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Chapter 4 - Risk and Rates of Return

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Remember, there s a tradeoff between risk and return. Return Risk Portfolios Combining several securities in a portfolio can actually reduce overall risk. – PowerPoint PPT presentation

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Title: Chapter 4 - Risk and Rates of Return


1
Chapter 4 - Risk and Rates of Return
Ó 2005, Pearson Prentice Hall
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, Capital Asset Pricing
    Model)

3
Inflation, Rates of Return, and the Fisher Effect
4
Interest Rates
Conceptually
5
Interest Rates
6
Interest Rates
7
Interest Rates
8
Interest Rates
9
Interest Rates
10
Interest Rates
11
Interest Rates
12
Interest Rates
13
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.

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.

17
Term Structure of Interest Rates
  • The yield curve may be downward sloping or
    inverted if rates are expected to fall.

18
Term Structure of Interest Rates
  • The yield curve may be downward sloping or
    inverted if rates are expected to fall.

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?
  • 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?
25
For a corporate stock or bond, what is the
required rate of return?
  • 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 .20 4
    -10
  • Normal .50 10
    14
  • Boom .30 14
    30
  • 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 .20 4
    -10
  • Normal .50 10
    14
  • Boom .30 14
    30
  • For each firm, the expected return on the stock
    is just a weighted average
  • k P(k1)k1 P(k2)k2 ... P(kn)kn

29
Expected Return
  • State of Probability Return
  • Economy (P) Orl. Utility
    Orl. Tech
  • Recession .20 4
    -10
  • Normal .50 10
    14
  • Boom .30 14
    30
  • k P(k1)k1 P(k2)k2 ... 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 .20 4
    -10
  • Normal .50 10
    14
  • Boom .30 14
    30
  • k P(k1)k1 P(k2)k2 ... 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.

36
What is Risk?
  • Uncertainty in the distribution of possible
    outcomes.

37
How do We Measure Risk?
  • To get a general idea of a stocks price
    variability, we could look at the stocks price
    range over the past year.

52 weeks Yld Vol
Net Hi Lo Sym Div PE 100s Hi
Lo Close Chg 134 80 IBM .52 .5 21
143402 98 95 9549 -3 115 40 MSFT
29 558918 55 52 5194
-475
38
How do We Measure Risk?
  • A more scientific approach is to examine the
    stocks 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
  • (ki - k)2 P(ki)

40
  • Orlando Utility, Inc.

41
  • Orlando Utility, Inc.
  • ( 4 - 10)2 (.2) 7.2

42
  • Orlando Utility, Inc.
  • ( 4 - 10)2 (.2) 7.2
  • (10 - 10)2 (.5) 0

43
  • Orlando Utility, Inc.
  • ( 4 - 10)2 (.2) 7.2
  • (10 - 10)2 (.5) 0
  • (14 - 10)2 (.3) 4.8

44
  • Orlando Utility, Inc.
  • ( 4 - 10)2 (.2) 7.2
  • (10 - 10)2 (.5) 0
  • (14 - 10)2 (.3) 4.8
  • Variance 12

45
  • Orlando Utility, Inc.
  • ( 4 - 10)2 (.2) 7.2
  • (10 - 10)2 (.5) 0
  • (14 - 10)2 (.3) 4.8
  • Variance 12
  • Stand. dev. 12

46
  • Orlando Utility, Inc.
  • ( 4 - 10)2 (.2) 7.2
  • (10 - 10)2 (.5) 0
  • (14 - 10)2 (.3) 4.8
  • Variance 12
  • Stand. dev. 12 3.46

47
  • Orlando Technology, Inc.

48
  • Orlando Technology, Inc.
  • (-10 - 14)2 (.2) 115.2

49
  • Orlando Technology, Inc.
  • (-10 - 14)2 (.2) 115.2
  • (14 - 14)2 (.5) 0

50
  • Orlando Technology, Inc.
  • (-10 - 14)2 (.2) 115.2
  • (14 - 14)2 (.5) 0
  • (30 - 14)2 (.3) 76.8

51
  • Orlando Technology, Inc.
  • (-10 - 14)2 (.2) 115.2
  • (14 - 14)2 (.5) 0
  • (30 - 14)2 (.3) 76.8
  • Variance 192

52
  • Orlando Technology, Inc.
  • (-10 - 14)2 (.2) 115.2
  • (14 - 14)2 (.5) 0
  • (30 - 14)2 (.3) 76.8
  • Variance 192
  • Stand. dev. 192

53
  • Orlando Technology, Inc.
  • (-10 - 14)2 (.2) 115.2
  • (14 - 14)2 (.5) 0
  • (30 - 14)2 (.3) 76.8
  • Variance 192
  • Stand. dev. 192 13.86

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 3.46 13.86

57
  • It depends on your tolerance for risk!
  • Remember, theres a tradeoff between risk and
    return.

58
  • It depends on your tolerance for risk!
  • Remember, theres a tradeoff between risk and
    return.

59
  • It depends on your tolerance for risk!
  • Remember, theres a tradeoff between risk and
    return.

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. The returns
on these stocks do not tend to move together over
time (they are not perfectly correlated).
62
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).
63
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).
64
What has happened to the variability of returns
for the portfolio?
65
What has happened to the variability of returns
for the portfolio?
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 companys labor force goes on strike.
  • A companys top management dies in a plane crash.
  • A huge oil tank bursts and floods a companys
    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.

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

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

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 stocks returns vary with market
    returns.
  • Its a measure of the sensitivity of an
    individual stocks returns to changes in the
    market.

79
The markets 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 gt 1 is more volatile than the
    market.

80
The markets 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 gt 1 is more volatile than the
    market.
  • (ex technology firms)

81
The markets 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 gt 1 is more volatile than the
    market.
  • (ex technology firms)
  • A firm with a beta lt 1 is less volatile than the
    market.

82
The markets 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 gt 1 is more volatile than the
    market.
  • (ex technology firms)
  • A firm with a beta lt 1 is less volatile than the
    market.
  • (ex utilities)

83
Calculating Beta
84
Calculating Beta
85
Calculating Beta
86
Calculating Beta
87
Calculating Beta
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
    investments risk.

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  • Required
  • rate of
  • return

Lets try to graph this relationship!
Beta
97
  • Required
  • rate of
  • return

.
98
  • Required
  • rate of
  • return

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

100
  • Required
  • rate of
  • return

.
101
  • Required
  • rate of
  • return

.
102
  • Required
  • rate of
  • return

.
Beta
103
  • Required
  • rate of
  • return

.
104
  • Required
  • rate of
  • return

.
105
  • Required
  • rate of
  • return

.
106
  • Required
  • rate of
  • return

.
107
The CAPM equation
108
The CAPM equation
b
  • kj krf j (km - krf )

109
The CAPM equation
  • kj krf j (km - krf )
  • 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 SP 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

.
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  • Required
  • rate of
  • return

.
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  • Required
  • rate of
  • return

.
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  • Required
  • rate of
  • return

.
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  • Required
  • rate of
  • return

.
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Simple Return Calculations
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Simple Return Calculations
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Simple Return Calculations
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Simple Return Calculations
Pt1 60 Pt 50
- 1 -1 20
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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.
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