CHAPTER 6
Risk, Return, & the Capital Asset
Pricing Model
1

Topics in Chapter





Basic return concepts
Basic risk concepts
Stand-alone risk
Portfolio (market) risk
Risk and return: CAPM/SML
2

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

> Risk, > Return, (both + & -)
Stand – Alone Risk


Risk in Portfolio Context a. Diversifiable 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: r i
= r
RF
+ (R
M
- r
RF
)b i

What are investment returns?



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

An investment costs $1,000 and is sold after 1 year for $1,100.
Dollar return:
$ Received - $ Invested
$1,100 - $1,000 = $100
Percentage return:
$ Return/$ Invested
$100/$1,000 = 0.10 = 10%
6

What is investment risk?

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

Risk & Return
Student Sue
Exam 1
70%
X weight
X 50%
Exam 2
80%
X wt.
X 50%
-----------
Final grade = 75 %
Student Bob
Exam 1 x weight
50% x .50
Exam 2 x wt
100% x .50
-------
Final grade = 75 %

Probability Distribution: Which stock is riskier? Why?
Stock A
Stock B
-30 -15 0 15
Returns (%)
30 45 60
9

WedTech Co




Normal 40% Return 20% = .08
Bad 30% Return 5% = .015
Good 30% Return 35% = .105
=Expected ave return = 20%

WedTech Co


Standard Deviation: Measure of standalone risk
Return-Exp Ret = Diff 2 x Prob =


Variance:
SD:

Standard Deviation and
Normal Distributions



1 SD = 68.26% likelihood
2 SD = 95.46%
3 SD = 99.74%

WedTech Co vs. IBM

Stand-Alone Risk


Standard deviation measures the standalone risk of an investment.
The larger the standard deviation, the higher the probability that returns will be far below the expected return.
14

WedTech Co & IBM in 2 stock
Portfolio

Ave Portfolio Return

Portfolio Standard Deviation


IBM
WedTech Co & IBM & adding other stocks to Portfolio
WedTech

Coke Microsoft

Historical Risk vs. Return
Risk: Hi - Lo





Return: Hi – Lo
Small Co stock
Large Co Stock
LT Corp Bonds
LT Treasuries
ST T-Bills

Reward-to-Variabilty Ratio (Sharpe’s)

Portfolio’s average return in excess of riskfree rate divided by standard deviation

Comparing Different Stocks


Coefficient of Variation:
= S.D. / Return; or Risk / Return




WalMart vs. Philip Morris
12% Return 12%
S.D.
= C.V. =

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

Comparing Different Stocks




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

Two-Stock Portfolios





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

Adding Stocks to a Portfolio


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


1 stock
≈ 35%

Many stocks
≈ 20%
1 stock
2 stocks
Many stocks
-75 -60 -45 -30 -15 0 15 30 45 60 75 90 10
5
Returns (%)
24

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

Stand-alone risk = Market risk
+ Diversifiable risk


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

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

Can an investor holding one stock earn a return commensurate with its risk?



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

How is market risk measured for individual securities?



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: b i
= ( r i,M
 i
) / 
M
29

How are betas calculated?

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

Using a Regression to
Estimate Beta


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

Use the historical stock returns to calculate the beta for PQU.
Year
1
2
3
6
7
4
5
8
9
10
Market
25.7%
8.0%
-11.0%
15.0%
32.5%
13.7%
40.0%
10.0%
-10.8%
-13.1%
PQU
40.0%
-15.0%
-15.0%
35.0%
10.0%
30.0%
42.0%
-10.0%
-25.0%
25.0%
32

Calculating Beta for PQU
50%
40%
30%
20%
10%
0%
-10%
-20%
-30% r
PQU
= 0.8308 r
R
2
M
+ 0.0256
= 0.3546
-30% -20% -10% 0% 10% 20% 30% 40% 50%
Market Return
33

Beta & PQU Co.





Beta reflects slope of line via regression y = mx + b m=slope + b= y intercept
R pqu
= 0.8308 r
M
+ 0.0256
So, PQU’s beta is .8308 & y-intercept @ 2.56%

Beta & PQU Co. & R 2



R 2 measures degree of dispersion about regression line (ie – measures % of variance explained by regression equation)
PQU’s R 2 of .3546 means about 35% of PQU’s returns are explained by the market returns (32% for a typical stock)
R 2 of .95 on portfolio of 40 randomly selected stocks would reflect a regression line with points tightly clustered to it.

Two-Stock Portfolios





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

Adding Stocks to a Portfolio


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


1 stock
≈ 35%

Many stocks
≈ 20%
1 stock
2 stocks
Many stocks
-75 -60 -45 -30 -15 0 15 30 45 60 75 90 10
5
Returns (%)
38

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

Stand-alone risk = Market risk
+ Diversifiable risk


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

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

Can an investor holding one stock earn a return commensurate with its risk?



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

How is market risk measured for individual securities?



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: b i
= ( r i,M
 i
) / 
M
43

How are betas calculated?

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

Using a Regression to
Estimate Beta


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

Use the historical stock returns to calculate the beta for PQU.
Year
1
2
3
6
7
4
5
8
9
10
Market
25.7%
8.0%
-11.0%
15.0%
32.5%
13.7%
40.0%
10.0%
-10.8%
-13.1%
PQU
40.0%
-15.0%
-15.0%
35.0%
10.0%
30.0%
42.0%
-10.0%
-25.0%
25.0%
46

Calculating Beta for PQU
50%
40%
30%
20%
10%
0%
-10%
-20%
-30% r
PQU
= 0.8308 r
R
2
M
+ 0.0256
= 0.3546
-30% -20% -10% 0% 10% 20% 30% 40% 50%
Market Return
47

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

Capital Asset Pricing Model





The Security Market Line (SML) is part of the
Capital Asset Pricing Model (CAPM).
Return = Risk Free + Beta (RetMrkt –Rf)
SML: r i
= r
RF
Assume r
RF
+ (RP
= 8%; r
M
M
)b i
= r
.
M
RP
M
= (r
M
= 15%.
- r
RF
) = 15% - 8% = 7%.
49

Use the SML to calculate each alternative’s required return.




The Security Market Line (SML) is part of the Capital Asset Pricing Model
(CAPM).
SML: r i
= r
RF
Assume r
RF
+ (RP
= 8%; r
M
M
)b i
= r
.
M
RP
M
= (r
M
= 15%.
- r
RF
) = 15% - 8% = 7%.
50

Required Rates of Return




 r r
Alta
M
= 8.0% + (7%)(1.29) = 17%.
= 8.0% + (7%)(1.00) = 15.0%.
r r
Am. F.
T-bill
= 8.0% + (7%)(0.68) = 12.8%.
= 8.0% + (7%)(0.00) = 8.0%.
r
Repo
= 8.0% + (7%)(-0.86) = 2.0%.
51

Expected versus Required
Returns (%)
Alta
Market
Exp.
r
17.4
15.0
Am. Foam 13.8
T-bills 8.0
Repo 1.7
Req.
r
17.0
Undervalued
15.0
Fairly valued
12.8
Undervalued
8.0
Fairly valued
2.0
Overvalued
52

SML: r i r i
= r
RF
+ (RP
M
) b i
= 8% + (7%) b i r i
(%) r
M
Repo
.
-1
= 15 r
RF
= 8
.
.
T-bills
0
Alta
.
.
1
Am. Foam
Market
2
Risk, b i
53

Calculate beta for a portfolio with 50% Alta and 50% Repo b p
= Weighted average
= 0.5(b
= 0.22.
Alta
) + 0.5(b
Repo
)
= 0.5(1.29) + 0.5(-0.86)
54

Required Return on the
Alta/Repo Portfolio?
r p
= Weighted average r
= 0.5(17%) + 0.5(2%) = 9.5%.
Or use SML: r p
= r
RF
+ (RP
M
) b p
= 8.0% + 7%(0.22) = 9.5%.
55

18
15
11
8
Impact of Inflation Change on
SML r (%)
New SML 
I = 3%
SML
2
SML
1
Original situation
0 0.5
1.0
1.5
Risk, b i
56

18
15
8
Impact of Risk Aversion
Change r (%)
SML
2
After change
SML
1

RP
M
= 3%
Original situation
Risk, b i 57 1.0

Has the CAPM been completely confirmed or refuted?

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

Below are per book mini-case

Consider the Following
Investment Alternatives
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
Avg.
0.40 8.0
-2.0
20.0
14.7
-10.0
0.0
7.0
1.0
15.0
Above avg.
0.20 8.0
Boom 0.10 8.0
1.00
35.0
-10.0
50.0
-20.0
45.0
30.0
29.0
43.0
60

What is unique about T-bill returns?

T-bill returns 8% regardless of the state of the economy.

Is T-bill riskless? Explain.
61

Alta Inds. and Repo Men vs. Economy

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

Calculate the expected rate of return on each alternative.
^
(think wtd average)
^ r
Alta
= 0.10(-22%) + 0.20(-2%)
+ 0.40(20%) + 0.20(35%)
+ 0.10(50%) = 17.4%.
n
∑ i=1 r i
P i
.
63

Alta has the highest rate of return. Does that make it best?
Alta
Market
Am. Foam
T-bill
Repo Men
Expected return
17.4%
15.0
13.8
8.0
1.7
64

What is the standard deviation of returns for each alternative?
σ = Standard deviation
σ = √ Variance = √ σ 2
=
n
∑ i=1
(r i
^
– r) 2 P i
.
65

Standard Deviation of Alta
Industries
 = [(-22 - 17.4) 2 0.10 + (-2 - 17.4) 2 0.20
+ (20 - 17.4) 2 0.40 + (35 - 17.4) 2 0.20
+ (50 - 17.4) 2 0.10] 1/2
= 20.0%.
66

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

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

Coefficient of Variation (CV)






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

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

Return vs. Risk (Std. Dev.):
Which investment is best?
20.0%
15.0% Mkt
Alta
Am. Foam
10.0%
T-bills
5.0%
Repo
0.0%
0.0% 5.0% 10.0% 15.0% 20.0% 25.0%
Risk (Std. Dev.)
71

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

Portfolio Expected Return
^ p is a weighted average (w portfolio in stock i): i is % of
^ p n
= Σ w i i = 1
^ i r
^ p
= 0.5(17.4%) + 0.5(1.7%) = 9.6%.
73

Alternative Method: Find portfolio return in each economic state
Economy
Bust
Below avg.
Average
Above avg.
Boom
Prob.
0.10
0.20
0.40
0.20
0.10
Alta
-22.0%
-2.0
20.0
35.0
50.0
Repo
28.0%
14.7
Port.=
0.5(Alta)
+
0.5(Repo)
3.0%
6.4
0.0
-10.0
10.0
12.5
-20.0
15.0
74

Use portfolio outcomes to estimate risk and expected return r
^ p
= (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) 2 0.10 + (6.4 - 9.6) 2 0.20
+(10.0 - 9.6) 2 0.40 + (12.5 - 9.6) 2 0.20
+ (15.0 - 9.6) 2 0.10) 1/2 = 3.3%
CV p
= 3.3%/9.6% = .34
75

Portfolio vs. Its Components



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

Two-Stock Portfolios





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

Adding Stocks to a Portfolio


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


1 stock
≈ 35%

Many stocks
≈ 20%
1 stock
2 stocks
Many stocks
-75 -60 -45 -30 -15 0 15 30 45 60 75 90 10
5
Returns (%)
79

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

Stand-alone risk = Market risk
+ Diversifiable risk


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

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

Can an investor holding one stock earn a return commensurate with its risk?



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

How is market risk measured for individual securities?



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: b i
= ( r i,M
 i
) / 
M
84

How are betas calculated?

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

Using a Regression to
Estimate Beta


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

Use the historical stock returns to calculate the beta for PQU.
Year
1
2
3
6
7
4
5
8
9
10
Market
25.7%
8.0%
-11.0%
15.0%
32.5%
13.7%
40.0%
10.0%
-10.8%
-13.1%
PQU
40.0%
-15.0%
-15.0%
35.0%
10.0%
30.0%
42.0%
-10.0%
-25.0%
25.0%
87

Calculating Beta for PQU
50%
40%
30%
20%
10%
0%
-10%
-20%
-30% r
PQU
= 0.8308 r
R
2
M
+ 0.0256
= 0.3546
-30% -20% -10% 0% 10% 20% 30% 40% 50%
Market Return
88

What is beta for PQU?

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

Calculating Beta in Practice



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

How is beta interpreted?





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?
91

Other Web Sites for Beta



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.
92

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

Use the SML to calculate each alternative’s required return.




The Security Market Line (SML) is part of the Capital Asset Pricing Model
(CAPM).
SML: r i
= r
RF
Assume r
RF
+ (RP
= 8%; r
M
M
)b i
= r
.
M
RP
M
= (r
M
= 15%.
- r
RF
) = 15% - 8% = 7%.
94

Required Rates of Return




 r r
Alta
M
= 8.0% + (7%)(1.29) = 17%.
= 8.0% + (7%)(1.00) = 15.0%.
r r
Am. F.
T-bill
= 8.0% + (7%)(0.68) = 12.8%.
= 8.0% + (7%)(0.00) = 8.0%.
r
Repo
= 8.0% + (7%)(-0.86) = 2.0%.
95

Expected versus Required
Returns (%)
Alta
Market
Exp.
r
17.4
15.0
Am. Foam 13.8
T-bills 8.0
Repo 1.7
Req.
r
17.0
Undervalued
15.0
Fairly valued
12.8
Undervalued
8.0
Fairly valued
2.0
Overvalued
96

SML: r i r i
= r
RF
+ (RP
M
) b i
= 8% + (7%) b i r i
(%) r
M
Repo
.
-1
= 15 r
RF
= 8
.
.
T-bills
0
Alta
.
.
1
Am. Foam
Market
2
Risk, b i
97

Calculate beta for a portfolio with 50% Alta and 50% Repo b p
= Weighted average
= 0.5(b
= 0.22.
Alta
) + 0.5(b
Repo
)
= 0.5(1.29) + 0.5(-0.86)
98

Required Return on the
Alta/Repo Portfolio?
r p
= Weighted average r
= 0.5(17%) + 0.5(2%) = 9.5%.
Or use SML: r p
= r
RF
+ (RP
M
) b p
= 8.0% + 7%(0.22) = 9.5%.
99

18
15
11
8
Impact of Inflation Change on
SML r (%)
New SML 
I = 3%
SML
2
SML
1
Original situation
0 0.5
1.0
1.5
Risk, b i
100

18
15
8
Impact of Risk Aversion
Change r (%)
SML
2
After change
SML
1

RP
M
= 3%
Original situation
Risk, b i 101 1.0

Has the CAPM been completely confirmed or refuted?

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.
102