Transcript bodie kane-ch 7-optimal risky portfolios

1
Optimal Risky Portfolios
Chapter 7
Bodi Kane Marcus Ch 5
p (%)
35
0
Total Risk
20
Unique Risk
(unsystematic risk)
Market Risk (systematic risk)
10
20
30
40
1,000+
Number Stocks in Portfolio
Portfolios of two risky assets
rˆP  w D  rˆD  w E  rˆE
Note : w E  1 - w D
(Cov rD , rE )
 P  w   w   2w D  w E  ρ DE D   E
2
D
2
D
2
E
2
E
rˆP  expected return of portfolio
rˆD  expected return of stock D
r̂E  expected return of stock E
 D  Standard deviation of Stock D
 E  Standard deviation of Stock E
 P  Standard deviation of Portfolio
w D  Proportion of stock D to the entire portfolio
w E  Proportion of stock E to the entire portfolio
 DE  the Coefficien t Correlatio n between Stock A and Stock B
Portfolios of two risky assets
rˆP  w D  rˆD  w E  rˆE
Note : w E  1 - w D
(Cov rD , rE )
 P  w   w   2w D  w E  ρ DE D   E
2
D
2
D
2
E
2
E
 P  (0.16 * 0.0225)  (0.36 * 0.09)  2 * 0.4  0.6  0.1* 0.15  0.3
=0.19 =19%
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Bodi Kane Marcus Ch 5
Covariance
• A measure of the degree to which returns on two
risky assets move in tandem. A positive
covariance means that asset returns move
together. A negative covariance means
returns move inversely.
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Bodi Kane Marcus Ch 5
Correlation Coefficient
A measure that determines the degree to which two
variable's movements are associated.
The correlation coefficient is calculated as:
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Bodi Kane Marcus Ch 5
Portfolios of two risky assets
• If
DE = 1
 P  wD   D  wE   E
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Expected Return,
Bodi Kane Marcus Ch 5
Portfolio Expected Return as a
function of investment proportion
13%
Equity Fund
8%
Debt Fund
- 0.5
0
1
2.0
W stocks
1.5
1
0
-1.0
W bonds
9
Expected Return,
Bodi Kane Marcus Ch 5
Problem 5
20%
Equity Fund
12%
Debt Fund
- 0.5
0
1
2.0
W stocks
1.5
1
0
-1.0
W bonds
10
Bodi Kane Marcus Ch 5
Expected Return, rp
Portfolio Expected Return as a function of
standard deviation
 =-1
E
 =.30
 =0
 =1
D
Risk, p
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The Optimal Risky Portfolio with Two Risky Assets
and a Risk-Free Asset
Bodi Kane Marcus Ch 5
E (rD )  E (rE )  A(   D E  DE )
wD 
2
2
A( D   E  2 D E  DE )
2
E
A = the risk aversion parameter
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Bodi Kane Marcus Ch 5
The reward-to-volatility (Sharpe) ratio
sA 
E (rA )  rf
Max sP 
A
E (rP )  rf
P
Expected
Return, rp
I2
^
rM
^
rR
.
.
I1
M
Opportunity Set of
Risky Assets
P
Optimal Risky
Portfolio
rRF
Optimal Complete
Portfolio
R
M
Risk, p
The Determination of Complete Portfolio
CAL(P)
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Bodi Kane Marcus Ch 5
The optimal Complete Portfolio
The
Expected Return, rp
Efficient frontier
Global
MinimumVariance
Portfolio
Individual Asset
Minimum-Variance Frontier
Risk, p
The Opportunity Set of The Debt and Equity funds with
the optimal CAL and the optimal risky portfolio
Expected
Return, (%)
The Capital Allocation
Line (CAL):
E
P
Opportunity set of risky asset
rRF
D
Risk,  (%)
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Bodi Kane Marcus Ch 5
The efficient portfolio set
E( r )
Efficient Frontier
Risky Assets
E( r 3)
E( r 2)
E( r 1)

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Tugas Kelompok
Klp
Felix -ffs
RDPU
Venny
Schroder Dana
Likuid
Schroder Dana Obl Panin Dana
Ekstra
Unggulan
Timothy
Manulife DK
Manulife Obl Ngr
Hilda
Mathew
Ivana
Gentry
Mandiri Investa PU Mandiri Investa DU Mandiri Investa
Mandiri Investa
Aktif
Atraktif
Mandiri Investa PU Fortis rUPIAH Plus Panin Dana
Schroder Dana
II
Unggulan
Prestasi Plus
Manulife
Manulife
Manulife Dana
Manulife Dana
DanaPasar Uang
Pendapatan Tetap Berimbang
Ekuitas
Batavia Dana Kas Manulife Obl Neg Manulife Dana
Panin Dana Prima
Maxima
Indonesia
Bertumbuh
Berimbang
Manulife Dana Kas Manulife Obl
Manulife Dan Stabil Manulife Dana
Unggulan
Berimb
Saham
Mandiri Investa PU Mandiri Investa DU Manulife Dana
Manulife Saham
Campuran II
Andalan
Danny
Dyson-ffs
RDPT
Bodi Kane Marcus Ch 5
Mandiri Investa PU Fortis Prima II
RDC
RDS
Fortis Pesona
Schroder Dana
Prestasi Plus
Panin Dana Maxima
Fortis Ekuitra
Manulife Saham
Andalan
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Bodi Kane Marcus Ch 5
In order to run this model, you must have your Excel's "solver add-in" installed to your
computer.
To install the "solver add-in",
1. From the menu, choose "TOOLS",
2. Choose, "ADD-INS",
3. In the "Add-Ins Available" list, have your "SOLVER ADD-IN" checked.
If you have not chosen the full installment option when you had been installing your Microsoft Office,
you might need your original Microsoft Office disks during this configuration.
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