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SENIOR RESEARCH
Asset Allocation and Spillovers in Global Equity Market
Narathorn Munsuvarn
544 55649 29
Advisor: Pongsak Luangaram, Ph.D.
May 19, 2015
Senior Research Submitted in Partial Fulfillment of the Requirements
for the Bachelor of Economics
Faculty of Economics
Chulalongkorn University
Academic Year 2014
Asset Allocation and Spillovers in Global Equity Market
Narathorn Munsuvarn
Abstract
This paper attempts to explain returns and volatility spillovers in global equity market
assuming that investors allocate their global equity portfolio optimally. Measures of market
spillovers are due to Diebold and Yilmaz (2009). In addition, I calculate efficient frontiers using
expected return from the standard Black-Litterman model to get optimal equity allocation for each
country. Using data from January 1991 to January 2015 and covering 18 countries (representing
over 60 percent of total world market capitalization), the paper finds that changes in optimal asset
allocation are able to explain the global returns and volatility spillover significantly. This paper
suggests that a proper analysis of returns and volatility spillovers needs to take into account of how
investors allocate their assets from the microeconomic point of view. In addition, it is found that
the VIX index (a standard measure of investor’s fear gauge) plays an important role in explaining
change in optimal portfolios and spillover indices.
Contents
Introduction ................................................................................................................................................. 1
Literature Review ....................................................................................................................................... 3
Model ............................................................................................................................................................ 5
Spillover Measures Model ........................................................................................................................ 5
Black-Litterman Model and Efficient Frontier ......................................................................................... 7
Black-Litterman Model .................................................................................................................... 7
Efficient Frontier ............................................................................................................................ 10
Panel Regression ..................................................................................................................................... 10
Data and Sample Analysis ........................................................................................................................ 11
Data ......................................................................................................................................................... 11
Sample Analysis ...................................................................................................................................... 14
Results ........................................................................................................................................................ 15
Spillover Results ..................................................................................................................................... 15
Black-Litterman Results ......................................................................................................................... 20
Panel Regression Results ........................................................................................................................ 22
Optimal Portfolios, Spillover indices and VIX index ............................................................................. 24
Concluding Remarks ................................................................................................................................ 27
References .................................................................................................................................................. 28
Figures
Figure 1 Asset Under Management 2007-2013 ........................................................................................ 2
Figure 2 An Example of Efficient Frontier ............................................................................................ 10
Figure 3 Return and Volatility Spillover Plots from 1994 to 2014 ......................................................... 19
Figure 4 Efficient Frontiers .................................................................................................................... 21
Figure 5 Risk-Return Trade-offs under Different Monetary Policies .................................................... 21
Tables
Table 1 Calculation of Spillover Table ..................................................................................................... 7
Table 2 Global Equity Market Return Descriptive Statistics from Dec 1991- Jan 2015 ....................... 12
Table 3 Global Equity Market Volatility Descriptive Statistics from Dec 1991- Jan 2015 .................... 13
Table 4 Global Equity Market Return Spillover Table from Dec 1991- Jan 2015 ................................. 16
Table 5 Global Equity Market Volatility Spillover Table from Dec 1991- Jan 2015 ............................. 17
Table 6 Optimal Portfolio at given risk .................................................................................................. 22
Table 7 Top 5 Highest R-squared in Explaining VIX ............................................................................. 24
Table 8 Top 5 Highest Coefficient in Explaining VIX .......................................................................... 25
Table 9 Top 5 Lowest Coefficient in Explaining VIX ........................................................................... 25
Table 10 Regression Result of VIX on Spillover Indices ...................................................................... 25
Table 11 Results from Granger Causality Test of VIX and Return Spillover ...................................... 26
Table 12 Results from Granger Causality Test of VIX and Volatility Spillover .................................. 26
1
I. Introduction
Nowadays, we can see high spillover of returns and volatility and flows of fund in the
global equity market, which seems to be difficult but important to understand it. Because financial
markets are highly interconnected worldwide and, consequently, negative shocks in one country
have spilled over into other countries (Shinagawa, 2014). Recent events show that financial market
is globally dominating world economy such as in Global Financial Crisis (GFC) in U.S. or
European Sovereign Debt Crisis. Thus, understanding financial market is important and urgent.
Moreover, financial spillover can be a good measure of systemic risks, because market is fragile
when the spillover is high. This fact supports Liu and Pan (1997) finding about stronger spillover
effects after stock market crash.
From some parts of a literature review, there are many articles try to explain the spillover
effects by finding factors determining the spillover behavior. For example, Chuhan et al (1998)
uses global factors to explain portfolio flows of Latin America and Asia. In addition, some studies
use spillover effects as a factor in explaining some economic phenomenon such as Global
Financial Crisis (Longstaff, 2010), Effect of U.S. equity market on emerging market (Cheung et
al., 2010) and 1987 stock market crash (Liu, 1997).
My research topic is mainly motivated by Disyatat and Gelos (2001) and Diebold and
Yilmaz (2009). Disyatat and Gelos (2001) attempt to explain asset allocation behavior of mutual
funds in emerging market. They use Markowitz’s mean-variance optimization to explain
movement of capital flows of emerging market mutual funds. Diebold and Yilmaz (2009) construct
an intuitive quantitative measurement of interdependence of asset returns and volatilities spillover,
which allows us to see a variation in one market contributed from other markets. This paper will
take a different route from others focusing on explaining spillover returns and volatility using
rationality of investor through portfolio optimization because understanding spillover needs micro
foundation to show underlying mechanism behind it, not only observable things. Thus, the paper
contributes to explain the financial spillover of the global equity market using portfolio choice of
investors.
In this paper, I use daily nominal stock market indexes of 18 countries from January 1991
to January to represent global equity market. By the end of 2013, these countries worth more than
40 trillion dollars (63% of global equity market capitalization compared to 64 trillion dollars1) I
divide my methodology into three main parts. First is about spillover measures, which I follow
Diebold and Yilmaz (2009) in creating spillover index and spillover table. Calculation based on
vector autoregressive models (VAR) focusing on variance decomposition. I roll samples 50 weeks
window and collect variance in each market contributed from others in spillover table as panel
data. This represents spillover measuring in global equity market.
Second, this part is about rationality of investor. The figure below shows us about size of
asset under management of financial institution such as a mutual fund, venture capital firm, or
1 According to 2013 WFE Market Highlights report.
2
brokerage house. Financial institutions are very important players in global financial market
because they hold almost 69 trillion dollars. Due to large amount of money, financial institutions
cannot just use discretionary for investing, but they need theory or model to support their decision.
In this case, portfolio optimization model represents investor rationality. I choose Black-Litterman
model to be portfolio optimization model in this paper instead of Markowitz model because the
Markowitz model has some limitations2when using the model in practice. For example, Markowitz
model does not consider market capitalization weights, so the model often suggests high weights
in assets with low level of capitalization. Moreover, Markowitz model uses historical data to
produce a sample mean return and replace the expected return only with the sample mean return,
which can contributes greatly to the error maximization.
Figure 1 Asset Under Management 2007-2013
The last part of methodology is about using panel regression to see if optimal portfolio is
able to explain the spillover returns and volatility of the global equity market.
As a result, an updated version of spillovers table calculating from December 1991 to
January 2015 indicates that U.S. market is more powerful in term of generating return and volatility
spillover since 2008. Return spillover from U.S. market increases by 43%, and volatility spillover
increases by 299% compared to a result of Diebold and Yilmaz in 2009 that calculate spillovers
table from 1992-2007. Moreover, the table also tells us about a higher volatility spillover after the
Global Financial Crisis (GFC). After GFC, amount of volatility spillover contribution increases by
34.8% after the crisis. This changing interprets that equity markets are more interdependence
during and after crisis. An optimal portfolio at risk 5% is the best portfolio in explaining the
2 See literature review for more detail
Figure 1 Asset Under Management 2007-2013 according to BCG Global Asset Management Market Sizing Database, 2014.
3
spillover effect of both return and volatility with 𝑅2 0.419652 and 0.508823 respectively. The
optimal portfolios at others level of risk are also able to explain the spillover effect but low level
of optimal portfolio is better at explanation. Although investors are rational and optimize their
portfolio, it still generates volatility across countries. Interestingly, VIX index plays an important
role between optimal weight and the volatility spillover.
This paper contains six sections. First section is an introduction. The second one is the
literature review. The third section is about deriving the model used in this paper. The forth section
is about data and samples analysis. Next is a result section. The last one is concluding remarks.
II. Literature Review
Since I cannot find any study that use both of Spillover Model and Black-Litterman model
in one paper, I divide the literature review into two main sections. The first section is about
spillover effect analysis containing various studies and model about spillover effects. The next
section is an overview of asset allocation model consists of two asset allocation models, which are
Markowitz’s mean-variance optimization model and Black-Litterman asset allocation model.
After all sections, I finish the literature review with some interesting empirical studies related to
this paper.
There are many dimensions of analysis about spillover effects. Most of studies use spillover
analysis to explain some economic phenomenon especially on equity market such as Global
Financial Crisis (Longstaff, 2010), Effect of U.S. equity market on emerging market (Cheung et
al., 2010) and 1987 stock market crash (Liu, 1997). The previous studies found that volatility of
stock returns is time–varying (Ross, 1989). Liu and Pan (1997) shows that return and volatility
spillovers from the U.S. market to other national stock markets is statistically significant, and the
U.S. market is more influential than the Japanese market in spilling over return and volatility to
the Asian markets. Moreover, there are stronger spillover effects after stock market crash. Another
aspect of spillover effects analysis is to quantify the spillover effect of exchange rate. According
to Mattoo et al (2010), they found that depreciation of the renminbi creates significantly negative
spillover effects on China’s competing exporting countries. They also found that spillover effect
is greater if products are homogenous than differentiated one. Another one is from Diebold and
Yilmaz (2008) which is about trends and bursts in spillovers. They found a divergent behavior in
the return and volatility spillovers. Return spillovers show a trend without bursts but vice versa for
volatility spillovers.
In construction of the model, various methods have been used to capture the spillover
effects. First, Liu and Pan (1997) use a two–stage GARCH model proposed by Engle (1982) to
test the return and volatility spillover effects from the U.S. and Japan to four Asian stock markets.
Furthermore, Kim and Whang (2012) develops the model by using value at risk as a measure of
risks in stock markets for testing a spillover effect of financial risks from a market to other markets.
They use the Threshold-GARCH (TGARCH) model to test if an extreme downside movement in
a market causes similar movement in another market. Another method shows in Diebold and
Yilmaz (2009). They propose an intuitive quantitative measurement of interdependence of asset
4
returns and volatilities spillover. For more in detail, they base their measurement of spillover
effects on vector autoregressive (VAR) models focusing on variance decompositions. In addition,
there is a study try to use of both GARCH model and VAR model on their work. Abidin et al
(2015) use VAR model to measure return spillover and use GARCH model to measure volatility
spillover. All above is an overview of analysis and modeling which is studying about the spillover
effects nowadays.
About an overview of asset allocation model, there are two of the widely used theories,
which are Markowitz’s mean-variance optimization model and Black-Litterman asset allocation
model. Let start with Markowitz model first, Harry Markowitz took some advice from stockbroker
and developed a theory when he was graduate student. That theory became a foundation of
financial economics and revolutionized investment practice (Kaplan, 1998). His work earned him
a share of 1990 Nobel Prize in Economics. Markowitz states that his work on portfolio theory
considers how an optimizing investor would behave3. He derived the expected return for a portfolio
of assets and an expected risk measure. In his theory, He illustrate that the variance of return is an
intuitive measure of portfolio risk under some reasonable assumptions, and he derives the formulas
for computing the variance of a portfolio. The combinations of the highest expected return at each
level of the expected risk are plotted as a frontier which now known as the efficient frontier (Kamil
et al, 2006). However, Markowitz’ mean-variance model has several problems arise when using
the model in practice (Mankert, 2006). Among the several problems, two of the most important
problems in using the model are reviewed here. First problem is about market capitalization
weights of asset. This is because the model does not consider market capitalization weights. It
means that if asset A has low level of capitalization but high expected returns, the model can
suggest a high portfolio weight. This is quite a serious problem, especially with a shorting
constraint (assume that investors cannot make a short selling of asset). The model then often
suggests high weights in assets with low level of capitalization (Michaud, 1989). Another problem
is that using historical data to produce a sample mean return and replace the expected return only
with the sample mean return can contributes greatly to the error maximization of the Markowitz
mean-variance model (Mankert, 2006).
From the problems above, Black-Litterman Model is a solution. As we can see that the
Markowitz model has problems when use it in practice, these problems motivate Fisher Black and
Robert Litterman to develop a more practicable model of portfolio choice. In 1992, Black and
Litter proposed their portfolio model with a new way of estimating expected returns developing
from the Markowitz model. Black-Litterman Model is known as a completely new portfolio model
(Mankert, 2006). In fact, the only difference of two models is the estimation of expected return of
asset. To calculate expected returns, Black-Litterman Model uses the Bayesian approach combines
investor's views with the mean return estimation4.
In the empirical studies about asset allocation topic, Disyatat and Gelos (2001) explain
asset allocation behavior of mutual funds in emerging market by using mean variance
optimization. The outcome is that a simple mean variance optimization has explanatory power
3 From Nobel Prize lecture by Markowitz in 1990 at Baruch College, The City University of New York, New York, USA 4 See the model part for more detail about expected return estimation
5
especially for high capitalization countries. Moreover, they found that fund managers’ view about
future returns implicit in weights they invest in each country because of a strong relationship
between weights and actual future returns. Another empirical work is Chuhan et al (1998) who use
global factors in explaining portfolio flows of Latin America and Asia. They found that global
factors like US interest rates and US industrial activity are able to explain portfolio flows. In
addition, Equity flows are more sensitive than bond flows to global factors. However, country-
specific factors still have more explanatory power than the global one.
III. Model
The model construction divides to three parts. First, I follow Spillover Measures Model
(SOM model) of Francis Diebold and Kamil Yilmaz (2009) to measure return and volatility
spillovers of the global equity market. Second, I use expected return calculation method from the
Canonical Black-Litterman Model modified by Jay Walters (2007) and Efficient Frontier to
compute optimal weights, which are a representative of investor behavior at given risks. Last, I
use Panel Regression to see if the optimal weight is able to explain return and volatility spillover.
Spillover Measures Model (SOM model)
Francis Diebold and Kamil Yilmaz (2009) create the spillover index and table. The
calculation of it based on vector autoregressive models (VAR) focusing on variance
decomposition. In this part, I will show a calculation with formulas similar to that used in Diebold
and Yilmaz (2009) in the case of two variables. For the case of more than two variables, you can
just add more inputs into a vector 𝑥𝑡 showing below.
First, they start with a covariance stationary first-order two-variable VAR
𝑥𝑡 = Φ𝑥𝑡−1 + 휀𝑡 (1)
𝑥𝑡 is (𝑥1,𝑡, 𝑥2,𝑡) can be a vector of stock returns or a vector of stock return volatilities.
Φ a 2x2 parameter matrix.
휀𝑡 an error term
With stationary covariance, the moving average representation of the VAR is
𝑥𝑡 = Θ(𝐿) 휀𝑡, (2)
, where Θ(𝐿) = (𝐼 − Θ𝐿)−1
6
Now I can rewrite the moving average coefficient representation as
𝑥𝑡 = A(𝐿) 𝑢𝑡 (3)
, where A(𝐿) = Θ(𝐿)𝑄−1 , 𝑢𝑡 = 𝑄𝑡휀𝑡, 𝐸(𝑢𝑡𝑢𝑡′ ) and 𝑄−1 is the unique lower-triangular Cholesky
factor of the covariance matrix of 휀𝑡
With one-step ahead forecasting, the optimal forecast is
𝑥𝑡+1,𝑡 = Φ𝑥𝑡 (4)
Thus, the one-step-ahead vector error is
𝑒𝑡+1,𝑡 = 𝑥𝑡+1 − 𝑥𝑡+1,𝑡 = 𝐴0𝑢𝑡+1 = [𝑎0,11 𝑎0,12
𝑎0,21 𝑎0,22] [
𝑢1,𝑡+1
𝑢2,𝑡+1] (5)
𝐸(𝑒𝑡+1,𝑡𝑒′𝑡+1,𝑡) = 𝐴0𝐴′0 (6)
Equation (5) shows a correlation matrix [𝑎0,11 𝑎0,12
𝑎0,21 𝑎0,22], and the variance of the 1-step-
ahead error in forecasting 𝑥1𝑡 is 𝑎0,112 + 𝑎0,12
2 . Now, we can see that 𝑎0,122 is a part of variance
of 𝑥1𝑡 caused by shocks in 𝑥2𝑡. Thus, we can calculate the spillover index by using the variance
of the 1-step-ahead error in forecasting as following
𝑎0,122 +𝑎0,21
2
𝑎0,112 +𝑎0,12
2 +𝑎0,212 +𝑎0,22
2 ×100 (7)
Equation (7) is the spillover index calculated by total spillover 𝑎0,122 + 𝑎0,21
2 relative to total
forecast error variation 𝑎0,112 + 𝑎0,12
2 + 𝑎0,212 + 𝑎0,22
2 . Moreover, we can build the spillover table
with variance decomposition
7
Table 1 Calculation of Spillover Table
𝑥1𝑡 𝑥2𝑡 Contribution
From Others
𝑥1𝑡 𝑎0,11
2
𝑎0,112 +𝑎0,12
2 +𝑎0,212 +𝑎0,22
2 𝑎0,12
2
𝑎0,112 + 𝑎0,12
2 + 𝑎0,212 + 𝑎0,22
2 𝑎0,12
2
𝑎0,112 + 𝑎0,12
2 + 𝑎0,212 + 𝑎0,22
2
𝑥2𝑡 𝑎0,21
2
𝑎0,112 + 𝑎0,12
2 + 𝑎0,212 + 𝑎0,22
2 𝑎0,22
2
𝑎0,112 + 𝑎0,12
2 + 𝑎0,212 + 𝑎0,22
2 𝑎0,21
2
𝑎0,112 + 𝑎0,12
2 + 𝑎0,212 + 𝑎0,22
2
Contribution
To Others
𝑎0,212
𝑎0,112 + 𝑎0,12
2 + 𝑎0,212 + 𝑎0,22
2 𝑎0,12
2
𝑎0,112 + 𝑎0,12
2 + 𝑎0,212 + 𝑎0,22
2 𝑎0,12
2 + 𝑎0,212
𝑎0,112 + 𝑎0,12
2 + 𝑎0,212 + 𝑎0,22
2
Thus, in a column of a contribution from other, we can see a part variation in a variable
contributed by other variables. It is a summation of contribution from all other variable excluding
itself (in case of more than two variables). In this paper, I use this contribution to measure return
and volatility spillovers of the global equity market.
Black-Litterman Model and Efficient Frontier
Black-Litterman Model
Starting with normally distributed expected returns
𝑟~𝑁(𝜇, Σ) (8)
The goal of the Black-Litterman model is to model these expected returns, which assumes
to have normally distribution with mean μ and variance Σ.
𝜇~𝑁(𝜋, Σ𝜋)
μ is the unknown mean return. π is the estimated mean called ‘prior return’ and Σ𝜋 is the
variance of the unknown mean.
𝜇 = 𝜋 + 𝜖 (9)
𝜖 is an distance between an actual mean and the estimated mean return
8
From above assumption, we can see that the prior return is varying around actual mean
return with distance 𝜖
Σ𝑟 = Σ + Σ𝜋 (10)
The equation (10) shows that variance of estimated return can increase from two reasons.
First, the actual return has more volatility. Second, it increases from more error of estimation.
Thus, the Black-Litterman model expected return is
𝑟~𝑁(𝜋, Σ𝑟) (11)
From this section, I will use the Quadratic Utility function, CAPM, and unconstrained
mean-variance follows Jay Walters (2007)
Deriving the equations for 'reverse optimization' starting from the quadratic utility function
𝑈 = 𝑤𝑡𝜋 −𝛿
2𝑤𝑡Σw (12)
U Investors utility, this is the objective function during Mean-Variance Optimization.
w Vector of weights invested in each asset
𝜋 Vector of equilibrium excess returns for each asset
δ Risk aversion parameter
Σ Covariance matrix of the excess returns for the assets
Now, maximize the investor utility function with respect to the weights (w)
𝑑𝑈
𝑑𝑤= 𝜋 − 𝛿Σw = 0 (13)
After that, solve for an optimal vector of equilibrium excess returns for each asset.
𝜋 = 𝛿Σw (14)
9
Apply Bayes Theorem to the Estimation Model
In the Black-Litterman model, there are two distributions combining into the posterior
distribution. The first one is the prior distribution and the second is the conditional distribution
from the investor's views.
The prior distribution depends on the equilibrium implied excess returns. The Black-
Litterman model assumes the proportional covariance of the prior estimate to the covariance of
the actual returns, but the two quantities are independent. The parameter τ will be the constant of
proportionality. Given that assumption, Σπ= τΣ, then the prior distribution P (A) for the Black-
Litterman model can be written as
𝑃(𝐴) = 𝑁~(𝜋, 𝜏𝛴) (15)
The conditional distribution from the investor's views can be written as
𝑃(𝐵|𝐴) = 𝑁~(𝑃−1𝑄, [𝑃𝑡𝛺−1𝑃]−1) (16)
P Investor’s view
Q Vector of the returns for each view
𝛺 The diagonal covariance of the views
Now, apply Bayes Theorem, and we have the posterior distribution ( 𝑃(𝐵|𝐴)) of asset
returns and the posterior return (�̂�) as the following5.
𝑃(𝐵|𝐴) = 𝑁~([(𝜏𝛴)−1𝜋 + 𝑃𝑡𝛺−1𝑄][(𝜏𝛴)−1 + 𝑃𝑡𝛺−1𝑃]−1, [(𝜏𝛴)−1 + 𝑃𝑡𝛺−1𝑃]−1 (17)
�̂� = 𝜋 + 𝜏𝛴𝑃𝑡[𝑃𝜏𝛴𝑃𝑡 + 𝛺]−1[𝑄 − 𝑃𝜋] (18)
I have made some assumptions about an investor’s view and parameters here. First, I
assume investor’s view equal to one (P=1) and assume Q to be a vector of 0.05 for neutral view of
investor. Second, I assume the parameter τ to be 0.05 following He and Litterman (1999). Last,
for 𝛺, I follow He and Litterman (1999) assume 𝛺 to be proportional to the variance of the prior
return (𝛺 = 𝑑𝑖𝑎𝑔(𝑃𝜏𝛴𝑃𝑡))
5 See Jay Walters (2007) for a full deriving of Bayes Theorem.
10
Efficient Frontier
Efficient Frontier is a set of optimal portfolios that offers the highest expected return for a
defined level of risk or the lowest risk for a given level of expected return. From the Black-
Litterman Model, we have the expected return, which is able to plot the Efficient Frontier as
showing below in figure 2
Figure 2 An Example of Efficient Frontier
With given risk, we have a portfolios choice containing a set of optimal weight investing in
each asset. Thus, we have investor behavior at many rates of risk from Efficient Frontier. Note that
we have return and volatility spillovers of the global equity market from the first part, and we have
optimal portfolios choices of investor in this part. In the next part, we will run a panel regression
to see if optimal portfolios choice from the model is able to explain return and volatility spillovers
of the global equity market.
Panel Regression
For a brief overview of Panel Regression, it is a method in econometrics dealing with two-
dimensional (cross sectional/times series) data. The data are collected over time and over the same
individuals and then a regression is run over these two dimensions. There are three types of panel
regression, which are a pooled regression model, a random effect model and a fixed effect model.
I will skip the first two models because in this paper, I choose the fixed effect model from the
following reasons. First, I assume that something within the individual may affect or bias the
dependent variables and I need to control for this. Second, I am only interesting in analyzing the
impact of variables that vary over time so the fixed effect model is a good answer. Last reason is
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
10.00%
12.00% 13.00% 14.00% 15.00% 16.00% 17.00%
Po
rtfo
lio
Ret
urn
(%
)
Portfolio Risk (%)
Efficient Frontier
11
that Hausman Test confirms the fixed effect model at low to middle level of risks. Fixed effect
model explore the relationship between independent and dependent variables within an entity
(country, person, company, etc.). Each entity has its own individual characteristics that may or
may not influence the predictor variables (for example, being a male or female could influence the
opinion toward certain issue; or the political system of a particular country could have some effect
on trade or GDP; or the business practices of a company may influence its stock price)6.
The model in this paper is very simple. The equation for the fixed effects model is
𝑌𝑖𝑡 = 𝛽1𝑥𝑡 + 𝛼𝑖 + 𝑢𝑖𝑡 (19)
Where
𝑌𝑖𝑡 A vector of dependent variable (return or volatility spillovers in this case)
𝑥𝑡 A vector of independent variable (optimal portfolios choice)
𝛽1 The coefficient for the independent variable
𝛼𝑖 n entity-specific intercepts
𝑢𝑖𝑡 An error term
Finally, we have all components of the model. In next section, I will describe about sample
data and model using in this paper.
IV. Data and Sample Analysis
Data
My data is daily nominal stock market indexes of 18 countries from January 1991 to
January 2015 and dollarize market capitalization of each country from January 2004 to January
2015 (due to limitation of accessing data in some countries), taken from Bloomberg. For the list
of countries, I follow Diebold and Yilmaz (2009) examining seven developed stock markets (for
the U.S., U.K., France, Germany, Hong Kong, Japan and Australia) and twelve emerging markets
from Asia and Latin America (Indonesia, South Korea, Malaysia, Philippines, Singapore, Taiwan,
Thailand, Argentina, Brazil, Chile, Mexico, and Turkey). However, because of data problem, I
need to cut Brazil from analysis. Thus, we have only 18 countries in the analysis.
I calculate weekly return in log index from Friday to Friday. When index data for Friday
are not available due to a holiday, I use Thursday instead. For volatility, I assume it to be fixed
within a week but vary over time. Thus, following Diebold and Yilmaz (2009), I can use weekly
6 See Panel Data Analysis Fixed and Random Effects lecture by Torres (2007) from Princeton University
12
high, low, opening and closing index obtained from daily data to estimate weekly stock return
volatility as showing below.
�̃�2 = 0.511(𝐻𝑡 − 𝐿𝑡)2 − 0.019[(𝐶𝑡 − 𝑂𝑡)(𝐻𝑡 + 𝐿𝑡 − 2𝑂𝑡) − 2(𝐻𝑡 − 𝑂𝑡)(𝐿𝑡 − 𝑂𝑡)] − 0.383(𝐶𝑡 − 𝑂𝑡)2
Where
𝐻𝑡 The highest index in a week
𝐿𝑡 The lowest index in a week
𝑂𝑡 Monday close7
𝐶𝑡 Friday close
Note that all variables is in natural logarithms when do a calculation.
After building the indices, I test both of return and volatility index with Unit Root Test to
see if the indices are stationary before running VARs in spillover calculation. The result is that
both of them are stationary at degree = 0 (at level). Test results and descriptive stat of data are
providing below
Table 2 Global Equity Market Return Descriptive Statistics from Dec 1991- Jan 2015
US UK HK FRA IND GER
Mean 0.001442 0.000939 0.001671 0.000903 0.00263 0.001628
Median 0.003236 0.002507 0.002932 0.002025 0.002964 0.004024
Max 0.121278 0.125845 0.139169 0.124321 0.192471 0.149421
Min -0.21735 -0.23632 -0.19921 -0.2505 -0.17375 -0.24347
S.D. 0.023078 0.023447 0.034037 0.029394 0.036011 0.030863
Skewness -0.94847 -0.90277 -0.40029 -0.70825 -0.04103 -0.64853
Kurtosis 9.300362 10.59596 3.028313 5.352864 2.427514 5.245828
PHI THA JAP CHL AUS KOR
Mean 0.002031 0.000786 -0.00023 0.002701 0.001181 0.000871
Median 0.002963 0.003103 0.001294 0.003078 0.002923 0.002532
Max 0.161846 0.218384 0.114496 0.14668 0.081012 0.170319
Min -0.21985 -0.26661 -0.27884 -0.21598 -0.1771 -0.22929
S.D. 0.034329 0.036706 0.030288 0.028526 0.019509 0.03852
Skewness -0.37946 -0.20918 -0.69736 -0.35092 -0.96336 -0.30809
Kurtosis 4.498278 4.36798 6.262199 4.607482 6.860882 3.27049
7 Due to problem of finding open index, I use Monday close as an open weekly index.
13
MAS SIN TW ARG MEX TUR
Mean 0.001052 0.002075 0.000785 0.003643 0.003422 0.006321
Median 0.001462 0.003094 0.003087 0.005833 0.004694 0.006207
Max 0.245786 0.18803 0.183182 0.433647 0.185786 0.329513
Min -0.19027 -0.23297 -0.16408 -0.31181 -0.17928 -0.33984
S.D. 0.028363 0.036523 0.034101 0.055701 0.034629 0.060395
Skewness 0.112523 -0.4197 -0.18539 0.419814 -0.19761 -0.04992
Kurtosis 9.77392 5.302243 2.386134 6.382205 3.353291 3.987157
Table 3 Global Equity Market Volatility Descriptive Statistics from Dec 1991- Jan 2015
US UK HK FRA IND GER
Mean 0.001305 0.000828 0.001527 0.000774 0.002558 0.001565
Median 0.003186 0.002342 0.002651 0.001949 0.002911 0.004014
Max 0.121278 0.125845 0.139169 0.124321 0.192471 0.149421
Min -0.21735 -0.23632 -0.19921 -0.2505 -0.17375 -0.24347
S.D. 0.023039 0.023456 0.034113 0.029419 0.03593 0.030841
Skewness -0.96162 -0.90194 -0.39169 -0.70588 -0.05634 -0.65332
Kurtosis 9.425823 10.656 3.012853 5.370409 2.445945 5.31445
PHI THA JAP CHL AUS KOR
Mean 0.001619 0.000477 -0.00034 0.002416 0.00108 0.000866
Median 0.002541 0.003025 0.00121 0.002974 0.002573 0.002532
Max 0.161846 0.218384 0.114496 0.14668 0.081012 0.170319
Min -0.21985 -0.26661 -0.27884 -0.21598 -0.1771 -0.22929
S.D. 0.033913 0.036512 0.030323 0.028137 0.019525 0.038592
Skewness -0.46441 -0.22285 -0.69621 -0.4381 -0.95965 -0.30962
Kurtosis 4.555812 4.498641 6.274446 4.698558 6.878824 3.267077
MAS SIN TW ARG MEX TUR
Mean 0.0009 0.002084 0.000559 0.00281 0.003208 0.006095
Median 0.001419 0.003114 0.003029 0.00571 0.004559 0.006115
Max 0.245786 0.18803 0.183182 0.284993 0.185786 0.329513
Min -0.19027 -0.23297 -0.16408 -0.31181 -0.17928 -0.33984
S.D. 0.028324 0.036491 0.033842 0.052625 0.034616 0.060057
Skewness 0.110079 -0.42881 -0.23602 -0.11668 -0.19427 -0.07775
Kurtosis 9.906778 5.348535 2.363488 3.464785 3.386302 4.076887
14
Sample Analysis
I use 50 weeks rolling sample in running in both of SOM model and Black-Litterman
model. In SOM model, I roll 50 weeks window in running to find return and volatility spillovers
table. After I got the table, I calculate for the contribution from other vector and collect it as a
panel data of financial spillover (collect it in two dimensions, which are vectors of contribution
from other, and time). Moreover, I calculate 50 weeks rolling return and volatility spillover index
and calculate for full-sample return and volatility spillover table too.
For Black-Litterman model, I roll 50 weeks window in calculating covariance matrix,
which is inputs of the model. After that, I use end of window weighted average dollarize market
capitalization as another component of input. However, since I have mentioned earlier that I have
problem about dollarize market capitalization due to limitation of accessing data in some countries,
every calculation before January 2004 has to use weighted average market capitalization of first
week of January 2004. After I have expected returns from Black-Litterman model, I use expected
returns and covariance matrix to calculate the efficient frontier. Then, I collect the optimal portfolio
choice at 5, 10 and 15 percentages of risks as a panel data the same way I did in SOM model.
While the calculation of the optimal portfolio is going on, as I have mentioned that we need
to calculate the efficient frontier before obtaining optimal portfolio, I collect the efficient frontier
of three periods for analyzing which are the periods between 1991-2006, 2007-2009, 2010-present
and found interesting result showing in next section.
Now, we have five vectors of panel data that are return spillover from others, volatility
spillover from others and optimal portfolio choices at 5, 10 and 15 percentages of risks. I run two
variables panel regression using fixed effect model on every possible relationships between
spillover and optimal portfolio on a condition that spillover is a dependent variable, and optimal
portfolio is an independent variable. Finally, we have six combinations of relationship discussing
results in next section.
After that, we will see an empirical study in a case of Thailand using weekly foreign net
purchases in Stock Exchange of Thailand (SET) to see whether optimal weights from the portfolio
are able to explain changes in foreign net purchases or not. A result is presenting in two parts,
which are a plot of weekly net capital flows against optimal weights of Thailand and a regression
using ordinary least square method.
In the last part of analysis, I attempt to find an intermediate mechanism between optimal
portfolio choices and spillover indices using Chicago Board Options Exchange Spx Volatility
Index (VIX index). This is because a relationship between spillover index and optimal portfolios
may has an intermediate transmission channel through VIX index referred as a global fear factor.
15
V. Results
In this section, I will analyze overall results and discuss it with other studies. I divide results
into four main parts. First part is about result from spillover calculation including an update version
of spillover plot and spillover table from Diebold and Yilmaz (2009). After that, I will show you
some interesting result from Black-Litterman model especially for the efficient frontier’s behavior.
The third part is results from panel regression in the earlier section. Lastly, I finish the result part
with VIX index analysis.
Spillover results
I will show the spillover table first. After that, I will discuss the result with result of Diebold
and Yilmaz (2009) to see how it changes in seven years later8.
8 Diebold and Yilmaz (2009) calculate spillover tables from 1992-2007
16
Table 4 Global Equity Market Return Spillover Table from Dec 1991- Jan 2015
US UK HK FRA IND GER PHI THA JAP CHL AUS KOR MAS SIN TW ARG MEX TUR Contribution from
others
US 99.2 0 0 0 0 0 0.2 0 0.1 0 0 0.1 0.1 0 0 0 0 0.1 0.8
UK 59.3 39.6 0 0 0 0.2 0.1 0 0.4 0 0 0.2 0 0 0 0 0 0 60.4
HK 25.8 5.6 67.4 0 0 0 0 0.1 0.5 0 0 0 0 0 0.2 0 0 0.1 32.6
FRA 56.7 14.7 0.1 27.7 0 0 0.2 0.1 0.1 0.1 0 0.1 0 0 0 0 0 0.1 72.3
IND 11.8 1.3 2.5 0.3 81.7 0 0.4 0 0.2 0.2 0.1 0.1 0.1 0.3 0.2 0 0.7 0.1 18.3
GER 55.3 10.6 0.4 9.4 0.2 23.2 0 0.1 0.1 0 0.1 0.5 0 0 0 0 0 0.1 76.8
PHI 12.5 1.2 8.3 0 0.2 0 74.3 1.4 0.1 0.3 0 0 0.1 0 0.1 1.4 0 0.1 25.7
THA 11.2 2.2 7.9 0.3 1.4 0.2 7.3 68.5 0 0 0.1 0 0 0 0 0.2 0.5 0 31.5
JAP 25.6 2.6 3.5 0.7 0.5 0.2 0.7 0.2 65.3 0 0 0 0 0.2 0.1 0 0.1 0.1 34.7
CHL 20.3 1.4 1.5 0.2 0.3 0.1 1.6 0.7 0.2 71.7 0.1 0 0 0.2 0.1 0.8 0.7 0 28.3
AUS 39.1 5.3 5.6 0.2 0.5 0 0.9 0.3 2.7 0.3 44.4 0.2 0 0.1 0.1 0 0.3 0.1 55.6
KOR 14.5 2.4 8.3 0.2 2.1 0.6 0.3 3.6 2.6 0.1 0.3 64.8 0 0.1 0 0 0 0.1 35.2
MAS 7.1 1 10.5 0 0.6 0.5 5.9 3.9 1.1 0 0.1 0 68.8 0.2 0.1 0.1 0.1 0.1 31.2
SIN 10 0.7 7.5 0.3 2.2 0.2 8.1 4.8 0.7 0.3 0.1 0.6 2 62.4 0 0 0 0 37.6
TW 11.2 0.7 6.2 0.9 0.9 1.1 2 0.7 1.6 0.2 0.6 1.3 0.4 0.5 71.6 0.1 0.1 0 28.4
ARG 16.8 1.1 1.2 0.8 0.2 0 0.8 0.6 0.1 2.3 0.2 0 0 0.1 0.5 74.9 0.5 0 25.1
MEX 36 0.9 2.6 0.1 0.1 0.3 1.2 0.1 0.1 1.5 0.1 0.1 0.4 0 0.1 3.2 53 0.1 47
TUR 7.3 1.6 0.3 0.3 0.9 0.7 1.2 0.5 0.4 0.1 0.1 0.1 0.2 0 0.1 0.1 0.1 86.1 13.9
Contribution
to others 420.2 53.2 66.5 13.8 10.3 4.3 30.9 17.1 11 5.3 1.8 3.5 3.4 1.9 1.8 6 3.1 1.1 655.2
Contribution
including its
own
519.5 92.9 134 41.4 92 27.5 105.2 85.6 76.3 77 46.2 68.3 72.2 64.3 73.5 80.9 56.1 87.2 Spillover Index
= 36.40%
17
Table 5 Global Equity Market Volatility Spillover Table from Dec 1991- Jan 2015
US UK HK FRA IND GER PHI THA JAP CHL AUS KOR MAS SIN TW ARG MEX TUR Contribution
from others
US 87.2 6.1 1.8 0.2 1.2 0.0 0.2 0.1 1.7 0.3 0.7 0.1 0.1 0.0 0.1 0.0 0.1 0.0 12.8
UK 63.0 30.8 1.1 0.1 0.7 0.4 0.8 0.2 1.0 0.5 0.2 0.2 0.6 0.0 0.1 0.0 0.1 0.3 69.2
HK 44.2 4.5 44.4 1.4 1.7 0.1 0.4 0.1 0.3 0.8 0.4 0.9 0.5 0.1 0.1 0.0 0.1 0.1 55.6
FRA 60.0 21.3 1.7 11.3 0.6 1.0 0.8 0.2 0.7 0.5 0.0 0.4 0.9 0.0 0.3 0.0 0.0 0.4 88.7
IND 30.0 6.6 3.9 0.7 53.7 0.1 1.0 1.1 0.6 0.5 0.0 0.6 0.6 0.1 0.2 0.1 0.0 0.2 46.3
GER 50.2 18.4 2.4 9.0 0.4 14.7 1.0 0.1 0.3 0.4 0.4 0.5 1.1 0.0 0.3 0.1 0.0 0.6 85.3
PHI 20.4 4.6 9.0 0.1 1.5 0.5 45.9 1.3 0.1 1.5 0.1 1.6 9.8 0.0 0.9 1.9 0.3 0.5 54.1
THA 17.0 5.0 8.2 0.2 5.2 0.5 8.0 49.4 0.1 0.8 0.0 1.6 2.0 0.0 1.3 0.3 0.1 0.3 50.6
JAP 57.0 6.5 6.1 1.0 3.9 0.5 0.5 0.2 22.0 0.4 0.5 0.4 0.5 0.0 0.2 0.1 0.0 0.1 78.0
CHL 13.5 5.8 2.0 0.5 0.8 1.6 6.3 0.6 0.1 60.3 0.1 0.7 2.8 0.0 1.9 2.4 0.2 0.5 39.7
AUS 55.7 7.2 8.7 0.2 3.3 1.5 0.3 0.1 0.4 1.2 20.3 0.2 0.2 0.2 0.1 0.1 0.1 0.1 79.7
KOR 33.0 8.7 6.2 0.3 1.4 0.9 2.2 2.9 0.1 0.4 0.3 40.0 2.3 0.6 0.3 0.1 0.0 0.3 60.0
MAS 1.8 1.8 6.1 0.4 0.2 0.6 2.5 1.0 0.5 0.4 0.6 1.5 80.2 0.0 0.7 0.1 0.7 0.8 19.8
SIN 27.2 6.9 12.8 0.1 1.3 1.0 9.2 1.9 0.1 0.5 0.8 4.1 3.4 30.2 0.2 0.1 0.0 0.3 69.8
TW 25.9 3.8 5.9 1.1 2.0 1.0 1.7 0.5 0.1 0.7 0.2 3.5 1.0 0.3 50.2 0.6 0.6 0.8 49.8
ARG 11.5 2.3 4.4 1.1 0.9 0.3 2.6 0.7 0.0 6.6 0.1 1.0 5.0 1.3 2.8 58.3 0.2 0.9 41.7
MEX 33.1 7.3 11.4 0.1 1.8 0.8 2.7 0.4 0.1 3.5 0.3 1.5 5.3 0.1 0.8 2.0 28.2 0.6 71.8
TUR 7.5 4.1 4.8 0.4 0.5 2.5 6.0 0.6 0.6 0.8 0.3 2.3 3.5 0.3 1.7 0.6 1.3 62.1 37.9
Contribution
to others 551.0 120.8 96.4 17.0 27.5 13.4 46.1 12.1 6.8 19.8 5.0 21.2 39.7 3.1 12.2 8.4 3.9 6.8 1010.9
Contribution
including its
own 638.2 151.5 140.7 28.2 81.1 28.1 92.0 61.5 28.8 80.1 25.3 61.2 119.9 33.2 62.3 66.7 32.1 68.9 Spillover Index
=56.16%
18
From the spillover table, we can see that U.S. stock market has very strong power in two
meanings. First, if we look at U.S.’s contribution to others market in volatility spillover table which
is 551.0, it tell us that more than a half of global equity market volatility is contributed from U.S.
market. Moreover, results in return spillover table also confirm the statement above that U.S.
market contributes more than a half of global equity market return. Second, if we now look at
contribution from others to U.S. market, we can see that there are only 0.8% of return spillover
and 12.8% of volatility spillover from other countries. It means that U.S. market contributes
spillover more than a half of all spillover in global equity market but receives a very low level of
spillover from other markets. Thus, we could say that U.S. is still powerful and dominating global
equity market.
Compared to result of Diebold and Yilmaz (2009), there are two main changes of the
results. First thing is about U.S. market, which is generating more spillover in both of return and
volatility. Compared to result in 2007, U.S. has 292 and 138 of return and volatility spillovers
contribution to others respectively, but it increases to 420 and 551 respectively in this paper. In
addition, return spillover from U.S. market increases by 43%, and volatility spillover increases by
299%. One of the most important reasons for this increasing in spillovers is Global Financial Crisis
during 2007-2009. The crisis encompasses the worst economic conditions seen in the United States
since the Great Depression. It is beginning with HSBC’s announcement in February 2007 that it
expected to see substantial losses from defaults on subprime loans. After that, two Bear Stearns
hedge funds collapsed in July 2007. Moreover, investors’ worrying about the effects the Global
Financial Crisis sent Dow Jones down by 387 points to close at 13,270.68 (the biggest one-day
decline since the previous February). However, this is only a little part of Global Financial Crisis
because after that U.S.’s banks and those who also invest in subprime mortgage faced huge loss.
Many of those banks, hedge funds and insurance companies bankrupted during the subprime crisis.
This crisis leaves a long lasting impact on the U.S. economic conditions until nowadays. More
detail on global equity market, when Global Financial Crisis spreads over the world especially in
America and Europe, all equity markets are very sensitive. They are very fluctuating responding
to subprime news. This is one reason of changing in the spillover tables.
Another important changing in results is a level of an aggregate contribution from and to
others. Diebold and Yilmaz (2009) show the spillover tables calculated from data in 1992-2007,
which is period before crisis. The aggregate values of contribution from and to other in return and
volatility spillover tables are 675 and 750 respectively, but in this paper, it is 655 and 1011. Thus,
we can see a big changing in amount of volatility spillover contribution that increases by 34.8%
after the crisis. This changing can be interpreted that equity markets are more interdependence
during and after crisis because there are much more volatility contributed by others than ever in
the past.
19
Figure 3 Return and Volatility Spillover Plots from 1994 to 2014
In the second part of result from spillover calculation, I show a figure of return and
volatility spillover plots above. We can see that nature of spillover indices (both of volatility and
return) is exactly what Diebold and Yilmaz state in their work that return spillover index show a
trends without bursts, but volatility spillover index captures bursts without trends. Thus, the indices
are able to capture major global economic events very well.
Starting from Asian Financial crisis in late 1997, Thailand decided to change exchange rate
regime from fixed exchange rate to the float one. The devaluation of Thai Baht in July 1997 spread
to Hong Kong in October and further spread to other major economies in the region in early of
1998. After that, Russia faces another financial crisis with same cause with Thailand. Declining
productivity and fixed exchange rate regime between the ruble and foreign currencies and a chronic
fiscal deficit were the reasons that led to the crisis. Russian government devalued the ruble in 17
August 1998, defaulted on domestic debt, and declared a moratorium on payment to foreign
creditors. This clash leads to very high volatility in both international exchange rates and global
equity market. Eight years later, volatility in global equity market rises again because an intense
capital flows from emerging markets flows back to U.S. caused by a strong signals from the
Federal Reserve tend to hikes the Fed Funds rate during May–June 2006. In August 2007, BNP
Paribas bank freeze three of their funds, indicating that they are unable to value the collateralized
debt obligations (CDOs), or packages of sub-prime loans. It is the first major bank to acknowledge
the risk of exposure to sub-prime mortgage markets. Five months later, the largest single-year drop
0
10
20
30
40
50
60
70
80
90
100
Ind
ex
Time (Year)
Return Spillover Volatility Spillover
Asian Financial Crisis
Russian Crisis
9/11
terrorists
attacks
Capital
outflows
from EMs
First sign
of GFC
Bear Stearns failure
Iceland and
UK banks
collapse Financial
markets turmoil
from Euro debt
crisis ECB decides to
hold the rates unexpectedly
20
in house sales in a quarter of century following by Bear Stearns failure, which was sold to
JPMorgan Chase at a fire-sale price in March 2008. After that, in the first half of October 2008,
Glitnir, Kaupthing, and Landsbanki bank collapsed (it is Iceland's three biggest commercial banks)
,and the British government has to bails out several banks, including the Royal Bank of Scotland,
Lloyds TSB, and HBOS. After big events of U.S., it is now European’s turn when European
sovereign debt crisis sends financial markets into turmoil. The sharp drop in stock prices in August
2011 in stock exchange markets across the United States, Middle East, Europe and Asia due to
fears of contagion of the European sovereign debt crisis. Last event happened in June 2013, during
European countries’ recession, ECB decided to hold rates steady and stopped cut interest rates
further.
In conclusion, by using 200 weeks rolling spillover calculation, the indices are very good
at explaining the economic events happening in the world. In the future, the volatility spillover
index could be a very good indicator for monitoring crisis due to its ability to capture economic
events
Black-Litterman results
As I have mentioned that I calculate the optimal portfolio choices at 5, 10 and 15
percentages of risks, I found the nature of asset allocation with different risk levels according to
the results. The optimal portfolio at low risk (at 5% level of risk) is more diversify compared to
the high-risk one (at 10% level of risk). It means that the low-risk portfolio diversifies risks by
investing in many countries while the high-risk portfolio usually suggests investing with high
weights but fewer countries. These results are intuitive with investors’ behavior in reality and link
with the panel regression result, which we will talk about it later.
In this part, I present the risk-return trade off (efficient frontier) behavior with an intuition
behind it. After that, I will present the empirical result in Thailand to see if the optimal weight has
a relationship with amount of foreign net purchases in Stock Exchange of Thailand (SET).
Let start with the frontiers first, figure below shows three efficient frontier calculating from
three period which are 2001-2006, 2007-2009, 2010-present. The reason I choose those periods is
that I want to see how risk-return trade off change before, during, and after Global Financial Crisis
(GFC).
21
Figure 4 Efficient Frontiers
As a result, two frontiers of pre and post GFC are not different, but interestingly, the GFC
shifts frontier to the right during crisis. This is because there is an increasing in systematic risk in
all markets. Thus, investor needs to take higher risk when they invest.
Figure 5 Risk-Return Trade-offs under Different Monetary Policies
Figure 5 Risk-Return Trade-offs under Different Monetary Policies according to IMF Global Financial Stability Report in 2014
0%
2%
4%
6%
8%
10%
12%
5% 10% 15% 20% 25% 30%
Po
rtfo
lio
Ret
urn
(%
)
Portfolio Risk (%)
Pre GFC (2001-2006) During GFC (2007-2009) Post GFC (2010-present)
X
x
Y
22
This result is different compared to IMF Global Financial Stability Report in 20149 about
risk-return trade off during crisis. The report suggests that when unconventional monetary policy
is implemented (during GFC), financial volatility diminishes and reduce market risk shifting the
risk-return trade off to the left (from X frontier to Y frontier), and investors become even more
willing to hold risky assets. On the other hand, the result in this paper shows that financial volatility
increases and raises market risk sending the efficient frontier to the right. Investors have to face
the risk-return trade off at higher risk during the crisis.
Our results here are not directly comparable to those in IMF Global Financial Stability
Report due to different asset universe. However, from a pure global equity market perspective, it
appears that the unconventional monetary policy in developed world does not seem to change the
risk-return profile significantly.
Panel Regression Results
A table below is the results from panel regression that we have talked about in the earlier
section. There are two types of model here which are a full-sample model using data from 1991-
present and sub-sample models using data only from some periods. For the sub-sample models, I
divide all samples into three periods depending on the Global Financial Crisis (GFC) called the
period of “Pre GFC”, “During GFC” and “Post GFC”
Table 6 Optimal Portfolio at given risk
Period Spillover
of
Low Risk (5%) Medium Risk (10%) High Risk (15%)
Weight 𝑅2 Weight 𝑅2 Weight 𝑅2
Pre GFC
(Before 2007)
Return −18.60423∗∗∗
(-18.32805) 0.469231
−8.670936∗∗∗
(-8.371898) 0.459231
0.841008
(1.209828) 0.456588
Volatility −29.03481∗∗∗
(-27.87977) 0.528426
−9.263116∗∗∗
(-8.587566) 0.504917
2.958966∗∗∗
(4.088817) 0.502908
During GFC
(2007- 2009)
Return −6.254966∗∗∗
(-5.322029) 0.739723
−4.415563∗∗∗
(-3.735245) 0.738389
−2.376007∗∗
(-2.285172) 0.737571
Volatility −3.525046∗∗∗
(-2.809278) 0.693383
−4.715076∗∗∗
(-3.749627) 0.694057
4.325790∗∗∗
(3.918145) 0.694198
Post GFC
(2010- present)
Return −11.10882∗∗∗
(-5.056597) 0.632582
0.178681
(0.140349) 0.630591
−0.345824
(-0.326483) 0.630597
Volatility −11.07589∗∗∗
(-6.876107) 0.693499
−3.325091∗∗∗
(-3.558760) 0.691255
1.968106∗∗ (2.530023)
0.690845
9 See p.12 of IMF Global Financial Stability Report, October 2014 for more detail.
23
Full-Sample
Return −13.32967 ∗∗∗
(-17.08749) 0.419652
−5.356799 ∗∗∗ (-6.78056)
0.413067 −0.080136 (-0.128834)
0.411820
Volatility −24.20652 ∗∗∗
(-35.43466) 0.508823
−10.60375 ∗∗∗ (-15.06336)
0.485710 1.814989 ∗∗∗ (3.261978)
0.480572
From a table above, sub-sample models shows us that the model fits more when use it with
sub-sample data. The models fit most with a period during crisis following by periods of post and
pre crisis respectively. During the global financial crisis, the model is able to explain up to nearly
74% of return spillover and 70% of volatility spillover in global equity market. Moreover, I also
find that the portfolio at 15% risk has highly significant with positive coefficient in all sub-sample
periods against volatility spillover index. It means that increasing weight of investment sometimes
also generates volatility spillover not just reducing weight. We will talk about it again later.
For full-sample analysis, we can see that optimal portfolios are able to explain the returns
and volatility spillovers of the global equity market quite well. Optimal portfolio at risk 5% is the
best portfolio in explaining the spillover effect of both return and volatility with highest 𝑅2. The
portfolio is able to explain 42% of return spillover, which is nearly a half of it. Moreover, the
portfolio can explain 50% of volatility spillover. With optimal portfolio at higher risk, it has a bit
lower 𝑅2compared to the lower risk portfolio in both of returns and volatility spillover. We can
see that the spillover indices are most sensitive to the low-risk portfolio as we can see the highest
𝑅2 of all periods in table 7. The reason behind these results is the nature of asset allocation with
different risk levels. As I have explained, the low-risk portfolio suggests investing in many
countries while the high-risk portfolio suggests investing in fewer countries. Thus, the portfolio
with low risk can explain more and better in some countries because the high-risk one suggests no
investment in those countries.
Intuitions behind results are that although investors are rational and optimize their
portfolio, it still generates volatility across countries. In this case, rebalancing portfolio by rational
investor can cause spillover effect of both return and volatility in the market. According to Chuhan
et al (1998) who use global factors in explaining portfolio flows, maybe the results in this paper
could be missing intermediate mechanisms in explaining portfolio flows. The explanation could
be that change in global factors such as US interest rates, US industrial activity or other external
shocks affects investor expected return, so they optimize their portfolio by rebalancing it and cause
portfolio flows, return and volatility spillovers. Moreover, the finding supports what has found in
Disyatat and Gelos (2001) that a mean variance optimization has explanatory power for asset
allocation behavior of mutual funds in emerging market, and the information contained in
historical return covariance is useful.
Interestingly, if we look at results of volatility spillover in every period, we can see that it
significantly has negative sign on 5% and 10% level of risk (which means reducing weight
generates volatility spillover) and positive sign on 15% level (which means increasing generates
weight volatility spillover) at every period including whole sample. In general, reducing
investment generates volatility spillover, but the result shows that if investors have higher
perception of risk, increasing investment could generate spillover too. The big question is that how
24
do we know risk perception of investor at all periods because a direction of volatility spillover is
depending on perception of risk. However, the answer could be the making risk endogenous in
modeling, but it is beyond the purpose of this paper.
To sum up, this could be evidence that the spillover returns and volatility have some micro
foundations behind it because portfolio optimization model can capture its changes. The results
also confirm us and give some senses that there are some mechanisms behind the spillover effect.
Moreover, this paper illustrates the effectiveness of using portfolio model in practice and its
intuition.
Optimal Portfolios, Spillover indices and VIX index
To see relationships between optimal portfolios, spillover indices and VIX index, I divide
the test into two parts under an assumption that VIX index is an intermediate mechanism between
the relationships of optimal portfolios and spillover indices resulting in earlier parts. The first part
is testing optimal portfolio in explaining changes in VIX index and see the individual effect of
each country to changes in VIX. Second part is to see direction of relationships between VIX and
spillover indices by using Granger Causality Test and to test VIX in explaining changing in
spillover indices.
Optimal Portfolio and VIX index
Let me start with result from testing optimal portfolio in explaining movement of VIX
index using ordinary least square method providing below.
Table 7 Top 5 Highest R-squared in Explaining VIX
5% risk 10% risk 15% risk
Coef P-value 𝑅2 Coef P-value 𝑅2 Coef P-value 𝑅2
US -16.33 0.00 0.12 US -18.85 0.00 0.22 MAS 19.40 0.00 0.24
KOR -59.17 0.00 0.07 MAS 13.32 0.00 0.19 US 9.44 0.00 0.15
MAS 5.53 0.00 0.04 GER -39.85 0.00 0.13 AUS 77.64 0.00 0.14
FRA -97.28 0.00 0.03 HK -48.66 0.00 0.13 GER -14.57 0.00 0.11
HK -72.59 0.00 0.03 AUS 15.00 0.00 0.12 ARG -26.09 0.00 0.11
We can see that U.S. has the highest 𝑅2at 5% and 10% risk and is the second rank at 15 %
risk. It tells us about the importance of the U.S. equity market on VIX. Moreover, coefficients of
U.S. are negative at 5% and 10% risk meaning that normally, increasing weight in U.S. represents
the confident of investor around the world (increasing weight in U.S. reduces VIX which
recognized as global fear factor). In addition, the optimal weights are statistically significant in
explaining VIX index in almost all countries.
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Table 8 Top 5 Highest Coefficient in Explaining VIX
5% risk 10% risk 15% risk
Coef P-value 𝑅2 Coef P-value 𝑅2 Coef P-value 𝑅2
ARG 35.86 0.01 0.01 TW 25.06 0.00 0.02 AUS 77.64 0.00 0.14
MEX 29.85 0.00 0.01 CHL 24.57 0.00 0.04 TW 48.31 0.00 0.03
IND 26.50 0.00 0.02 PHI 20.95 0.00 0.01 CHL 39.86 0.00 0.03
PHI 15.88 0.02 0.00 IND 16.93 0.00 0.01 SIN 31.83 0.00 0.02
JAP 10.18 0.07 0.00 AUS 15.00 0.00 0.12 MAS 19.40 0.00 0.24
Table 9 Top 5 Lowest Coefficient in Explaining VIX
5% risk 10% risk 15% risk
Coef P-value 𝑅2 Coef P-value 𝑅2 Coef P-value 𝑅2
FRA -97.28 0.00 0.03 TUR -95.65 0.00 0.02 TUR -71.71 0.00 0.04
HK -72.59 0.00 0.03 ARG -81.65 0.00 0.10 ARG -26.09 0.00 0.11
KOR -59.17 0.00 0.07 HK -48.66 0.00 0.13 THA -21.97 0.00 0.03
TUR -41.06 0.00 0.01 KOR -45.85 0.00 0.05 JAP -19.12 0.00 0.07
GER -27.28 0.00 0.02 JAP -43.91 0.00 0.08 HK -17.59 0.00 0.06
The top 5 of highest and lowest coefficient indicates effects of investing on change in VIX.
It means that if a country has a positive coefficient, increasing weight in that country increases
VIX index. On the other hand, if a country has a negative coefficient, increasing weight in that
country reduces VIX index. These results imply investors’ perception about risk in each country.
This is because when the investors have low confidence (when they fear), they invest in some
countries (countries with positive coefficient) and they invest in other countries (countries with
negative coefficient) when they have confidence.
VIX index and Spillover indices
In this part, testing results of the relationship between VIX index and spillover indices
show in a table below. After that, I apply the Granger Causality tests to test whether spillovers
cause a change in VIX index or vice versa. The Granger Causality tests divide into two tests
explained below.
Table 10 Regression Result of VIX on Spillover Indices
Coef T-stat P-value 𝑅2
Return spillover 0.33 7.16 0.00 0.05
Volatility spillover 0.52 11.77 0.00 0.12
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The results of testing the relationship between VIX index and spillover indices indicate
that VIX index is statistically significant in explaining return and volatility spillovers. With a
positive relationship, it means that return and volatility spillovers also increase when VIX index
increase. However, we still do not know whether VIX index causes a change in return and volatility
spillovers or the spillovers cause a change in VIX index. Thus, the Granger Causality test is used
to find directions of relationships. Here I provide two tests, which are VIX index-Return spillover
and VIX index-Volatility spillover.
Table 11 Results from Granger Causality Test of VIX and Return Spillover
Chi-sq df Prob.
Dependent variable: VIX
RETURN 101.2345 2 0
Dependent variable: RETURN
VIX 17.6896 2 0.0001
The first test is the VIX index-Return spillover’s test. You will see two ways testing in the
table. First two rows are a result from Granger Causality testing when the VIX index is a dependent
variable and the return spillover is an independent variable, and the next two rows are vice versa.
A result from the test indicates that both of VIX index and Return spillover are able to explain
changing of each other. Thus, it still has an ambiguous direction of the relationship between VIX
index and Return spillover.
Table 12 Results from Granger Causality Test of VIX and Volatility Spillover
Chi-sq df Prob.
Dependent variable: VIX
VOLATILITY 0.89 2 0.63
Dependent variable: VOLATILITY
VIX 26.29 2 0
Another test is the VIX index-Volatility spillover’s test. Interestingly, I have found that in
this case, VIX index is able to explain changes in Volatility spillover but Volatility spillover is
unable to explain changes in VIX index all over time. This means that it is only a one-way direction
of relationships in a case of VIX index-Volatility spillover, which is changing in Volatility
spillover.
As a conclusion, optimal weights calculated from Black-Litterman model are able to
explain changes in VIX index, and VIX index is able to explain spillover indices. However, the
result from the last part indicates that VIX index has one-way relationship to explain changes in
volatility spillover but not for return spillover. Thus, it means that VIX index can be an
intermediate mechanism between optimal weights and volatility spillover, but it not confirms for
a case of return spillover.
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VI. Concluding remarks
This paper attempts to find an underlying micro mechanism behind spillover in global
equity markets. I have found that when investor optimizes their portfolio, which means
optimization in microeconomics unit, it still creates fluctuation in macroeconomics unit likes
global equity markets. This would be beneficial to policy makers to consider microeconomics unit
when making decision because a policy affects microeconomics unit can cause fluctuation in
macroeconomics. In addition, this paper also attempts to illustrate the practical use of portfolio
optimization model, and try to make it compatible with the reality.
The key findings of this paper can be summarized as follows:
U.S. equity market generates more return and volatility spillovers during and after
the Global Financial Crisis (GFC).
More return and volatility spillovers in global equity markets indicates their more
interdependence since 2008.
Spillover indices are able to capture major global economic events very well
especially for the volatility spillover index.
During GFC, financial volatility increases and raises market the risk-return trade
off in a case of global equity market.
The optimal portfolio from the model is able to explain spillovers. Moreover,
reducing weight generates volatility spillover in cases of low and medium risk level
but opposite for a case of high-risk level.
VIX index has significant relationships with optimal portfolios and spillover
indices
For further research, this paper gives a new framework about describing the
macroeconomics by micro foundations. Thus, it still has many ways to conduct the research in this
framework. One of the interesting topics is applying this framework to explain exchange rate
spillover or other assets. Another aspect is to make risk endogenous by using monetary policy to
determine appropriate level of risk in model. This is because the policy directly affects risk-return
tradeoff of investor, which means it affects risk-taking behavior of investor too. Some types of
monetary policy might promote risk-taking behavior unintentionally.
28
References
Abidin, Sazali, Krishna Reddy, Chun Zhang, and Zhenfei Tien. 2015. "Intensity of Price and
Volatility Spillover Effects: Evidence from Asia-Pacific Basin ." The University of
Waikato.
Cheung, William, Scott Fung, and Shih-Chuan Tsai. 2010. "Global Capital Market
Interdependence and Spillover Effect of Credit Risk: Evidence from the 2007–2009
Global Financial Crisis." Applied Financial Economics, vol 20, issue 1-2, 85-103.
Chuhan, Punam, Stijn Claessens, and Nlandu Mamingi. 1998. "Equity and Bond Flows to Latin
America and Asia: The Role of Global and Country Factors." Journal of Development
Economics, vol 55, 2 439-463.
Diebold, Francis X., and Kamil Yilmaz. 2009. "Measuring Financial Asset Return and Volatility
Spillovers, With Application to Global Equity." The Economic Journal, vol.119, 158-
171.
Disyatat, Piti, and Gaston R. Gelos. 2001. "The Asset Allocation of Emerging Market Mutual
Funds." IMF working paper.
Engle, R. 1982. "Autoregressive conditional heteroscedasticity with estimates of the variance of
United Kingdom inflation." Econometrica 50 987-1007.
Kamil, Anton Abdulbasah, Chin Yew Fei, and Lee Kin Kok. 2006. "Portfolio analysis based on
Markowitz model ." Journal of Statistics and Management Systems, 9:3, 519-536.
Kaplan, Paul D. 1998. "Asset Allocation Models Using the Markowitz Approach."
Kim, Jae Young, and Jung-Bin Hwang. 2012 . "Risk Spillover Effects in International Financial
Markets: Evidence from the Recent Financial Crisis ." Seoul National University .
Liu, Y. Angela, and Ming-Shiun Pan. 1997. "Mean and Volatility spillover effects in the U.S.
and Pacific-Basin stock markets." Multinational Finance Journal, 1, 47-62.
Mankert, Charotta. 2006. "The Black-Litterman Model- Mathematical and Behavioral Finance
Approaches Towards Its Use in Practice." Stockholm School of Economic.
Markowitz, Harry M. 1990. "Foundation of Portfolio Theory." Nobel Lecture in Economic
Sciences .
Mattoo, Aaditya, Prachi Mishra, and Arvind Subramanian. 2012. "Spillover Effects of Exchange
Rates: A Study of the Renminbi." IMF working paper.
Ross, S. 1989. "Information and volatility: The no-arbitrage martingale approach to timing and
resolution irrelevancy." Journal of Finance, 45, 1-17.
Shinagawa, Yoko. 2014. "Determinants of Financial Market Spillovers: The Role of Portfolio
Diversification, Trade, Home Bias, and Concentration ." IMF working paper.
Walters, Jay. 2007. "The Black-Litterman Model In Detail ."
