Σ(r) mvp e(r) standard deviation of return c a b expected return % 15% 10%
TRANSCRIPT
σ(r)
MVP
E(r)
Standard deviation of return
C
A
B
Expecte
d re
turn
%
15%
10%
Standard deviation of return
E(r)
σ(r)10% 20% 30% 40% 50%
Exp
ecte
d re
turn
%
MVP
N
Consolidated
Z
Q
W
Acme
Brown
XA
Portfolio weight in stock B
1.00
1.00
-1.00
-1.00
Q
U
S
L
Y’
XB
Portfolio weight in stock A
0
X
XA
Portfolio weight in stock B
1.00
1.00
-1.00
-1.00
Q
U
S
L
Y’
XB
Portfolio weight in stock A
0
X
T
R
1.00
1.00
-1.00
-1.00
XB
Portfolio weight in stock A
0XA
Portfolio weight in stock B
Isoexpected return line
10%12%
16%
18%
20%
B
XB
MVP
-1.00 0 1.00XA
30%
28%
21%
26%
17%
C
W
X
Portfolio weight in stock A
Portfolio weight in stock B
XB
MVP
-1.00
0
1.00XA
30%
28%
21%
26%
17%
Q
WN
Z
0.5
1.00
Y
Critical Line
-0.5
Isovariance ellipse
Isoexpected return line
10%12%16%
18%20%
D
E
F
-1.00
-0.5
XA
Portfolio weight in stock B
1.0
1.0
-1.00
-1.00
Q
S
Z
XB
Portfolio weight in stock A
0 .5-.5
R
T
Standard deviation of return
E(r)
σ(r)10% 20% 30% 40% 50%
Exp
ecte
d re
turn
%
MVP
N
Consolidated
Z
Q
W
Acme
Brown
XA
Portfolio weight in stock B
1.0
1.0
-1.00
-1.00
Q
S
Z
XB
0 .5-.5
R
TAC
B
Standard deviation of return
E(r)
σ(r) 10% 20% 30% 40% 50%
Exp
ecte
d re
turn
%
MVP
N
CS
Z
Q
W
AT
BR
資本市場線 (CML)
一個無風險資產, N 個風險性資產 ( 投資組合M) 下的效率前緣
Pr =
Fx
Fr +
Mx
Mr =(1-
Mx )
Fr +
Mx
Mr (1)
2
p = 22
MMx ,
Mx =
M
p (2) 將(2) 代入(1)
可得 )(PrE =
Fr +〔
M
)(
FMrrE 〕
P
CML v. s. SML(CAPM)
CML:
SML:
)(PrE =
Fr +〔
M
)(
FMrrE
〕P
E (Jr )=
Fr +﹝E (
Mr )-
Fr ﹞
J
10% =γFγF
E (γ)E (γ)
E (γM )M
σ (γ)o o
Capita
l mar
ket l
ine
Exp
ecte
d r
etu
rn
15% = E (γM )
Securit
y m
arke
t lin
e
17.5%
β
Standard deviation 1 1.5Beta
A
M
E (γM) ﹣γF
FIGURE 8.8 CAPITAL MARKET LINE FIGURE 8.9 SECURITY MARKET LINE
βM = 1.00
CAPM v.s.Market Model
同 : 均與市場組合報酬有關 異 :1. 截距項 2. 均衡概念 (CAPM); 無 3. 殘差項相關 (CAPM); 獨立
E (Jr )=
Fr +﹝E (
Mr )-
Fr ﹞
J
tJr
,=
JA +
J
tMr
,+
tJ ,
(Fr ,
JA )
SML v.s. Characteristic lineE (
Jr )=
Fr +﹝E (
Mr )-
Fr ﹞
J
=Fr (1-
J )+
J E (
Mr )
tJr
,=
Fr (1-
J )+
J
tMr
,+
tJ ,
=JA +
J
tMr
,+
tJ ,
if Mr =
Fr then E (
Jr )=
Fr
all Characteristic lines 均相交於共同點(Fr ,
Fr )
C
FIGURE 8.10 CHARACTERISTIC LINES UNDER THE CAPITAL ASSET PRICING MODEL
E(γA )
E(γB )
γJ A
B
E(γM )γF
10% =γF = E(γB )
-10%
5%
γM
Market return
o
FIGURE 8.11 POSITIONS OF INDIVIDUAL STOCKS IN E(γ), σ (γ) SPACE
10% =γF Exp
ecte
d r
etu
rn 15% = E(γM )
Standard deviation
17.5%
E(γ)
σ (γ)
AA’
M
CML
15% 22.5% 30%
β = 1.50
β = 1.00
β = .50
β = .00
SML(CAPM) in (E (r), σ)
E (Jr )=
Fr +﹝E (
Mr )-
Fr ﹞
J
J =
JM / 2
M ;
JM =
JM /
MJ
E (Jr )=
Fr +〔
JM
FMrrE
M
)( 〕
P
FIGURE 8.12 POSITIONS OF STOCKS ACCORDING TO THEIR CORRELATION COEFFICIENTS
γF
Exp
ecte
d r
etu
rn
Standard deviation
E(γ)
σ (γ)
M
ρ = -1.00
ρ = 1.00
ρ = .50
ρ = .00
Capital market lin
e
ρ = -.50
o
資本資產定價模式 (CAPM)
Where is the price?E (
Jr )=
Fr +﹝E (
Mr )-
Fr ﹞
J
0P =
)(1
)()(11
rE
DEPE
(由E ( r ) =0
011)()(
P
PDEPE )
Pricing:
1. 預測Fr ,E (
Mr ),
J 依 CAPM得 E(r)
2. 預測 E(P1),E(D
1)再與前所得之 E(r)共同設定 P
0
FIGURE 8.13 MARKET PRESSURE TO FORCE A STOCK TO ITS EQUILIBRIUM PRICE
γF = 10%
Standard deviation
E(γ)
σ (γ)
M
Capital m
arket line
o
15%
E(γ)
BM’
.10
5%
C’
C
C’’
A
CAPM之應用 投資風險評估-系統風險 ( 貝他係數 ) 投資績效評估-風險調整績效評估
Jensen Index Treynor Index Sharpe Index
資本預算評估-估計權益資金成本
風險控管 個別風險;非系統風險- 分散多種證券
(cross-sectional diversification) 例如,共同基金; ETF 。 市場風險;非系統風險-分散不同時間點 (time-series diversification) 。
例如,定時定額投資;期貨避險。 What risk take , what return make
投資績效評估-風險調整績效評估 Jensen Index (Based on CAPM) Treynor Index Sharpe Index
Jensen Index Based on CAPM(SML)
母體
樣本
PJ = E(r
p)-﹛r
F+﹝E(r
M)-r
F﹞
p ﹜
J =pr -﹝
Fr +(
Mr -
Fr )
p
﹞
FIGURE 11.4 ESTIMATED SML (BULL MARKET)
o
γP
βPPortfolio beta
Ave
rag
e p
ort
foli
o r
etu
rnB
A
Treynor Index Based on
CAPM(SML)
母體
樣本
T P =p
)(
FPrrE
P
FP
P
rrT
FIGURE 11.6 LEVERING ALPHA TO DOMINATE OMEGA
γF Exp
ecte
d r
etu
rn
E(γ)
β
M
o
A’
A’’
O’
1.501.00
Beta
Sharpe Index Based on
CAPM(CML)
母體
樣本
S P =p
)(
FPrrE
P
FP
P
rrS
FIGURE 11.7 PERFORMANCE OF ALPHA AND OMEGA ACCORDING TO THE SHARPE INDEX
γF
Exp
ecte
d r
etu
rn
Standard deviation
E(γ)
σ (γ)
M
o
A’
A
O
O’
資本預算-估計權益資金成本 估計 β ,依 CAPM 決定權益資金成本 E(r) 預測投資方案現金流量,估計淨現值 (NPV)
NPV=
N
t
in
rE
CF1 )(1
-
N
t
out
rE
CF1 )(1
獨立方案:NPV 0 ;互斥方案:選 NPV最大者