7 投資組合理論 - mail.nhu.edu.twmail.nhu.edu.tw/~ysliau/ch07.pdf · 第7 章...
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7 3
ISBN 978-957-41-7812-4
7
7-1
7-2 12%8% 0.5
1w
Var 0
w1
7-3
7-4
0
7-5 CAPM
CAPM
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4
ISBN 978-957-41-7812-4
7-6 APT
CAPM
1. 2
1 2 3 4 5 6 7 8 -1% 5% 4% 1% 8% 2% -1% -5%
20% 15% 11% 5% -5% 2% -10% -8%
(1)
(2)
(3) 50%
(4) 2(3)
Ans
(1)1.63%4.07%
3.75%11.03%
(2)
L %)75.3%15(%)63.1%5(%)75.3%20(%)63.1%1[(81
)R,R(Cov 21
%)]75.3%8(%)63.1%5(
0.087%
1938.0%03.11%07.4
%087.0)R(Var)R(Var
)R,R(Cov)R,R(Cor
21
2121
(3)Var
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ISBN 978-957-41-7812-4
%39.0%087.05.05.02)03.11(5.0%)07.4(5.0
),(2)()(2222
212122
212
1
RRCovWWRVarWRVarW
6.24%
(4) 2 7.55%
1
2. 10%
5%-1
Ans :
-1()
22112
2211
212122
22
21
21P
ww)ww(
)1(ww2ww
==
++=
0ww 1P ==
ww1 =
=ww
( w + w =1)
21
10%5%
ww
==
w + w =1
w =1/3 w =2/3
1/3 2/3
3.
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6
ISBN 978-957-41-7812-4
Ans :
4.
Ans
(1)
(2)
5.
Ans
( M1M2)
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ISBN 978-957-41-7812-4
6. CAPM APT
Ans
CAPM
APT
CAPM
APT
7. 0
Ans
0
8. 10% 2% 0.5
Ans :
%6%]2[10%5.0%2)E(Ri =+=
9.
Ans : (1) CAPM : ]R)[E(RR)E(R fmifi +=
(2)
fR [ fm R)E(R ](SML)
(3)( fR )
[ )E(R m ]
( )
fR [ fm R)E(R ]
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ISBN 978-957-41-7812-4
10. APT 1 12% 2
10% 3 8% 2%
b 0.51.20.8
Ans : %4.21%]2%8[8.0%]2%01[2.1%]2%12[5.0%2)R(E i =+++=
11. A B
A 5% 10%
B 10% 20%
0.001
(1) AB
wAwB1
(2)
(3) -0.02
(4)
2009 -
Ans
(1)
81.25%0.0012-20%10%
0.001-20%),(2
),(w 222
BA2B
2A
BA2B
min,A =+=
+
=RRCov
RRCov
18.75%81.25%-1w1w min,Bmin,B ===
(2)81.25%5%+18.75%10%=5.94%
(3) 3
2(-0.02)2-20%10%
(-0.02)-20%),(2
),(w 222
BA2B
2A
BA2B
min,A =+=
+
=RRCov
RRCov
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ISBN 978-957-41-7812-4
31
32-1w1w min,Bmin,B ===
(4)
)R,Cov(Rww2ww BABA2B
2B
2A
2AP ++=
0(-0.02)31
322%
3120%
3210% 22
22 =++=
12. 8% 12%A 1.2
(1)
(2) CAPM A A
(1)
(3) 3%
5% 9% A
(4)
12% 15% 8%(3)
A
2007 -
ANS
(1)
(2) A =8%1.2(12%8%)=12.8%
8% 12.8%
1.2
E(Ri) E(Ri)8%i(12%8%)
i
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ISBN 978-957-41-7812-4
(3) A =5%1.2(9%5%)=9.8%
(4) A =8%1.2(15%8%)=16.4%
13.
12% 1.00 -1.00 0.20
15% -1.00 1.00 -0.20
10% 0.20 -0.20 1.00
(1) 20% 80%
(2) 40% 20% 40%
(3)
0
5%
9.8%
1.2 i
8%
16.4%
1.2
E(Ri) E(Ri)8%i(15%8%)
i
E(Ri)5%i(9%5%)
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ISBN 978-957-41-7812-4
2007 -
ANS
(1)
9.6%80%15%20%12%wwP ===
(2)
4.7%)2.0(%10%15%40%2022.0%10%1240%40%2
)1(%15%1220%40%2 10%40%15%20%12%40%
),(ww2),(ww2),(ww2www
222222
B
222222
=
+++++
=
++
+++=
RRCovRRCovRRCov
P
(3) 0wwP ==
ww = 45
12%15%
ww
===
( w +w =1)
: 95w = 9
4w =
1. CAPM (A)
(B)(C) (D)
2010Q3
Ans(D)
2.
(A) 100% (B) 100% (C) 0 100% (D) 0
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ISBN 978-957-41-7812-4
2010Q3 Ans(D)
3. A 0.5B 1.5
(A)B A (B)B
A (C)B (D)B
A
2010Q3 Ans(B)
4. Markowitz
(A) W (B) X (C)
Y (D) Z
2010Q3
Ans(B)
5. U=E(R)1.5(S2)
(E(R)) (S) (A)12%20% (B)10%
15%(C)10%10% (D)8%10%
2010Q3
Ans(C)
6. (/)
(A) (B)(C)
(D)
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ISBN 978-957-41-7812-4
2010Q2
Ans(B)
13.00 8.50
21.50(A)0.125 (B)0.195 (C)0.285
(D)0.365
2010Q2
Ans(B)
7. (Capital Asset Pricing Model)
15.5% 3.5% 1.2(implied
market risk premium)(A)6.5% (B)12.0% (C)10.0% (D)15.5%
2010Q2
Ans(C)
8. (A)
(B)
(C)
(D)
2010Q2
Ans(D)
9. (capital allocation line)(A)
(expected profit)(B)(C)
(D)
2010Q2 Ans(D)
11. 0(A)
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ISBN 978-957-41-7812-4
0(B) 0(C) 0(D)
-1
2010Q2
Ans(D)
12. C12. 5%
6% 1.2 0.7
17%(A)6.0% (B)6.5% (C)6.8%
(D)7.4%
2010Q2
Ans(C)
13. (marginal utility)
(A) (B) (C) (D)(A)(B)(C)
2010Q1
Ans(C)
14. 0.2 0.005
0.5(A)0.1 (B)0.05 (C)0.15 (D)0.2
2010Q1
Ans(B)
15. (CML)(SML) .CML
SML .CML
SML .CML SML
(A) (B) (C) (D)
2010Q1
Ans(A)
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ISBN 978-957-41-7812-4
16. (Capital Asset Pricing Model)(A)
beta (B) alpha (C) beta (D) alpha
2010Q1
Ans(D)
17. ?(A)
(B)
(C)(D)
2010Q1
Ans(D)
18. ?(A)
(B)(C)(D)
2010Q1
Ans(A)
19. A B A
B (A)
(B) (C) (D)
2009Q4
Ans(A)
20. (short sale)
(A)+1.00 (B)0.00 (C)-1.00
(D)0.5
009Q4
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ISBN 978-957-41-7812-4
Ans(C)
21.
(A) (B) (C) (D)
2009Q4
Ans(A)
22. (CAPM)
V
(A)V (B) (C) V (D)
2009Q4
Ans(C)
23. P
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ISBN 978-957-41-7812-4
10 5 P W
0.002 P 0.8 P Beta
P W (A)1.250.66 (B)1.250.76 (C)1.050.66 (D)1.05
0.76
2009Q4
Ans(D)
24. A. B. 0
0C. 1(A) B. (B)
A.C.(C) B.C. (D)A.B.C.
2009Q3
Ans(A)
25. 14% 8%
13% 25%
(A)9% (B)30% (C)36% (D)40%
2009Q3
Ans(C)
26.
SML(A) (B) (C)
(D)
2009Q2
Ans(B)
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ISBN 978-957-41-7812-4
27. (Beta)
(A) (B) (C) (D)
2009Q2
Ans(C)
28.
(A) (B)
(C) (D)
2009Q2
Ans(B)
29. (CAPM) (A) CAPM
(B) CAPM (Capital
Market Line CML) (Security Market Line SML)
(C)
(D) CML SML
2009Q2
Ans(C)
30. ()
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ISBN 978-957-41-7812-4
A B -1 rB =
a0 + a1rA a1 A B
B
(A) -2 0.4 (B) -1.5 0.4 (C) -2 0.6 (D)-1.5 0.6
2009Q2
Ans(B)
31. E(r) = 25 S = 20 5
U = E(r) (A/3)S2 A
(A) 13 (B) 14 (C)15 (D) 16
2009Q2
Ans(C)
32. APT ?
APT (efficient portfolio)
APT
(factor beta)
APT
(A) (B)(C) (D)
2009Q2
Ans(C)
33. (zero-beta portfolio)
(A) (B)
(C) (D)
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ISBN 978-957-41-7812-4
2009Q2 Ans(C)
1. A B
(1)AB (2)AB (3)AB (4)()35%A65%B()
2010Q3
Ans
(1) E(RA)=0.158%+0.2013%+0.1512%+0.314%+0.216%=13%
E(RB)=0.158%+0.207%+0.156%+0.39%+0.211%=8.4%
(2) =
=n
1ss
2s Prob]E(R)[R
2.45%0.2013%)-(16%0.3013%)-(14%
0.1513%)-(12%0.2013%)-(13%0.1513%)-(8%22
222
A =++
++=
1.66%0.208.4%)-(11%0.308.4%)-(9%
0.158.4%)-(6%0.208.4%)-(7%0.158.4%)-(8%22
222
B =++
++=
(3)
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ISBN 978-957-41-7812-4
0.59
1.66%2.45%0.208.4%)-(11%13%)-(16%
0.308.4%)-(9%13%)-(14%0.158.4%)-(6%13%)-(12%0.208.4%)-(7%13%)-(13%0.158.4%)-(8%13%)-(8%
)R,Cov(R
BA
BA2,A
=
+++
+
=
=
(4) E(RP)=35%13%+65%8.4%=10.01%
1.73%0.591.66%2.45%65%35%21.66%65%2.45%35% 2222P =++=
2. 10%
16% 8% 12%(1)
(global minimum variance portfolio)
(2)
2010Q2
Ans
(1) :
wwP =
0wwP ==
ww = 43
16%12%
ww
===
( w +w =1)
: 73w = 7
4w =
(2) E(RP)= 7310%+
748%=8.86%
3. (separation theorem)(utility theory)
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ISBN 978-957-41-7812-4
2010Q2
Ans
:
(1)
()
(2)
4. (Capital Asset Pricing Model)(Arbitrage Pricing
Model)
2010Q1
Ans
(1)APT :APT
(2) APT :
5.X Y Z
(1) X Y Z 12%16% 25%
(2) X Y Z 12%14% 18% X
Y 0.6Y Z 0.2X
Z -0.3
2007Q1
Ans
(1) = %67.17%)25%16%12(31
=++
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ISBN 978-957-41-7812-4
(2)
%9298.0
%18%12)3.0(31
312%18%142.0
31
312
%14%126.031
312)
31(%18)
31(%14)
31(%12 222222
=
++
+++=
6.
0.6 2 1.0
3 1.6 5
5% 11.1%
0.8
2006Q3
Ans :
22.1532
56.1532
31532
26.0 =++
+++
+++
5% 11.1% CAPM
%]}5)[E(R22.1%5%{1.11 m += 10%)E(R m =
0.82
82.0532
58.0532
31532
26.0 =++
+++
+++
9.1% %1.9%]5[10%82.0%5)E(Ri =+=
7. CAPM
2006Q3
Ans :
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24
ISBN 978-957-41-7812-4
(1) CAPM
(2) CAPM
(3) CAPM
8. Chen,Roll&Ross APTFama&French CAPM
Merton CAPM( ICAPM)
2006Q1
Ans
(1) APT
APT
]R)E(R[b.......]R)E(R[b]R)E(R[bR)R(E fnn,if22,if11,ifi ++++=
(2) CAPM CAPM (Firm Size)
(Book-to-Market Ratio) E(HML)HE(SMB)S]R)[E(RR)E(R iifmifi +++=
E(SMB)(Size Premium) iS i E(HML)
(Value Premium) iH i CAPM
(3) CAPM CAPM CAPM(Intertemporal CAPM
ICAPM)
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ISBN 978-957-41-7812-4
CAPM
CAPM
ICAPM
=
+=n
1jfjji,fi ]R)[E(RR)E(R
)E(R j j ji, i
j ICAPM
9.
(1)
(2)
(3)
(4)
2001Q4
Ans
(1)
(2)
(3)
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26
ISBN 978-957-41-7812-4
(4)
10.CAPM CAPM
Security Market Line
2000Q4
Ans
(Security Market Line)
B
B
(B*)
Ri
i
B
B*
A*
A
E(Ri)
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ISBN 978-957-41-7812-4
11.
CAPM
CAPM rF M (1) A C A C
(2) B C
B C
(3) 12% 8%
AB C A, B C
2000Q4
Ans
(1)
6%6%(11%6%)AA0
14%6%(11%6%)CC1.6
(2) CAPM B C
B C
(3) (RZ)8%(Rm)
12% A B
C
M
C
B
A
0.5 0.7 0.9
0.14
0.11
rF=0.06
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ISBN 978-957-41-7812-4
RARfA (RmRf)A 0
RBRfB (RmRf)B0.83
RCRzC (RmRz)C1.50
12. 18 22 10
30
(1)
(2)(1)
1996Q1
Ans
(1)
(2)
13.
(1)
(2)
1995Q2
Ans
(1)
n
li
n
lj)ji(ijjj
2i
n
li
2i
2P WWW
= ==
n
li
n
lj)ji(ijiijji
2i
n
li
2i WWW
= ==
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ISBN 978-957-41-7812-4
ij 1
n
1iiiP W
=
ij 1
(2)
A.
B.
C.
Mini-Case
(1980 ~1993 )
()
15.70% 21.1% 1.00 0.37 0.53 0.26 0.43 0.73 0.44 21.70% 25.0% 0.37 1.00 0.47 0.36 0.29 0.36 0.63
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ISBN 978-957-41-7812-4
18.30% 23.5% 0.53 0.47 1.00 0.43 0.50 0.54 0.51 17.30% 26.6% 0.26 0.36 0.43 1.00 0.26 0.29 0.42 14.80% 27.6% 0.43 0.29 0.50 0.26 1.00 0.56 0.34 10.50% 23.4% 0.73 0.36 0.54 0.29 0.56 1.00 0.39 17.20% 26.6% 0.44 0.63 0.51 0.42 0.34 0.39 1.00
1.
2.
EXCEL