### PPT

```Part III 風險
9 資本市場理論
10 風險與報酬：資本資產定價模式
11 風險與報酬：套利定價理論
12 風險、資金成本與資本預算

1

9.1

9.2

9.3

9.4

10.1

10.2

10.3

10.4

10.5

10.6

2

12.1

12.2

12.3

12.4

12.5

3





9.1
9.2
9.3
9.4

4
9.1

：分成股利收益與資本所得兩項。
Dividends
Ending
market value
Time
0
1
Initial
investment

percentage return  dividend yield  capital gains yield

5
【例題】Suppose you bought 100 shares of Wal-Mart (WMT) one year ago today at
\$25. Over the last year, you received \$20 in dividends (= 20 cents per share ×
100 shares). At the end of the year, the stock sells for \$30. How did you do?
【解】

\$20  \$500
 20.8%
\$2,500


\$0.20 \$30  \$25

 0.8%  20%  20.8%
\$25
\$25

6
9.2

holding period return  (1  r1 )  (1  r2 ) 

 (1  rn )  1
, rn 是持有期間各期的報酬率

7
【例題】四年的報酬率如下：
Year Return
1
10%
2
-5%
3
20%
4
15%

【解】

 (1.10)  (.95)  (1.20)  (1.15)  1
 0.4421  44.21%

(1  rg ) 4  (1  r1 )  (1  r2 )  (1  r3 )  (1  r4 )
rg  4 (1.10)  (.95)  (1.20)  (1.15)  1  0.095844  9.58%

r  r  r  r 10%  5%  20%  15%
（算數）平均報酬  1 2 3 4 
 10%
4
4

8

1000
10
Common Stocks
Long T-Bonds
T-Bills
0.1
1930
1940
1950
1960
1970

1980
1990
2000
9
9.3

Series
Average
Annual Return
Standard
Deviation
Large Company Stocks
12.2%
20.5%
Small Company Stocks
16.9
33.2
Long-Term Corporate Bonds
6.2
8.7
Long-Term Government Bonds
5.8
9.4
U.S. Treasury Bills
3.8
3.2
Inflation
3.1
4.4
– 90%
Distribution
0%
+ 90%
Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by

10
9.4

：因承擔風險所多出來的報酬。

：無需承擔風險的報酬。

：報酬的標準差（報酬的變動大小）
。

11

18%
Small-Company Stocks
Annual Return Average
16%
14%
Large-Company Stocks
12%
10%
8%
6%
T-Bonds
4%
T-Bills
2%
0%
5%
10%
15%
20%
25%
30%
35%
Annual Return Standard Deviation
60
40
20
0
-20
Common Stocks
Long T-Bonds
T-Bills
-40
-60 26
30
35
40
45
50
55
60
65
70
75
80
85
90
95 2000
Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by

12
【例題】四種資產的報酬率分別為： 5% 、 5% 、10% 、18% ，請計算其報酬率之標

。
【解】

r1  r2  r3  r4 5%  5%  10%  18%

 7%
4
4
 r1  r 2   r2  r 2   r3  r 
4 1

2
  r4  r 
2
 9.63%
13

r  r   rn r
r 1 2

n
n
 r1  r 
sr 
2
  rn  r  
  r2  r  
2
2
 r1  r 2   r2  r 2 
r12

  rn  r 
n 1
r22
2


rn2
 n  r  r
2
2
2
r 


n
r 2   r  n
2

n 1

r
-5
5
10
18
28
2
r
25
25
100
324
474
n  4, r  28, r 2  474
r 28
r

7
n
4
sr 
r 2   r 

n 1
2
282
474 
n
4  278  9.63

4 1
3
14







10.1
10.2
10.3
10.4
10.5
10.6

15
10.1

Rate of Return
Scenario Probability Stock fund Bond fund
Recession
33.3%
-7%
17%
Normal
33.3%
12%
7%
Boom
33.3%
28%
-3%

1/3
1/3
1/3

-7%
17%
12%
7%
28%
-3%

Xf
-0.0233
0.0400
0.0933
0.1100
ΣX
Yf
0.0567
0.0233
-0.0100
0.0700
ΣY
2
Xf
0.0016
0.0048
0.0261
0.0326
2
ΣX
2
Yf
0.0096
0.0016
0.0003
0.0116
2
ΣY
XYf
-0.0040
0.0028
-0.0028
-0.0040
ΣXY

2

2
s X  X 2   X   14.3%
sY  Y 2   Y   8.2%
2
2

s X ,Y
s X sY

0.0117
 0.9950
0.1430  0.0820

16

Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Rate of Return
Stock fund Bond fund Portfolio
-7%
17%
5.0%
12%
7%
9.5%
28%
-3%
12.5%
11.00%
0.0205
14.31%
7.00%
0.0067
8.16%

squared deviation
0.160%
0.003%
0.123%
9.0%
0.0010
3.08%
17

% in stocks
Risk
Return
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
8.2%
7.0%
5.9%
4.8%
3.7%
2.6%
1.4%
0.4%
0.9%
2.0%
3.1%
4.2%
5.3%
6.4%
7.6%
8.7%
9.8%
10.9%
12.1%
13.2%
14.3%
7.0%
7.2%
7.4%
7.6%
7.8%
8.0%
8.2%
8.4%
8.6%
8.8%
9.0%
9.2%
9.4%
9.6%
9.8%
10.0%
10.2%
10.4%
10.6%
10.8%
11.0%
Portfolio Return
10.2
Portfolo Risk and Return Combinations
12.0%
11.0%
10.0%
9.0%
8.0%
7.0%
6.0%
5.0%
0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0%
Portfolio Risk (standard deviation)

18
return

100%
stocks
 = -1.0
100%
bonds
 = 1.0
 = 0.2


19
10.3


Diversifiable Risk;
Nonsystematic Risk;
Firm Specific Risk;
Unique Risk
Portfolio risk
Nondiversifiable risk;
Systematic Risk;
Market Risk
n

(1)可藉由投資組合分散的風險：可分散風險、非系統風險、廠商特有風險。
(2)無法藉由投資組合分散的風險：不可分散風險、系統風險、市場風險。

20
return

c
effi
ier
t
n
t fro
ien
minimum
variance
portfolio
Individual
Assets
P

21
10.4

return

L
CM
efficient frontier
rf
P

22

return
（風險  與報酬 r 為一直線關係。）
L
CM
100%
stocks
Optimal
Risky
Portfolio
rf
100%
bonds


23

：資本市場線（CML）的存在隱含以下性質
(1)所有人有共同的 CML 與最適投資組合（M 點）
(2)風險取向不同的投資者，會選擇在相同 CML 上的不同位置

24
return

1
f
0
f
r
r
C
L 0 CML 1
M
100%
stocks
First
Optimal
Risky
Portfolio
Second Optimal
Risky Portfolio
100%
bonds

（下一階段：整合各種不同風險的資本市場線。）

25
10.5

i 
Cov( Ri , RM )
 2 ( RM )

26
Security Returns

ne
i
L
c
i
ist
r
cte
a
ar
h
C
Slope = i
Return on
market %
Ri =  i + iRm + ei
（個別資產之報酬 ri 與市場報酬 rM 間的關係。）

27
10.6

RM  RF  Market Risk Premium

R i  RF  βi  ( R M  RF )

28
Expected return

：
R i  RF  β i  ( R M  RF )
RM
RF
1.0


29
【例題】市場投資組合報酬為 10%，無風險報酬為 3%，某資產的   1.5，請以 CAPM

【解】
Ri  3%  1.5  (10%  3%)  13.5%

30



31
Slide 32
Arbitrage Pricing Theory
Arbitrage arises if an investor can
construct a zero investment portfolio
with a sure profit.
– Since no investment is required, an
investor can create large positions to
secure large levels of profit.
– In efficient markets, profitable arbitrage
opportunities will quickly disappear.
McGraw-Hill/Irwin

33
Slide 34
11.1 Factor Models: Announcements,
Surprises, and Expected Returns
• The return on any security consists of two
parts.
– First, the expected returns
– Second, the unexpected or risky returns
• A way to write the return on a stock in the
coming month is:
R  R U
where
R is the expected part of the return
U is the unexpected part of the return
McGraw-Hill/Irwin

R  R U

35
Slide 36
Risk: Systematic and
Unsystematic
We can break down the total risk of holding a stock into
two components: systematic risk and unsystematic risk:
2
R  R U
becomes
Total risk

R Rmε
Nonsystematic Risk: 
Systematic Risk: m
where
m is 系統風險
ε is 非系統風險
n
McGraw-Hill/Irwin
Slide 37
Systematic Risk and Betas
• For example, suppose we have identified
three systematic risks: inflation, GNP
growth, and the dollar-euro spot exchange
rate, S(\$,€).
• Our model is:
R Rmε
R  R  βI FI  βGNP FGNP  βS FS  ε
βI is the inflation beta（通貨膨脹）
βGNP is the GNP beta
βS is the spot exchange rate beta（匯兌）
ε is the unsystematic risk
McGraw-Hill/Irwin
Systematic Risk and Betas:
Example
Slide 38
R  R  βI FI  βGNP FGNP  βS FS  ε
• Suppose we have made the following estimates:
1. I = -2.30
2. GNP = 1.50
3. S = 0.50
• Finally, the firm was able to attract a “superstar”
CEO, and this unanticipated development
contributes 1% to the return.
ε  1%
R  R  2.30  FI  1.50  FGNP  0.50  FS  1%
McGraw-Hill/Irwin
Systematic Risk and Betas:
Example
Slide 39
R  R  2.30  FI  1.50  FGNP  0.50  FS  1%
We must decide what surprises took place in the
systematic factors.
If it were the case that the inflation rate was
expected to be 3%, but in fact was 8% during
the time period, then:
FI = Surprise in the inflation rate = actual –
expected
= 8% – 3% = 5%
R  R  2.30  5%  1.50  FGNP  0.50  FS  1%
McGraw-Hill/Irwin
Systematic Risk and Betas:
Example
Slide 40
R  R  2.30  5%  1.50  FGNP  0.50  FS  1%
If it were the case that the rate of GNP
growth was expected to be 4%, but in
fact was 1%, then:
FGNP = Surprise in the rate of GNP growth
= actual – expected = 1% – 4% = –
3%
R  R  2.30  5%  1.50  (3%)  0.50  FS  1%
McGraw-Hill/Irwin
Systematic Risk and Betas:
Example
Slide 41
R  R  2.30  5%  1.50  (3%)  0.50  FS  1%
If it were the case that the dollar-euro spot
exchange rate, S(\$,€), was expected to
increase by 10%, but in fact remained
stable during the time period, then:
FS = Surprise in the exchange rate
= actual – expected = 0% – 10% = –
10%
R  R  2.30  5%  1.50  (3%)  0.50  (10%)  1%
McGraw-Hill/Irwin
Systematic Risk and Betas:
Example
Slide 42
R  R  2.30  5%  1.50  (3%)  0.50  (10%)  1%
Finally, if it were the case that the
expected return on the stock was 8%,
then:
R  8%
R  8%  2.30  5%  1.50  (3%)  0.50  (10%)  1%
R  12%
McGraw-Hill/Irwin
Slide 43
11.6 CAMP 與 APT
• APT applies to well diversified portfolios and
not necessarily to individual stocks.
• With APT it is possible for some individual
stocks to be mispriced - not lie on the SML.
• APT is more general in that it gets to an
expected return and beta relationship without
the assumption of the market portfolio.
• APT can be extended to multifactor models.
McGraw-Hill/Irwin
Slide 44
11.7 Empirical Approaches to Asset
Pricing
• Both the CAPM and APT are risk-based models.
• Empirical methods are based less on theory and
more on looking for some regularities in the
historical record.
• Be aware that correlation does not imply
causality.
• Related to empirical methods is the practice of
classifying portfolios by style, e.g.,
– Value portfolio
– Growth portfolio
McGraw-Hill/Irwin






12.1
12.2
12.3
12.4
12.5

45
12.1

Firm with
excess cash
Pay cash dividend
Shareholder
invests in
financial
asset
A firm with excess cash can either pay a
dividend or make a capital investment
Invest in project
Shareholder’s
Terminal
Value

Ri  RF  βi ( RM  RF )

46
【例題】Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint
presentations, has a beta of 2.5. The firm is 100-percent equity financed.
Assume a risk-free rate of 5-percent and a market risk premium of 10-percent.
What is the appropriate discount rate for an expansion of this firm?
【解】

Ri  RF  βi (RM  RF )  5%  2.5 10%  30%

47
IRR
Project

SML
Good
A
project
30%
B
5%
C
Firm’s risk (beta)
2.5

48
12.2

Beta 的公式：
βi 
Cov( Ri , RM ) σ i , M
 2
Var ( RM )
σM

(1)時間、(2)樣本大小、(3)融資與風險狀況。

49
【例題】某 g 公司與其產業在過去四年的報酬資料如下，請計算 g 公司的 Beta 值。

1
2
3
4
Rg
-10%
3%
20%
15%
RM
-40%
-30%
10%
20%
【解】

1
2
3
4

Rg
-10%
3%
20%
15%
0.2800
ΣRg
0.30   0.40  4
RM
-40%
-30%
10%
20%
-0.4000
ΣRM
2
RM
0.1600
0.0900
0.0100
0.0400
0.3000
ΣRM2
2
 M2 
βg 
4 1
Cov( Rg , RM )
Var ( RM )

σ g ,M
σ M2
 0.0867

 g ,M 
Rg×RM
0.0400
-0.0090
0.0200
0.0300
0.0810
Σ(Rg×RM)
0.081   0.28    0.40  4
4 1
 0.0363
0.0363
 0.42
0.0867

50
12.3

(1)收益週期循環性（Cyclicity of Revenues）
(2)營運槓稈（Operating Leverage）

(3)財務槓桿（Financial Leverage）

51

：衡量固定成本對營收得影響。

：
EBIT
DOL  EBIT
Sales
Sales
\$
 EBIT
Total
costs
Fixed costs
 Volume
Fixed costs
Volume

52

：衡量固定資金成本對營收得影響。
 Asset 
Debt
Equity
  Debt 
  Equity
Debt  Equity
Debt  Equity











 資產 負債  權益




53
【例題】某全部權益的 g 公司之 Beta 值為 0.8。若該公司將財務槓桿調整為 1 比 2
（1 份負債比 2 份權益）
，則該公司權益的 Beta 值為何？（假設負債的 Beta 值

【解】
負債  0

 資產 

 負債 

1
  權益    權益  0.8

1
  資產   權益  0.8

資產 

  權益 
 負債 

  權益 
2
  權益  0.8
1 2
3
3
 資產   0.8  1.2
2
2

54
12.4

Project IRR

The SML can tell us why:
Incorrectly accepted
negative NPV projects
RF  βFIRM ( R M  RF )
Hurdle
rate
rf
FIRM
SML
Incorrectly rejected
positive NPV projects
Firm’s risk (beta)

55

rWACC 
S
B
 rS 
 rB  1  TC 
BS
BS

rS  RF     RM  RF 

56
【例題】某公司負債的市值為 4000 萬，權益的市值為 6000 萬。該公司給付負債 15%

【解】

rS  RF     RM  RF   11%  1.41 9.5%  24.40%
rWACC 
6000
4000
 24.40% 
15%  1  0.34  18.60%
4000  6000
4000  6000

57
12.5

：資產、有價證券的變現能力。

Cost of Capital

Liquidity

58

。投資時預期之景氣狀態與報酬率資料如下表：

0.2
0.5
0.3

-3%
10%
18%

4%
6%
8%
5. 該公司預期之投資組合報酬為何？
6. 該公司之投資組合之風險為何？
7. 若想要讓投資組合風險最低，則投資於高科技產業的權重（比例）應為何？
【解】

0.2
0.5
0.3

1.90%
7.20%
11.00%
E  X   7.28%
Xf
0.0038
0.0360
0.0330
0.0728
X2f
0.000072
0.002592
0.003630
0.006294
  E  X 2   E  X   0.006294  0.07282  3.15%
2

59
8. A 公司的平均報酬率為 20%，標準差 8%；市場的平均報酬率為 12%，標準差 6%。

【解】
 B  8%,  M  6%, B,M  0.8
A 
 AM  AM  A 0.8  8%


 1.07
M
6%
 M2

60

9. 該公司的權益成本（ rS ）為為何？
10. 該公司的實質（稅後）負債成本為何？
11. 該公司的加權資金成本（ rWACC ）為為何？
【解】
rS  rf    rM  rf   4%  1.5 12%  4%  16%
rB 1  TC   9%  1  30%  6.3%
rWACC 
S
B
60
40
rS 
rB 1  TC  
16% 
 6.3%  12.12%
BS
BS
100
100

61