Investment returns measure financial results of an investment. Returns may be historical or prospective (anticipated). Returns can be expressed in: ($) dollar terms. (%) percentage terms. Typically, investment returns are not known with certainty. Investment risk pertains to the probability of earning a return less than expected. Greater the chance of a return far below the expected return, greater the risk

1. Risk, Return, & the Capital Asset Pricing
Model
1

2. Basic return concepts
Basic risk concepts
Stand-alone risk
Portfolio (market) risk
Risk and return: CAPM/SML
2

3. Value = + + +
FCF1 FCF2 FCF∞
(1 + WACC)1 (1 + WACC)∞(1 + WACC)2
Free cash flow
(FCF)
Market interest rates
Firm’s business riskMarket risk aversion
Firm’s debt/equity mixCost of debt
Cost of equity
Weighted average
cost of capital
(WACC)
Net operating
profit after taxes
Required investments
in operating capital
−
=
Determinants of Intrinsic Value:
The Cost of Equity
...

4. STAND – ALONE RISK
RISK IN PORTFOLIO
CONTEXT

 b. Market Risk
• Quantified by Beta & used in
 CAPM: Capital Asset Pricing Model
 Relationship b/w market risk & required
return as depicted in SML
 Req’d return =
• Risk-free return + Mrkt risk Prem(Beta)
• SML: ri = rRF + (RM - rRF )bi
a. Diversifiable

5. Investment returns measure financial results
of an investment.
Returns may be historical or prospective
(anticipated).
Returns can be expressed in:
• ($) dollar terms.
• (%) percentage terms.
5

6. 6
Dollar return:
Percentage return:
$ Received - $ Invested
$1,100 - $1,000 = $100
$ Return/$ Invested
$100/$1,000 = 0.10 = 10%

7. Typically, investment returns are not known
with certainty.
Investment risk pertains to the probability of
earning a return less than expected.
Greater the chance of a return far below the
expected return, greater the risk.
7

8. STUDENT SUE STUDENT BOB
Exam 1
70%
Exam 2
80%
X weight
X 50%
X wt.
X 50%
-----------
Final grade = 75 %
Exam 1 x weight
50% x .50
Exam 2 x wt
100% x .50
-------
Final grade = 75 %

9. 9
-30 -15 0 15 30 45 60
Returns (%)
Stock A
Stock B

10. Normal 40% Return 20% = .08
Bad 30% Return 5% = .015
Good 30% Return 35% = .105
 =Expected ave return = 20%

11. Standard Deviation: Measure of stand-
alone risk
Return-Exp Ret = Diff2 x Prob =
 Variance:
 SD:

12.  1 SD = 68.26% likelihood
 2 SD = 95.46%
 3 SD = 99.74%

14. Standard deviation measures the stand-
alone risk of an investment.
The larger the standard deviation, the
higher the probability that returns will be
far below the expected return.
14

15.  Ave Portfolio Return
 Portfolio Standard Deviation

16.  IBM WedTech
 Coke Microsoft

17. RETURN: HI – LO RISK: HI - LO
 Small Co stock
 Large Co Stock
 LT Corp Bonds
 LT Treasuries
 ST T-Bills

18. Portfolio’s average return in excess of risk-
free rate divided by standard deviation

19.  Coefficient of Variation:
= S.D. / Return; or Risk / Return
WalMart vs. Philip Morris
12% Return 12%
 S.D.
 = C.V. =

20. 20
Security
Expected
Return
Risk:

Risk:
CV
Alta Inds 17.4% 20.0% 1.1
Market 15.0 15.3 1.0
Am. Foam 13.8 18.8 1.4
T-bills 8.0 0.0 0.0
Repo Men 1.7 13.4 7.9

21.  Correlation coefficient = r (rho):
Measures tendency of 2 variables to move
together. Rho (r) = 1 = perfect + correlation &
variables move together in unison.
Does not help with diversification
See text figures 6-9 thru 6-11

22. Two stocks can be combined to form a
riskless portfolio if r = -1.0.
Risk is not reduced at all if the two stocks
have r = +1.0.
In general, stocks have r ≈ 0.35, so risk is
lowered but not eliminated.
Investors typically hold many stocks.
What happens when r = 0?
22

23. What would happen to the risk of an
average 1-stock portfolio as more
randomly selected stocks were added?
p would decrease because the added
stocks would not be perfectly correlated,
but the expected portfolio return would
remain relatively constant.
23

24. 24
-75 -60 -45 -30 -15 0 15 30 45 60 75 90 10
5
Returns (%)
1 stock
2 stocks
Many stocks

25. 25
10 20 30 40 2,000 stocks
Company Specific
(Diversifiable) Risk
Market Risk
20%
0
Stand-Alone Risk, p
p
35%

26. Market risk is that part of a security’s
stand-alone risk that cannot be eliminated
by diversification.
Firm-specific, or diversifiable, risk is that
part of a security’s stand-alone risk that
can be eliminated by diversification.
26

27.  As more stocks are added, each new stock has
a smaller risk-reducing impact on the portfolio.
 p falls very slowly after about 40 stocks are
included. The lower limit for p is about 20% =
M .
 By forming well-diversified portfolios, investors
can eliminate about half the risk of owning a
single stock.
27

28. No. Rational investors will minimize risk
by holding portfolios.
They bear only market risk, so prices and
returns reflect this lower risk.
The one-stock investor bears higher
(stand-alone) risk, so the return is less
than that required by the risk.
28

29. Market risk, which is relevant for stocks
held in well-diversified portfolios, is defined
as the contribution of a security to the
overall riskiness of the portfolio.
It is measured by a stock’s beta coefficient.
For stock i, its beta is:
bi = (ri,M i) / M
29

30. In addition to measuring a stock’s
contribution of risk to a portfolio, beta also
measures the stock’s volatility relative to
the market.
30

31. Run a regression with returns on the stock
in question plotted on the Y axis and
returns on the market portfolio plotted on
the X axis.
The slope of the regression line, which
measures relative volatility, is defined as
the stock’s beta coefficient, or b.
31

32. 32
Year Market PQU
1 25.7% 40.0%
2 8.0% -15.0%
3 -11.0% -15.0%
4 15.0% 35.0%
5 32.5% 10.0%
6 13.7% 30.0%
7 40.0% 42.0%
8 10.0% -10.0%
9 -10.8% -25.0%
10 -13.1% 25.0%

33. 33
rPQU = 0.8308 rM + 0.0256
R2
= 0.3546-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
-30% -20% -10% 0% 10% 20% 30% 40% 50%
Market Return
PQUReturn

34. Beta reflects slope of line via regression
y = mx + b
 m=slope + b= y intercept
Rpqu = 0.8308 rM + 0.0256
 So, PQU’s beta is .8308 & y-intercept @ 2.56%

35. R2 measures degree of dispersion about regression
line (ie – measures % of variance explained by
regression equation)
 PQU’s R2 of .3546 means about 35% of PQU’s returns are
explained by the market returns (32% for a typical stock)
 R2 of .95 on portfolio of 40 randomly selected stocks would
reflect a regression line with points tightly clustered to it.

36. Two stocks can be combined to form a
riskless portfolio if r = -1.0.
Risk is not reduced at all if the two stocks
have r = +1.0.
In general, stocks have r ≈ 0.35, so risk is
lowered but not eliminated.
Investors typically hold many stocks.
What happens when r = 0?
36

37. What would happen to the risk of an
average 1-stock portfolio as more
randomly selected stocks were added?
p would decrease because the added
stocks would not be perfectly correlated,
but the expected portfolio return would
remain relatively constant.
37

38. 38
-75 -60 -45 -30 -15 0 15 30 45 60 75 90 10
5
Returns (%)
1 stock
2 stocks
Many stocks

39. 39
10 20 30 40 2,000 stocks
Company Specific
(Diversifiable) Risk
Market Risk
20%
0
Stand-Alone Risk, p
p
35%

40. Market risk is that part of a security’s
stand-alone risk that cannot be eliminated
by diversification.
Firm-specific, or diversifiable, risk is that
part of a security’s stand-alone risk that
can be eliminated by diversification.
40

41.  As more stocks are added, each new stock has
a smaller risk-reducing impact on the portfolio.
 p falls very slowly after about 40 stocks are
included. The lower limit for p is about 20% =
M .
 By forming well-diversified portfolios, investors
can eliminate about half the risk of owning a
single stock.
41

42. No. Rational investors will minimize risk
by holding portfolios.
They bear only market risk, so prices and
returns reflect this lower risk.
The one-stock investor bears higher
(stand-alone) risk, so the return is less
than that required by the risk.
42

43. Market risk, which is relevant for stocks
held in well-diversified portfolios, is defined
as the contribution of a security to the
overall riskiness of the portfolio.
It is measured by a stock’s beta coefficient.
For stock i, its beta is:
bi = (ri,M i) / M
43

44. In addition to measuring a stock’s
contribution of risk to a portfolio, beta also
measures the stock’s volatility relative to
the market.
44

45. Run a regression with returns on the stock
in question plotted on the Y axis and
returns on the market portfolio plotted on
the X axis.
The slope of the regression line, which
measures relative volatility, is defined as
the stock’s beta coefficient, or b.
45

46. 46
Year Market PQU
1 25.7% 40.0%
2 8.0% -15.0%
3 -11.0% -15.0%
4 15.0% 35.0%
5 32.5% 10.0%
6 13.7% 30.0%
7 40.0% 42.0%
8 10.0% -10.0%
9 -10.8% -25.0%
10 -13.1% 25.0%

47. 47
rPQU = 0.8308 rM + 0.0256
R2
= 0.3546-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
-30% -20% -10% 0% 10% 20% 30% 40% 50%
Market Return
PQUReturn

48. 48
Security
Expected
Return (%) Risk, b
Alta 17.4 1.29
Market 15.0 1.00
Am. Foam 13.8 0.68
T-bills 8.0 0.00
Repo Men 1.7 -0.86

49. The Security Market Line (SML) is part of the
Capital Asset Pricing Model (CAPM).
 Return = Risk Free + Beta (RetMrkt –Rf)
SML: ri = rRF + (RPM)bi .
Assume rRF = 8%; rM = rM = 15%.
RPM = (rM - rRF) = 15% - 8% = 7%.
49

50. The Security Market Line (SML) is part of
the Capital Asset Pricing Model (CAPM).
SML: ri = rRF + (RPM)bi .
Assume rRF = 8%; rM = rM = 15%.
RPM = (rM - rRF) = 15% - 8% = 7%.
50

51. rAlta = 8.0% + (7%)(1.29) = 17%.
rM = 8.0% + (7%)(1.00) = 15.0%.
rAm. F. = 8.0% + (7%)(0.68) = 12.8%.
rT-bill = 8.0% + (7%)(0.00) = 8.0%.
rRepo = 8.0% + (7%)(-0.86) = 2.0%.
51

52. 52
Exp. Req.
r r
Alta 17.4 17.0 Undervalued
Market 15.0 15.0 Fairly valued
Am. Foam 13.8 12.8 Undervalued
T-bills 8.0 8.0 Fairly valued
Repo 1.7 2.0 Overvalued

53. 53
.
.Repo
.Alta
T-bills
.
Am. Foam
rM = 15
rRF = 8
-1 0 1 2
.
ri (%)
Risk, bi
Market

54. 54
bp = Weighted average
= 0.5(bAlta) + 0.5(bRepo)
= 0.5(1.29) + 0.5(-0.86)
= 0.22.

55. 55
rp = Weighted average r
= 0.5(17%) + 0.5(2%) = 9.5%.
Or use SML:
rp = rRF + (RPM) bp
= 8.0% + 7%(0.22) = 9.5%.

56. 56
SML1
Original situation
r (%)
SML2
0 0.5 1.0 1.5 Risk, bi
18
15
11
8
New SML  I = 3%

57. 57
SML1
Original situation
r (%)
SML2
After change
Risk, bi
18
15
8
1.0
 RPM = 3%

58. No. The statistical tests have problems
that make empirical verification or rejection
virtually impossible.
• Investors’ required returns are based on future
risk, but betas are calculated with historical data.
• Investors may be concerned about both stand-
alone and market risk.
58

60. 60
Econ. Prob. T-Bill Alta Repo Am F. MP
Bust 0.10 8.0% -22.0% 28.0% 10.0% -13.0%
Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0
Avg. 0.40 8.0 20.0 0.0 7.0 15.0
Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0
Boom 0.10 8.0 50.0 -20.0 30.0 43.0
1.00

61. T-bill returns 8% regardless of the state of
the economy.
Is T-bill riskless? Explain.
61

62. Alta moves with economy, so it is positively
correlated with economy. This is typical
Repo Men moves counter to economy.
Such negative correlation is unusual.
62

63. 63
r = expected rate of return
(think wtd average)
rAlta = 0.10(-22%) + 0.20(-2%)
+ 0.40(20%) + 0.20(35%)
+ 0.10(50%) = 17.4%.
^
^ n
∑r =
^
i=1
riPi.

64. 64
Expected return
Alta 17.4%
Market 15.0
Am. Foam 13.8
T-bill 8.0
Repo Men 1.7

65. 65
σ = Standard deviation
σ = √ Variance = √ σ2
n
∑
i=1= √ (ri – r)2 Pi.
^

66. 66
 = [(-22 - 17.4)20.10 + (-2 - 17.4)20.20
+ (20 - 17.4)20.40 + (35 - 17.4)20.20
+ (50 - 17.4)20.10]1/2
= 20.0%.

67. 67
T-bills = 0.0%.
 Alta = 20.0%.
 Repo = 13.4%.
 Am Foam = 18.8%.
Market = 15.3%.

68. 68
Security
Expected
Return Risk, 
Alta Inds. 17.4% 20.0%
Market 15.0 15.3
Am. Foam 13.8 18.8
T-bills 8.0 0.0
Repo Men 1.7 13.4

69. CV = Standard deviation / Expected return
CVT-BILLS = 0.0% / 8.0% = 0.0.
CVAlta Inds = 20.0% / 17.4% = 1.1.
CVRepo Men = 13.4% / 1.7% = 7.9.
CVAm. Foam = 18.8% / 13.8% = 1.4.
CVM = 15.3% / 15.0% = 1.0.
69

70. 70
Security
Expected
Return
Risk:

Risk:
CV
Alta Inds 17.4% 20.0% 1.1
Market 15.0 15.3 1.0
Am. Foam 13.8 18.8 1.4
T-bills 8.0 0.0 0.0
Repo Men 1.7 13.4 7.9

71. 71
Alta
MktAm. Foam
T-bills
Repo0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
18.0%
20.0%
0.0% 10.0% 20.0% 30.0%
Return
Risk (Std. Dev.)

72. 72
Assume a two-stock portfolio with
$50,000 in Alta Inds. and $50,000 in
Repo Men.
Calculate rp and p.^

73. 73
rp = Σ wi ri
rp is a weighted average (wi is % of
portfolio in stock i):
rp = 0.5(17.4%) + 0.5(1.7%) = 9.6%.^
^
^ ^
n
i = 1

74. 74
Economy Prob. Alta Repo
Port.=
0.5(Alta)
+
0.5(Repo)
Bust 0.10 -22.0% 28.0% 3.0%
Below
avg.
0.20 -2.0 14.7 6.4
Average 0.40 20.0 0.0 10.0
Above
avg.
0.20 35.0 -10.0 12.5
Boom 0.10 50.0 -20.0 15.0

75. 75
rp = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40
+ (12.5%)0.20 + (15.0%)0.10 = 9.6%
^
p = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20
+(10.0 - 9.6)20.40 + (12.5 - 9.6)20.20
+ (15.0 - 9.6)20.10)1/2 = 3.3%
CVp = 3.3%/9.6% = .34

76. Portfolio expected return (9.6%) is
between Alta (17.4%) and Repo (1.7%)
returns.
Portfolio standard deviation is much lower
than:
• either stock (20% and 13.4%).
• average of Alta and Repo (16.7%).
The reason is due to negative correlation
(r) between Alta and Repo returns.
76

77. Two stocks can be combined to form a
riskless portfolio if r = -1.0.
Risk is not reduced at all if the two stocks
have r = +1.0.
In general, stocks have r ≈ 0.35, so risk is
lowered but not eliminated.
Investors typically hold many stocks.
What happens when r = 0?
77

78. What would happen to the risk of an
average 1-stock portfolio as more
randomly selected stocks were added?
p would decrease because the added
stocks would not be perfectly correlated,
but the expected portfolio return would
remain relatively constant.
78

79. 79
-75 -60 -45 -30 -15 0 15 30 45 60 75 90 10
5
Returns (%)
1 stock
2 stocks
Many stocks

80. 80
10 20 30 40 2,000 stocks
Company Specific
(Diversifiable) Risk
Market Risk
20%
0
Stand-Alone Risk, p
p
35%

81. Market risk is that part of a security’s
stand-alone risk that cannot be eliminated
by diversification.
Firm-specific, or diversifiable, risk is that
part of a security’s stand-alone risk that
can be eliminated by diversification.
81

82.  As more stocks are added, each new stock has
a smaller risk-reducing impact on the portfolio.
 p falls very slowly after about 40 stocks are
included. The lower limit for p is about 20% =
M .
 By forming well-diversified portfolios, investors
can eliminate about half the risk of owning a
single stock.
82

83. No. Rational investors will minimize risk
by holding portfolios.
They bear only market risk, so prices and
returns reflect this lower risk.
The one-stock investor bears higher
(stand-alone) risk, so the return is less
than that required by the risk.
83

84. Market risk, which is relevant for stocks
held in well-diversified portfolios, is defined
as the contribution of a security to the
overall riskiness of the portfolio.
It is measured by a stock’s beta coefficient.
For stock i, its beta is:
bi = (ri,M i) / M
84

85. In addition to measuring a stock’s
contribution of risk to a portfolio, beta also
measures the stock’s volatility relative to
the market.
85

86. Run a regression with returns on the stock
in question plotted on the Y axis and
returns on the market portfolio plotted on
the X axis.
The slope of the regression line, which
measures relative volatility, is defined as
the stock’s beta coefficient, or b.
86

87. 87
Year Market PQU
1 25.7% 40.0%
2 8.0% -15.0%
3 -11.0% -15.0%
4 15.0% 35.0%
5 32.5% 10.0%
6 13.7% 30.0%
7 40.0% 42.0%
8 10.0% -10.0%
9 -10.8% -25.0%
10 -13.1% 25.0%

88. 88
rPQU = 0.8308 rM + 0.0256
R2
= 0.3546-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
-30% -20% -10% 0% 10% 20% 30% 40% 50%
Market Return
PQUReturn

89. The regression line, and hence beta, can
be found using a calculator with a
regression function or a spreadsheet
program. In this example, b = 0.83.
89

90. Many analysts use the S&P 500 to find the
market return.
Analysts typically use four or five years’ of
monthly returns to establish the regression
line.
 Some analysts use 52 weeks of weekly
returns.
90

91. 91
If b = 1.0, stock has average risk.
If b > 1.0, stock is riskier than average.
If b < 1.0, stock is less risky than
average.
Most stocks have betas in the range of
0.5 to 1.5.
Can a stock have a negative beta?

92. 92
Go to http://finance.yahoo.com
Enter the ticker symbol for a “Stock
Quote”, such as IBM or Dell, then click
GO.
When the quote comes up, select Key
Statistics from panel on left.

93. 93
Security
Expected
Return (%) Risk, b
Alta 17.4 1.29
Market 15.0 1.00
Am. Foam 13.8 0.68
T-bills 8.0 0.00
Repo Men 1.7 -0.86

94. The Security Market Line (SML) is part of
the Capital Asset Pricing Model (CAPM).
SML: ri = rRF + (RPM)bi .
Assume rRF = 8%; rM = rM = 15%.
RPM = (rM - rRF) = 15% - 8% = 7%.
94

95. rAlta = 8.0% + (7%)(1.29) = 17%.
rM = 8.0% + (7%)(1.00) = 15.0%.
rAm. F. = 8.0% + (7%)(0.68) = 12.8%.
rT-bill = 8.0% + (7%)(0.00) = 8.0%.
rRepo = 8.0% + (7%)(-0.86) = 2.0%.
95

96. 96
Exp. Req.
r r
Alta 17.4 17.0 Undervalued
Market 15.0 15.0 Fairly valued
Am. Foam 13.8 12.8 Undervalued
T-bills 8.0 8.0 Fairly valued
Repo 1.7 2.0 Overvalued

97. 97
.
.Repo
.Alta
T-bills
.
Am. Foam
rM = 15
rRF = 8
-1 0 1 2
.
ri (%)
Risk, bi
Market

98. 98
bp = Weighted average
= 0.5(bAlta) + 0.5(bRepo)
= 0.5(1.29) + 0.5(-0.86)
= 0.22.

99. 99
rp = Weighted average r
= 0.5(17%) + 0.5(2%) = 9.5%.
Or use SML:
rp = rRF + (RPM) bp
= 8.0% + 7%(0.22) = 9.5%.

100. 10
0
SML1
Original situation
r (%)
SML2
0 0.5 1.0 1.5 Risk, bi
18
15
11
8
New SML  I = 3%

101. 101
SML1
Original situation
r (%)
SML2
After change
Risk, bi
18
15
8
1.0
 RPM = 3%

102. No. The statistical tests have problems
that make empirical verification or rejection
virtually impossible.
• Investors’ required returns are based on future
risk, but betas are calculated with historical data.
• Investors may be concerned about both stand-
alone and market risk.
10
2