Crisis-robust portfolios

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					Université Libre de Bruxelles – Solvay Business School – Centre Emile Bernheim ULB CP145/1 50, Av. F.D. Roosevelt 1050 Bruxelles - BELGIUM

Research Institute in Management Sciences

Centre Emile Bernheim

WORKING PAPER: WP-CEB 07-030

=(

K

)
Σ

Σ

Φ = (φ K φ

) ∑φ
=

=

φ

σ

(

⎧σ ⎪ ⎪ )=⎨ ⎪ ⎪σ ⎩

( )=Φ ( )=Φ

Σ Φ Σ Φ

σ σ

( (

) = )

∈⎧ ⎨ ⎩

σ ⎫ σ ⎬
⎭

( ) ( )

Φ = φ Kφ

(

)

∑φ
=

=

Φ =

Φ Σ Φ ΦΣ Φ

(

=

)

σ

(

=

)
γ

σ

(
ρ

=

)
ρ

ρ =γ ρ
γ

β

σ σ

=

σ σ

=β >

φ ∈[

]
+ ( −φ ) σ + ( −φ ) σ + φ ( − φ )σ σ ρ + φ ( − φ )σ σ ρ

−φ ∈[

]

σ σ

( ) =φ σ

( ) =φ σ

σ σ

( ) ( )

(γ − ) ⎡ φ ( − φ ) (φσ ⎣
γ≠ φ σ − ( −φ ) σ
=

− ( − φ )σ

)− (

− φ) φ σ

(

+ ( −φ ) σ

)⎤ = ⎦

φ
−φ

=

σ σ

Φ = φ φ

(

)

σ ⎧ ⎪ φ = σ +σ ⎪ ⎨ ⎪φ = − φ = σ ⎪ σ +σ ⎩

δ

δ = ρ (γ −

)=ρ

⎛ρ ⎞ − ⎟=ρ −ρ ⎜ ⎜ρ ⎟ ⎝ ⎠

δ

(δ > )

(δ < )

(
ρ <ρ

=

)

σ σ

=

σ σ

>

σ σ

( ) ( )
(
=

φ = −

σ σ +σ

)

δ =ρ σ
= ×
−

(γ − ) = ρ
−

−ρ

σ

= ×

β=

ρ =

δ=−0.6

δ=−0.3

δ=0

δ=0.3

δ=0.6

δ =ρ σ
= ×
−

(γ − ) = ρ
−

−ρ

σ

= ×

β=

ρ =

δ=−1

δ=−0.9

δ=−0.6

δ=0

δ=0.6

σ σ

( (
=

) )
+ρ

φ

φ

σ σ

( (

+ρ )= ) ( +γ ρ )β

( +ρ )β

(
ρ <ρ

=

)

σ σ

=

σ σ

>

σ σ

( (

) )

+ρ +ρ

=β

δ = ρ −ρ

+ρ +ρ

= β ⇔δ =δ

δ =⎜

⎞ − ⎟( + ρ ⎝β ⎠

⎛

)

β>

− ≤ρ ≤

δ
>δ >δ

δ

δ >δ = −

β

δ =δ = −

δ = − <δ


				
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posted:5/29/2009
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Description: Crisis-robust portfolios
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