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
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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.
Literature Review ....................................................................................................................................... 3
Model ............................................................................................................................................................ 5
Spillover Measures Model ........................................................................................................................ 5
Black-Litterman Model and Efficient Frontier ......................................................................................... 7
Black-Litterman Model .................................................................................................................... 7
Data and Sample Analysis ........................................................................................................................ 11
Data ......................................................................................................................................................... 11
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.