Transcript Learning about Return and Risk from The Historical Record

1
Risk Aversion and Capital
Allocation to Risky Asset
Chapter 6
Bodi Kane Marcus Ch 5
Risk and Risk Aversion
• Risk, Speculation, and Gambling
• Risk Aversion and Utility Values
• Estimating Risk Aversion
Risk and Risk Aversion
• Risk, Speculation, and Gambling
• Risk: The chance that an investment's actual
return will be different than expected.
• Speculation: the assumption consider-able
investment risk to obtain commensurate
gain
▫ Considerable = the risk is sufficient to affect the
decision
• Gamble = bet or wager on an uncertain
outcome
▫ Speculation gambling
Risk and Risk Aversion
• Risk Aversion and Utility Values
Portfolio
Risk
Premium
(%)
Expected
Return (%)
Risk (SD)
(%)
L (Low Risk)
2
7
5
M (Medium Risk)
4
9
10
H (High Risk)
8
13
20
Risk and Risk Aversion
• Risk Aversion and Utility Values
Portfolio L
U = E ( r ) – ½ A 2
Investor Risk
Aversion (A)
Utility Score Of Portfolio L
[E(r) = 0.07;  = 0.05]
2.0
.07 – ½ x 2 x .052
.0675
3.5
07 – ½ x 3.5 x .052
.0656
5.0
07 – ½ x 5 x .052
.0638
Risk and Risk Aversion
• Risk Aversion and Utility Values
Portfolio M
U = E ( r ) – ½ A 2
Investor Risk
Aversion (A)
Utility Score Of Portfolio L
[E(r) = 0.09;  = 0.10]
2.0
.09 – ½ x 2 x .102
.0800
3.5
09 – ½ x 3.5 x .102
.0725
5.0
09 – ½ x 5 x .102
.0650
Risk and Risk Aversion
• Risk Aversion and Utility Values
Portfolio H
U = E ( r ) – ½ A 2
Investor Risk
Aversion (A)
Utility Score Of Portfolio L
[E(r) = 0.13;  = 0.20]
2.0
.13 – ½ x 2 x .202
.09
3.5
.13 – ½ x 3.5 x .202
.06
5.0
.13 – ½ x 5 x .202
.03
Risk Aversion and Utility Values
• The Trade-off Risk and Return
P
I
II
E(r p)
III
IV
p
Risk Aversion and Utility Values
• Indifference Curve
Indifference Curve
Q
E(r p)
P
p
Risk and Risk Aversion
• Estimating Risk Aversion
Expected Return Standard Devi- Utility = E ( r ) - ½ A  2
(E(r))
ation ()
.10
.200
.10 - .5 x 4 x .04
.02
.15
.255
.02
.20
.300
.02
.25
.339
.02
Risk and Risk Aversion
• Rate of Return
r (loss) = -1 (i.e., -100%)
r (no loss) = 0
E (r ) = p x (-1) + (1-p) x 0 = -p
Risk and Risk Aversion
• Variance and Standard Deviation
-1 – (-p) = p-1
0- (-p) = p
2 ( r ) = p (1-p)
(6.3)
Capital Allocation across Risky and
Risk-Free Portfolios
• The risk of long-term Bonds > the risk of T-Bills
Ready Asset Money
Market Fund
Initial portfolio
W to
total
$ 90,000
Equities
(30%)
$ 113,400 (54%)
.378
$ 300,000
Risky Securities
$ 210,000
Long-Term bonds
(70%)
$ 96,600 (46%)
.322
.70
Portfolios of One Risky Asset and a
Risk-Free Asset
The Risky
rate of
return of P
The
Expected
rate of
return
Standard
Deviation
The rate of
return 0n
the risk
free asset
Risk
Premium
rp
E (r p)
p
rf
E (r p)-r f
15%
22%
7%
8%
Proportion risky
portfolio
Proportion risk free
portfolio
y
1-y
The Expectation of the portfolio rate of return
E ( r C ) = The Complete portfolio
E ( r C ) = y.E( R p ) + (1-y) r f =
rf + y [ E (rp) –rf ]= 7 + y ( 15-7) = 7 + 8y
(6.8)
Portfolios of One Risky Asset and a
Risk-Free Asset
The Risky
rate of
return of P
The
Expected
rate of
return
Standard
Deviation
The rate of
return 0n
the risk
free asset
Risk
Premium
rp
E (r p)
p
rf
E (r p)-r f
15%
22%
7%
8%
Proportion risky
portfolio
Proportion risk free
portfolio
y
1-y
The Expectation of the Standard Deviation of portfolio
 C = The Standard Deviation of Complete portfolio
 C = y p = 22y
(6.9)
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Portfolios of One Risky Asset and a
Risk-Free Asset
Bodi Kane Marcus Ch 5
• If investor:
▫ Invest solely in the risky asset; y = 1 ; the complete
portfolio = P
▫ Invest y = 0; (1-y) = 1; the complete portfolio =
the risk free portfolio = F
▫ The extra return per extra risk = 8/22 = .36
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Bodi Kane Marcus Ch 5
Portfolios of One Risky Asset and a
Risk-Free Asset
• The extra return per extra risk = 8/22
E(rC)=
rf +y
[ E (rp) –rf ] =
rf + c /p [ E (rp) –rf] =
7 + 8/22
c
(6.10)
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Bodi Kane Marcus Ch 5
Portfolios of One Risky Asset and a
Risk-Free Asset
E(r p) =15%
P
CAL = Capital Allocation
Line
E(r p )-r f = 8%
r f = 7%
F
 p = 22%
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Portfolios of One Risky Asset and a
Risk-Free Asset
Bodi Kane Marcus Ch 5
Differential borrowing and lending rates
E(r p) =15%
P
S(y > 1) = .27
rB f = 9%
r f = 7%
S(y  1) = .36
 p = 22%
CAL
Risk Tolerance and Asset Allocation
Utility as function of allocation to the risky asset y
Utility
.10
.05
0
0.2
0.4
0.6
0.8
Allocation to
risky asset
1
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Bodi Kane Marcus Ch 5
Indifference Curve
.60
Highly risk averse
A= 4
A= 4
A= 2
A= 2
.30
Slightly risk averse
U =.09
U =.05
0
.10
.20
.30
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Bodi Kane Marcus Ch 5
Note Fig 6.7
• Steeper curve (kurva yang lebih curam)
menandakan investor menuntut peningkatan
expected return untuk setiap satu satuan
tambahan risiko atau investor relatif lebih
enggan terhadap risiko
• The higher curve (kurva pada posisi lebih tinggi)
menunjukkan tingkat kepuasan yang lebih tinggi
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Bodi Kane Marcus Ch 5
Table 6.6
• Expected return of :
 Given Risk Aversion (A)
 Given Utility (U)
 Certain Standard Deviation ()
• Higher risk (standard deviation)  higher
Expected return
• It is possible the same risk aversion (A= 4) has
different Utility (U = .05 and U= .09)
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Bodi Kane Marcus Ch 5
Finding optimal complete portfolio
CAL
E(r p )= 15%
E(r C= .1028
r f = 7%
 C = .0902
 p = .22
Passive Strategies: The Capital Market
Line
• Menggambarkan keputusan baik yang langsung
atau tidak langsung berupaya menghindari
pembuatan analisa
• Tab 6.8
• Portofolio yang ditiru : S&P 500; T-Bills
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Bodi Kane Marcus Ch 5
Tugas Kelompok
Klp
RDPU
RDPT
RDC
RDS
Felix
Bahana
BNP Paribas
Makinta
Schroder
Venny
Schroders
Schroders
Panin
Panin
Timothy
Fortis
Fortis
Fortis
Manulife
Hilda
Schroders
Schroders
Schroders
Mandiri
Mathew
AXA
AXA
Fortis
Fortis
Ivana
GMT
Gentry
Batavia
Batavia
Batavia
Batavia
Danny
Bahana
Bahana
Bahana
Bahana