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||||||| Journal of Money and Finance | Vol.23 | No. 2 | 2009. 6 1)
: GARCH
*
. ,
(risk premium) , (risk averseness),
(asymmetric volatility) .
, EGARCH-M
, .
, .
.
: , , ,
JEL : C32, E32, G12
.
(risk averseness parameter) ( )
(risk premium = - )
CAPM(capital asset pricing model) (asset pricing
* (Tel : 02-3277-4467, E-mail : [email protected])
2 23 2 2009
theory) .1) Merton(1973) Intertemporal CAPM
(+) ,
(+) (-)
. (tradeoff)
, . Kim
and Lee(2008) , (risk-aversion)
(state-dependent),
.
,
(+) .
(time-varying) ,
.2)
(asymmetric volatility) (business cycle)
. , EGARCH-M -
, - .
.
, ( )
.
.
.
(intertemporal substitute relation)
1) CAPM Consumption CAPM , CAPM
U = E(R)-A2( E(R) : , 2 : , A : ) Consump-
tion-CAPM Constant Relative Risk Averseness(CRRA) (
C : ) A
. A . 2) Kim and Lee(2008) .
3
. , French, Schwert and Stambaugh
(1987) Campbell and Hentschel(1992) (+)
, Fama and Schwert(1977), Campbell(1987), Breen, Glosten, and
Jagannathan(1989), Turner, Startz and Nelson(1989), Pagan and Hong(1991), Nelson, Glosten,
Jagannathan and Runkle(1993), Whitelaw(2000) (-) . Harvey
(1989)
. (volatility feedback)
. Brown(1988)
, . , Potera and Summers(1986)
. French, Schwert and
Stambaugh(1987) (shock return) (innovation)
(-) . Haugen, Talmor, and Torous(1991)
.
(asymmetric)
. ,
(-) . ,
. Black(1976) (leverage)
. Christie(1982), Schwert
(1989)
.
, . Engle, Lilien,
and Robin(1987) ARCH (
) ARCH-M .
Engle(1982) Bollerslev(1986) GARCH-M .3)
3) GARCH (moving average)
(persistence) . Attannasio
and Wadhwani(1989), Chou(1988)
GARCH .
4 23 2 2009
French, Schwert, and Stambaugh(1987) GARCH-M
(+) . Chou(1988) GARCH-M
(-) ,
.
. , Schwert(1990) Fama(1990)
. McQueen and Roley(1993)
(stage) .
. Hamilton and Lin(1996) (state)
(Markov Chain)
.
Whitelaw(1994)
(unconditional contemporaneous relation) ,
(non-contermporaneous relation) .
,
. Wu(2001) (moment method)
. DeGoeji and Marquering(2002) GARCH
(Treasury bond)
.
. Duffe(2005) (wealth)
,
. Li(2007, 2008)
(Consumption Asset Pricing Model)
(equity premium puzzle)
. Lundblad(2007)
. Mele(2007)
5
(countercyclical)
, -
.
,
, Fama and French(1989)
(IP) . Kim and Lee(2008) NBER
(boom) (recession) .4)
GARCH
-, , -
. (+),
(-) ,
.
,
,
.
, , (1993) GARCH(1, 1)-M MA(1)-
GARCH(1, 1)-M , . (1994)
ARCH(3)-M GARCH(1, 1)-M
. (1999)
, GARCH
7
. (2002)
, GJR-GARCH
-, ,
, .
4) NBER employment, sales, income, industrial production(IP)
, NBER business cycle()
. .
6 23 2 2009
. , (1999) , ,
(2005) (symmetric)
(asymmetric) ,
. (good news) (bad
news) .
(1999)
.
,
. (2002) 9.11
. (2003)
, , ,
. (2005) Markov- Switching ARCH
, .
13
. (2008) AR(1)-GARCH(1, 1)
.
KOSPI .
(2009) (Consumption Asset Pricing Model)
1978 2008 .
.
,
, .
,
.
Kim and Lee(2008) (risk
averseness) (procyclical) ,
, 3
.
7
Kim and Lee(2008) Kim
and Lee(2008) ,
, 3 3
. , , , 3 ,
3 .
.
, AR(1)-EGARCH(1, 1)-M
. ,
. .
.
1. EGARCH-M
EGARCH-M 5)
(time-varying)
,
.
(specification test) (parsimo-
nious) AR(1)-EGARCH(1, 1)-M .6)
(stationarity condition) (unit root
5) Engle and Ng(1993) GARCH ARCH
EGARCH .
EGARCH .6) AR(p) p .
(Akaike Information Criterion : AIC)
p = 1 . AR(p) ARCH
Ljung-Box (autocorrelation)
. , KOSPI
p-value = 0.96 ,
p-value = 0.00 GARCH .
8 23 2 2009
test) , .7)
AR(1)-EGARCH(1, 1)-M (1) (2) .
(1)
(2)
: (KOSPI -3 )
: (conditional variance)
(1) t (rt) t-1 (rt-1)
(t), .
(+) (-)
, ,
. (2) 1
. t (lnt) t-1 ( )
. , (fat-tail)
, t- .8)
(risk premium) .
(1) .
7) Augmented Dicky-Fuller Unit Root KOSPI () 1% ,
3 ( time trend) 5% , (KOSPI
-3 ) ( ) 1% (unit root) . 8) ,
. Jarque and Bera(1986)
(normality) , Jarque-Bera 1.2469(p-value
= 0.0000) KOSPI .
. t .
9
. (2)
EGARCH-M (asymmetry) (leverage effect)
2 (exponential) ,
(-) .
. , , ( , )
, , ( , ) ,
. t-1 , t
, (asymmetry) (leverage effect)
.
(asset pricing theory) (time varying)
, ,
. (1)
,
. 3 , ,
3 , 4 .
2. EGARCH-M
( ) () AR(1)-
EGARCH(1, 1)-M .9)
.
(3)
9) (state)
(Markov regime switching model) .
. (Markov
regime switching model)
, (state)
. ,
, (ex-post)
.
, .
10 23 2 2009
(4)
,
(3) , (constant term, )
(volatility term, ) . (, )
(volatility feedback), (risk averseness)
. (4) ()
(asymmetric volatility term, ) . ,
() (/) , .
Kim and Lee(2008) / ()
, .
() (boom) 3 , 3
1 , 0 . ()
(recession) 3 , 3 1 ,
0 . ( ) ,
.
.
: , ( = 1, = 0)
: 3 ( 3 = 1, = 0)
: 3 ( 3 = 1, = 0)
AR(1)-EGARCH(1, 1)-M (3)
(4) .
(3)
11
(4)
3
. , -
1 , 3
.
3 ,
3
. 2(6)
3(1)
.
.
1.
KOSPI 3
1 .
. 3
3
(risk-free) .10)
(1995 52008 12)
. -0.0017%(), 8.0951%()
.
10) 1 Treasury Bill . Treasury
Bill 1 . 3
.
12 23 2 2009
(non-normality) . (skewness) -0.0715 (long tail),
3.7325 (kurtosis) .
KOSPI Return(%, 1995. 52008. 12)
This figure shows dynamics of the representative Korean stock market index(or KOSPI) return from May
1995 to December 2008 on monthly basis. The data has been retrieved from Korea Exchange data archive.
-. 3
-. 2
-. 1
. 0
. 1
. 2
. 3
1 9 9 6 1 9 9 8 2 00 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8
3-Year Maturity Koran Government Bond Return(%, 1995. 52008. 12)
This figure shows dynamics of the 3-year maturity Korean government bond return from May 1995
to December 2008 on monthly basis. The data has been retrieved from Bank of Korea data archive.
. 0 0 0
.0 02
.0 04
.0 06
.0 08
.0 10
.0 12
.0 14
.0 16
1996 1998 2000 2002 2004 2006 2008
13
Excess Stock Return(%, 1995. 52008. 12)
This figure shows dynamics of excess stock return(KOSPI return-3-year maturity Korean government
bond return) from May 1995 to December 2008 on monthly basis. The data has been calculated by
author from the data retrieved from Bank of Korea and Korea Exchange data archive.
- . 3
- . 2
- . 1
. 0
. 1
. 2
. 3
1 9 9 6 1 9 9 8 2 00 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8
Statistic Summary of Excess Stock Return(KOSPI return-3-year maturity
Korean Government Bond Return)(1995. 52008. 12)
This table summarized basic statistics of excess stock return(KOSPI return-3-year maturity Koran
government bond return) from May 1995 to December 2008 on monthly basis. Along with the whole
period, there are 4 sub-period(boom, recession, 3-month before boom starts, 3-month before recession
starts) defined with the Korea National Statistic Office's business cycle announcement.
WholePeriod
3-month before boom
startsboom
3-month before
recession startsrecession
Number of Observation
164 18 104 18 60
average(%) -0.0017 5.9787 -1.4882 -3.7027 2.8342
standard deviation(%)
8.0950 4.9057 6.8904 10.5462 8.7347
, . ,
-1.4882%, 6.8904%. , ,
2.8342%, 8.7347% .
14 23 2 2009
, .
.
, , 3 , 3
, , . 2002
,
. ,
(coincident composite index : CCI) .
, .11)
.
, ,
.
100
100 .
(trough), (peak) .
,
. .
, .
1995 5 2008 12 (business cycle) 5 (troughs)
6 (peaks) . , 3 18, 3
18 . ,
(, ) .
3 , 5.9787% ,
11)
(CI) .
. , , ,
, ,
. ,
( ), , ,
, , , 8 .
15
4.9057% .
8.0950% . 3
, -3.7027% 10.5462%
.
Business Cycle Turning Points(1995. 52008. 12)
This table lists official troughs and peaks of Korean business cycle based on the announcement of Korea
National Statistics Office from May 1995 to December 2008 on monthly and quarterly basis. The data
is retrieved from the Korea National Statistic Offices data archive.
Trough Peak
1998. 8(I)2001. 8(III)2003. 7(III)2005. 3(I)
2006. 7(III)
1996. 5(II)2000. 8(III)
2002. 11(IV)2004. 2(I)2006. 1(I)
2008. 8(III)
Note : (I) : 1/4 Quarter, (II) : 2/4 Quarter, (III) : 3/4 Quarter, (IV) : 4/4 Quarter.
Business Cycle Coincident Composite Index(CCI)(1995. 52008. 12)
This figure shows dynamics of Korean Business Cycle Coincident Composite Index(CCI) from May 1995
to December 2008 on monthly basis. The data has been retrieved from Korea National Statistic Office
data archive.
92
94
96
98
100
102
104
106
1996 1998 2000 2 00 2 2004 2006 2008
16 23 2 2009
,
, . (-)
, (+) (+) ,
(-) . 6.8904% , 4.9057%
, 8.7347% , 10.5462% .
.
Excess Stock Return and Business Cycle(%, 1995. 52008. 12)
This figure shows dynamics of excess stock return(KOSPI return-3-year maturity Korean government bond
return) from May 1995 to December 2008 on monthly basis with business cycle changes. The gray parts
represent recession periods and the white parts represent boom period. The data has been retrieved from
Bank of Korea, Korea Exchange, and Korea National Statistics Office data archive respectively.
-.3
-.2
-.1
.0
.1
.2
.3
95 96 97 98 99 00 01 02 03 04 05 06 07
, (quarter)
, .
(frequency) , 1996 2008 50
. GARCH
t-distribution .
.
17
Excess Stock Return in the 3-month Before Boom Starts Period
(%, 1995. 52008. 12)
This figure shows dynamics of excess stock return(KOSPI return-3-year maturity Korean government bond
return) from May 1995 to December 2008 on monthly basis with business cycle changes. The gray parts
represent the 3-month before the boom periods and the white parts represent the remaining period. The
data has been retrieved from Bank of Korea, Korea Exchange, and Korea National Statistics Office data
archive respectively.
- . 3
- . 2
- . 1
. 0
. 1
. 2
. 3
9 5 9 6 9 7 9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7
Excess Stock Return in the 3-month Before Recession Starts Period
(%, 1995. 52008. 12)
This figure shows dynamics of excess stock return(KOSPI return-3-year maturity Korean government
bond return) from May 1995 to December 2008 on monthly basis with business cycle changes. The
gray parts represent the 3-month before the recession periods and the white parts represent the remaining
period. The data has been retrieved from Bank of Korea, Korea Exchange, and Korea National Statistics
Office data archive respectively.
- . 3
-. 2
-. 1
. 0
. 1
. 2
. 3
9 5 9 6 9 7 9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7
18 23 2 2009
2. AR(1)-EGARCH(1, 1)-M
AR(1)-EGARCH(1, 1)-M . 4
(, , - (d1) , 3
(d2) , 3 (d3) )
.
AR(1)-EGARCH-(1, 1)-M
() () .
() -0.0700 (-) , . ,
-0.0912 , .
AR(1)-EGARCH-(1, 1)-M (
) .
- .
() (+)
. ( )
.
. (conditional mean) (
= 1), = -0.0373 1% .
(structural break) ,
.12)
.
.
3
. 3 , ( ) 5% 0.8772
, (pre-boom) ( )
.
12) -1.4882%, 2.8342%.
19
Estimations of EGARCH-M Model with and without Business Cycle Dummy
Variable(d1)
This table summarizes estimation results of EGARCH-M with and with business cycle dummy variable
(d1). For each estimation, equations (1) and (2) are for without dummy case and (3) and (4) are for with dummy case.
EGARCH-M(Without dummy variable)
EGARCH-M(With boom-recession dummy
variable : d1)
coefficient Estimate t-value Estimate t-value
0.0061 0.3213 0.0217 0.9201
--- --- -0.0373* -2.9953
0.3425* 4.2876 0.2952* 3.4585
-0.0700 -0.2920 -0.0201 -0.0824
--- --- 0.1130 0.5813
-0.3312* -1.8211 -0.7277 -1.5243
--- --- 0.05201 0.4813
0.9254* 28.1410 0.9125* 17.2154
0.1778* 2.5073 0.4012 1.6879
-0.09142 -1.4720 -0.0601 -0.5518
--- --- -0.0001 -0.1789
Log Likelihood
197.1820 --- 199.3258 ---
Adjusted R-squared
0.1023 --- 0.1258 ---
Auto(2)Auto(6)
0.12290.0970
---0.05900.0620
---
Note : * implies significant at 5% level.
Auto(k) implies residual autocorrelation P-values.
, .
,
. 3 5.8787%
.
( ) . 3
, .
20 23 2 2009
3 (pre-boom) 1% -0.4322 .
,
.
Estimations of EGARCH-M Model with Business Cycle Dummy Variables(d2 and d3)
This table summarizes estimation results of EGARCH-M with business cycle dummy variables of (d2
and d3). The d2 is for the 3-month before the boom period and d3 is for the 3-month before the recession
period respectively. For both estimations, equations (3) and (4) show estimation specification.
EGARCH-M(3-month before boom dummy : )
EGARCH-M(3-month before recession dummy : )
coefficient Estimate t-value Estimate t-value
-0.0312* 2.1578 0.0154 1.2543
-0.0342 -0.8925 -0.0052 -0.5246
0.2992* 4.4442 0.2856* 3.8915
-0.6215* -2.8465 0.2004 0.8886
0.8772* 2.3242 -0.1356 -0.5765
-0.1351* -2.8421 -0.5886 -1.5951
-0.4934* -2.3214 0.0023 0.0022
0.9853* 185.2743 0.9612* 17.5138
-0.0683 -1.5576 0.4527* 2.5714
0.1722* 2.5675 -0.1532 -1.4281
-0.4322* -2.9689 0.0311** 1.8972
Log Likelihood
207.1409 --- 205.5146 ---
Adjusted R-squared
0.2046 --- 0.2626 ---
Auto(2)Auto(6)
0.05400.1000
---0.06800.0590
---
Note : * implies significant at 5% level.
Auto(k) implies residual autocorrelation P-values.
3
.
21
. 10% 0.0311
, .
, ( )
.
3 3
.
3 3
(asset pricing theory) .
3 164 18
. -
, Kim and Lee(2008) .
, 3 -0.1532
, .
.
3 ,
Lucas(1978) consumption asset pricing
theory . CRRA utility function,
, ( )
.13)
(5)
, , discount factor
risk premium
( ) , 3
13) Asset Pricing, Cochrane(2001) .
22 23 2 2009
( ), ( )
.
.
(
)
. Kim and
Lee(2008) Kim and Lee(2008)
, , 3
3 . ,
, , 3 , 3
.
EGARCH-M ,
.
.
Merton(1980) ()
(risk-aversion) . Kim and
Lee(2008) (procyclical)
.
, (
) .
.
.
.
.
23
, (, )
,
.
(state-dependent)
(business cycle) .
,
.
,
. Kim and Lee(2008)
,
3 .
KOSPI
, .
.
24 23 2 2009
1. , , , 10 3, 2009, 33-49.
2. , 9.11 ,
, 2002.
3. , , , 16 1, 1999, 155-170.
4. , , , 52 3, 2004, 177-207.
5. , , , 14 1, 2008, 97-117.
6. , , , 16 2, 2003, 31-65.
7. , 1995 ,
, 2007.
8. , , , 1 3, 2002, 53-96.
9. , , . 12 2, 1999, 315-340.
10. , , , , 22 2, 2005, 165-187.
11. ,
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27
< Abstract >14)
Stock Returns and Its Volatility under Business Cycles Changes :
Using Asymmetric GARCH Model
Sei-Wan Kim*
We study how three interrelated phenomena-excess stock returns
and risk relation, risk aversion, and asymmetric volatility movement-
change over business cycles in Korean stock market. In a single framework
of asymmetric GARCH in mean models, we significantly find that the risk
averseness in Korean stock market is dependent on the business cycle and
it increases before the boom periods start (i.e., precyclical risk aversion).
And also the asymmetric volatility is weakened before the boom periods
start.
In Korean stock market, while there is a general agreement about
the trade-off between risk and expected return for cross-sectional secur-
ities within a given time period, there seems to be no such an agreement
about the relation between risk and return over time. There is an extensive
empirical literature that has tried to establish the existence of such an
intertemporal tradeoff between risk and return for stock market indices.
Unfortunately, the results have been inconclusive. Related to this, recently
it has been debated whether risk aversion is state-dependent and whether
it is pro-cyclical or counter-cyclical.
In this paper, we have explored these issues using an empirical model.
We have employed a representative asymmetric GARCH-M model allowing
for potential business cycle effects to examine a time-varying inter-
temporal relation between excess return and risk using a series of business
cycle dummy variables.
Given our finding of a time-varying risk-return relation over busi-
ness cycles, we have attempted to infer its implication for time-varying
risk aversion over the business cycles.
Our findings can be summarized as follows. First, in the simple
GARCH models without allowing for the business cycle effect, the risk pre-
* Ewha Womans University, Department of Economics, 11-1 Daehyun-Dong, Seodaemun-Gu, Seoul,
Korea(Tel : 02-3277-4467, E-mail : [email protected])
28 23 2 2009
mium coefficient does not show any clear and significant relation between
risk and excess return in Korean stock market over 1995 to 2008 period.
Even though we allow for a business cycle factor (boom and recession),
the risk premium coefficient is still insignificantly changed between the
boom and recession periods. This result is quite consistent over previous
studies about Korean stock market.
However the risk premium coefficient significantly increases in the
3-month before the boom start period. Since the coefficient of volatility
in the excess mean return equation is usually characterized as measuring
the time-varying risk aversion parameter [e.g., Merton (1980)], our finding
suggests increased risk aversion in the 3-month before the boom start
period or a precyclical movement of risk aversion.
Secondly, we find that the asymmetric movement of volatility is also
state-dependent, and the intensity of it changes over business cycles.
Specifically, we find that asymmetric volatility is weakened significantly
in the 3-month before the boom start period.
Our finding of state-dependent and procyclical risk aversion helps
us understand not only the larger risk premium for a given risk in the
3-month before the boom start period but also weakened asymmetric vola-
tility during the 3-month before the boom start period, in particular by
extending Campbell and Hentschels (1992) argument, both of which are
observed based on GARCH-M models with business cycle dummies. Regard-
ing the asymmetric volatility movement, Black (1976) argues that it could
be due to an increase in leverage that occurs when the market value of
a firm declines.
However, we find that investors are strongly risk-averse during the
3-month before the boom start period. As such, investors become more
sensitive to the leverage effect, and the leverage effect hypothesis antici-
pates that asymmetric volatility will get stronger in the 3-month before
the boom start period. This prediction is not easily compatible with our
finding of weakened asymmetric volatility during the 3-month before the
boom start period.
Key words : Stock Return, Asymmetric Volatility, Risk Averseness, Business
Cycle
JEL Classification : C32, E32, G12
/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False
/Description > /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ > /FormElements false /GenerateStructure true /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles true /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /NA /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /LeaveUntagged /UseDocumentBleed false >> ]>> setdistillerparams> setpagedevice