This paper describes three measures of financial risk –Value at Risk (VaR) based on the Gaussian distribution, VaR based on extreme value theory and conditional VaR (expected shortfall) – and shows an application of these measures to the withdrawals of deposits in the Bolivian financial system. The results suggest that it’s important to consider the statistical assumptions of these measures, in order to avoid underestimate or overestimate the true financial risks

Gonzales-Martínez, Rolando

German

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Risk Measures and an Application to the
Withdrawals of Deposits in the Bolivian
Financial System
Rolando Gonzales-Mart´ınez
Superintendencia de Bancos y Entidades Financieras de Bolivia
September 2008
Online at http://mpra.ub.uni-muenchen.de/14700/
MPRA Paper No. 14700, posted 17. April 2009 06:49 UTC
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A
2001 2002 2003 2004 2005 2006 2007 2008
2000
2500
3000
3500
4000
4500
Observaciones (evolucion en el tiempo)
M
M
U
S
$
2001 2002 2003 2004 2005 2006 2007 2008
0
200
400
600
800
1000
Observaciones (evolucion en el tiempo)
M
M
U
S
$
2001 2002 2003 2004 2005 2006 2007 2008
150
200
250
300
350
Observaciones (evolucion en el tiempo)
M
U
S
$
2001 2002 2003 2004 2005 2006 2007 2008
300
350
400
450
500
Observaciones (evolucion en el tiempo)
M
M
U
S
$
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
0
50
100
150
200
250
300
VaR
Gaussiano
VaR
(EVT)
Variaciones de los Depósitos
y Valor-en-Riesgo de
Retiros de Depósitos
SISTEMA FINANCIERO BOLIVIANO
Variaciones de depósitos del sistema finaciero
Histograma de las variaciones de depósitos del
sistema finaciero y medidas de riesgo VaR
Sistema Bancario Fondos Financieros Privados
Cooperativas de Ahorro y Crédito Mutuales de Ahorro y Préstamo
Evolución de Depósitos
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-3
-2
-1
0
1
2
3
4
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-6
-4
-2
0
2
4
6
8
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-10
-5
0
5
-3 -2 -1 0 1 2 3 4
0
50
100
150
200
250
300
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
50
100
150
200
250
300
-10 -5 0 5
0
200
400
600
800
1000
1200
1400
-6 -4 -2 0 2 4 6 8
0
200
400
600
800
1000
1200
1400
-4 -3 -2 -1 0 1 2 3
0
0.5
1
1.5
2
2.5
3
3.5
4
Umbral
E
x
c
e
s
o
 
d
e
 
l
a
 
M
e
d
i
a
 
(
M
e
a
n
 
E
x
c
e
s
s
)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
0
1
2
3
4
5
6
7
8
Umbral
E
x
c
e
s
o
 
d
e
 
l
a
 
M
e
d
i
a
 
(
M
e
a
n
 
E
x
c
e
s
s
)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Umbral
E
x
c
e
s
o
 
d
e
 
l
a
 
M
e
d
i
a
 
(
M
e
a
n
 
E
x
c
e
s
s
)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Umbral
E
x
c
e
s
o
 
d
e
 
l
a
 
M
e
d
i
a
 
(
M
e
a
n
 
E
x
c
e
s
s
)
Sistema Bancario Fondos Financieros Privados Mutuales de Ahorro y Préstamo Cooperativas de Ahorro y Crédito


Medidas de Riesgo Financiero y una Aplicación a las Variaciones de Depósitos del Sistema Financiero Boliviano

Munich RePEc Personal Archive

MPRAMunich Personal RePEc ArchiveRisk Measures and an Application to theWithdrawals of Deposits in the BolivianFinancial SystemRolando Gonzales-Mart´ınezSuperintendencia de Bancos y Entidades Financieras de BoliviaSeptember 2008Online at http://mpra.ub.uni-muenchen.de/14700/MPRA Paper No. 14700, posted 17. April 2009 06:49 UTC !"#"$% "! &#!%'( )#*$*+#!,( - .*$ /01#+$+#2* $ 1$%3$,#$+#(*!% "! 4!02%#5(% "!1 6#%5!7$ )#*$*+#!,( 8(1#9#$*( !"#$%! &!$'#"() *#+,-$(' !"#$!% !"# #!"$%&' %#!()&*# ")#! +#%&%,! %# )&#!-' fi/,/(&#)' 01,2') #/ 3&#!-' 41,35 *,!,%' #/ 2,%&!")&*$(&6/ %# 7,$!!8 1,3 *,!,%' #/ 9#'):, %# 1,2')#!  ;")#+'! < 1,3 ('/%&(&'/,2 4 !"#$%#&'()*%+,--50 < #=#+>2&fi(, !$ $!' 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X-#:D<` M-: D` 33: D$@RDA@:A2001 2002 2003 2004 2005 2006 2007 2008200025003000350040004500Observaciones (evolucion en el tiempo)MMUS$2001 2002 2003 2004 2005 2006 2007 200802004006008001000Observaciones (evolucion en el tiempo)MMUS$2001 2002 2003 2004 2005 2006 2007 2008150200250300350Observaciones (evolucion en el tiempo)MUS$2001 2002 2003 2004 2005 2006 2007 2008300350400450500Observaciones (evolucion en el tiempo)MMUS$0 200 400 600 800 1000 1200 1400 1600 1800 2000-2-1.5-1-0.500.511.522.53-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3050100150200250300VaRGaussianoVaR(EVT)Variaciones de los Depósitosy Valor-en-Riesgo deRetiros de DepósitosSISTEMA FINANCIERO BOLIVIANOVariaciones de depósitos del sistema finacieroHistograma de las variaciones de depósitos delsistema finaciero y medidas de riesgo VaRSistema Bancario Fondos Financieros PrivadosCooperativas de Ahorro y Crédito Mutuales de Ahorro y PréstamoEvolución de Depósitos0 200 400 600 800 1000 1200 1400 1600 1800 2000-3-2-1012340 200 400 600 800 1000 1200 1400 1600 1800 2000-6-4-2024680 200 400 600 800 1000 1200 1400 1600 1800 2000-2-1.5-1-0.500.511.520 200 400 600 800 1000 1200 1400 1600 1800 2000-10-505-3 -2 -1 0 1 2 3 4050100150200250300-2 -1.5 -1 -0.5 0 0.5 1 1.5 2050100150200250300-10 -5 0 50200400600800100012001400-6 -4 -2 0 2 4 6 80200400600800100012001400-4 -3 -2 -1 0 1 2 300.511.522.533.54UmbralExceso de la Media (Mean Excess)-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4012345678UmbralExceso de la Media (Mean Excess)-2 -1.5 -1 -0.5 0 0.5 1 1.5 200.20.40.60.811.21.41.61.82UmbralExceso de la Media (Mean Excess)-5 -4 -3 -2 -1 0 1 2 3 4 5 600.511.522.533.544.55UmbralExceso de la Media (Mean Excess)Sistema Bancario Fondos Financieros Privados Mutuales de Ahorro y Préstamo Cooperativas de Ahorro y Crédito

http://mpra.ub.uni-muenchen.de/14700/1/MPRA_paper_14700.pdf

Medidas de Riesgo Financiero y una Aplicación a las Variaciones de Depósitos del Sistema Financiero Boliviano

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