csv analysis - qwafafew
TRANSCRIPT
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Jose Menchero
Global Cross-Sectional
Volatility Analysis
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2009. All rights reserved.
Outline
Global Factor Model
Industry versus Country
Diversification Potential, Correlation, and MAD
Regional and Size Differences
Cross-Sectional Volatility (CSV) Analysis
Why is CSV important?
CSV Factor Decomposition
Empirical Results: Styles, Industries, Countries
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Global Factor Model
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Global Factor Model
Model derived from Barra Global Equity Model (GEM2):
1 World factor
Country factors with (0,1) exposure
24 Industry Groups (GICS) with (0,1) exposure
8 style factors (derived from GEM2)
Estimate factor returns by regression:
4
n
s
sns
i
ini
c
cncwn ufXfXfXfr
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Factor Models for Study
Build separate factor models for each region:
48 countries in MSCI ACWI IMI
24 emerging markets in MSCI ACWI IMI
16 countries in MSCI Developed Europe (ACWI IMI)
Use global-relative standardization for style factors
Estimate models using cap-weighted (WLS) and equal-
weighted (OLS) regression
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Estimating Factor Returns
6
is the weight of stock n in factor portfolio k
n
s
sns
i
ini
c
cncwn ufXfXfXfr
nnknk rf Pure factor returns
Constraint: 0c c
c
w f Cap-weighted country factor returnssum to zero
Constraint: 0i ii
w f Cap-weighted industry factor returnssum to zero
kn
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Interpreting Factor Portfolios
Pure country factor portfolios go long the country and go
short the World; they have zero industry exposure
Pure industry factor portfolios go long the industry and go
short the World; they have zero country exposure
Pure style factor portfolios have unit exposure to the style
and zero exposure to all other factors
Adding World factor to country (industry) factor creates
100% net-long factor with neutral industry (country)
exposures
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Pure Pure Pure Pure PureMarket World Japan US Auto Volatility
Segment Factor Factor Factor Factor Factor
World (Net) 100.00 0.00 0.00 0.00 0.00
Long 100.00 109.75 66.03 128.46 62.32
Short 0.00 -109.75 -66.03 -128.46 -62.32
Japan (Net) 10.72 89.28 -10.72 0.00 0.00
Long 10.72 89.28 0.35 45.98 5.76Short 0.00 0.00 -11.07 -45.98 -5.76
US (Net) 35.42 -35.42 64.58 0.00 0.00
Long 35.42 6.31 64.64 20.30 22.91
Short 0.00 -41.73 -0.06 -20.30 -22.91
Auto (Net) 2.41 0.00 0.00 97.59 0.00
Long 2.41 6.71 0.84 97.59 1.29
Short 0.00 -6.71 -0.84 0.00 -1.29Japan Auto (Net) 1.15 6.71 -0.47 45.98 0.16
Long 1.15 6.71 0.09 45.98 0.41
Short 0.00 0.00 -0.56 0.00 -0.25
US Auto (Net) 0.18 -0.90 0.55 8.18 0.45
Long 0.18 0.00 0.55 8.18 0.46
Short 0.00 -0.90 0.00 0.00 0.00
Example of Pure Factor Portfolios (6-30-2009)
Country factorshave zero
exposure to
industries.
Industry factors
have zeroexposure to
countries.
Adding World
factor to country
factors produces100% net-long
portfolio in a single
country, with
neutral industry
exposures
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Industry vs Country
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The Algebra of Country/Industry Risk
10
wf (return of World factor)
kf (return of long/short country/industry factor)
return of net long country/industry factork w kf f f
1/22 2
,2k w k w k k w Volatility of net long
country/industry factor
World factor can be added to country (industry) factor to create
100% net long factor with neutral industry (country) exposure
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The Geometry of Country/Industry Risk
11
k k
kk
w
2 2 2
,2k w k w k k w Variance of net long factor
cosk k
cosk k
Correlation of long/short factor with World
Correlation of net long factor with World
kAs decreases, net longfactor becomes more
correlated with the World
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Diversification Potential (DP) and Correlation
Diversification Potential measures volatility reduction that canbe achieved by investing in the World portfolio rather thanthe country factor or industry factor
Use either equal-weighted or regression-weighted averages
12
kk
w
DP
k
k
k w
DP w
DiversificationPotential
k k
k
w Mean correlation between countriesor industries and the World
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DP and Correlation for World (48 Countries)
13
Countries dominated
from 1997-1999
Industries dominated
from 2000-2002
Overall, the two effects
are comparable strength
DPwas high during
internet bubble period
DP is now at an all-time
low
Year
1997 1999 2001 2003 2005 2007 2009
Value
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Countries (World)Industries (World)
DiversificationPotential
Correlation
Cap-weighted Results
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DP and Correlation for EM (24 Countries)
For emerging markets,
country effects always
dominate industries
Even before Oct 2008,DPseemed to be in
secular decline
DP is now at an all-time
low
14
Year
1997 1999 2001 2003 2005 2007 2009
Value
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Countries (EM)Industries (EM)
DiversificationPotential
Correlation
Cap-weighted Results
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DP and Correlation for Dev. Europe (16 Countries)
For developed Europe,
industry effects clearly
dominate countries
Industry diversificationwas particularly strong
during internet bubble
15
Year
1997 1999 2001 2003 2005 2007 2009
Value
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Countries (Euro 16)Industries (Euro 16)
DiversificationPotential
Correlation
Cap-weighted Results
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Diversification Potential: Empirical Results
Period: Jan-97 to Jul-09, Cap-Weighted Regression
Industries dominate countries in Europe
Countries dominate industries in emerging markets
Country DPincreases for equal-weighted case due to
effect of highly volatile small countries
16
Country (Cap Weighted) (Equal Weighted)
Scheme Countries Industries Countries Industries
48 ACWI 1.21 1.19 1.68 1.18
16 Europe 1.11 1.22 1.22 1.26
24 Emerging 1.41 1.17 1.54 1.21
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Diversification Potential: Small-cap vs Large-cap
Sample period: Jan-97 to Jul-09 (151 months)
OLS probes small-cap stocks, WLS probes large-caps
Countries dominate industries when using OLS regression
Country effects remain strong for small-cap stocks
Industry effects are weaker at the small-cap level
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Country Regression (Regression Weighted)
Scheme Scheme Countries Industries
48 ACWI WLS 1.21 1.19
48 ACWI OLS 1.38 1.09
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World Volatility: Cap-weighted vs Equal-weighted
Volatility of World
portfolio is largely
insensitive to stock-
weighting scheme
18
Year
1997 1999 2001 2003 2005 2007 2009
WorldFactorVo
latility
0
5
10
15
20
25
30
35
40
45
Cap Weighted (WLS)
Equal Weighted (OLS)
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Volatility Ratio of OLS-to-WLS (48 Countries)
Country factors retain
strength in small-cap
segment
Industry factors weaken
in the small-cap regime
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Year
1997 1999 2001 2003 2005 2007 2009
V
olatilityRatio(OLS/WLS)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Countries (OLS/WLS)
Industries (OLS/WLS)
(OLS)
(WLS)
kk
k
VR
1k
k
VR VRK
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Mean Absolute Deviation (MAD) Measure
MAD measures the cap-weighted active return from
tactical allocation to the segment with perfect foresight
Compute rolling 12-month average
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( ) k kk C
MAD C w f
( ) k kk I
MAD I w f
Mean Absolute Deviation, Countries
Mean Absolute Deviation, Industries
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MAD for World (48-Country Model)
Use 12-month rolling
average
Countries dominate prior to1999
Industries dominate from
2000-2003
Industries and countries
are comparable since 2003
21
Year
1997 1999 2001 2003 2005 2007 2009
MAD(percentmonthly)
0
1
2
3
4
5
Countries (World)
Industries (World)
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MAD for Developed Europe (16-Country Model)
At start of period,
industries and countries
were comparable
Industries have stronglydominated countries in
Europe since 1998
22
Year
1997 1999 2001 2003 2005 2007 2009
MAD(percentmo
nthly)
0
1
2
3
4
5
Countries (Dev. Europe)
Industries (Dev. Europe)
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MAD for Emerging Markets (24-Country Model)
Country effects were
strongest in 1998-1999
For Emerging Markets,
countries stronglydominate industries over
entire sample period
23
Year
1997 1999 2001 2003 2005 2007 2009
MAD(percentmo
nthly)
0
1
2
3
4
5
6
7
8
Countries (EM)
Industries (EM)
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Cross-Sectional Volatility
(CSV) Analysis
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What is Cross-Sectional Volatility (CSV)?
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Return (percent)
-100 -80 -60 -40 -20 0 20 40 60 80 100
Count
0
200
400
600
800
1000
1200
MSCI All Country
World Investable
Market Index(ACWI IMI)
October 2008:
Mean Return: -23%
CSV: 18%
Return Distribution
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Why is CSV Important?
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CSV measures the opportunity for active management:
Aggressiveness Opportunity Skill
AA n nn
R w r R Active Return
22
22
1( )
( )
A
n nA nA n n
An nn n
n n
w r RR N w r R
N w r R
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Active Weight (Percent)
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
RelativeReturn(Percent)
-80
-60
-40
-20
0
20
40
60
80
100
120
Example: October 2008
27
Portfolio: MSCI World ValueBenchmark: MSCI ACWI IMI
Portfolio Return -15.80%Benchmark Return -17.36%
Aggressiveness 5.11
Opportunity (CSV) 17.80%
Skill 0.0172
Active Return 1.56%
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A Brief Digression: Risk Attribution
Identifies three drivers of time series volatility
Risk contributions are intuitive and fully additive
Aligns risk attribution model with investment process
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t m mt
m
R x g Return Attribution, Period t
mx Source Exposure;
,m m mm
R x g g R Risk Attributionx-sigma-rho formula
mtg Source Return
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Exact CSV Decomposition
Identifies three drivers of cross-sectional volatility
Volatility contributions are intuitive and fully additive
CSV can be attributed to individual factors!
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n n nr u Return Decomposition (factor vs specific)
Explained CS Volatility
x-sigma-rho formula ( ) ,k k k
k
f X X
n k nk
k
f X Linear Factor Structure
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Approximate CSV Decomposition
Collinearity among GEM2 factors is typically small
Reasonable and useful approximation:
Contribution to explained CSV is roughly proportional tothe squared factor return and the variance of factor
exposures
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22( ) k
k
k
Xf
No-collinearity
Approximation
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Percent in Segment (p)
0 10 20 30 40 50
VarianceofExposures
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Variance of Factor Exposures
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Style factors have cross-
sectional variance of 1
Country & Industry factors have
maximum CS variance of 0.25
2var( ) /100kX p p
TypicalCS variance of Country
& Industry factors may be 0.02
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Explained vs Total CSV (12m Rolling Average)
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Year
1997 1999 2001 2003 2005 2007 2009
MonthlyCSV(Percent)
0
2
4
6
8
10
12
14
16
Explained CSV
Total CSV
Wide variation in
CSV over time:
CSV peaks above
14% in 2000
CSV dips below 7%
from 2005-2007
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Explained-to-Total CSV Ratio
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Year
1997 1999 2001 2003 2005 2007 2009
CSVRatio(rolling1
2maverage)
0.3
0.4
0.5
0.6
0.7
CSV Ratio (Explained/Total)
CSV Ratio is
remarkably stable
about 0.5
Square of CSV
ratio is the Relative
R-squared of model
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Explained CSV Attributed by Factor Type
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Year
1997 1999 2001 2003 2005 2007 2009
MonthlyCSV(Percent)
0
2
4
6
8
10
Explained CSV
Countries
Industries
Styles
Contributions to
explained CSV vary
greatly over time
Countries dominate
prior to 1999
Styles dominatefrom 2000-2004
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Attribution of Styles CSV
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Year
1997 1999 2001 2003 2005 2007 2009
MonthlyCSV(Percent)
0
1
2
3
4
5
Styles
Volatility
Momentum
Volatility factor islargest contributor to
Styles CSV
In 2001, Volatility
contributes one-fourth
of total explained CSV
(about 2% of 8%):
2
2 21
48
kk
Xf
Monthly volatility of
Volatility factor
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Year
1997 1999 2001 2003 2005 2007 2009
MonthlyCSV(P
ercent)
0
1
2
3
Countries
Japan
USA
Attribution of Countries CSV
36
In 2006, Japan
contributes one-tenth of
the total explained CSV
Thats 40 bps (of 4%)
2
2 2 (0.1)4
4
k
k
Xf
Monthly volatility of
Japan factor
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Summary
CSV represents the opportunity for active management
CSV can be attributed to individual factors
Styles, countries, and industries dominate over different periods
The relative strength of countries versus industries can be
measured by the Diversification Potential (DP) or MAD
Countries dominate industries in EM, vice versa in Dev. Europe
Country factors persist in small-cap regime; industries weaken
Recent decline of DP due to increased volatility of World factor,
not decline in volatility of country or industry factors
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39
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China North 10800.852.1032 (toll free)
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Notice and Disclaimer
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