Evaluating Market Risk Evaluating Market Risk Factors in Positive and Factors in Positive and Negative World MarketsNegative World Markets
Buhdy BokBuhdy BokFrank LiuFrank Liu
Jeff LuJeff LuBrad NewcomerBrad Newcomer
Ron YeeRon Yee
AgendaAgenda
HypothesisHypothesis OverviewOverview AnalysisAnalysis ApplicationsApplications Next StepsNext Steps
HypothesisHypothesis
Country market risk differ depending upon Country market risk differ depending upon market conditionsmarket conditions
Skewness is an important factor in Skewness is an important factor in evaluating country market riskevaluating country market risk
OverviewOverview
CAPM assumes an average beta CAPM assumes an average beta Volatility varies in different market conditionsVolatility varies in different market conditions Betas vary depending upon market conditionsBetas vary depending upon market conditions
CAPM assumes returns are normally CAPM assumes returns are normally distributeddistributed Returns are not generally symmetricalReturns are not generally symmetrical Returns typically exhibit positive or negative Returns typically exhibit positive or negative
skewness skewness
Data SourceData Source
Compared Monthly Compared Monthly Returns - Equity Markets Returns - Equity Markets from 37 Countries vs. from 37 Countries vs. World Market (MSCI World Market (MSCI Indices)Indices) 16 Developed Nations16 Developed Nations 21 Emerging Markets21 Emerging Markets
Developed Emerging MarketCountry CountryAustralia ArgentinaAustria BrazilBelgium ChileCanada ChinaDenmark ColombiaFrance GreeceGermany IndiaItaly IndonesiaJapan JordanNetherlands KoreaNorway MexicoSpain PakistanSweden PeruSwitzerland PhilippinesUK PolandUS Portugal
South_AfricaTaiwanThailandTurkeyVenezuela
Standard Deviation with Positive vs. Negative World Market Returns(Developed Countries)
-
0.0100
0.0200
0.0300
0.0400
0.0500
0.0600
0.0700
0.0800
0.0900
Austra
lia
Austri
a
Belgium
Canad
a
Denm
ark
Franc
e
Germ
any
Italy
Japa
n
Nethe
rland
s
Norway
Spain
Sweden
Switzer
land
UK US
Std Dev-
Std Dev
Std Dev+
Standard Deviation with Positive vs. Negative World Market Returns(Emerging Market Countries)
-
0.0500
0.1000
0.1500
0.2000
0.2500
Argen
tina
Brazil
Chile
China
Colom
bia
Greec
eIn
dia
Indo
nesia
Jord
an
Korea
Mex
ico
Pakist
anPer
u
Philipp
ines
Poland
Portu
gal
South
_Afri
ca
Taiwan
Thaila
nd
Turke
y
Venez
uela
Std Dev-
Std Dev
Std Dev+
Diversion from Standard CAPMDiversion from Standard CAPM
We want to split the CAPM Beta into 2 BetasWe want to split the CAPM Beta into 2 Betas BetaBeta++ when world market return is positive when world market return is positive BetaBeta-- when world market return is negative when world market return is negative
r = α + β( Rm - Rf ) + errorr = α + β( Rm - Rf ) + error
toto
r = α + βr = α + β++( Rm( Rm++ - Rf ) + β - Rf ) + β--( Rm( Rm-- - Rf ) + error - Rf ) + error
Betas with Positive vs. Negative World Market Returns(Developed Countries)
-
0.2000
0.4000
0.6000
0.8000
1.0000
1.2000
1.4000
Austra
lia
Austri
a
Belgium
Canad
a
Denm
ark
Franc
e
Germ
any
Italy
Japa
n
Nethe
rland
s
Norway
Spain
Sweden
Switzer
land
UK US
Beta-
Beta
Beta+
Confidence in Betas with Positive World Returns(Developed Countries)
-
0.2000
0.4000
0.6000
0.8000
1.0000
1.2000
1.4000
1.6000
Austra
lia
Austri
a
Belgium
Canad
a
Denm
ark
Franc
e
Germ
any
Italy
Japa
n
Nethe
rland
s
Norway
Spain
Sweden
Switzer
land
UK US
Beta
Beta+ (L95%)
Beta+
Beta+ (U95%)
Confidence in Betas with Negative World Returns(Developed Countries)
-
0.2000
0.4000
0.6000
0.8000
1.0000
1.2000
1.4000
1.6000
1.8000
Austra
lia
Austri
a
Belgium
Canad
a
Denm
ark
Franc
e
Germ
any
Italy
Japa
n
Nethe
rland
s
Norway
Spain
Sweden
Switzer
land
UK US
Beta
Beta- (L95%)
Beta-
Beta- (U95%)
Betas with Positive vs. Negative World Market Returns(Emerging Market Countries)
(1.0000)
(0.5000)
-
0.5000
1.0000
1.5000
2.0000
2.5000
3.0000
Argen
tina
Brazil
Chile
China
Colom
bia
Greec
eIn
dia
Indo
nesia
Jord
an
Korea
Mex
ico
Pakist
anPer
u
Philipp
ines
Poland
Portu
gal
South
_Afri
ca
Taiwan
Thaila
nd
Turke
y
Venez
uela
Beta-
Beta
Beta+
Confidence in Betas with Positive World Returns(Emerging Market Countries)
(2.0000)
(1.5000)
(1.0000)
(0.5000)
-
0.5000
1.0000
1.5000
2.0000
2.5000
3.0000
3.5000
Argen
tina
Brazil
Chile
China
Colom
bia
Greec
eIn
dia
Indo
nesia
Jord
an
Korea
Mex
ico
Pakist
anPer
u
Philipp
ines
Poland
Portu
gal
South
_Afri
ca
Taiwan
Thaila
nd
Turke
y
Venez
uela
Beta
Beta+ (L95%)
Beta+
Beta+ (U95%)
Confidence in Betas with Negative World Returns(Emerging Market Countries)
(2.0000)
(1.0000)
-
1.0000
2.0000
3.0000
4.0000
5.0000
Argen
tina
Brazil
Chile
China
Colom
bia
Greec
eIn
dia
Indo
nesia
Jord
an
Korea
Mex
ico
Pakist
anPer
u
Philipp
ines
Poland
Portu
gal
South
_Afri
ca
Taiwan
Thaila
nd
Turke
y
Venez
uela
Beta
Beta- (L95%)
Beta-
Beta- (U95%)
Coskewness RegressionCoskewness Regression
Coskewness: The amount of skewness Coskewness: The amount of skewness that an asset adds to the diversified that an asset adds to the diversified portfolio (systematic skewness)portfolio (systematic skewness)
r = r = αα + β + β11( R( RM M ) + β) + β22( R( RM M ))2 2 + error+ error
Beta and Coskew Coefficient Analysis(Developed Countries)
(4.0000)
(3.0000)
(2.0000)
(1.0000)
-
1.0000
2.0000
3.0000
Austra
lia
Austri
a
Belgium
Canad
a
Denm
ark
Franc
e
Germ
any
Italy
Japa
n
Nethe
rland
s
Norway
Spain
Sweden
Switzer
land
UK US Beta
Coskew
Beta and Coskew Coefficient Analysis(Emerging Market Countries)
(14.0000)
(12.0000)
(10.0000)
(8.0000)
(6.0000)
(4.0000)
(2.0000)
-
2.0000
4.0000
Argen
tina
Brazil
Chile
China
Colom
bia
Greec
eIn
dia
Indo
nesia
Jord
an
Korea
Mex
ico
Pakist
anPer
u
Philipp
ines
Poland
Portu
gal
South
_Afri
ca
Taiwan
Thaila
nd
Turke
y
Venez
uela
Beta
Coskew
Application of the ModelApplication of the Model
Results demonstrate the significance of Results demonstrate the significance of separate betas for up/down marketsseparate betas for up/down markets
A simple, intuitive refinement of the CAPMA simple, intuitive refinement of the CAPM Incorporating this concept into tactical Incorporating this concept into tactical
allocation decisions will generate excess allocation decisions will generate excess returnsreturns
Application of the ModelApplication of the Model
Requires a predictive model to forecast Requires a predictive model to forecast up/down marketsup/down markets
New procedure:New procedure:1.1. Create a predictive model to forecast +/- Create a predictive model to forecast +/-
market signalsmarket signals
2.2. Calculate the appropriate correlation matrixCalculate the appropriate correlation matrix
3.3. Run optimization model (either up/down)Run optimization model (either up/down)
4.4. Use output to determine asset allocationsUse output to determine asset allocations
Application of the ModelApplication of the Model
Mean - SD Frontiers
-4.00%
-3.00%
-2.00%
-1.00%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
2.00% 3.00% 4.00% 5.00% 6.00% 7.00%
Standard Deviation
Exp
ecte
d R
etu
rn
Traditional Frontier Upmarket frontier Downmarket Frontier
Application of the ModelApplication of the Model
One Beta Model Two Beta Model Two Beta ModelUp- & Down- Markets Up-Market Down-Market
% weighting:
Australia 4.80% 18.96% 4.77%
Austria 28.33% -2.25% 50.00%
Germany -4.73% 24.62% -12.72%
Japan 22.86% 28.39% 16.02%
Spain 0.90% 6.44% 13.72%
Sweden 29.80% 16.76% 7.04%
UK 18.04% 7.08% 21.17%
Total 100.00% 100.00% 100.00%
Portfolio Mean 1.08% 3.57% -1.79%Portfolio SD 4.63% 3.30% 4.46%
Next StepsNext Steps
Run an out-of-sample test of the modelRun an out-of-sample test of the model Parse market risk over more bucketsParse market risk over more buckets Examine performance of market risk factor Examine performance of market risk factor
using different parsing criteriausing different parsing criteria e.g., recession vs. expansione.g., recession vs. expansion
Goal: create a more accurate pricing Goal: create a more accurate pricing model that allows the market risk factor to model that allows the market risk factor to be more dynamic over a range of market be more dynamic over a range of market conditionsconditions
