev. = =

53. s S = (ki - k)2 P(ki) Orlando Technology, Inc.
(-10% - 14%)2 (.2) =
(14% %)2 (.5) =
(30% %)2 (.3) =
Variance =
Stand. dev. = = %

54. Which stock would you prefer?
How would you decide?

55. Which stock would you prefer?
How would you decide?

56. Summary Orlando Orlando Utility Technology Expected Return 10% 14%
Standard Deviation % %

57. It depends on your tolerance for risk!
Remember, there’s a tradeoff between risk and return.

58. It depends on your tolerance for risk!
Remember, there’s a tradeoff between risk and return.
Return
Risk

59. It depends on your tolerance for risk!
Remember, there’s a tradeoff between risk and return.
Return
Risk

60. Portfolios
Combining several securities in a portfolio can actually reduce overall risk.
How does this work?

61. Suppose we have stock A and stock B
Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated).
rate of
return
time

62. Suppose we have stock A and stock B
Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated).
rate of
return
time kA

63. Suppose we have stock A and stock B
Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated).
rate of
return
time kA kB

64. What has happened to the variability of returns for the portfolio?
rate of
return
time kA kB

65. What has happened to the variability of returns for the portfolio?
rate of
return
time kp kA kB

66. Diversification Investing in more than one security to reduce risk.
If two stocks are perfectly positively correlated, diversification has no effect on risk.
If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified.

67. If you owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified?
YES!
Would you have eliminated all of your risk?
NO! Common stock portfolios still have risk.

68. Some risk can be diversified away and some cannot.
Market risk (systematic risk) is nondiversifiable. This type of risk cannot be diversified away.
Company-unique risk (unsystematic risk) is diversifiable. This type of risk can be reduced through diversification.

69. Market Risk Unexpected changes in interest rates.
Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.

70. Company-unique Risk A company’s labor force goes on strike.
A company’s top management dies in a plane crash.
A huge oil tank bursts and floods a company’s production area.

71. As you add stocks to your portfolio, company-unique risk is reduced.

72. As you add stocks to your portfolio, company-unique risk is reduced.
number of stocks

73. As you add stocks to your portfolio, company-unique risk is reduced.
number of stocks
Market risk

74. As you add stocks to your portfolio, company-unique risk is reduced.
number of stocks
Market risk
company-
unique

75. Do some firms have more market risk than others?
Yes. For example:
Interest rate changes affect all firms, but which would be more affected:
a) Retail food chain
b) Commercial bank

76. Do some firms have more market risk than others?
Yes. For example:
Interest rate changes affect all firms, but which would be more affected:
a) Retail food chain
b) Commercial bank

77. Note
As we know, the market compensates investors for accepting risk - but only for market risk. Company-unique risk can and should be diversified away.
So - we need to be able to measure market risk.

78. This is why we have Beta. Beta: a measure of market risk.
Specifically, beta is a measure of how an individual stock’s returns vary with market returns.
It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market.

79. The market’s beta is 1
A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.
A firm with a beta > 1 is more volatile than the market.

80. The market’s beta is 1
A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.
A firm with a beta > 1 is more volatile than the market.
(ex: technology firms)

81. The market’s beta is 1
A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.
A firm with a beta > 1 is more volatile than the market.
(ex: technology firms)
A firm with a beta < 1 is less volatile than the market.

82. The market’s beta is 1
A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.
A firm with a beta > 1 is more volatile than the market.
(ex: technology firms)
A firm with a beta < 1 is less volatile than the market.
(ex: utilities)

83. Calculating Beta

84. Calculating Beta -5
-15 5 10 15
-10
XYZ Co. returns
S&P 500
returns

85. Calculating Beta . . . . . . . -5 -15 5 10 15 -10 XYZ Co. returns
S&P 500
returns
. . .

86. Calculating Beta . . . . . . . -5 -15 5 10 15 -10 XYZ Co. returns
S&P 500
returns
. . .

87. Calculating Beta . . . . . . . Beta = slope = 1.20 -5 -15 5 10 15 -10
XYZ Co. returns
S&P 500
returns
. . .
Beta = slope
= 1.20

88. Summary:
We know how to measure risk, using standard deviation for overall risk and beta for market risk.
We know how to reduce overall risk to only market risk through diversification.
We need to know how to price risk so we will know how much extra return we should require for accepting extra risk.

89. What is the Required Rate of Return?
The return on an investment required by an investor given market interest rates and the investment’s risk.

90. Required
rate of
return =

91. Required
rate of
return
= +
Risk-free

92. Required
rate of
return
= +
Risk-free
Risk
premium

93. market
risk
Required
rate of
return
= +
Risk-free
Risk
premium

94. = + market risk company- unique risk Required rate of return Risk-free
= +
Risk-free
Risk
premium

95. = + market risk company- unique risk Required rate of return Risk-free
can be diversified
away
Required
rate of
return
= +
Risk-free
Risk
premium

96. Let’s try to graph this relationship!
Required
rate of
return
Let’s try to graph this
relationship!
Beta

97. Required
rate of
return .
Risk-free
rate of
return
(6%)
Beta
12% 1

98. . security market line (SML) 1 12% Beta Required rate of return
Risk-free
rate of
return
(6%)
Beta
12% 1
security
market
line
(SML) .

99. This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM).

100. Required
rate of
return
Risk-free
rate of
return
(6%)
Beta
12% 1
SML .

101. . SML Is there a riskless (zero beta) security? 1 12% Beta Required
rate of
return
Risk-free
rate of
return
(6%)
Beta
12% 1
SML
Is there a riskless
(zero beta) security? .

102. . SML Is there a riskless (zero beta) security? Treasury
12% 1
SML
Is there a riskless
(zero beta) security?
Treasury
securities are
as close to riskless
as possible.
Risk-free
rate of
return
(6%)
Required
rate of
return .
Beta

103. . SML Where does the S&P 500 fall on the SML? 1 12% Beta Required
rate of
return
Beta
12% 1
SML
Where does the S&P 500
fall on the SML?
Risk-free
rate of
return
(6%) .

104. . SML Where does the S&P 500 fall on the SML? The S&P 500 is a good
Required
rate of
return
Beta
12% 1
SML
Where does the S&P 500
fall on the SML?
The S&P 500 is
a good
approximation
for the market
Risk-free
rate of
return
(6%) .

105. . SML Utility Stocks 1 12% Beta Required rate of return Risk-free
(6%) .

106. . SML High-tech stocks 1 12% Beta Required rate of return Risk-free
(6%) .

107. The CAPM equation:

108. The CAPM equation: b
kj = krf j (km - krf )

109. b kj = krf + j (km - krf ) The CAPM equation:
where:
kj = the required return on security j,
krf = the risk-free rate of interest,
j = the beta of security j, and
km = the return on the market index.

110. Example:
Suppose the Treasury bond rate is 6%, the average return on the S&P 500 index is 12%, and Walt Disney has a beta of 1.2.
According to the CAPM, what should be the required rate of return on Disney stock?

111. kj = krf + (km - krf ) b kj = .06 + 1.2 (.12 - .06) kj = .132 = 13.2%
According to the CAPM, Disney stock should be priced to give a 13.2% return.

112. Required
rate of
return
Beta
12% 1
SML
Risk-free
rate of
return
(6%) .

113. . SML Theoretically, every security should lie on the SML 1 12% Beta
Required
rate of
return
Beta
12% 1
SML
Theoretically, every
security should lie
on the SML
Risk-free
rate of
return
(6%) .

114. . SML Theoretically, every security should lie on the SML
Required
rate of
return
Beta
12% 1
SML
Theoretically, every
security should lie
on the SML
If every stock
is on the SML,
investors are being fully
compensated for risk.
Risk-free
rate of
return
(6%) .

115. . SML If a security is above the SML, it is underpriced. 1 12% Beta
Required
rate of
return
Beta
12% 1
SML
If a security is above
the SML, it is
underpriced.
Risk-free
rate of
return
(6%) .

116. . SML If a security is above the SML, it is underpriced.
Required
rate of
return
Beta
12% 1
SML
If a security is above
the SML, it is
underpriced.
If a security is
below the SML, it
is overpriced.
Risk-free
rate of
return
(6%) .

117. Simple Return Calculations

118. Simple Return Calculations
$50
$60

119. Simple Return Calculations
$50
$60
= = 20%
Pt+1 - Pt Pt

120. Simple Return Calculations
$50
$60
= = 20%
Pt+1 - Pt Pt
- 1 = = 20% Pt Pt

121. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
Feb
$63.80
Mar
$59.00
Apr
$62.00
May
$64.50
Jun
$69.00
Jul
Aug
$75.00
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

122. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
Mar
$59.00
Apr
$62.00
May
$64.50
Jun
$69.00
Jul
Aug
$75.00
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

123. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
Apr
$62.00
May
$64.50
Jun
$69.00
Jul
Aug
$75.00
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

124. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
May
$64.50
Jun
$69.00
Jul
Aug
$75.00
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

125. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
Jun
$69.00
Jul
Aug
$75.00
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

126. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
Jul
Aug
$75.00
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

127. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
Aug
$75.00
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

128. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
0.000
Aug
$75.00
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

129. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
0.000
Aug
$75.00
0.087
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

130. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
0.000
Aug
$75.00
0.087
Sep
$82.50
Oct
$73.00
Nov
$80.00
$86.00

131. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
0.000
Aug
$75.00
0.087
Sep
$82.50
Oct
$73.00
-0.115
Nov
$80.00
$86.00

132. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
0.000
Aug
$75.00
0.087
Sep
$82.50
Oct
$73.00
-0.115
Nov
$80.00
0.096
$86.00

133. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
0.000
Aug
$75.00
0.087
Sep
$82.50
Oct
$73.00
-0.115
Nov
$80.00
0.096
$86.00
0.075

134. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
0.049
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
0.000
Aug
$75.00
0.087
Sep
$82.50
Oct
$73.00
-0.115
Nov
$80.00
0.096
$86.00
0.075

135. (a)
(b)
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
0.049
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
0.000
Aug
$75.00
0.087
Sep
$82.50
Oct
$73.00
-0.115
Nov
$80.00
0.096
$86.00
0.075

136. St. Dev: sum, divide by (n-1), and take sq root:
monthly
expected
month
price
return
(a - b)2
Dec
$50.00
Jan
$58.00
0.160
0.049
Feb
$63.80
0.100
Mar
$59.00
-0.075
Apr
$62.00
0.051
May
$64.50
0.040
Jun
$69.00
0.070
Jul
0.000
Aug
$75.00
0.087
Sep
$82.50
Oct
$73.00
-0.115
Nov
$80.00
0.096
$86.00
0.075
0.0781
St. Dev: sum, divide by (n-1), and take sq root:

137. Calculator solution using HP 10B:
Enter monthly return on 10B calculator, followed by sigma key (top right corner).
Shift 7 gives you the expected return.
Shift 8 gives you the standard deviation.