examining international stock market integration: effects

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12-2016

Examining International Stock Market Integration: Effects on Examining International Stock Market Integration: Effects on

Portfolio Statistical Moments, Changes to Systematic Risk Portfolio Statistical Moments, Changes to Systematic Risk

Significance, and Investor Purchasing of Foreign Equities Significance, and Investor Purchasing of Foreign Equities

Justin Kingsley Hanig Western Michigan University, [email protected]

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EXAMINING INTERNATIONAL STOCK MARKET INTEGRATION: EFFECTS ON

PORTFOLIO STATISTICAL MOMENTS, CHANGES TO SYSTEMATIC RISK

SIGNIFICANCE, AND INVESTOR PURCHASING OF FOREIGN EQUITIES

by

Justin Kingsley Hanig

A dissertation submitted to the Graduate College

in partial fulfillment of the requirements

for the degree of Doctor of Philosophy

Economics

Western Michigan University

December 2016

Doctoral Committee:

C. James Hueng, Ph.D., Chair

Mark Wheeler, Ph.D.

David Burnie, Ph.D.

EXAMINING INTERNATIONAL STOCK MARKET INTEGRATION: EFFECTS ON

PORTFOLIO STATISTICAL MOMENTS, CHANGES TO SYSTEMATIC RISK

SIGNIFICANCE, AND INVESTOR PURCHASING OF FOREIGN EQUITIES

Justin Kingsley Hanig, Ph.D.

Western Michigan University, 2016

The internet provides individuals with the ability to find instantaneous information on nearly

every corner of the earth. Increasing correlations of international stock markets suggests investors may

use information from different parts of the world to assess the value of the assets they hold in their

portfolios. This dissertation examines changes in international stock market behavior to identify the

effects of international market integration across a time. More specifically, this dissertation studies the

effects of integration on the ability of diversification to reduce risk and skewness of portfolios, how

global-wide risks significantly impact country-level index returns, and the equity purchasing behavior of

foreign investors.

The first paper in this dissertation measures the benefit to international portfolio diversification

through time. The investigation observes the change in the standard deviation and skewness of

increasingly more diversified portfolio returns from 1973 to 2010. Previous literature implies

diversification reduces standard deviation, but diversification also reduces positive skewness in a

portfolio. Increasing correlations of international stock markets suggests the reduction in standard

deviation and positive skewness of a portfolio could be mitigated in recent time periods. This paper

studies the changes of risk and positive skewness of international index portfolios over time. The results

show that the reduction in standard deviation and skewness occurs at a much faster rate in more recent

time periods. Robustness checks demonstrate the rate of standard deviation and skewness reduction varies

across different investment strategies.

The second paper examines the impact of global-wide risk measures on country-level asset prices

in an international capital asset pricing model (ICAPM). Integrated international markets imply assets

returns with similar risks should not vary across countries, but segmented international markets suggest

asset returns vary only through risks within a particular country. Previous literature documents that

international financial markets became more correlated and integrated in the late 1990s. This investigation

in this paper, therefore, studies the impact of global-wide risks on returns in an integrated international

stock market environment. The results show insignificant global-market risk factors on returns before and

after 2000, which implies world financial markets have not become integrated in the recent time period

when looking across a sample of 37 stock markets. However, global-wide risk factors significantly

impact index returns for a sub-set of advanced economies.

The third paper investigates the effect of international equity market integration on equity

purchasing behavior of investors in different countries across different time periods. This study observes

the relationship between net equity purchases by U.S. residents from foreign investors on stock market

index returns in a segmented and integrated international stock market environment. The results of the

examination indicate international equity integration did not affect equity purchasing differences across

foreign and domestic investors.

Copyright by


2016

ii

ACKNOWLEDGMENTS

I would like to acknowledge all those who helped me along my academic journey,

especially the faculty and staff in the Department of Economics and the Graduate College at

Western Michigan University. The passion and interest of the faculty in teaching economics and

the scientific method touched me well beyond the classroom, and their enthusiasm led to the

production of this dissertation.

I would like to express my complete gratitude to Dr. C. James Hueng, Dr. Mark Wheeler,

and Dr. David Burnie for their effort, time, and patience in helping me finish this project. Their

wisdom, support, and guidance were the cornerstone for my success at Western Michigan. I

would like to thank Dr. Michael Ryan for giving me an example of how to be a great teacher and

connect with students, and I would particularly like to thank Dr. Eskander Alvi for his endless

amount of class, poise, and intelligence during my career at Western Michigan that I will

constantly seek to emulate.

I cannot be thankful enough for the love and support of my family throughout my pursuit

of my degree. My wife and children are the center of my world, and I would never be able to be

in the place that I am today without their unconditional love. My father’s endless and persistent

interest in my progress and my mother’s limitless support inspired me towards completing this

degree. I love you all dearly.


iii

TABLE OF CONTENTS

ACKNOWLEDGMENTS .............................................................................................................. ii

LIST OF TABLES .......................................................................................................................... v

LIST OF FIGURES ...................................................................................................................... vii

1. INTRODUCTION ..................................................................................................................... 1

2. INTERNATIONAL PORTFOLIO DIVERSIFICATION: THE COSTS AND

BENEFITS ................................................................................................................................. 7

2.1 Introduction ...................................................................................................................... 7

2.2 Data and Methodology ................................................................................................... 12

2.3 Results ............................................................................................................................ 15

2.3.1 Summary Statistics ................................................................................................. 15

2.3.2. Portfolio Formation Results .................................................................................... 16

2.4 Robustness Checks ......................................................................................................... 25

2.4.1 Highest Historical Return Portfolio Creation ......................................................... 26

2.4.2 Lowest Historical Risk Portfolio Creation .............................................................. 33

2.5 Conclusion ...................................................................................................................... 41

3. SHOWING WORLD MARKET INTEGRATION THROUGH TIME ................................... 43

3.1 Introduction .................................................................................................................... 43

3.2 Literature Review ........................................................................................................... 46

3.3 Methodology .................................................................................................................. 53

3.4 Data ................................................................................................................................ 58

3.5 Regression Results and Discussion ................................................................................ 62

CHAPTER

iv

Table of Contents - Continued

CHAPTER

3.5.1 The Entire World Market ........................................................................................ 62

3.5.2 Developed and Emerging Markets ......................................................................... 65

3.6 Conclusion ...................................................................................................................... 69

4. INTERNATIONAL CAPITAL FLOWS IN AN INTEGRATED MARKET ......................... 71

4.1 Introduction .................................................................................................................... 71

4.2 Data and Methodology ................................................................................................... 74

4.3 Results ............................................................................................................................ 79

4.3.1 Summary Statistics ................................................................................................. 79

4.3.2 Comparable Regressions ......................................................................................... 81

4.3.3 Additional Regressions ........................................................................................... 85

4.4 Conclusion ...................................................................................................................... 91

5. CONCLUSION ......................................................................................................................... 93

BIBLIOGRAPHY ......................................................................................................................... 98

v

LIST OF TABLES

1 Summary Statistics of International Market Indices .................................................................. 13

2 Diversified Structure of Standard Deviation Risk Results – Portfolios

Built by Randomly Choosing Indices ....................................................................................... 21

3 Diversified Structure of Skewness Results – Portfolios Built by Randomly Choosing Indices 23

4 Percent Diversified Structure of Standard Deviation and Skewness for Each

Portfolio – Portfolios Built by Randomly Choosing Indices ..................................................... 24

5 Diversified Structure of Standard Deviation Risk Results – Portfolios Built by Adding

Indices with Highest Historical Average Return ....................................................................... 27


Portfolio – Portfolios Built by Adding Indices with Highest Historical Return ........................ 28

7 Diversified Structure of Skewness Results –Portfolios Built by Adding Indices

with Highest Historical Return .................................................................................................. 30

8 Diversified Structure of Standard Deviation Risk Results – Portfolios Built by

Adding Indices with Lowest Historical Standard Deviation ..................................................... 36

9 Diversified Structure of Skewness Results – Portfolios Built by Adding Indices

with Lowest Historical Standard Deviation ............................................................................... 39


Portfolio – Portfolios Built by Adding Indices with Lowest Historical Standard Deviation .. 40

11 Summary Statistics................................................................................................................... 59

12 F-test Results of Equal-Weighted Average Correlations of Countries Indices

with the World Market ............................................................................................................. 61

13 Cross-Sectional Results over Time .......................................................................................... 63

14 Cross-Sectional Results over Time of Developed Countries ................................................... 67

vi

List of Tables - Continued

15 Cross-Sectional Results over Time of Emerging Countries .................................................... 68

16 F-test Results of Equal-Weighted Average Correlations of Countries Indices

with the World Market ............................................................................................................. 77

17 Summary Statistics – Monthly Purchases of Equities by U.S. Residents from

Foreign Investors(in Millions of U.S. Dollars from January 1977 to October 2010) .............. 79

18 Summary Statistics - Monthly Stock Market Index Returns

(in % from January 1977 to October 2010) ............................................................................. 80

19 U.S. Purchases of Stocks in Foreign Markets – Comparable Regressions .............................. 81

20 U.S. Purchases of Stocks in Foreign Markets Pre-2000 – Additional Regressions -

Panel (a) ........................................................................................................................................ 87


Panel (a) - Continued ............................................................................................................... 88


Panel (b) ........................................................................................................................................ 89


Panel (b) - Continued .................................................................................................................... 90

vii

LIST OF FIGURES

1 Standard Deviation against Diversification – Portfolios Built by Randomly

Choosing Indices ........................................................................................................................ 17

2 Skewness against Diversification - Portfolios Built by Randomly Choosing Indices ............... 17

3 Scaled Standard Deviation against Diversification - Portfolios Built by Randomly

Choosing Indices ........................................................................................................................... 18

4 Scaled Skewness against Diversification – Portfolios Built by Randomly

Choosing Indices ........................................................................................................................ 18

5 Standard Deviation against Diversification – Portfolios Built by Adding Indices

with Highest Historical Average Return ....................................................................................... 26

6 Skewness against Diversification - Portfolios Built by Adding Indices with

Highest Historical Average Return ............................................................................................ 29

7 Scaled Standard Deviation against Diversification – Portfolio Built by Adding

Indices with Highest Historical Average Return ....................................................................... 32

8 Scaled Skewness against Diversification - Portfolio Built by Adding Indices

with Highest Historical Average Return .................................................................................... 33

9 Standard Deviation against Diversification – Portfolios Built by Adding Indices

with Lowest Historical Standard Deviation ............................................................................... 34

10 Scaled Standard Deviation against Diversification – Portfolio Built by Adding

Indices with Lowest Historical Standard Deviation ................................................................ 35

11 Skewness against Diversification - Portfolios Built by Adding Indices with

Highest Historical Average Return .......................................................................................... 37

12 Scaled Skewness against Diversification - Portfolio Built by Adding Indices

with Lowest Historical Standard Deviation ............................................................................. 37

13 Equal-Weighted Average Correlation of Countries’ Indices with World Market ................... 60

14 Equal-Weighted Average Correlation of Countries’ Indices with World Market ................... 76

1

CHAPTER 1

INTRODUCTION

An investor can trade securities across the globe every hour of the day. When an

individual wakes up in the morning, they may see European and Asian stock market indices

showing gains. A natural question would be how these gains affected the individual’s portfolio,

and whether the United States’ stock market will see gains as well. This dissertation aims to

shed light on the answers to these questions.

In a speech at the Federal Reserve Bank in Chicago, Janet Yellen (2011), then Vice Chair

of the Federal Reserve, stated, “…concerns about European fiscal and banking issues have

contributed to strains in global financial markets that pose significant downside risks to the U.S.

economic outlook.” This indicates that domestic stock markets can vary due to risks implicit in

foreign countries, and Dr. Yellen suggests global financial markets are interconnected, or

integrated. An integrated international market implies that returns on assets with the same risk

will remain the same regardless of their geographic location. Segmented international markets,

though, imply that assets vary based on risks within a given country, and country-level assets do

not fluctuate based on global-wide risk factors. Dr. Yellen implicitly assumes integrated

international stock markets by suggesting European risks pose threats to all assets, regardless of

whether the assets reside in Europe or the United States.

Several factors across international markets could drive country-specific stock market

returns to vary independently from each other. Monetary policy can differ across markets,

causing differences in asset returns in different countries through policy programs set in place by

central banks. Individual countries may also differ in their openness for foreign investment.

2

Fiscal policy differences, especially in regards to tax policies, can also reduce asset return

correlations of international stock markets. Finally, foreign investors’ inability to interpret the

economic and financial data of a country with the same clarity as domestic investors may cause

differences in asset returns across geographic locations. All of these factors can mitigate the

integration of international financial markets.

The remarks by Dr. Yellen, though, indicate that international markets may have

overcome these barriers to integration. With the formation of the European Union, the European

Central Bank conducts policy in a harmonized fashion, leaving no ambiguity between monetary

policies of individual countries for investors to decipher across countries. Many foreign

governments have also opened their financial markets to foreign investment. Some studies [e.g.

- French and Poterba (1991)] using investor-level data found that tax policies of a certain country

do not play a significant role in investment strategies, and the speed and availability of

information made possible through the internet allows for easy interpretation of information

regarding foreign economies and businesses. The main question then becomes whether the

international financial markets have become integrated through the reduction in the barriers

viewed in previous time periods.

This dissertation focuses on analyzing the changes in stock market behavior to identify

the effects of international market integration across a time. Correlations across stock markets

increased in the first decade of the new millennium, which suggests diminishing benefits to

diversification. Also, international market integration implies increasing significance of

systematic risk on returns, while lessening the impact idiosyncratic risk plays on returns. With

increasing importance of systematic risk on country-level returns, investors in different

3

geographies should adjust their return predictions based on global-wide risk. Consequently,

international equity flows should follow changes in global-wide risk variation. The dissertation

that follows investigates each of these three behaviors.

The first paper, “International Portfolio Diversification: The Costs and Benefits,”

observes the changes in benefits to diversification of portfolios built with country-level stock

market indices for the past four decades. The paper also studies how skewness changes over

time with differing levels of diversification in a portfolio. Previous literature [e.g. – Sharpe

(1964)] shows that diversification decreases risk, measured as the standard deviation of returns in

a portfolio, by adding securities to a portfolio. Additionally, investors seek positive skewness in

the return distribution of their portfolios to improve the probability of positive returns [Scott and

Horvath (1980)]. As international markets became more correlated over time, the benefits to

diversification in risk reduction should diminish, and positive skewness reduction should also be

mitigated. The first paper observes the relationship between diversification and risk and

skewness over time to test whether the benefits to diversification decreased in recent time

periods.

Using Datastream Global Indices [Thomson Reuters (2016)], portfolios were built by

adding indices to a portfolio. The standard deviations and skewness of the portfolios exhibited

normal risk-return and skewness behavior with decreasing standard deviations and skewness of

portfolios with higher levels of diversification. This suggests a trade-off between lower variance

and positively skewed returns.

Yield curve literature models were employed to estimate the amount of standard

deviation and skewness reduced from a given level of diversification for each decade [Nelson

4

and Siegel (1987)]. The percentage of standard deviation and positive skewness reduced through

diversification occurs at a much faster rate and with less diversification in the most recent time

period.

This result corresponds to an increase in the correlations of international stock market

index returns, suggesting international market integration could have decreased the amount of

diversification needed to eliminate risk. The results imply an international investor can achieve

the same level of risk reduction with less diversification currently than in previous decades, but

the loss of positive skewness also increases at a faster diversification rate than in the twentieth

century.

The second paper examines whether the relationship between returns and systematic and

idiosyncratic risk changed over time. Previous literature using international capital asset pricing

models (CAPM) show systematic risk does not affect country-level index returns, suggesting

segmented international markets. However, increasing correlations after the year 2000 among

stock market indices over time imply that markets across countries vary through global-wide

risks. Therefore, the second paper tests the impact of systematic risk and country-level risks on

index returns before and after the year 2000.

Similar to previous studies, this paper finds measures of systematic and country-level risk

using an international CAPM. The risk measures were conditioned on the positive or negative

environment of excess world market returns to reduce bias created from differing trading

environments, a procedure observed in domestic and international CAPM studies [Pettengill et al

(1995) and Fletcher (2000)]. Returns were regressed on the conditioned systematic and country-

level index risk measures.

5

The results show that systematic risk did not significantly affect returns in either time

period from regressions when looking at developed and emerging economies. The results remain

consistent for a sub-group of emerging economies when separating countries into developed and

emerging economies. However, systematic risk did significantly affect returns after the year

2000 in developed nations, a result most likely driven by the formation of the European Union.

Consequently, developed country stock market indices vary with global-wide risk factors when

making investment decisions, but systematic risks do not affect the variability in emerging

country markets.

The third paper observes the effect of integration on equity purchasing behavior of

investors across different countries. Investor forecasts across different countries should not

differ in an integrated market. Integrated international equity markets imply that index returns

vary according to global-wide risk factors, which would align domestic and foreign residents’

assessment of future equity returns. The third paper examines the equity purchasing behavior of

investors across two different time periods to digest the effect of integration on equity purchases

of investors in different countries.

Previous literature [Brennan and Cao (1997)] theoretical and empirically describes a

model of foreign investors equity purchasing, and the model states that foreign investors will

exhibit trend-following equity purchasing behavior when they possess an information

interpretation disadvantage to domestic investors. That is, foreign investors will purchase

foreign equities at a more rapid rate than domestic investors when indices in foreign markets see

an increase in returns, and vice versa. Accordingly, this paper tests the relationship between net

6

purchases of equities in foreign markets by U.S. investors and the stock market indices of those

markets.

The results of the regressions show that increases in foreign equity market returns

significantly affect U.S. investor purchases of foreign equities across time periods identified as

segmented and integrated international equity environments. The results suggest international

market integration did not affect the purchasing behavior of international investors, meaning

differences between foreign and domestic investor forecasts still exist. Alternative theoretical

models indicate foreign investors may see an incentive to specialize in domestic investing, even

though diversification benefits exist by adding international assets to a portfolio. This results in

foreign investor forecasts not aligning to their domestic counterparts.

Overall, this dissertation observes evidence resulting from the integration of international

equity markets. The investigation will provide international investors with incremental

information to more precisely build portfolios with international equities.

7

CHAPTER 2

INTERNATIONAL PORTFOLIO DIVERSIFICATION: THE COSTS AND BENEFITS

2.1 Introduction

This paper observes changes in diversification standard deviations and skewness of

international stock portfolios over a 37 year period. Contemporary finance literature states that

international markets have become more correlated in recent time periods, suggesting that

country-specific risks do not affect international portfolio returns with as much magnitude as in

past time periods. The integration of international markets implies a reduction in the amount of

diversification needed to eliminate the maximum amount of country-specific risk, or standard

deviation of returns, in a portfolio over time. Integration also implies a reduction in the amount

of positive skewness eliminated from diversification due to a trade-off between standard

deviation and skewness.

This study observes the change in the standard deviation and skewness of increasingly

more diverse international asset portfolios across different time segments to examine the effect

of international financial market integration on portfolio return moments. This research, thus,

observes the impact of financial market integration on portfolios of a typical international

investor.

Standard financial literature says that an investor can reduce risk in their portfolio by

diversifying with a wide range of assets. As an investor adds assets to their portfolio, the

investor will reduce the standard deviation of the returns of the portfolio, which allows them to

more accurately achieve a given level of return from the assets with less risk. The work of

Markowitz (1952), Sharpe (1964), and Lintner (1965) asserts that the total risk of a portfolio is

8

comprised of two types of risk, systematic risk and non-systematic risk. These papers present

the notion that diversification can eliminate non-systematic risk, but assets will always contain

some level of risk that varies with economic swings, or systematic risk. Thus, total risk of a

portfolio equals diversifiable risk plus the amount of systematic risk in a portfolio, or:

𝜎𝑇 = 𝜎𝑆 + 𝜎𝑁

where 𝜎𝑇 represents total risk, 𝜎𝑆 represents systematic risk, and 𝜎𝑁 represents non-systematic

risk. Diversification will eliminate 𝜎𝑁 by combining varying assets in a portfolio, but 𝜎𝑆 will

always remain due to systematic risks. The investor, therefore, aims to reduce as much non-

systematic risk as possible through diversification.

Early empirical studies of U.S. markets provide evidence to support the theoretical

diversification literature. Evans and Archer (1968) set the standard of such studies by conducting

an analysis of diversification and portfolio return variance using 470 stocks listed in the Standard

& Poor 500 index, where they found a statistically significant negative relationship between

diversification and risk. Specifically, they showed that adding stocks to a portfolio predictably

and stably reduced the standard deviation of portfolio returns. The authors indicate that adding

more than 10 different stocks to a portfolio provides limited additional benefit of risk reduction

when compared to the transaction costs. Many different authors since then support the

conclusions of Evans and Archer (1968) [e.g. – Reilly and Brown (2011)], and the academic and

investment communities alike adopted this corollary into common investment practice.

Several different studies point out that optimal diversification requires more

heterogeneous assets than Evans and Archer (1968) suggest. Statman (1987) provides similar

evidence to Evans and Archer (1968), but he implies that 30 to 40 stocks are necessary to

(1)

9

eliminate non-systematic risk in a portfolio. Campbell et al. (2001) advocate around 50 stocks is

needed for diversification benefits due to increased idiosyncratic risk in U.S. markets. Ang et al.

(2009) suggest that wide-ranging anomalies within financial markets caused the increase in the

amount of stocks needed to eliminate non-systematic risk. Ang et al. (2009) also provide

evidence of an inverse relationship between idiosyncratic risk and returns, which runs contrary to

the widely-held belief that higher risk is rewarded with higher returns. These papers all

consistently stress the importance of diversification in U.S. markets, especially in more recent

time periods of increased risk in the market, but the combined conclusions of these papers

suggest changing diversification behaviors of markets over time.

An investor can also reduce risk in their portfolio by diversifying with international

assets. Levy and Sarnat (1970) and Solnik (1974a) both indicate that an investor can significantly

reduce the risk of their portfolios when investing in a wide range of international stocks. Solnik

(1974b) and Grauer, Litzenberger, and Stehle (1976) used the studies of Levy and Sarnat (1970)

and Solnik (1974a) to build an international capital asset pricing model (iCAPM) similar to the

Markowitz (1952), Sharpe (1964), and Lintner (1965) model. The Solnik (1974b) and Grauer,

Litzenberger, and Stehle (1976) iCAPM substitutes the domestic market portfolio with an

international market portfolio. The domestic CAPM implies an investor should reduce risk

through diversification, which implicitly suggests international investors can achieve less risk

through diversification by investing in a broad range of international securities through the

iCAPM. Several studies thereafter showed that the iCAPM may not suffice as the only equation

to model international asset markets (e.g. – Bekaert, Hodrick, and Zhang (2009)), but Lewis

(2011) states that the iCAPM supplies the basis for arguing that investors can reduce domestic

portfolio risk by purchasing international securities.

10

Some recent bodies of research, though, provide evidence that investors may not choose

to fully eliminate all non-systematic risk in their portfolios through diversification. For example,

Goetzmann and Kumar (2004) use portfolio holdings of investors at a large U.S. brokerage firm

to show that most domestic investors hold four stocks or less in their portfolios, which hardly

comes close to the necessary 10 of Evans and Archer (1968) or 50 of Campbell et al. (2001).

Arditti (1967) and Scott and Horvath (1980), though, explain that investors prefer positive

skewness when building portfolios, and Simkowitz and Beedles (1978) and Hueng and Yau

(2006) empirically show that a trade-off exists between diversification and positive skewness.

Tang and Choi (1998) show the same trade-off exists across international equity index markets

as well. Consequently, investors may hold under-diversified portfolios in order to add positive

skewness.

Recent literature also indicates a decrease in the benefit of diversifying internationally in

the past few decades. Goetzmann et al. (2001) suggest investors gain from globalization through

increasing opportunities for investment internationally, but they lose out on this benefit due to

increasing cross-country stock market correlations. Goetzmann et al. (2001) also imply that the

diversification benefits available to an international investor mainly reside in emerging markets.

You and Daigler (2010) offer further support that international stock markets are becoming more

correlated by showing results that are robust to time-varying calculations of the correlation

statistics. They demonstrate that, through time, international indices exhibit higher standard

deviations with higher returns, but their result of recently high international index correlations

implies decreasing gains from diversification. They conclude that decreasing gains to

diversification provide a reasonable explanation for why an investor may under-diversify.

11

Some authors state that results showing increased international stock market correlations

imply that markets across the globe are becoming more integrated. Bekaert, Harvey, and

Lumsdaine (2002) indicate that returns in almost all international stock markets have become

integrated with each other since the mid-1990s. Hardouvelis, Malliaropulos, and Priestley

(2006) find that European markets became fully integrated in the second half of the 1990s due to

the formation of the European Union, and Carrieri, Errunz, and Hogan (2007) provide evidence

of integration within emerging markets. Consequently, increasing correlations of stock markets

across the globe imply international markets are affected by global-wide risk factors, which

reduces an investor’s ability to completely mitigate risk in their portfolios.

The studies discussed above indicate that an investor can reduce the standard deviation of

a portfolio by diversifying assets globally, and a trade-off exists between diversification and

positive skewness. However, this literature does not observe how these relationships change

over time in increasingly more correlated international stock markets.

This paper tests whether diversification directly impacts the standard deviation and

skewness of increasingly larger portfolios built from the perspective of an international investor.

The results show that investors can reduce volatility in their portfolios by increasingly adding

assets to their holdings, but portfolios built in recent time periods can eliminate more risk with

fewer assets than in previous decades. Additionally, increasingly more diverse portfolios deplete

their positive skewness, but the portfolios see higher reductions in positive skewness with less

diversification in more recent decades. Robustness checks reveal that investors building

portfolios with the highest historical return indices do not reduce as much risk in recent decades

than a naïve investor or an investor building portfolios with the lowest risk historical risk. This

12

suggests an investor sees less of an incentive to diversify in more recent time periods, depending

on the investment strategy of an individual.

2.2 Data and Methodology

This paper observes the statistical behavior of increasingly more diverse portfolios built

with international stock market indices. The analysis observes the standard deviation and

skewness of a portfolio with increasing diversification from the perspective of the international

index investor. This will examine how the statistical moments of a portfolio change with varying

levels of diversification using a broad range of country-level asset indices. The results will

illuminate if recent increases in international index correlations decreased benefits to

diversification across international stock markets over time.

The portfolio formation will follow the methodology conducted by Hueng and Yau

(2006). The data used represents U.S. dollar-dominated, daily stock-market index returns from

17 different countries obtained from Datastream. The indices represent a minimum of 75% to

80% of the market capitalization for each market, and the indices are called the Datastream

Global indices. The first column of Table 2.1 lists the different countries used. The sample

starts in January 1973 and ends in November of 2010 for a total of 9,892 daily observations over

four decades. Hong Kong presents the highest return and the highest standard deviation, and

Japan presents the lowest return. The U.S. gives the lowest standard deviation for the sample.

The Denmark index provides the highest value for the skewness of the distribution of returns, but

the Australian index donates the lowest skewness level.

In order to observe the moments on increasingly more diversified portfolios, the

following process was used to form the portfolios. First, a randomly chosen index constituted a

13

Table 1 Summary Statistics of International Market Indices

Country Mean Std. Dev. Skewness

Australia 0.050 1.370 -1.183

Austria 0.045 1.165 -0.025

Belgium 0.046 1.140 -0.075

Canada 0.044 1.067 -0.635

Denmark 0.055 1.259 0.345

France 0.052 1.307 -0.039

Germany 0.045 1.200 0.128

Hong Kong 0.063 1.817 -0.860

Ireland 0.047 1.328 -0.253

Italy 0.040 1.480 -0.044

Japan 0.036 1.282 0.049

Netherlands 0.052 1.192 -0.113

Singapore 0.044 1.447 -0.170

South Africa 0.059 1.650 -0.257

Switzerland 0.049 1.079 -0.170

UK 0.049 1.263 -0.020

US 0.043 1.035 -0.626

Mean 0.048 1.299 -0.232

Std. Dev. 0.007 0.208 0.385

Max 0.063 1.817 0.345

Min 0.036 1.035 -1.183

portfolio of one index. This portfolio represented a completely under-diversified portfolio. The

average return, variance, and skewness of this portfolio were found for each decade in the

sample period. The years from 1973 to 1979 comprised the 1970s1, the years from 1980 to 1989

compromised the 1980s, the years from 1990 to 1999 compromised the 1990s, and the years

from 2000 to 2010 compromised the 2000s. Then, another randomly chosen index was

combined with the first randomly chosen index to create a two-index portfolio. The average

daily return between these two indices was computed to find the portfolio returns for the sample

period. The standard deviation and skewness of the average daily returns of the newly formed

1 The 1970s time period begins in 1973 instead of 1970 because Datastream did not track global indices prior to

1973.

14

portfolio was then found for each decade in the sample period. Next, a third randomly chosen

index was added to the two-index portfolio to create a three-index portfolio, and the average

returns were computed for the newly formed, three-index portfolio. The standard deviation and

skewness of this portfolio were then computed for each decade over the sample period. This

process was repeated until a portfolio was formed that includes all of the available indices. This

gave the standard deviation and skewness of the average portfolio returns for each decade over

the sample period for increasingly more diversified portfolios. These observations show how the

risk statistics of a portfolio changed as it becomes increasingly more diversified for each decade.

This process was repeated 100 times to give further robustness to the portfolio creation process.

The standard deviation and skewness measures for each decade for each portfolio were averaged

over the 100 simulations to yield the final results.

The moments of the portfolio were calculated using the usual statistical calculations. The

portfolio average returns are calculated as the average of the returns of all of the indices in the

portfolio for each day in the sample period:

Rp,t = 1

N ∑ ri,t

N1 (1)

where ri,t represents the ith individual index return of day t and N gives the number of indices in

the portfolio. The simple mean formula defines the first moment of the average portfolio returns

for each decade:

𝜇𝑑 =1

𝑇∑ 𝑅𝑝,𝑡

𝑇1 (2)

15

where t still represents the days in the decade d, and T represents the total days in each decade d.

The standard deviation gives the second moment of the average portfolio returns, which is

defined as:

𝜎𝑑 = √∑ (Rp,t − μd

)2𝑇1 (3)

The sample skewness gives the third moment of the average portfolio returns:

𝛾𝑑 = √ 𝑛(𝑛−1)

(𝑛−2)∙

μ3

𝜎³ (4)

The standard deviation and skewness was calculated for each portfolio for each decade from the

1970s to the 2000s. The statistics for each decade was plotted against the number of indices in

the portfolio to observe how each statistic changes with increasing diversification. Comparing

the graphs of the different decades will allow for the observation on how the diversification

trade-off changes over time.

2.3 Results

2.3.1 Summary Statistics

Table 1 gives the summary statistics for the countries’ data used in the analysis. The first

column lists the countries included in the data set. The second column gives the means of the

daily returns over the entire date range of each country. The return averages range from the

highest coming in at 6.3% (Hong Kong) and the lowest at 3.6% (Japan). The third column states

the standard deviation of the returns for each country over the sample period, which ranges from

1.817 to 1.035 for Hong Kong and the United States, respectively. In terms of the traditional,

16

mean-variance framework, Hong Kong achieves the highest level of average return over this

period with the highest associated risk, but the U.S. achieves the lowest risk of the sample, even

though the United States does not see the lowest return. The fourth column gives the sample

skewness for each country, which ranges from 0.345 to -1.183 for the Denmark and Australia,

respectively. The data set contains 3 countries with positive skewness measures for the entire

period studied. The method described above will proceed to obtain the effect portfolio formation

has on higher moments of the return distribution.

2.3.2. Portfolio Formation Results

This paper seeks to observe the statistical behavior of portfolios as diversification of a

portfolio increases. Portfolio formation occurred by sequentially adding indices randomly to a

portfolio, and the statistical properties of each marginal portfolio were found for each decade in

the sample period, or from the 1970s to the 2000s. Daily data was used to observe the standard

deviation and skewness for each decade over the entire sample period. The results appear in

Figures 1 and 2. Figure 1 gives the standard deviation of each portfolio for each decade, and

Figure 2 gives the skewness of each portfolio for each decade. These graphs give the level of

standard deviation and skewness relative to each decade. Each graph gives the respective statistic

on the vertical axis of the graph, and the number of indices in the portfolio resides on the

horizontal axis of the graph. Therefore, each line in the graph gives the statistic with one

through 17 indices in the portfolio. The graphs were then scaled to the 1970 decade, so the lines

in each figure starts at the same point. This gives perspective on how the slopes of the graphs

change over time. The scaled graphs appear in Figures 3 and 4 for standard deviation and

skewness, respectively.

17

Figure 1 Standard Deviation against Diversification – Portfolios Built by Randomly

Choosing Indices

Figure 2 Skewness against Diversification - Portfolios Built by Randomly Choosing Indices

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Sta

nd

ard

Dev

iati

on

Number of Indices in the Portfolio

70s

80s

90s

00s

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Sk

ewn

ess


70s

80s

90s

00s

18

Figure 3 Scaled Standard Deviation against Diversification - Portfolios Built by Randomly

Choosing Indices

Figure 4 Scaled Skewness against Diversification – Portfolios Built by Randomly Choosing

Indices

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Sta

nd

ard

Dev

iati

on

Number of Indicies in the Portfolio

70s

80s

90s

00s

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Sk

ewn

ess


70s

80s

90s

00s

19

Figure 1 shows that the standard deviation of a portfolio decreases as more indices are

added to the portfolio for all decades. This conforms to standard financial literature that

indicates the riskiness of a portfolio decreases with diversification when using standard deviation

as a measure of riskiness. The result seen in Figure 1 corresponds with the same general

conclusions as Hueng and Yau (2006) and Tang and Choi (1998) in that increases in

diversification correspond to lower levels of risk. Figure 1 also shows that the overall level of

standard deviation increased from the 1970s to the 2000s. The level of risk increased from the

1970s to the 1980s, but the level of risk fell slightly from the 1980s to the 1990s. However, the

risk level increased, again, over that of all other decades for the 2000s, so the general results

reveal that the level of risk increased over the sample period.

Previous literature shows increasing correlations of international stock markets

throughout the world, so this increase in the levels of risk corresponds to the increase in

correlation. However, this does not give a full analysis of the gains from diversification. The

graphs obviously show that an investor gains from diversifying by decreasing the risk, but the

percentage change in standard deviation from increasing diversification will indicate the benefit

from diversification for each decade.

A non-linear estimation of the diversifiable and diversified risk at each portfolio will

indicate the effect of diversification on risk. The literature modeling yield curves will provide a

model for this estimation (Nelson and Siegel (1987); Hueng and Yau (2006)) The model follows

as:

𝑅𝑖,𝑛 = 𝑎𝑖 + 𝑏𝑖 ∙ 1

exp (𝑛) + 𝑐𝑖 ∙

𝑛

exp (𝑛) + 𝑒𝑖,𝑛 (5)

20

where R represents either the standard deviation or skewness, i = 1, 2, …, 100 repetitions, and

n = 1, 2, …, 17 indices in the portfolio. Each statistic contains an asymptote a, and the second

and third terms of Equation (5) both decay as n increases relative to the values of b and c. The

coefficient a in this model represents the long-term risk that is systematic, or non-diversifiable.

The coefficients b and c represent the low and medium term risks, respectively, seen in the

standard deviation curves, since they both decay based on the number of indices in the portfolio.

This model allows for monotonic, humped, or S-shapes of the statistics if the values of b and c

call for it. The diversifiable risk is described as:

𝑏+𝑐

exp (1)(6)

The diversified risk is, then, is :

𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑓𝑖𝑒𝑑 𝑅𝑖𝑠𝑘: 𝑏+𝑐

exp (1)− [b ·

1

exp (𝑛) + c ·

𝑛

exp (𝑛)] (7)

Panel (A) of Table 2 gives the estimated results of the coefficients of Equation 5 for each

decade averaged over the 100 simulations and the t-statistics of the averages. All coefficients are

positive and statistically significant, indicating that all levels of diversification significantly

affect risk. Panel (B) gives the estimated diversified risk, and how much of this risk is

diversified when adding n indices to the portfolio. Table 4 combines the results for an easy

comparison. The percentage diversified when adding 1 index to the portfolio (meaning n = 2) is

39.0% in the 1970s, but the percentage diversified at this level of diversification is 44.9% in the

2000s. Consequently, the benefit, in terms of reduced standard deviation, to diversification at

this diversification level increased from the 1970s to the 2000s. This remains true for all levels

21

Table 2 Diversified Structure of Standard Deviation Risk Results – Portfolios Built by

Randomly Choosing Indices

(A)

70s t-statistic 80s t-statistic 90s t-statistic 00s t-statistic

a 0.595 191.195 0.771 324.449 0.726 309.945 1.141 360.310

b 0.597 4.432 0.537 5.495 0.405 4.556 0.430 5.257

c 1.149 13.362 0.801 11.050 0.537 7.826 0.425 5.634

(B)

Diversifiable

Risk: 0.642 0.492 0.346 0.315

Diversified

Risk: Level % Change Level % Change Level % Change Level % Change

n = 2 0.250 39.0% 0.203 41.2% 0.146 42.2% 0.141 44.9%

3 0.441 68.7% 0.346 70.3% 0.246 71.0% 0.230 73.0%

4 0.547 85.2% 0.424 86.1% 0.300 86.5% 0.276 87.6%

5 0.599 93.3% 0.462 93.8% 0.325 94.0% 0.297 94.5%

6 0.623 97.1% 0.479 97.3% 0.337 97.4% 0.307 97.7%

7 0.634 98.8% 0.487 98.9% 0.342 98.9% 0.312 99.0%

8 0.639 99.5% 0.490 99.5% 0.345 99.5% 0.313 99.6%

9 0.641 99.8% 0.491 99.8% 0.346 99.8% 0.314 99.8%

10 0.641 99.9% 0.492 99.9% 0.346 99.9% 0.314 99.9%

11 0.642 100.0% 0.492 100.0% 0.346 100.0% 0.315 100.0%

12 0.642 100.0% 0.492 100.0% 0.346 100.0% 0.315 100.0%

13 0.642 100.0% 0.492 100.0% 0.346 100.0% 0.315 100.0%

14 0.642 100.0% 0.492 100.0% 0.346 100.0% 0.315 100.0%

15 0.642 100.0% 0.492 100.0% 0.346 100.0% 0.315 100.0%

16 0.642 100.0% 0.492 100.0% 0.346 100.0% 0.315 100.0%

17 0.642 100.0% 0.492 100.0% 0.346 100.0% 0.315 100.0%

of diversification when comparing the 1970s to the 2000s, that is, until diversification eliminates

99% of the diversifiable risk in each decade. Diversification in the 2000s decade eliminates

87.6% of the diversifiable risk in the portfolios after adding 4 indices, whereas 85.2% of

diversifiable risk was eliminated after adding 4 indices to the portfolios in the 1970s. This

implies that most of the diversifiable risk was eliminated after adding 4 indices to the portfolio,

since further index additions produce marginal results when considering adding additional

22

indices will increase transaction costs. However, the results show that more risk was eliminated

with 4 indices in the 2000s than in the 1970s. The 1980s and 1990s present similar percentage

values, both of which are larger than the percentages seen in the 1970s. The 2000s decade sees

larger percentage diversifiable risk reduction values than all other decades. These observations

all indicate that the benefits to diversification are greater in more recent periods than in the past.

Figure 2 shows that the skewness of a portfolio decreases as more indices are added to

the portfolio. Again, this corresponds to Hueng and Yau (2006) and Tang and Choi (1998) by

showing that higher levels of diversification cause lower levels of skewness. The results shown

here confirm these two previous paper’s conclusions that diversification decreases risk in a

portfolio at the cost of more positively skewed portfolios. Also, the overall level of skewness

decreased from the 1970s to the 2000s, but the results for skewness do not present a clear enough

implication to make a straightforward conclusion. The skewness level decreased dramatically

from the 1970s to the 1980s2, and the level of skewness increased from the 1980s to the 1990s.

The 1990s and 2000s present similar levels, but the paths of the 1990s line and the 2000s cross.

Therefore, the results of the change in the levels of skewness do not clearly suggest a complete

increase or decrease in their levels. However, the crossing of the curves of the 1990s and 2000s

indicates that the costs of diversification changed over time, so the costs to diversification

changed over at least this time period.

Figure 4 shows the same graphs produced in Figure 3 scaled to the 1970s line to allow for

the analysis of how the slopes change relative to the passage of time. Again, the results do not

present a clear conclusion. Overall, the slope of skewness across diversification appears to have

2 Increased world-wide economic and political turmoil most likely caused the dramatic decrease of skewness in the

1980s.

23

increased from the 1970s to the 2000s, which indicates that the costs of diversification when

measured by skewness have increased. This suggests that the increase in the benefits to

diversification accompany increases in the costs to diversification.

Estimations of Equation 5 for skewness are presented in Panel (A) of Table 3. The

Table 3 Diversified Structure of Skewness Results – Portfolios Built by Randomly

Choosing Indices

(A)


a 0.038 4.554 -1.428 -55.348 -0.377 -55.775 -0.310 -58.337

b -0.349 -1.539 0.850 1.418 -0.500 -2.924 0.273 1.837

c 0.824 4.243 0.467 0.812 1.324 8.272 0.316 2.333

(B)

Diversifiable

Skewness: 0.175 0.484 0.303 0.217

Diversified

Skewness: Level % Change Level % Change Level % Change Level % Change

n = 2 -0.001 -0.6% 0.243 50.2% 0.013 4.1% 0.094 43.5%

3 0.069 39.5% 0.372 76.9% 0.130 43.0% 0.156 72.0%

4 0.121 69.1% 0.435 89.7% 0.215 71.0% 0.189 87.0%

5 0.149 85.5% 0.463 95.6% 0.262 86.4% 0.204 94.2%

6 0.163 93.5% 0.475 98.1% 0.285 93.9% 0.211 97.5%

7 0.170 97.2% 0.481 99.2% 0.295 97.4% 0.215 99.0%

8 0.173 98.8% 0.483 99.7% 0.300 98.9% 0.216 99.6%

9 0.174 99.5% 0.484 99.9% 0.302 99.5% 0.216 99.8%

10 0.174 99.8% 0.484 99.9% 0.303 99.8% 0.217 99.9%

11 0.175 99.9% 0.484 100.0% 0.303 99.9% 0.217 100.0%

12 0.175 100.0% 0.484 100.0% 0.303 100.0% 0.217 100.0%

13 0.175 100.0% 0.484 100.0% 0.303 100.0% 0.217 100.0%

14 0.175 100.0% 0.484 100.0% 0.303 100.0% 0.217 100.0%

15 0.175 100.0% 0.484 100.0% 0.303 100.0% 0.217 100.0%

16 0.175 100.0% 0.484 100.0% 0.303 100.0% 0.217 100.0%

17 0.175 100.0% 0.484 100.0% 0.303 100.0% 0.217 100.0%

estimated coefficients of a are negative and significant at the 5% level for all decades. The

significance of the a coefficient suggests that complete diversification negatively affected

24

Table 4 Percent Diversified Structure of Standard Deviation and Skewness for Each

Portfolio – Portfolios Built by Randomly Choosing Indices

Standard

Deviation Skewness

n 70s 80s 90s 00s n 70s 80s 90s 00s

2 39.0% 41.2% 42.2% 44.9% 2 -0.6% 50.2% 4.1% 43.5%

3 68.7% 70.3% 71.0% 73.0% 3 39.5% 76.9% 43.0% 72.0%

4 85.2% 86.1% 86.5% 87.6% 4 69.1% 89.7% 71.0% 87.0%

5 93.3% 93.8% 94.0% 94.5% 5 85.5% 95.6% 86.4% 94.2%

6 97.1% 97.3% 97.4% 97.7% 6 93.5% 98.1% 93.9% 97.5%

7 98.8% 98.9% 98.9% 99.0% 7 97.2% 99.2% 97.4% 99.0%

8 99.5% 99.5% 99.5% 99.6% 8 98.8% 99.7% 98.9% 99.6%

9 99.8% 99.8% 99.8% 99.8% 9 99.5% 99.9% 99.5% 99.8%

10 99.9% 99.9% 99.9% 99.9% 10 99.8% 99.9% 99.8% 99.9%

11 100.0% 100.0% 100.0% 100.0% 11 99.9% 100.0% 99.9% 100.0%

12 100.0% 100.0% 100.0% 100.0% 12 100.0% 100.0% 100.0% 100.0%

13 100.0% 100.0% 100.0% 100.0% 13 100.0% 100.0% 100.0% 100.0%

14 100.0% 100.0% 100.0% 100.0% 14 100.0% 100.0% 100.0% 100.0%

15 100.0% 100.0% 100.0% 100.0% 15 100.0% 100.0% 100.0% 100.0%

16 100.0% 100.0% 100.0% 100.0% 16 100.0% 100.0% 100.0% 100.0%

17 100.0% 100.0% 100.0% 100.0% 17 100.0% 100.0% 100.0% 100.0%

skewness of the portfolios. All coefficients of b are insignificant from zero, except the in 1990s

with the coefficient negative and significant. The insignificance of the b coefficient in the 1970s,

1980s, and 2000s indicates low levels of diversification do not affect total skewness of the curve

in those time periods. The negative and significant b coefficient in the 1990s states that low

levels of diversification impacted skewness in the 1990s. All c coefficients are positive and

significant for all decades other than the 1980s, where the coefficient is not significantly

different from zero. The significance c coefficient, other than in the 1980s, indicates that mid-

levels of diversification affected the total skewness of the curve in those time periods.

Panel (B) gives the estimated diversified skewness, and how much of this risk is diversified

when adding n indices to the portfolio. Similar to the values observed with standard deviations,

the 2000s decade sees the largest reduction in positive skewness at 43.5% with two indices added

25

to the portfolio than any other decade. In the 2000s, 87% of all skewness is reduced with a 4

index portfolio, while only 69.1% of skewness was reduced in the 1970s with 4 indices added to

the portfolio. The larger percentage of diversified skewness at the increasing levels of

diversification indicates increasing diversification decreases skewness across the overall time

period, which implies a trade-off to diversification exists, similar to results seen in other studies.

However, the increase in percent of positive skewness diversified away in more recent periods

shows that investors lose out on positive skewness more rapidly in the new millennium than in

previous decades. The percentage reduction of positive skewness occurs with almost the same

percentage as the reduction in standard deviations of the same portfolios, indicating a symmetric

trade-off. However, the level of positive skewness increased since the 1980s, as seen in Figures

2 and 4, suggesting a benefit to consumers.

2.4 Robustness Checks

Malkiel (1973) stated, “a blindfolded monkey throwing darts at a newspaper’s financial

pages could select a portfolio that would do just as well as one carefully selected by experts.”

Investors, therefore, may choose to follow the naïve investment strategy outlined in (3) above.

The naïve portfolio creation strategy may not reflect an investment strategy used by the typical

investor. In order to test the robustness of the results seen above, the standard deviation,

skewness, diversifiable risk, and diversified risk of sequentially larger portfolios was calculated

in the manner outlined above using two different portfolio creation strategies. The first strategy

assumes an investor will build a portfolio by choosing to invest in the index with the highest

historical average out of the dataset first to build a portfolio with one index. The investor will

then add the index to the portfolio with the second highest historical average return. Then, the

26

investor will add the index to the portfolio with the third highest historical average return, and

this will continue until the portfolio contains all 17 indices in the data set. The second strategy

will use the same format, but the investor will sequentially add indices to the portfolio with the

lowest historical risk, or standard deviation.

2.4.1 Highest Historical Return Portfolio Creation

An investor building a portfolio by sequentially adding indices to the portfolio with the next

highest historical returns will see similar standard deviations characteristics as the naïve investor,

indicating the diversification-risk relationship consistently appears regardless of investment

strategies. Figure 5 shows the standard deviations of portfolios of a high-return minded

Figure 5 Standard Deviation against Diversification – Portfolios Built by Adding Indices

with Highest Historical Average Return

investor as indices are added to the portfolio for each decade, similar to Figure 1 of the naïve

investor. Figure 5 shows that the standard deviation of the portfolio decreases as indices are

added to the portfolio, suggesting that the investor decreases the risk of the portfolio by

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Sta

nd

ard

Dev

iati

on

Number of Indices in Portfolio

70s

80s

90s

00s

27

diversifying assets. Figure 5 also shows that overall standard deviation increased from the 1970s

to 2000s. This indicates an overall increase in systematic risk, similar to the results seen in

Figure 1.

Table 5 shows the diversifiable risk and diversified risk associated with each portfolio for the

high-return minded investor as described by equations (5) – (7). Panel (A) shows all of the


Adding Indices with Highest Historical Average Return

(A)


a 0.630 36.178 0.830 50.957 0.752 81.566 1.216 98.417

b 2.477 5.303 1.359 3.110 1.147 4.639 0.071 0.215

c 1.733 4.350 1.749 4.694 1.296 6.146 0.698 2.468

(B)

Diversifiable

Risk: 1.549 1.143 0.899 0.283

Diversified


n=2 0.744 48.1% 0.486 42.5% 0.393 43.7% 0.084 29.8%

3 1.167 75.3% 0.814 71.2% 0.648 72.1% 0.175 61.9%

4 1.376 88.9% 0.990 86.6% 0.783 87.1% 0.231 81.5%

5 1.474 95.2% 1.075 94.0% 0.848 94.3% 0.259 91.5%

6 1.517 97.9% 1.114 97.4% 0.877 97.5% 0.272 96.3%

7 1.535 99.1% 1.131 98.9% 0.890 99.0% 0.278 98.4%

8 1.543 99.6% 1.138 99.5% 0.895 99.6% 0.281 99.3%

9 1.546 99.9% 1.141 99.8% 0.897 99.8% 0.282 99.7%

10 1.548 99.9% 1.142 99.9% 0.898 99.9% 0.283 99.9%

11 1.548 100.0% 1.143 100.0% 0.899 100.0% 0.283 100.0%

12 1.549 100.0% 1.143 100.0% 0.899 100.0% 0.283 100.0%

13 1.549 100.0% 1.143 100.0% 0.899 100.0% 0.283 100.0%

14 1.549 100.0% 1.143 100.0% 0.899 100.0% 0.283 100.0%

15 1.549 100.0% 1.143 100.0% 0.899 100.0% 0.283 100.0%

16 1.549 100.0% 1.143 100.0% 0.899 100.0% 0.283 100.0%

17 1.549 100.0% 1.143 100.0% 0.899 100.0% 0.283 100.0%

28

coefficients are positive and significant at the 5% level, except the b coefficient in the 2000s

decade. The significant coefficients show that all levels of diversification significantly affect

risk for most all decades. This result mimics the results observed with the naïve investor,

suggesting the diversification reduces risk regardless of the investment strategy.

Panel (B) shows the diversifiable risk and the risk diversified away with each associated

portfolio. Table 6 combines the percentages of Table 5 in a concise manner to make the

comparisons between decades easier to read. The standard deviation sections of Table 6 shows


Portfolio –Portfolios Built by Adding Indices with Highest Historical Return Standard

Deviation Skewness

n 70s 80s 90s 00s n 70s 80s 90s 00s

2 48.1% 42.5% 43.7% 29.8% 2 28.8% 87.5% 93.4% 117.2%

3 75.3% 71.2% 72.1% 61.9% 3 61.1% 104.3% 108.7% 126.2%

4 88.9% 86.6% 87.1% 81.5% 4 81.0% 104.9% 107.3% 116.9%

5 95.2% 94.0% 94.3% 91.5% 5 91.3% 103.0% 104.2% 108.9%

6 97.9% 97.4% 97.5% 96.3% 6 96.2% 101.5% 102.1% 104.3%

7 99.1% 98.9% 99.0% 98.4% 7 98.4% 100.7% 101.0% 101.9%

8 99.6% 99.5% 99.6% 99.3% 8 99.3% 100.3% 100.4% 100.8%

9 99.9% 99.8% 99.8% 99.7% 9 99.7% 100.1% 100.2% 100.4%

10 99.9% 99.9% 99.9% 99.9% 10 99.9% 100.1% 100.1% 100.2%

11 100.0% 100.0% 100.0% 100.0% 11 100.0% 100.0% 100.0% 100.1%

12 100.0% 100.0% 100.0% 100.0% 12 100.0% 100.0% 100.0% 100.0%

13 100.0% 100.0% 100.0% 100.0% 13 100.0% 100.0% 100.0% 100.0%

14 100.0% 100.0% 100.0% 100.0% 14 100.0% 100.0% 100.0% 100.0%

15 100.0% 100.0% 100.0% 100.0% 15 100.0% 100.0% 100.0% 100.0%

16 100.0% 100.0% 100.0% 100.0% 16 100.0% 100.0% 100.0% 100.0%

17 100.0% 100.0% 100.0% 100.0% 17 100.0% 100.0% 100.0% 100.0%

that the percent of risk diversified away increases as indices were added to the portfolios,

coinciding with the graphical result seen in Figure 5. The data in the third row of Table 6 shows

the percent of risk diversified with only two indices in the portfolio (i.e. – n = 2). The percent of

risk diversified away with this portfolio decreases in more recent decades. The 1970s showed

29

88.9% of risk reduced through diversification with four indices, but later decades showed less

risk reduced. The reduction in the amount of risk diversified away in later time periods with this

investment strategy differs from the results of the naïve investor where less diversified portfolios

eliminated more risk in more recent time periods than older decades.

Figure 6 displays the skewness of portfolios built by the high-return minded investor for the

four different decades in the data set used in this study. Similar to Figure 2, skewness decreases

as indices are added to the portfolio for the 1970s and 1990s. Skewness decreases as

Figure 6 Skewness against Diversification - Portfolios Built by Adding Indices with Highest

Historical Average Return

the first three indices are added to the portfolio for the 2000s decade, but the skewness increases

and decreases in low magnitudes as additional indices are added to the portfolio. Skewness for

the 1980s shows a pattern much different from the other decades and the naïve investor

approach. Skewness increases as portfolios are added to the portfolio, and the skewness level for

the portfolio with a single index was far below the other decades. The skewness level continues

-3.5

-3

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80s

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30

to increase and decrease as more indices are added to the portfolio. Otherwise, the skewness

level shifts follow the same pattern as the naïve investor, shown in Figure 2. The skewness level

shifts downward from the 1970s to the 1980s, but increases for the 1990s and, subsequently, the

2000s. The overall skewness level decreased from the 1970s to the 2000s, but the decrease and

increase arrangement does not present a clear implication.

The estimated coefficients of Equation 5 for skewness of the high-return minded investor are

shown in Panel (A) of Table 7. All coefficients are statistically significant at the 5% level for

Table 7 Diversified Structure of Skewness Results –Portfolios Built by Adding Indices with

Highest Historical Return

(A)


a 0.038 2.069 -1.325 -28.747 -0.477 -76.059 -0.289 -23.488

b 0.073 0.148 -8.244 -6.665 3.871 23.028 1.533 4.649

c 1.068 2.555 3.276 3.106 -1.744 -12.165 -0.911 -3.241

(B)

Diversifiable

Risk: 0.420 -1.828 0.783 0.229

Diversified


n=2 0.121 28.8% -1.599 87.5% 0.731 93.4% 0.268 117.2%

3 0.256 61.1% -1.907 104.3% 0.850 108.7% 0.289 126.2%

4 0.340 81.0% -1.917 104.9% 0.839 107.3% 0.267 116.9%

5 0.383 91.3% -1.882 103.0% 0.815 104.2% 0.249 108.9%

6 0.403 96.2% -1.856 101.5% 0.799 102.1% 0.238 104.3%

7 0.413 98.4% -1.841 100.7% 0.790 101.0% 0.233 101.9%

8 0.417 99.3% -1.834 100.3% 0.786 100.4% 0.231 100.8%

9 0.418 99.7% -1.830 100.1% 0.784 100.2% 0.230 100.4%

10 0.419 99.9% -1.829 100.1% 0.783 100.1% 0.229 100.2%

11 0.419 100.0% -1.828 100.0% 0.783 100.0% 0.229 100.1%

12 0.419 100.0% -1.828 100.0% 0.783 100.0% 0.229 100.0%

13 0.419 100.0% -1.828 100.0% 0.783 100.0% 0.229 100.0%

14 0.420 100.0% -1.828 100.0% 0.783 100.0% 0.229 100.0%

15 0.420 100.0% -1.828 100.0% 0.783 100.0% 0.229 100.0%

16 0.420 100.0% -1.828 100.0% 0.783 100.0% 0.229 100.0%

17 0.420 100.0% -1.828 100.0% 0.783 100.0% 0.229 100.0%

31

all decades, except the b coefficient in the 1970s. Again, the significant coefficients show that

all levels of diversification significantly affect risk for most all decades. Panel (B) provides the

estimated diversified skewness and the amount of skewness diversified away as indices were

added to the portfolio. Table 6 combines the percentages of skewness diversified in a condensed

format for easier comparison across decades and diversification levels. The results for the 1970s

shows a similar pattern to those of the naïve investor with the percent of skewness diversified

increasing as indices are added to the portfolio, starting from a low percentage and eventually

reaching 99% skewness diversified with eight indices. However, the 1980s, 1990s, and 2000s

show greater than 100% skewness diversified with three indices added to the portfolio. The

2000s decade indicates that 117% of skewness was reduced with only two indices. The

estimation of diversified skewness in equations (5) – (7) imply that the total level of skewness

will converge to a given level after a certain number of indices are added to the portfolio. This

characteristic of the estimation technique is observed as all of the decades reach 100%

diversification with 11 indices, and the percentage does not change as more indices are added.

Thus, the percentages greater than 100% indicate that the percent of skewness reduced exceeds

that of the converging level attained with a portfolio of 11 indices or more.

The skewness percentages in Table 6 increase at every level of diversification when

observing the values from the 1970s to the 2000s. The larger percentages in more recent time

periods follows the same pattern as the naïve investor displayed in Table 4. Investors value

higher positive levels of skewness, and diversification presents a cost of skewness to the investor

because diversification reduces positive skewness. This cost increased in more recent time

periods for the high-return minded investor. However, a high-return minded investor in more

recent time periods needs more diversification compared to an investor in older decades to

32

reduce the standard deviation of a portfolio. Consequently, in more recent decades, the high-

return minded investor has less of an incentive to diversify in more recent time periods than

previous decades.

Figure 7 and Figure 8 show the same graphs formed in Figure 5 and Figure 6, respectively,

scaled to the 1970s line to more easily analyze how the slopes change over time. Figure 7 shows

that the percentage of risk reduced through diversification in the 2000s is less than the 1970s,

which mirrors the results seen in Tables 5 and 6. Figure 8 also emulates the data seen in Tables

6 and 7 with skewness decreasing steadily in the 1970s. The over- reduction of skewness with

Figure 7 Scaled Standard Deviation against Diversification – Portfolio Built by Adding

Indices with Highest Historical Average Return

0

0.5

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

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80s

90s

00s

33

Figure 8 Scaled Skewness against Diversification - Portfolio Built by Adding Indices with

Highest Historical Average Return

diversification also is apparent in Figure 8. For example, the 2000s line shows a reduction to a

skewness level with a portfolio comprised of two indices greater than the skewness level with a

portfolio with 11 indices.

2.4.2 Lowest Historical Risk Portfolio Creation

The standard deviations of the low-risk minded investor follow similar trends as the naïve

and high-return minded investors. Figure 9 shows line graphs of the standard deviations as

sequentially more indices are added to the portfolio across the four different decades in the

dataset. Overall, the standard deviation of the portfolio decreases as additional indices are added

to the portfolio. Also, the standard deviation levels increased from the 1970s to the 2000s,

signifying an increase in systematic risk in more recent time periods. The non-smooth line

-1

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0

0.5

1

1.5

2

2.5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

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70s

80s

90s

00s

34

Figure 9 Standard Deviation against Diversification – Portfolios Built by Adding Indices

with Lowest Historical Standard Deviation

graphs of the 1980s, 1990s, and 2000s stem from the standard deviations for different countries

varying over time. Even though the lines do not show a smooth slope similar to Figure 1, the

overall trend and level shifts between the decades remains consistent for all three portfolio

creation strategies. This is more clearly seen in Figure 10, which shows the same graphs formed

in Figure 9 scaled to the 1970s line to more easily analyze how the slopes change over time.

Panel (A) of Table 8 shows the results for equation (5) for the standard deviations of the

portfolios of the low-risk minded investor. All of the coefficients are statistically significant at

the 5% level except coefficients b and c in the 2000s decade. The significant coefficients show

that all levels of diversification significantly affect risk for most all decades. The significance of

the a coefficient suggests that complete diversification positively affected the standard deviation

of the portfolios in all decades, but the insignificance of the b and c coefficients in the 2000s

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

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80s

90s

00s

35

Figure 10 Scaled Standard Deviation against Diversification – Portfolio Built by Adding

Indices with Lowest Historical Standard Deviation

indicates that low and mid-levels of diversification on their own do not affect the total standard

deviation of the curve in that decade.

Panel (B) shows the diversifiable risk and risk diversified at a given level of

diversification. Table 10 condenses the percentages of Panel (B) in Table 8 into a format that

eases the comparison between the decades. Similar to the naïve investor, the low-risk minded

investor needs less diversification to reduce portfolio risk in recent decades than in the more

distant past. A low-risk minded investor reduced 87.6% of risk with four indices in the 1970s,

while an investor in the 2000s reduced 96.1%. Alternatively, an investor with a portfolio

containing only two indices reduced 45% of the diversifiable risk in the 1970s, but an investor in

the 2000s reduced 66% of the diversifiable risk with a two index portfolio. This shows that a

low-risk minded investor saw similar increases in risk diversified away in more recent times as

0

0.1

0.2

0.3

0.4

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0.6

0.7

0.8

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80s

90s

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36


Adding Indices with Lowest Historical Standard Deviation

(A)


a 0.540 175.001 0.723 133.599 0.696 145.525 1.140 123.718

b 0.506 6.109 0.464 3.194 0.748 5.829 0.484 1.957

c 0.497 7.042 0.294 2.378 -0.400 -3.652 -0.033 -0.159

(B)

Diversifiable

Risk: 0.369 0.279 0.128 0.166

Diversified

Risk Level % Change Level % Change Level % Change Level % Change

n=2 0.166 45.0% 0.136 48.9% 0.135 105.4% 0.109 65.9%

3 0.269 73.0% 0.212 76.0% 0.151 117.5% 0.147 88.5%

4 0.323 87.6% 0.249 89.2% 0.144 112.2% 0.159 96.1%

5 0.349 94.5% 0.266 95.3% 0.137 106.6% 0.163 98.7%

6 0.36 97.7% 0.273 98.0% 0.132 103.2% 0.165 99.6%

7 0.365 99.0% 0.277 99.2% 0.13 101.5% 0.165 99.9%

8 0.367 99.6% 0.278 99.7% 0.129 100.6% 0.166 100.0%

9 0.368 99.8% 0.279 99.9% 0.128 100.3% 0.166 100.0%

10 0.369 99.9% 0.279 99.9% 0.128 100.1% 0.166 100.0%

11 0.369 100.0% 0.279 100.0% 0.128 100.0% 0.166 100.0%

12 0.369 100.0% 0.279 100.0% 0.128 100.0% 0.166 100.0%

13 0.369 100.0% 0.279 100.0% 0.128 100.0% 0.166 100.0%

14 0.369 100.0% 0.279 100.0% 0.128 100.0% 0.166 100.0%

15 0.369 100.0% 0.279 100.0% 0.128 100.0% 0.166 100.0%

16 0.369 100.0% 0.279 100.0% 0.128 100.0% 0.166 100.0%

17 0.369 100.0% 0.279 100.0% 0.128 100.0% 0.166 100.0%

the naïve investor. This differs from the high-return minded investor that saw decreases in the

amount of risk diversified over time within the same levels of diversification. Consequently, the

change in diversification benefits over time depends on the investment strategy of an investor.

The line graphs in Figure 11 depict the skewness of portfolios built by the low-risk

minded investor across the four decades in this study. Figure 12 shows the same graph formed

37

Figure 11 Skewness against Diversification - Portfolios Built by Adding Indices with

Highest Historical Average Return

Figure 12 Scaled Skewness against Diversification - Portfolio Built by Adding Indices with

Lowest Historical Standard Deviation

-3

-2.5

-2

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-1

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0

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

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80s

90s

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38

in Figure 10 scaled to the 1970s line to more easily analyze how the slopes change over time.

The 1970s line decreases in a pattern similar to the other portfolio creation strategies with

decreases in skewness as diversification increases. However, skewness increases after 10 indices

are added to the portfolio. The 1980s overall trend is similar to the trend viewed with the high-

return minded investor, where skewness starts at a lower level compared to the other decades,

then increases with increased diversification. After 12 indices are added to the portfolio,

skewness decreases in the 1980s. The 1990s and 2000s graphs follow comparable trends.

Creating a two-index portfolio reduces skewness in the portfolio from a single-index portfolio,

but skewness increases to a fairly steady level as more indices were added to the portfolio. The

level shifts between the different decades, however, remain consistent across all three investment

strategies. The skewness level drops from the 1970s to the 1980s, and then increases in the

1990s. The 2000s saw a full diversification level (i.e. – the 17-index portfolio) above the 1990s.

This clearly shows that the skewness level changed over the sample period to a level less than

that of the 1970s.

The data displayed in Panel (A) of Table 9 show the estimated coefficients and their

respective t-statistics for skewness for equation (5). All of the coefficients are statistically

significant in all decades, except the c coefficient in the 1970s and the b coefficient in the 1980s.

The significant coefficients demonstrate that all levels of diversification significantly affect

skewness for most all time periods. The insignificance of the b coefficient in the 1980s indicates

that low levels of diversification do not affect the total skewness of the curve in that decade, and

the insignificance of the c coefficient signifies that mid-levels of diversification do not affect

total skewness in the 1970s. Panel (B) shows the diversifiable risk and amount of risk

diversified at each level of diversification for each decade according to equations (6) and (7).

39

Table 9 Diversified Structure of Skewness Results – Portfolios Built by Adding Indices with

Lowest Historical Standard Deviation

(A)


a -0.158 -7.151 -1.073 -10.762 -0.324 -19.004 -0.263 -21.187

b 1.714 2.897 1.544 0.577 1.797 3.928 3.360 10.093

c -0.519 -1.029 -4.967 -2.176 -1.809 -4.637 -2.807 -9.886

(B)

Diversifiable

Risk: 0.439 -1.259 -0.004 0.204

Diversified


n=2 0.348 79.2% -0.124 9.8% 0.242 -5378.3% 0.509 249.9%

3 0.432 98.2% -0.594 47.2% 0.176 -3917.1% 0.455 223.8%

4 0.446 101.5% -0.924 73.3% 0.095 -2114.2% 0.348 170.8%

5 0.445 101.4% -1.102 87.5% 0.044 -985.5% 0.275 135.3%

6 0.443 100.8% -1.189 94.4% 0.018 -399.0% 0.237 116.4%

7 0.441 100.4% -1.229 97.6% 0.005 -120.2% 0.218 107.3%

8 0.440 100.2% -1.246 99.0% -0.000 5.5% 0.210 103.1%

9 0.440 100.1% -1.254 99.6% -0.003 60.3% 0.206 101.3%

10 0.439 100.0% -1.257 99.8% -0.004 83.6% 0.205 100.6%

11 0.439 100.0% -1.258 99.9% -0.004 93.3% 0.204 100.2%

12 0.439 100.0% -1.259 100.0% -0.004 97.3% 0.204 100.1%

13 0.439 100.0% -1.259 100.0% -0.004 98.9% 0.204 100.0%

14 0.439 100.0% -1.259 100.0% -0.004 99.6% 0.204 100.0%

15 0.439 100.0% -1.259 100.0% -0.004 99.8% 0.204 100.0%

16 0.439 100.0% -1.259 100.0% -0.004 99.9% 0.204 100.0%

17 0.439 100.0% -1.259 100.0% -0.004 100.0% 0.204 100.0%

The percentages of Panel (B) are condensed into a format that makes an easy comparison

between the different decades in Table 10. Table 10 shows inconsistent results across the

different decades. Similar to the percentages seen in Table 7, greater than 100% of the

diversifiable skewness was eliminated with low levels of diversification in the 1990s and 2000s.

This indicates that skewness decreased to a level less than the convergent level of skewness at

full diversification (i.e. – the 17-index portfolio) in portfolios with lower levels of diversification.

The low value of diversifiable risk in the 1990s and 2000s causes the percent of risk diversified

40


Portfolio – Portfolios Built by Adding Indices with Lowest Historical Standard Deviation Standard

Deviation Skewness

n 70s 80s 90s 00s n 70s 80s 90s 00s

2 45.0% 48.9% 105.4% 65.9% 2 79.2% 9.8% -5378.3% 249.9%

3 73.0% 76.0% 117.5% 88.5% 3 98.2% 47.2% -3917.1% 223.8%

4 87.6% 89.2% 112.2% 96.1% 4 101.5% 73.3% -2114.2% 170.8%

5 94.5% 95.3% 106.6% 98.7% 5 101.4% 87.5% -985.5% 135.3%

6 97.7% 98.0% 103.2% 99.6% 6 100.8% 94.4% -399.0% 116.4%

7 99.0% 99.2% 101.5% 99.9% 7 100.4% 97.6% -120.2% 107.3%

8 99.6% 99.7% 100.6% 100.0% 8 100.2% 99.0% 5.5% 103.1%

9 99.8% 99.9% 100.3% 100.0% 9 100.1% 99.6% 60.3% 101.3%

10 99.9% 99.9% 100.1% 100.0% 10 100.0% 99.8% 83.6% 100.6%

11 100.0% 100.0% 100.0% 100.0% 11 100.0% 99.9% 93.3% 100.2%

12 100.0% 100.0% 100.0% 100.0% 12 100.0% 100.0% 97.3% 100.1%

13 100.0% 100.0% 100.0% 100.0% 13 100.0% 100.0% 98.9% 100.0%

14 100.0% 100.0% 100.0% 100.0% 14 100.0% 100.0% 99.6% 100.0%

15 100.0% 100.0% 100.0% 100.0% 15 100.0% 100.0% 99.8% 100.0%

16 100.0% 100.0% 100.0% 100.0% 16 100.0% 100.0% 99.9% 100.0%

17 100.0% 100.0% 100.0% 100.0% 17 100.0% 100.0% 100.0% 100.0%

to reach high values at lower levels of diversification. The convergent level of skewness occurs

when 100% of diversified skewness is reached. The convergent level of skewness occurs with a

10-index portfolio in the 1970s, a 12-index portfolio in the 1980s, a 17-index portfolio in the

1990s, and a 13-index portfolio in the 2000s.

Overall, a higher level of diversification is needed to reach the convergent level of skewness

in the 2000s than in the 1970s, but the amount of skewness reduced is greater at every level of

diversification in the 2000s than in the 1970s before a 13-index portfolio was formed. This,

combined with the fact that the amount of standard deviation reduced from diversification was

greater in the 2000s than in the 1970s, provides less incentive for an investor to diversify in the

2000s than in the 1970s.

41

The robustness checks illustrate similar results for the naïve investor and an investor who

builds their portfolios based on adding assets with the lowest risk. Both of these portfolio

formation strategies imply an investor in the 2000s can reduce the standard deviation of their

portfolio with less diversification than an investor in the 1970s, but both of these portfolio

formation strategies show a greater reduction in the skewness of portfolios with less

diversification. However, the results differ for the investor building portfolios with the highest

historical return from the naïve investor. An investor building portfolios by adding indices with

the highest return will need more diversification in the 2000s to reduce the standard deviation of

a portfolio than in the 1970s. Consequently, the ability to reduce standard deviation of a

portfolio differs across the portfolio formation strategies.

2.5 Conclusion

This paper looks at behavior of the statistical moments of portfolios sequentially

increasing in diversification. Portfolios were formed by randomly adding indices to a portfolio,

and the first three statistical moments of each portfolio was found for each decade in the entire

time period. The study uses U.S. dollar-dominated, daily stock-market index returns from 17

different countries, which was obtained from Datastream. The sample starts in January 1973 and

ends in November of 2010 for a total of 9,892 daily observations. The standard deviation and

skewness calculations for the portfolios for each decade were regressed using a model that

separates diversified risk from non-diversified risk, a practice found in bond yield research. The

relative change in the levels of standard deviation and skewness of each portfolio within each

decade show decreasing standard deviation and decreasing skewness with increasingly more

diverse portfolios, which suggests a trade-off exists between lower variance and positively

42

skewed returns. However, the graphs show an overall increase in the level of risk and an

increase in the level of skewness over time, a cost to diversification.

Though the standard deviation and skewness levels increased over time, the percentage of

standard deviation and positive skewness reduced through diversification occurs at a much faster

rate and with less diversification in the most recent time period. This result corresponds to an

increase in the correlations of international stock market index returns, suggesting international

market integration could have decreased the amount of diversification needed to eliminate risk.

The results imply an international investor can achieve the same level of risk reduction with less

diversification currently than in previous decades, but the loss of positive skewness also

increases at a faster diversification rate than in the twentieth century.

The results differ for an investor building a portfolio by sequentially adding indices to a

portfolio with highest historical return. An investor seeking to build a portfolio with indices

having the highest historical return saw a decrease in the percent of diversifiable risk reduced in

recent decades than in previous time periods at every level of diversification. An investor that

builds a portfolio by sequentially adding indices to a portfolio with the lowest historical standard

deviation, however, will see similar diversification benefits over time as the naïve investor.

Consequently, the trade-off between risk and positive skewness reduction depends on the

investment strategy of an individual when building a portfolio.

43

CHAPTER 3

SHOWING WORLD MARKET INTEGRATION THROUGH TIME

3.1 Introduction

This paper investigates how country-specific risk factors affect country-level assets in an

international capital asset pricing model (ICAPM) and examines world financial market

integration over a 37 year time period. Specifically, this study observes the time series

significance of systematic and non-systematic risk factors from pooled cross-sectional

regressions of 37 different country-level stock market indices. Significant non-systematic risk

factors over time in the pooled cross-sectional regressions imply world market segmentation, but

insignificant non-systematic risk factors with significant systematic risk factors suggest world

financial markets are integrated. Thus, the procedure in this study directly examines if world

capital markets have integrated over time.

In a completely integrated market, the return on any asset with relatively the same risk should

remain consistent across investors, regardless of the location of the asset. Thus, the returns on

assets in integrated markets will fluctuate only through variation in global-wide market risk

factors. Conversely, completely segmented markets indicate that the returns of assets within a

certain country vary through risks observed in that specific location, and any global risk factor

should not cause variation in country-specific assets. Assets in completely segmented markets,

therefore, vary only through country-specific risks [Bekaert, Harvey, and Lumsdaine (2002)].

Investors, consequently, need to know whether the risk exposure of their investments in any

country-level asset comes from a single, global, factor or influences pertinent only to a specific

country.

44

Previous literature on this topic supports arguments for both international financial market

integration [You and Daigler (2010); Carrieri, Errunza, and Hogan (2007); Bekaert, Harvey, and

Lumsdaine (2002); Hardouvelis, Malliaropulos, and Priestley (2006)] and segmentation [Adler

and Dumas (1983); Brennan and Cao (1997); Bali and Cakici (2010)]. Additionally, authors

imply that world market integration changed over time [e.g. – Bekaert and Harvey (1995); You

and Daigler (2010)], leaving investors without the ability to confidently build their portfolios

based on evidence presented in academic research. The investigation of this paper aims to

resolve this issue by providing evidence showing that world market integration exists in current

times, giving investors the ability to make fully informed decisions.

This study will observe the significance of systematic risk factors over two different time

periods to decipher if integration changed in recent time periods as opposed to the more distant

past. Choosing the break point to observe if, and when, international capital markets have

become integrated provides a challenge with little evidence available to suggest a specific date

for the integration of the overall world market. However, some authors offer various

suggestions as to when this break point occurred for some regions of the globe or for specific

countries.

A variety of studies imply that the integration of most developing markets occurred before or

during the year of 1994 [Carrieri, Errunza, and Hogan (2007); Bekaert, Harvey, and Lumsdaine

(2002)], and Hardouvelis, Malliaropulos, and Priestley (2006) show that European countries

became more integrated in the second half of the 1990s due to the formation of the European

Union. Collectively, these studies indicate that the integration of the returns of most countries’

indices with global market returns starting around 1995, which implies global market integration

45

during and after this year. However, this study conducts F-tests on the average of monthly

correlations of country-specific indices with the global market index indicate a break-point at the

year 2000. Consequently, this paper will investigate if the significance of non-systematic risk

factors differs from before to after 2000.

In addition to observing the significance of non-systematic risk factors over time, this study

uses a procedure that conditions systematic risk on up or down markets, which differs from

previous studies that did not incorporate this conditioning procedure when observing country-

specific risks across countries [e.g. – Bali and Cakici (2010)]. Finance theory states that more

risky investments should earn higher returns, but investors understand that a non-zero probability

exists of the event that assets with larger systematic risk exposures will realize larger negative

returns during down market environments than assets with less risk exposures [Pettengill,

Sundaram, and Mathur (1995)]. Consequently, investors expect higher returns on more risky

assets during up markets than less risky assets, but they also expect lower returns on more risky

assets during down markets than less risky assets. This means systematic risk affects returns

differently across up and down markets. The procedure used in this experiment conditions

global-risk factors on up or down market environments when determining the significance of

these variables. Previous research shows that this procedure produces an effective result in both

domestic and international stock markets [Fletcher (2000)], so the investigation detailed in this

study uses the procedure to test the significance of integrated global-wide risk factors.

The results of the cross-sectional regressions using all countries in the dataset in this

paper show that global risk factors did not significantly affect country-level index returns before

or after 2000. The results also show country-specific factors did not significantly affect index

46

returns. When sub-setting the data into emerging and developed countries, the outcome stays

robust for the emerging market countries specifically. Alternatively, global-wide risk factors

significantly affected the sub-set of developed economies in the post-2000 period, indicating

stock markets in developed economies vary in an integrated manner. These findings provide

evidence to support the argument that international stock market indices overall vary in a

segmented manner, but certain segments of global financial markets, particularly those in more

developed economies, have become integrated in recent periods. This paper supports previous

research indicating integrated international stock markets for Europe, but also supports literature

indicating overall segmentation of international financial markets.

3.2 Literature Review

This paper observes the effect of world financial market country-specific risk on international

index returns to show international market integration. Previous literature shows an increasing

trend towards international financial market integration, but some evidence indicates country-

specific risk factors significantly affect country-level index returns. This investigation uses an

international capital asset pricing model (ICAPM) to define world market and country-specific

risks, and uses these variables to study the pricing behavior of them on country-level index

returns. The results of the analysis show that the trends toward world market integration did not

cause global-wide risk factors to significantly affect index returns across all countries, but

global-wide risks significantly influenced index returns in developed economies. The following

literature provides some background on the evidence of this topic.

Financial managers and policymakers often base their decisions on how international

financial markets behave, which led to a large amount of academic research studying whether or

47

not financial markets are integrated or segmented. Completely integrated markets imply the

index returns of a market within country co-vary only with a global market index, but completely

segmented markets mean only the variance of the index returns of a country affect the expected

excess returns of a country’s index [Lewis (2011)]. A more integrated market will reduce the

cost of capital, increase the investment opportunity set for local and foreign investors, and

welfare will increase from economic growth made possible through international risk sharing.

From those benefits, society will gain from studying the world’s ability to integrate financial

markets [Lewis (2011)]. The extension of the traditional capital asset pricing model (CAPM) of

Sharpe (1964), Lintner (1965), and Black (1972) to international markets (ICAPM) by Solnik

(1974a,b), Stehle (1977), Sercu (1980), and Stulz (1981) first initiated the study of international

financial market behavior, but the augmentation of the CAPM from domestic to international

markets caused a debate among researchers for the viability of the ICAPM to accurately model

returns due to the model’s implicit assumption of integration.

The ICAPM states that only the variability of the global market basket impacts the

variability of returns of an asset in a country, which follows this basic equation:

𝑅𝑖 = 𝛼𝑖 + 𝛽𝑖𝑅𝑤 + 𝜀𝑖

where 𝑅𝑖 represents the return of an asset in country i, 𝛼𝑖 represents the abnormal return of asset,

𝑅𝑤 represents the return on the global market basket of assets, 𝛽𝑖 is the coefficient on the global

market basket that represents systematic risk, and 𝜀𝑖 represents the residual return of the ICAPM.

The ICAPM implicitly assumes integrated international financial markets in order for the global

market basket of assets to significantly affect country-level returns [Fletcher (2000)]. Authors

suggesting that country-specific (or idiosyncratic) factors influence index returns inherently infer

(1)

48

segmented markets due to the inefficiency of the ICAPM to correctly model returns. The

inefficiencies of the country-specific risks, therefore, reside in the residuals of the ICAPM,

which provides for a proxy for all inefficiencies of the ICAPM due to global market

segmentation.

For a domestic market, the CAPM presumes that investors hold diversified portfolios, but

recent research indicates most individual investors do not meet this condition [e.g. – Goetzmann

and Kumar (2008)]. Failure for a market to meet this condition causes idiosyncratic risks to

impact individual asset returns [Levy (1978)]. Merton (1987) indicated that investors who do

not hold a completely diversified portfolio will only care about total risk instead of market risk.

Campbell, Lettau, Malkiel, and Xu (2001) show that the number of stocks needed to achieve a

given level of diversification increased from 1962 to 1997 in the U.S. stock market. From this,

Ang, Hodrick, Xing, and Zhang (2006) take the idea that most investors hold under-diversified

portfolios to illustrate that idiosyncratic risk exists in the U.S. financial market. This

corresponds to Goetzmann and Kumar (2008) demonstrating that most investors hold under-

diversified portfolios.

Some recent research extends the proficiency of the CAPM to markets beyond the U.S.

Ang, Hodrick, Xing, and Zhang (2008) expand the work of Ang, Hodrick, Xing, and Zhang

(2006) to 23 developed markets, and they show that the results seen in the U.S. hold for the stock

markets in each of the countries in their sample. This work, though, only observes the behaviors

of domestic markets. Bali and Cakici (2010) conducted an experiment across international

financial markets using country-level index data and a global market risk factor. Their results

imply a significant and positive relationship of expected index returns and country-specific

49

factors using Fama and MacBeth (1973) methodology within the ICAPM framework, but the

relationship between global-wide factors and expected returns remained flat. The work of Bali

and Cakici (2010) echoes the conclusions of Ang, Hodrick, Xing, and Zhang (2006, 2008) across

international markets that idiosyncratic risk affects stock returns. These works expand the debate

over whether the CAPM can efficiently model international markets due to lack of investor

diversification.

The dispute about whether or not the ICAPM can efficiently capture international stock

returns spawned several explanations for why country-specific risks could change the pricing

behavior of international assets outside of systematic risk. Adler and Dumas (1983) state that

deviations from the purchasing power parity (PPP) effect asset returns across countries, which

would increase the residual return and, hence, idiosyncratic risk in the ICAPM. The deviations

from PPP provide country-specific factors that affect index returns, thus offering evidence to

suggest segmented markets. Bekaert and Harvey (1995, 2000) imply that barriers to trade can

cause international financial market segmentation, and the liberalization of financial markets

closed off to foreign investors, especially in emerging countries, did not occur until the middle

1990s. Also, Brennan and Cao (1997) develop a model where asymmetric information differs

across foreign and domestic investors, and the difference in information causes differences in

opinion upon the equilibrium price of financial assets. These studies provide different

explanations of how country-specific factors can affect international stock market returns, and

these authors often contend that international financial markets are segmented.

Even though research suggests country-specific factors can affect index returns, the

following researchers state that markets are becoming more integrated. You and Daigler (2010)

50

show increasing time-varying correlations of international index returns, which suggests the

international financial market is growing more towards integration because the markets are

varying together more closely. Bekaert, Harvey, and Lumsdaine (2002) show that significant

break points exist for index returns of financial markets within several countries where their

governments officially allowed foreign investment. This implies continued growth towards

integration of these markets with the rest of the globe. These authors note that the change in

policy towards allowing foreign investment resulted in a large amount of capital flows into these

countries, and they found capital flows significantly affected portfolio returns. Carrieri,

Errunza, and Hogan (2007) also supply evidence of growing market integration by creating a

time-varying integration index. The index values, which are similar to the R² of a regression of a

world market return on the return of securities available to all investors (foreign and domestic),

show significant variation during different time periods, but all of their indices point towards

international financial market integration. Carrieri, Errunza, and Hogan (1997) support the

conclusion of Bekaert, Harvey, Lumsdaine (2002) by implying the liberalization of closed off

markets caused world integration to increase. Therefore, evidence offered in the literature would

suggest global risk factors as well as country-specific factors should affect index returns.

Authors, such as Ang, Hodrick, Xing, and Zhang (2006, 2008) and Bali and Cakici

(2010), argue that the CAPM and ICAPM cannot efficiently predict domestic and international

stock market returns, but one line of research offers a methodological explanation to the

inadequacy. Pettengill, Sundaram, and Mathur (1995) (PSM henceforth) state that a negative

relationship between risk and returns occurs during negative return markets, and, during these

times, high beta portfolios will see lower returns than low beta portfolios. Therefore, PSM

(1995) conduct the traditional Fama-MacBeth regressions conditioned on positive and negative

51

excess market return and betas. The results of PSM (1995) show a significant and consistent

relationship between beta and expected excess stock returns, which supports the traditional

CAPM. Fletcher (2000) extends the PSM analysis to international equity returns, and finds

similar results as PSM in international markets using the ICAPM. The results shown by these

authors suggest that improper methodology explains why some research found idiosyncratic risk

affecting returns.

The arguments formed by PSM and Fletcher (2000) suggest that the market-wide risk

factor significantly relates to individual excess asset returns when separating excess market

returns into positive and negative groups. Their conclusions state that the risk-return relationship

between the market betas and returns exists because high betas correspond to lower returns

during periods when excess market returns are negative. The PSM and Fletcher arguments

coupled with evidence showing increasing international stock market integration indicate a

significant relationship should exist between the covariance of a global market index and

country-level indices in the ICAPM, and the same argument would imply that a significant

relationship should be present between systematic risk and country-level index returns.

Additionally, any idiosyncratic risk measures should not cause significant changes in equilibrium

prices in the ICAPM.

Previous research also estimates dates when certain markets show signs of integration

with the rest of the globe. The research in the current paper will investigate the influence of

global and country-specific risk factors on asset returns in different time periods, since previous

research argues the significance of these factors vary over time. A global-wide event marking

when overall integration occurred does not exist from the literature, which makes choosing a

52

particular way to divide the sample into sub-periods fairly arbitrary. However, a few researchers

indicate that the market in the late 1990s contains more significantly integrated factors than the

market in earlier time periods.

The investigation of Bekaert, Harvey, and Lumsdaine (2002) observes break points from

regulatory policy changes to indicate world financial market integration for several countries

throughout the world. Their inquiry mainly focuses on whether the market integration dates of

20 different countries differ from the officially stated date of the policy change. The results of

this analysis show all 20 countries in their sample display break points in these factors, and 1994

is the most recent date for one of these break points. This result provides one motivation for

studying the impact of global and country-level risk factors on international asset returns.

Other authors also provide evidence to suggest 1995 as a break point to divide the sample

period into sub-samples. Carrieri, Errunza, and Hogan (2007) use an integration index to show

that some countries’ markets became more integrated after 1992. However, the authors state that

the 1992 date is rather arbitrary, but the integration index and other tests support the conclusion

that markets became more integrated with other global markets after 1992. You and Daigler

(2010) use time-varying correlations to show that the correlations of international index markets

increased since the late 1990s. Finally, Hardouvelis, Malliaropulos, and Priestley (2006) find

that European markets became fully integrated in the second half of the 1990s due to the

formation of the European Union. These authors provide evidence to support the argument that

the degree of world financial market integration increased since the later 1990s. This evidence

provides a good basis for observing the significance of global and country-specific risk factors

on international asset returns in times after the late 1990s.

53

In order to define a specific year to use as a breakpoint, F-tests were run on the averages

of correlations of country-level indices with a global market index to identify a shift from a low-

correlation to a high-correlation environment with the global market index. The results of the F-

tests suggest the year 2000 as year for the division by showing a significant break-point exists in

that particular year, further supporting previous literature that a breakpoint occurred after the

early 1990s. Consequently, the statistical tests in this paper will compare how a global market

risk factor affects country-level market returns in times before and after the year 2000.

3.3 Methodology

This paper observes if country-specific risk factors affect returns in recent time periods

compared to the more distant past to observe if world financial markets have become more

integrated. The investigation determines whether the returns of international financial market

securities vary with global-wide risk factors or with risk factors observed in a specific country.

Previous research suggests international markets have become more integrated over time, but

some studies found statistically insignificant systematic risk factors and significant idiosyncratic

and total risk factors, implying international financial market segmentation [Bali and Cakici

(2010)]. Thus, the procedure, developed from the methodology of Pettengill et al. (1995) and

Fletcher (2000), re-investigates the significance of the relationship between country-specific risk

factors and international asset returns in two different time periods.

Fama and MacBeth (1973) outlined a procedure that most studies [e.g. – Bali and Cakici

(2010)] use for identifying the effects of risk on returns, and this procedure will serve as the basis

for conducting the analysis here, as well. The Fama-MacBeth methodology uses a two-step

regression scheme that first estimates risk for securities through the CAPM, and, then, regresses

54

the return of those securities on the risk measures. The time-series significance of the

coefficients of the risk variables in the second step regression indicates whether risk significantly

affects returns. The following explanation will sketch out how this paper will adopt the Fama-

MacBeth methodology to observe international financial market integration.

In the first step, systematic risk for month t is measured by the world market betas of

international securities using daily returns within month t. The equation regresses each country’s

market portfolio returns on world market portfolio returns over each month in the data set using

daily returns, and the slope coefficient in the ICAPM equation gives the β statistic in the

following equation:

𝑅i,d,t = Ci,t + βi,t

∙𝑅w,d,t + εi,d,t,

where 𝑅i,d,t represents the market return on country i’s market portfolio on day d in month t,

𝑅w,d,t represents the market return on the world market portfolio on day d in month t, and 𝐶𝑖,𝑡 and

𝜀𝑖,𝑑,𝑡 represent the intercept and residual of the equation, respectively.

Two variables measure country-specific risk factors: country-specific total risk and

country-specific idiosyncratic risk. The monthly standard deviation of country i’s market

portfolio returns in month t, which includes all of the days d in the month, measures country-

specific total risk:

TVOLi,t = √Vart(Ri,t) = √∑ (Ri,d - R̅i,t)2D

t-1

d=1

(2)

(3)

55

where R̅ represents the average return in month t of country i. The monthly standard deviation

of the residuals from equation (2) for each country i in month t, including all days d in the

month, measures country-specific idiosyncratic risk:

IVOLi,t = √∑ (εi,d - ε̅i,t)2D

t-1

d=1.

where ε̅i,t represents the average of the residuals in month t of country i.

In the second stage, the Fama-MacBeth methodology assesses the effect of risk on returns

by observing the statistical significance of the time-series averages over all t’s from cross-

sectional regressions of one-month-ahead country returns on systematic risk (β) in the following

equation:

Ri,t+1 = γ0,t

+ γ1,t

βi,t

+ εi,t+1,

where Ri,t+1 represents the return on country i’s market portfolio in month t+1. The coefficients

γ0,t

and γ1,t

are obtained for each month in the data set. The time-series averages of the

coefficients are, then, tested using t-statistics to obtain their significance from zero.

However, the conditioning procedure of the Fama and MacBeth (1973) methodology

presented by Pettengill et al (1995) for U.S. markets and Fletcher (2000) for international

markets allows for the study of international financial market integration significance in up and

down markets. Both of these papers theorize that using ex post, realized, data with an

expectations model creates downward bias on the systematic risk coefficient, which causes these

coefficients to become statistically insignificant. These authors state an investor assigns a non-

zero probability to an event where market returns become less than the risk-free rate (i.e. – down

(4)

(5)

56

markets), and portfolios and assets with higher betas will see lower returns during these events

than portfolios and assets with lower betas. This implies that a positive relationship should exist

between returns and risk in up markets and a negative relationship should exist between returns

and risk in down markets.

Pettengill et al (1995) and Fletcher (2000) suggest a specification for the conditional

relationship between risks and return that will reduce this bias. The following equation shows

the conditional equation (5):

Ri,t+1 = γ0,t

+ γ1,t

Dβi,t

+ γ2,t

(1-D)βi,t

+ εi,t+1

where D represents a dummy variable that equals one if return on the world market portfolio is

positive and zero if return on the world market portfolio is negative, γ1,t

represents the monthly

risk premium in positive markets, and γ2,t

represents the risk premium in negative markets.

Essentially, the regression splits the systematic risk regression into up and down markets. PSM

(1995) and Fletcher (2000) point out that two conditions must be met in order for a positive risk-

return continuum to exist. First, the market return should be positive on average, and, second,

the risk premium in up and down markets should be symmetrical. The first condition is tested

using summary statistics, and the second condition is tested with a two-population t-test.

Previous literature indicates that international financial markets have become more integrated,

and PSM (1995) and Fletcher (2000) show that the conditioning procedure brings to light that

systematic risk is significant. Therefore, the coefficient on the systematic risk factor is expected

to be statistically significant.

(6)

57

The focus of this investigation, though, also intends to observe the significance of the

effect country-specific risks have on country-level index returns. Consequently, the second stage

of the procedure will also include substituting the systematic risk variable with the country-

specific risk variables. The following two equations represent these regressions:

Ri,t+1 = γ0,t

+ γ3,t

IVOLi,t +εi,t+1

Ri,t+1 = γ0,t

+ γ4,t

TVOLi,t +εi,t+1

,

where γ3,t

and γ4,t

represent the risk premium on the idiosyncratic risk variable, IVOL, and the

total risk variable, TVOL, respectively.

Previous literature [e.g. - Brennan and Cao (1997)] suggest that systematic risk and

country-specific risks could both influence returns. Thus, the following two equations will also

be included in the procedure:

Ri,t+1 = γ0,t

+ γ1,t

Dβi,t

+ γ2,t

(1-D)βi,t

+γ3,t

IVOLi,t + εi,t+1

Ri,t+1 = γ0,t

+ γ1,t

Dβi,t

+ γ2,t

(1-D)βi,t

+ γ4,t

TVOLi,t + εi,t+1

,

where the definitions of the variables in the previous equations are carried over to equations (9)

and (10).

The literature discussing more integrated world capital markets suggests that most

markets in countries throughout the globe have become more integrated with each other in the

second half of the 1990s. Therefore, this investigation will observe if the significance of

systematic and country-specific risk factors differs over the two time periods. The regressions of

(8)

(7)

(9)

(10)

58

(5) through (10) will be calculated from the beginning of the sample in January 19733 to

December 1999 for the first sub-sample period. Regressions (5) through (10) will also be

calculated from January 2000 through the end of the sample, or November 2010. Any

differences in the time-series averages of the coefficients and their respective t-statistics in these

regressions will show if asset returns have become more or less integrated in more recent time

periods.

3.4 Data

The experiment’s model above uses daily and monthly U.S. dollar denominated returns of

stock market indices for 37 different countries plus an index for a world market portfolio. The

data set contains data from the following countries: Argentina, Australia, Austria, Belgium,

Brazil, Canada, Chile, China, Denmark, Finland, France, Germany, Greece, Hong Kong, India,

Ireland, Italy, Japan, Korea, Malaysia, Mexico, the Netherlands, New Zealand, Norway,

Philippines, Poland, Portugal, Singapore, South Africa, Spain, Sweden, Switzerland, Taiwan,

Thailand, Turkey, the United Kingdom, and the United Sates. The data set also includes a world

index that is calculated as the value-weighted average of all the stocks in the entire data set. The

observations come from Datastream, called the Datastream Global Indices, and the observations

represent percent returns of closed-out, long U.S. dollar positions of each index at the two

different frequencies. The Datastream Global Equity Indices User Manual gives a detailed

description of the collection and calculation methods of the indices for the interested reader.

The information in Table 11 gives some summary statistics of the monthly data used in this

experiment. The table reports the mean, standard deviation, minimum, maximum, skewness,

3 The 1970s time period begins in 1973 instead of 1970 because Datastream did not track global indices prior to

1973.

59

Table 11 Summary Statistics

Country Start Mean Std Min Max Skew Corr Beta Idio

Argentina Aug-93 0.82 9.21 -30.40 27.49 -0.32 0.53 1.05 7.81

Australia Jan-73 1.14 7.22 -43.25 25.13 -0.74 0.64 1.04 5.52

Austria Jan-73 1.04 6.71 -34.25 37.29 0.39 0.50 0.75 5.80

Belgium Jan-73 1.03 5.90 -32.33 24.42 -0.41 0.68 0.89 4.34

Brazil Jul-94 1.75 10.91 -33.24 39.71 -0.22 0.67 1.56 8.06

Canada Jan-73 0.99 5.53 -26.50 20.33 -0.57 0.76 0.93 3.61

Chile Jul-89 1.72 6.61 -24.03 18.00 -0.22 0.44 0.63 5.93

China Jul-93 1.75 11.25 -26.57 48.37 0.61 0.40 0.96 10.32

Denmark Jan-73 1.16 5.89 -26.39 22.99 -0.21 0.61 0.80 4.68

Finland Mar-88 1.15 8.63 -28.70 29.83 0.11 0.66 1.24 6.47

France Jan-73 1.16 6.74 -22.71 28.17 -0.18 0.72 1.08 4.69

Germany Jan-73 0.98 5.94 -20.65 19.33 -0.32 0.70 0.93 4.21

Greece Jan-90 1.03 10.14 -33.60 58.53 1.20 0.46 1.00 8.99

Hong Kong Jan-73 1.47 10.00 -45.39 75.44 0.48 0.52 1.17 8.51

India Jan-90 1.52 10.70 -32.53 54.34 0.60 0.34 0.78 10.06

Ireland Jan-73 1.08 7.27 -25.06 43.11 0.23 0.67 1.08 5.42

Italy Jan-73 0.94 7.59 -23.11 27.37 0.16 0.56 0.95 6.28

Japan Jan-73 0.80 6.23 -17.55 27.10 0.30 0.71 0.98 4.40

Korea Sep-87 1.06 11.19 -32.20 70.52 1.05 0.55 1.32 9.33

Malaysia Jan-86 1.31 8.79 -33.12 46.15 0.28 0.43 0.81 7.93

Mexico May-89 1.72 8.73 -33.76 24.09 -0.78 0.59 1.11 7.02

Netherlands Jan-73 1.12 5.52 -30.92 24.16 -0.85 0.82 1.01 3.16

New Zealand Jan-88 0.91 6.48 -18.58 29.95 0.11 0.62 0.87 5.09

Norway Jan-80 1.22 7.95 -30.62 24.79 -0.63 0.66 1.16 5.98

Philippines Nov-88 1.22 9.22 -27.18 48.62 0.56 0.47 0.94 8.12

Poland Mar-94 1.00 10.91 -33.35 37.50 -0.04 0.59 1.39 8.77

Portugal Jan-90 0.66 6.09 -28.00 17.71 -0.49 0.65 0.85 4.61

Singapore Jan-73 1.08 8.48 -37.02 63.12 0.62 0.63 1.20 6.56

South Africa Jan-73 1.36 8.28 -35.35 19.78 -0.56 0.56 1.03 6.87

Spain Mar-87 0.98 6.50 -24.09 21.61 -0.46 0.77 1.08 4.11

Sweden Jan-82 1.41 7.30 -26.12 22.43 -0.27 0.74 1.18 4.92

Switzerland Jan-73 1.06 5.14 -18.25 16.34 -0.33 0.72 0.82 3.58

Taiwan May-88 0.96 10.99 -33.21 56.95 0.75 0.44 1.04 9.88

Thailand Jan-87 1.56 10.81 -32.53 40.89 0.11 0.52 1.21 9.23

Turkey Jun-89 2.57 16.94 -40.83 70.53 0.69 0.38 1.37 15.67

UK Jan-73 1.12 6.52 -21.23 54.94 1.14 0.73 1.07 4.45

US Jan-73 0.94 4.48 -21.17 18.53 -0.43 0.82 0.82 2.59

World Jan-73 0.90 4.48 -20.67 13.93 -0.55 1.00

correlation with the world market portfolio, world market beta coefficient of the ICAPM, and the

idiosyncratic risk statistic respective to the ICAPM over the entire sample period for each

60

country and world market portfolios. Each time series ends in November 2010, but the start date

of each series varies. The table also lists the start date of each series. The earliest start date

begins in January 1973, which, when looking at the largest sample series, gives a maximum of

455 observations.

The data outlined in Figure 13 gives the equal-weighted, monthly averages of the

Figure 13 Equal-Weighted Average Correlation of Countries’ Indices with World Market

correlations between the world market index and the individual indices for the 37 countries for

each month in the sample. This graph shows an upward trend in the average of the correlations,

which suggests an increasing trend towards integration, especially in the later 1990s through the

end of the time series. The average correlation of country-level indices with the world index in

the pre-2000 time period is 0.36, and the average correlation value in the post-2000 time period

is 0.61. The average correlation of country-level indices with the world index for developed

economies in the pre-2000 time period is 0.40, and the average correlation value in the post-2000

time period is 0.62. The average correlation of country-level indices with the world index for

-0.2

0

0.2

0.4

0.6

0.8

1

1973

-01

1974

-05

1975

-09

1977

-01

1978

-05

1979

-09

1981

-01

1982

-05

1983

-09

1985

-01

1986

-05

1987

-09

1989

-01

1990

-05

1991

-09

1993

-01

1994

-05

1995

-09

1997

-01

1998

-05

1999

-09

2001

-01

2002

-05

2003

-09

2005

-01

2006

-05

2007

-09

2009

-01

2010

-05

Aver

age

Corr

elati

on

wit

h W

orl

d M

ark

et

61

emerging economies in the pre-2000 time period is 0.24, and the average correlation value in the

post-2000 time period is 0.53. This corresponds with previous studies [e.g. – You and Daigler

(2010)] showing increasing integration in more recent times, and the increase in the graph in

later time periods further supports sub-sampling the data into two different time periods.

In order to establish a firm breakpoint, Andrews (1993) suggests calculating F statistics for

suspected breakpoints in the data. When the p-value of the statistic reaches an acceptable level

of significance, the breakpoint is established. Therefore, F statistics were calculated on the

correlation data used to create Figure 1 with each year from 1995 to 2004 as breakpoints. Table

12 shows the breakpoint year, F statistic, and associated p-value of each statistic. The table

Table 12 F-test Results of Equal-Weighted Average Correlations of Countries Indices with

the World Market

Year Break F-Statistic p-value 1995 1.0258 0.8560

1996 1.0108 0.9446

1997 1.0875 0.5523

1998 1.1276 0.4039

1999 1.1058 0.4960

2000 1.2649 0.1213

2001 1.2992 0.0946*

2002 1.6815 0.0018**

2003 2.0143 0.0001**

2004 2.9257 0.0000**

** - significant at the 5% level. * - significant at the 10% level.

shows the 2001 breakpoint as significant at the 10% confidence level. However, a significant

drop in the correlation data in the last quarter of 2000 and early 2001 could potentially create

downward bias in the regressions. Choosing the year 2000 as the breakpoint in the dataset will

provide additional data in the later subset to mitigate any downward bias created the sharp drop

62

in the correlations seen in the later and early months of 2000 and 2001, respectively. Thus, the

year 2000 will serve as the breakpoint for sub-setting the dataset.

3.5 Regression Results and Discussion

3.5.1 The Entire World Market

The objective of this study is to test the significance of world-market risk factors on country-

specific stock market index returns in international financial markets over time, which, in effect,

determines if world market integration exists in recent time periods. Previous studies found that

systematic risk does not affect asset returns using the Fama and MacBeth (1973) methodology

within the ICAPM framework, and these authors also showed country-level risk variables

significantly cause asset return variability. These results suggest world financial markets vary in

a segmented manner instead of an integrated one. However, other strands of literature and the

data in Figure 3.1 imply systematic risks should affect asset returns and country-specific risk

should not. Therefore, this study looks at systematic risk measures influence on returns over

time to show whether international financial markets have become more integrated in recent time

periods.

The information contained in Table 13 shows the results from the procedure conducted with

equations (6) through (10) using the data set described above over two sub-sample periods, pre-

2000 and post-2000. The table shows the positive and negative systematic risk, or beta,

coefficient value, the idiosyncratic risk coefficient value, and total risk coefficient value and their

respective t-statistics for each sub-sample. Panel A of the table reports the regression results

using data for the period prior to 2000, and Panel B reports the regression results using data for

2000 and after.

63

Table 13 Cross-Sectional Results over Time

Panel A: Pre-2000

Equation Positive Beta Negative Beta Ivol Tvol

(6) 0.0794

(1.22)

-0.0774

(-0.95)

(7) 0.0063

(0.17)

(8) 0.0000

(0.03)

(9) 0.0526

(0.62)

-0.1945

(-1.32)

0.0514

(0.87)

(10) 0.2053

(1.81)

-0.0464

(-0.30)

-0.0002

(-1.27)

Panel B: Post 2000


(6) 0.2290

(1.70)

-0.3193*

(-2.29)

(7)

0.0895*

(2.40)

(8)

0.0001

(1.66)

(9) 0.1833

(1.22)

-0.3035

(-1.89)

0.0770

(1.77)

(10) 0.2837

(1.73)

-0.3961*

(-2.24)

0.0000

(0.28)

* - significant at the 5% level; t-statistics are reported in parenthesis

Panel A of Table 13 indicates, overall, neither country-specific risks or systematic risk

significantly affected country-level index returns prior to 2000. The idiosyncratic and total risk

variables, which represent country-specific risks, were not significant in all regression

specifications at the 5% confidence level. This provides a clearly consistent conclusion that

systematic risk and country-specific risks did not significantly affect country-level asset returns

in this sub-sample, indicating stocks vary from market-specific information.

64

The results shown in Panel A of Table 13 provides evidence to indicate international

financial markets were segmented prior to 2000. The insignificance of the country-specific risk

and total risk variables on index returns suggests that returns on these indices varied in a non-

integrated manner, and the insignificance of the systematic risk variables specifically suggests

any information regarding world financial markets not directly pertinent to a country did not

affect index returns in that country [Brennan and Cao (1997)]. This observable behavior

parallels the definition of a segmented market provided by Lewis (2011).

Panel B of Table 13 does not provide clear and consistent evidence to suggest that systematic

risk significantly affected index returns during 2000. The coefficients for negative systematic

risk was significant at the 5% confidence level for equations (6) and (10), and the coefficient for

the idiosyncratic risk variable was significant at the 5% confidence level in for equation (7). The

significance of the systematic risk variables indicate that global-wide risk factors affected index

returns in the most recent sub-sample period during negative market return environments.

However, the negative systematic risk variable in equation (9) was not significant, which does

not provide a clear conclusion that systematic risks consistently affected returns before or after

the year 2000. Though some evidence does exist in Panel B of Table 13 that systematic risk

factors affected index returns significantly, the inconsistency of the results does not provide a

clear indication that market index returns vary with both global-wide characteristics across all

countries in this data set.

The results in Panel A and B in Table 13 do not provide evidence to support the claim in

previous literature [e.g. - Carrieri, Errunza, and Hogan (2007)] that international financial

markets have become more integrated in recent time periods. The results in these two panels

65

support the assertion that systematic risk does not significantly affect index returns [e.g. – Bali

and Cakici (2010)]. Bali and Cakici (2010) conduct an experiment that uses the Fama and

MacBeth (1973) methodology to show systematic risk factors do not affect index returns from

the time frame of 1973 to 2006, but they also claim that country-specific risk factors affect these

returns in this same time period. The evidence in the current paper indicates that integration of

financial markets across all countries did not take place in recent or previous time periods, but

the evidence also suggests that country-level risks did not affect index returns, either. Dumas,

Lewis, and Osambela (2011) indicate that domestic investors interpret information differently

than foreign investors, and this difference explains the anomalies seen in research studying

international asset returns. The results viewed in Table 13 suggest that different interpretations

of information across countries may prevent international agreement on worldwide information

to significantly caused index returns to vary.

3.5.2 Developed and Emerging Markets

Some of the literature that indicates international financial markets have become more

integrated mainly relies on evidence from emerging markets. Therefore, the results suggesting

integration seen in part (a) of this section potentially could be driven by behaviors exhibited by

emerging markets. This section serves as a robustness check for the results seen in (a) by

conducting the experiment using data from developing countries and emerging countries

separately. Consistent results across the two sets of countries would support the conclusions

developed in section (a), which would invalidate claims that emerging countries are the main

driver of international market integration.

66

The data set used in section (a) contains 37 countries, but the sample can be separated into

developed and emerging markets. There are 23 developed countries: Australia, Austria,

Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy,

Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland,

United Kingdom, and the United States. The 14 remaining countries are considered developing:

Argentina, Brazil, Chile, China, India, Korea, Malaysia, Mexico, Philippines, Poland, South

Africa, Taiwan, Thailand, and Turkey.

The data in Table 14 shows the results from regressions run on the developed countries. The

table shows the positive and negative systematic risk, or beta, coefficient value, the idiosyncratic

risk coefficient value, and total risk coefficient value and their respective t-statistics for each sub-

sample. Panel A of the table reports the regression results using data for the period prior to 2000,

and Panel B reports the regression results using data for the period 2000 and after.

Panel A of Table 14 shows that country-specific and systematic risks did not significantly

affect country-level index returns prior to 2000 for developed countries. The idiosyncratic and

total risk variables were insignificant, as well, in all regression specifications at the 5%

significance level. This shows that country-specific and systematic risks do not appear to have

significantly affected returns in this sub-sample period, indicating that global-wide factors did

not affect index-level returns within individual countries.

Country-specific risk did not significantly affect index returns during or after 2000, as shown

in Panel B of Table 14. The coefficients for either country-specific risk variables were not

significant in any of the regressions, which indicate that country-specific risk did not

significantly affect index returns in this time period for developed countries. Alternatively, the

67

Table 14 Cross-Sectional Results over Time of Developed Countries

Panel A: Pre-2000


(6) 0.0608

(0.98)

-0.0689

(-1.03)

(7) -0.0128

(0.37)

(8) 0.0000

(0.53)

(9) 0.0040

(0.04)

-0.1837

(-1.28)

0.0551

(0.82)

(10) 0.1641

(1.61)

-0.0640

(-0.42)

-0.0002

(-1.36)

Panel B: Post 2000


(6) 0.3128*

(2.62)

-0.4759*

(-3.30)

(7) 0.0182

(0.63)

(8) 0.0001

(1.53)

(9) 0.4468*

(2.84)

-0.5591*

(-2.81)

-0.0052

(-0.10)

(10) 0.4504*

(2.57)

-0.8122*

(-3.71)

0.0002

(1.21)


systematic risk variables significantly affected index returns in all regressions at the 1%

significance level. The consistent insignificance of country-specific risk and significance of

systematic risk shows that international index markets were integrated in the most recent sub-

sample period for developed countries.

Table 15 shows the results for the emerging market countries. The table shows the positive

68

Table 15 Cross-Sectional Results over Time of Emerging Countries

Panel A: Pre-2000


(6) 0.0111

(0.06)

-0.0094

(-0.03)

(7)

0.1493

(1.29)

(8)

0.0002

(0.46)

(9) -0.0015

(-0.01)

-0.0521

(-0.13)

0.1824

(1.42)

(10) -0.0646

(-0.29)

-0.0673

(-0.17)

0.0002

(0.55)

Panel B: Post 2000


(6) 0.0895

(0.57)

-0.0796

(-0.23)

(7)

-0.1018

(-0.96)

(8)

-0.0004

(-1.22)

(9) 0.1377

(0.87)

-0.1864

(-0.49)

-0.1225

(-1.12)

(10) 0.1341

(0.82)

-0.0826

(-0.22)

-0.0004

(-1.30)


and negative systematic risk, or beta, coefficient value, the idiosyncratic risk coefficient value,

and total risk coefficient value and their respective t-statistics for each sub-sample. Panel A of

the table reports the regression results using data for the period prior to 2000, and Panel B reports

the regression results using data for the period 2000 and after.

None of the risk variables in Panel A of Table 15 show significance at the 5% level, implying

that the risk variables, as configured here, cannot explain future asset returns. However, country-

specific risk did not significantly affect index returns during or after 1999 either, as shown in

69

Panel B of Table 14. Additionally, the systematic risk variables did not significantly affect index

returns in any regressions in the pre- or post-2000 time period, indicating emerging market

countries do not seem to have become integrated in the more recent time period. The

insignificance of country-specific risk and systematic risk shows that emerging international

index markets did not drive the overall results seen in Table 13.

The observations in Tables 14 and 15 show that systematic risk factors significantly affect

asset returns during and after 2000 for developed countries, whereas the country-specific risk

factors did not cause variation in stock returns during the same period. Therefore, the results and

conclusions viewed in part (a) of this section remain robust across developed economies, but the

results do not stay consistent across emerging economies. Hardouvelis, Malliaropulos, and

Priestley (2006) state that European economies became integrated in the late 1990s due to the

formation of the European Union, which explains the consistency of the results seen in Table 14.

Brennan and Cao (1997) indicate that foreign investors interpret information differently than

domestic investors, and the interpretation difference typically does not favor the foreign investor.

The results from Table 14 indicate consistent interpretation of investment information across

foreign and domestic investors in developed countries, but the discrepancy of information

interpretation across foreign and domestic investors across emerging economies does not allow

for the indices in these countries to move in an integrated manner.

3.6 Conclusion

This paper investigates the significance of global risk factors when modeling

international stock market index returns in order to show international financial markets vary in

an integrated manner. Previous literature studying world financial market integration through an

70

international capital asset pricing model or other models conclude international index markets

fluctuate from country-level risk factors, which indicates segmented global capital markets

instead of integrated markets. This paper investigates if systematic and country-specific risks

affect international asset returns differently in the pre-2000 time period relative to the post-2000

time period. The empirical experiments of this paper, therefore, analyze the significance of

conditioned systematic risk factors, or betas from an international capital asset pricing model,

through time in regressions of expected international index returns.

The conditioned regressions show that systematic risk factors did not significantly affect

expected international index returns in the pre-2000 time period. The result stays robust for

emerging economies. Systematic risks significantly affected index returns in developed

countries, which support results seen in previous literature indicating that European markets

became integrated after the formation of the European Union. Consequently, investors should

take into account that developed stock market indices vary with global-wide risk factors when

making investment decisions, but systematic risks do not affect the variability in emerging

country markets.

71

CHAPTER 4

INTERNATIONAL CAPITAL FLOWS IN AN INTEGRATED MARKET

4.1 Introduction

This paper examines the affect of international stock market integration on international

capital flows. Specifically, the investigation observes differences in forecasts of capital market

investments of investors in different countries across two time periods that differ in their level of

market integration. An investor in a foreign country should not digest information regarding an

asset differently than an investor in the home country if international markets move in an

integrated manner. However, the results of this study show through international capital flows

that investors across countries differ in their expected stock market outcomes, even though recent

literature suggests international stock markets are integrated. The results can be explained by

theoretical implications that investors may choose not to learn about foreign assets because

larger payoffs exist when specializing in home assets.

The instantaneous and continuous delivery of information through the internet indicates that

a foreign investor can become informed about foreign markets as easily as a domestic investor.

However, a seminal paper by Brennan and Cao (1997) detailed a theoretical model that foreign

investors will interpret information differently than a domestic investor, regardless of the speed

the information is delivered. The researchers provided a theoretical model that suggests foreign

investors produce overly optimistic outlooks of domestic stock markets during periods when

foreign stock market index increase compared to domestic investors, and foreign investors

construct overly negative outlooks during domestic stock market index decreases. This causes

foreign investors to purchase domestic assets from domestic investors with a greater magnitude

than domestic investors when domestic stock market returns increase, and foreigners will sell the

72

assets to domestic investors with greater magnitude than domestic investors when domestic stock

market returns fall.

Brennan and Cao (1997) provided a theoretical foundation that shows the relationship

between asset transactions and stock prices is linear, and they showed that the theoretical

foundations of their theory held true empirically. Brennan and Cao (1997), though, indicate that

when foreign market participants can interpret information in a similar manner as domestic

participants, the relationship will no longer exist, due to the fact that foreign and domestic

investor stock market index outlooks equal each other.

The 2007 financial crisis displayed the global nature of investing. In a completely integrated

market, the returns on assets will fluctuate only through variation in global-wide market risk

factors, regardless of their geographical location. Individual markets varying with global-wide

risk factors will reduce the misalignment of interpreting data between foreign and domestic

investors because investors will outlook stock market returns based on risks not associated with

an individual market, thereby suggesting integrated markets will not stay in line with the

implications of Brennan and Cao (1997).

Previous literature on this topic supports arguments for international financial market

integration [You and Daigler (2010); Carrieri, Errunza, and Hogan (2007); Bekaert, Harvey, and

Lumsdaine (2002); Hardouvelis, Malliaropulos, and Priestley (2006)]. Additionally, authors

imply that world market integration changed over time [e.g. – Bekaert and Harvey (1995); You

and Daigler (2010)], in that markets have become more integrated in recent time periods.

Collectively, these studies indicate that the integration of the returns of most countries’ indices

with global market returns occurred in the late 1990s.

73

This study observes the relationship between purchases of foreign equities and the returns of

those assets in two different time periods. The observations will signal if the interpretation of

data does not differ between foreign and domestic investors in an integrated market. Significant

relationships between foreign purchases of equities and foreign stock market indices suggest

foreign and domestic investors differ in their future stock market index outlooks. If international

stock markets are integrated, then foreign and domestic investor forecasts should not differ

because returns on assets with similar risks vary only with global-wide risk factors, regardless of

the location of the assets.

The study will use seemingly unrelated regressions of equity purchases of U.S. residents on

to the returns of foreign equity indices before and after 2000. A variety of studies imply that the

integration of most developing markets occurred before or during the year of 1994 (Carrieri,

Errunza, and Hogan (2007); Bekaert, Harvey, and Lumsdaine (2002), and Hardouvelis,

Malliaropulos, and Priestley (2006) show that European countries became more integrated in the

second half of the 1990s due to the formation of the European Union. F-tests conducted in this

study confirm that country-level stock market indices correlate with a world market index after

the year 1999.

The results of the statistical analysis in this study suggest that the linear relationship between

purchases of foreign equities and their returns holds regardless of the time period studied.

Therefore, the results imply that interpretation of information differs across investors in different

countries, even in more recent, integrated, time periods. The results can be explained by

Nieuwerburgh and Veldkamp (2009) who theoretically find that when domestic investors

possess a slight information interpretation advantage of domestic markets over foreign investors,

74

they profit more by interpreting domestic information signals than foreigners, which provides an

incentive for domestic investors to specialize in domestic assets rather than learning and

investing in foreign markets. This suggests investors will continue to learn and specialize in

purchasing domestic assets, even though foreign holdings will increase the diversification of

their portfolios. Dong (2009) empirically shows this remains true, even in cross-listing of

foreign firms on domestic exchanges. Consequently, the work of Nieuwerburgh and Veldkamp

(2009) and Dong (2009) explain results seen in this study that foreigners still exhibit trend-

following investment strategies in integrated markets.

4.2 Data and Methodology

This paper observes differences in the relationship between purchases of equities by

foreigners and equity returns across two time periods, before and after the year 2000. Brennan

and Cao (1997) state that foreign investors interpret information regarding a foreign stock market

more fervently than investors of the host country, and, therefore, foreign investors follow trend-

driven purchasing behavior with greater magnitude than domestic investors. Therefore, a

positive and linear relationship exists between foreign purchases of equities in another country

and the returns of the stock market in that country. However, several pieces of literature state

that stock markets across the globe are becoming more integrated (e.g. - Bekaert and Harvey

(1995)), which indicates that investors will receive similar signals leading to predictions of future

stock market behavior in any country. Consequently, this examination studies the differences in

the relationship between equity purchases and stock market return in segmented and integrated

global stock market environments.

75

The analysis will incorporate daily and monthly U.S. dollar denominated returns of stock

market indices for each of the countries observed. The data set also includes a world index that

is calculated as the value-weighted average of all the stocks in the entire data set. The

observations come from Datastream, called the Datastream Global Indices, and the observations

represent percent returns of closed-out, long U.S. dollar positions of each index at the two

different frequencies. The Datastream Global Equity Indices User Manual gives a detailed

description of the collection and calculation methods of the indices for the interested reader.

The investigation will use monthly net sales of foreign stocks by foreigners to U.S. residents

for four developed countries and 13 developing countries. The four developed countries are:

Canada, Germany, Japan, and the United Kingdom. The 13 developing countries are: Argentina,

Brazil, Chile, Greece, India, South Korea, Malaysia, Mexico, Philippines, Portugal, Taiwan,

Thailand, and Turkey. These countries were chosen to directly estimate the relationship found

by Brennan and Cao (1997) across the two given time periods.4 The observations come from the

publicly available U.S. Treasury International Capital website, and they span from January 1977

to November 2010. The data represents net purchases of stocks by U.S. residents from

foreigners for capital flows for each month for each country.

Though literature (e.g. - Bekaert, Harvey, and Lumsdaine (2002)) implicitly suggests the year

2000 as a break point for integration, no specific piece of literature explicitly states a specific

year for this investigation to use. To seek out a specific year, the correlations were calculated

between the world market index and the individual indices for the 37 countries available in the

4 Columbia, Indonesia, and Pakistan were in the original data set of Brennan and Cao (1997), but the Datastream

stock market data set used in this paper does not include data on those countries. Consequently, those three

countries were left out of the investigation.

76

Datastream Global Equity Indices dataset for each month in the sample. The data outlined in

Figure 14 gives the equal-weighted, monthly averages of the correlations between the world

Figure 14 Equal-Weighted Average Correlation of Countries’ Indices with World Market

market index and the individual indices for the 37 countries for each month in the sample. This

graph shows an upward trend in the average of the correlations, which suggests an increasing

trend towards integration, especially in the later 1990s through the end of the time series. The

average correlation of country-level indices with the world index in the pre-2000 time period is

0.36, and the average correlation value in the post-2000 time period is 0.61. The average

correlation of country-level indices with the world index for developed economies in the pre-

2000 time period is 0.40, and the average correlation value in the post-2000 time period is 0.62.

The average correlation of country-level indices with the world index for emerging economies in

the pre-2000 time period is 0.24, and the average correlation value in the post-2000 time period

is 0.53. This corresponds with previous studies [e.g. – You and Daigler (2010)] showing

-0.2

0

0.2

0.4

0.6

0.8

1

1973

-01

1974

-05

1975

-09

1977

-01

1978

-05

1979

-09

1981

-01

1982

-05

1983

-09

1985

-01

1986

-05

1987

-09

1989

-01

1990

-05

1991

-09

1993

-01

1994

-05

1995

-09

1997

-01

1998

-05

1999

-09

2001

-01

2002

-05

2003

-09

2005

-01

2006

-05

2007

-09

2009

-01

2010

-05

Aver

age

Corr

elati

on

wit

h W

orl

d M

ark

et

77

increasing integration in more recent times, and the increase in the graph in later time periods

further supports sub-sampling the data into two different time periods.

In order to establish a firm breakpoint, Andrews (1993) suggests calculating F statistics for

time periods suspected as breakpoints in the data. When the p-value of the statistic reaches an

acceptable level of significance, the breakpoint is established. Therefore, F statistics were

calculated on the correlation data used to create Figure 1 with each year from 1995 to 2004 as

breakpoints. Table 16 presents F-tests results run on equal-weighted, monthly averages of the

Table 16 F-test Results of Equal-Weighted Average Correlations of Countries Indices with

the World Market

Year Break F-Statistic p-value 1995 1.0258 0.8560

1996 1.0108 0.9446

1997 1.0875 0.5523

1998 1.1276 0.4039

1999 1.1058 0.4960

2000 1.2649 0.1213

2001 1.2992 0.0946*

2002 1.6815 0.0018**

2003 2.0143 0.0001**

2004 2.9257 0.0000**

** - significant at the 5% level. * - significant at the 10% level

correlations of the world market index with the individual country indices from 1973 to 2010

using daily data. The table shows the breakpoint year, F statistic, and associated p-value of each

statistic. Table 16 shows the 2001 breakpoint as significant at the 10% confidence level.

However, a significant drop in the correlation data in the last quarter of 2000 and early 2001

could have been potentially created by downward bias in the regressions. Choosing the year

2000 as the breakpoint in the dataset will provide additional data in the later subset to mitigate

any downward bias created by the sharp drop in the correlations seen in late months of 2000 and

78

early months of 2001. Thus, the year 2000 will serve as the breakpoint for sub-setting the

dataset.

The linear relationship will be tested using seemingly unrelated regressions (SUR), the same

statistical method used by Brennan and Cao (1997). The tests use net purchases of equities as

the dependent variable, and the stock market index returns compromise the independent

variables. The four developed countries will be examined first, followed by the developing

countries. The analysis conducts regressions over three models within both subsets of countries.

The first model regresses net purchases of equities by U.S. investors from investors in each

country individually on stock market index returns of all countries:

𝑆𝑖 = 𝑐 + 𝛾𝑖𝑅𝑖 + 𝛾𝑈𝑆𝑅𝑈𝑆 + ∑ 𝛾𝑗𝑅𝑗𝐽𝑛=1

where c represents a constant term, 𝑆𝑖 represents net purchases of equities by U.S. investors from

investors in country i, 𝑅𝑖 represents index returns in country i, 𝑅𝑈𝑆 represents index returns in the

U.S., and 𝑅𝑗 represent index returns in returns in country j, and the gamma coefficients represent

the coefficients for each independent variable.

Brennan and Cao (1997) state that foreigner investors demand equities at a greater magnitude

than domestic investors during increases in domestic stock market indices due to overly

optimistic market forecasts. Also, foreigners will sell equities to domestic market participants

when domestic stock market indices decrease. This explains the use of net sales as the

dependent variable over gross sales. Therefore, Equation (1) tests whether foreign investors are

at an information disadvantage to investors in a host country, and the signs of the coefficient

within these regressions also tests whether U.S. investors follow trend-following behavior. From

(1)

79

the theoretical implications and empirical results in Brennan and Cao (1997), the coefficients on

the stock market variables are predicted to be significantly positive. These regressions were run

in all time periods before and including December 1999, and then, again, run on all time periods

after and including January 2000.

4.3 Results

4.3.1 Summary Statistics

Table 17 shows the summary statistics of the U.S. Treasury equity transaction data and

Table 17 Summary Statistics – Monthly Purchases of Equities by U.S. Residents from

Foreign Investors(in Millions of U.S. Dollars from January 1977 to October 2010)

Country Mean Standard Deviation Skewness

Australia 75.64 342.49 1.00

Austria 1.73 48.69 1.42

Belgium -31.18 282.54 0.09

Canada 132.85 674.87 0.84

Denmark 9.43 105.87 4.75

France 67.27 438.96 0.59

Germany 16.24 523.87 -0.51

Hong Kong 156.19 1,134.45 0.73

Ireland -1.71 236.79 -3.34

Italy 15.98 235.77 -0.21

Japan 584.83 1,856.69 1.29

Netherlands -41.12 350.15 -0.72

Singapore 3.74 342.08 -0.14

South Africa 20.17 102.35 4.92

Switzerland 22.75 378.59 2.55

United Kingdom 743.83 2,982.67 0.79

returns on country-level equity indices. Table 17 shows the summary statistics of the U.S.

Treasury data, and Table 18 summarizes the equity index return data. Both tables report the

mean, standard deviation, and skewness of the two different data sets for each country over the

80

Table 18 Summary Statistics - Monthly Stock Market Index Returns (in % from January

1977 to October 2010)

Country Mean Standard Deviation Skewness

Australia 1.31 6.90 -0.85

Austria 1.13 6.88 0.37

Belgium 1.13 5.73 -0.53

Canada 1.08 5.51 -0.69

Denmark 1.24 5.66 -0.33

France 1.31 6.51 -0.29

Germany 1.01 5.92 -0.41

Hong Kong 1.56 8.62 -0.52

Ireland 1.31 6.86 -0.22

Italy 1.16 7.37 0.26

Japan 0.84 6.29 0.32

Netherlands 1.19 5.41 -1.07

Singapore 1.23 7.36 -0.32

South Africa 1.54 8.18 -0.60

Switzerland 1.14 5.02 -0.38

UK 1.24 5.41 -0.32

US 1.01 4.30 -0.63

World 0.99 4.40 -0.69

entire time span of the data set. The data set starts in January 1977, and runs through October

2010. The stock return data was truncated to start on January 1977 because the Treasury data set

begins in 1977, which yielded 406 data points for each country for each data set.

Within the U.S. Treasury data of Table 17, U.S. investors trade the most with investors in

the United Kingdom, with an average of 743.83 in transactions occurring each month. U.S.

investors traded with investors in The Netherlands the least, with more U.S. investors selling

equities to investors in The Netherlands on average than investors in The Netherlands selling to

U.S. investors, as shown by an average value of -41.12. Looking at Table 18, the stock market

index in Hong Kong realized the largest average monthly return gain of 1.56%, where investors

in Japan saw the lowest return with 0.84% achieved per month on average. Even though

investors in the Hong Kong stock market saw the largest return over the given time period out of

81

the other countries in the data set, the Hong Kong stock market also varied the most. However,

the U.S. stock market realized the lowest average return standard deviation over the sample

period.

4.3.2 Comparable Regressions

Table 19 gives the results from the seemingly unrelated regressions of U.S. investors net

Table 19 U.S. Purchases of Stocks in Foreign Markets – Comparable Regressions

Panel (a)

Pre-2000 Constant 𝜸𝑼.𝑺. 𝜸𝑪𝒂𝒏𝒂𝒅𝒂 𝜸𝑮𝒆𝒓𝒎𝒂𝒏𝒚 𝜸𝑱𝒂𝒑𝒂𝒏 𝜸𝑼.𝑲.

Canada 63.95* -11.91* 10.65* 0.65 -0.58 1.96

(3.90) (-2.17) (2.30) (0.20) (-0.23) (0.51)

Germany 31.30 -12.91* 13.17* 9.13* -5.23 -4.44

(1.62) (-2.00) (2.41) (2.36) (-1.73) (-0.99)

Japan 378.40* 17.45 25.18 -3.20 48.79* -26.41

(4.64) (0.64) (1.09) (-0.20) (3.82) (-1.39)

U.K. 126.43 37.62 -35.85 -2.95 -27.75* 20.50

(1.69) (1.50) (-1.70) (-0.20) (-2.37) (1.18)

N = 276 for each variable in each equation

Panel (b)

Post-2000 Constant 𝜸𝑼.𝑺. 𝜸𝑪𝒂𝒏𝒂𝒅𝒂 𝜸𝑮𝒆𝒓𝒎𝒂𝒏𝒚 𝜸𝑱𝒂𝒑𝒂𝒏 𝜸𝑼.𝑲.

Canada 201.89* -18.71 68.72* -4.87 -24.64 3.40

(2.01) (-0.41) (2.35) (-0.17) (-1.02) (0.07)

Germany -3.44 -95.83* 2.67 37.80 12.51 27.01

(-0.05) (-2.92) (0.13) (1.81) (0.72) (0.80)

Japan 949.64* -95.72 -20.60 -45.89 253.54* 124.64

(4.44) (-0.98) (-0.33) (-0.74) (4.91) (1.24)

U.K. 1873.98* -217.23 150.59 81.15 4.94 154.25

(4.50) (-1.15) (1.24) (0.67) (0.05) (0.79)

N = 130 for each variable in each equation


purchases of equities from foreign investors. Panel (a) shows the regression results using data

spanning from January 1977 to December 1999, a time period already established as an

environment of non-integrated global stock markets [e.g. – Bekaert, Harvey, and Lumsdaine

(2002)]. Panel (b) displays the results from regressions run on the time period from January

2000 to October 2010, the designated time period of integration international markets. Though

82

more data points exist from 1977 to 1999 than 2000 to 2010, the large sample size in both time

periods does not suggest differences should exist in the results across time periods from

disproportionate sample sizes. The selection of countries corresponds to the initial country set

used by Brennan and Cao (1997) as a group of developed countries. The same set of countries is

used here in order to directly compare the results of Brennan and Cao (1997) across two different

levels of integration. The results of the table test the linear relationship between portfolio flows

to the host country and stock market indices for all other countries in the group.

Upon investigation of Panel (a), the coefficient of the stock market index for purchases in

the host country (e.g. – Row Canada and Column Canada) is positive and statistically significant

for the stock market indices of Canada, Germany, and Japan. The coefficient for the United

Kingdom stock market index is statistically insignificant at the 5% level. These results align

with the results seen in Brennan and Cao (1997), which indicates that this data set does not

produce differing results than the theory established by Brennan and Cao (1997). The significant

coefficients in the regressions of portfolio flows into these countries signal that foreign investors

forecast returns in foreign markets with greater magnitude than domestic investors, and the

positive sign on the coefficients indicate foreign investors exhibit trend-following behavior. The

insignificant coefficient for the United Kingdom stock market index implies that U.S. investors

form equal forecasts about the U.K. stock market as investors from the United Kingdom, or that

any advantage investors in the U.K. have over U.S. investors does not accumulate over time.

Brennan and Cao (1997) suggest this stems from a large presence of U.S. investors in London.

The results in Panel (a) of Table 19 also showed statistically significant coefficients on

the stock market indices of non-host countries. The coefficient for the U.S. stock market index

83

in the regression of U.S. investor purchases of Canadian equities showed statistical significance

and a negative sign. This suggests that negative returns of equities from the U.S. stock market

caused an increase of purchases of Canadian equities. The coefficients on the U.S. and Canadian

stock market index variables displayed significance in regression of U.S. investor purchases of

German equities, and the coefficient on the Japanese stock market index variable exhibited

significance in the regression of U.S. investor purchases of U.K. equities. The significance of

these coefficients infers that returns on indices other than the host country influence the

purchases of foreign equities from U.S. investors. The inconsistency of the significant

coefficients of non-host country stock market indices do not reveal any pattern that suggest one

or multiple non-host country stock market indices influences the purchases of foreign equities by

U.S. investors.

Panel (b) of Table 19 reports results of regressions run using data from January 2000 to

October 2010. The regressions contain similar results as those seen in the pre-2000 period. The

coefficients on the Canadian and Japanese stock market variables for the Canadian and Japanese

equity purchase equations are significantly positive at the 5% level. The coefficient for the

German and United Kingdom stock market variable in the German and United Kingdom equity

purchase equations, respectively, is statistically insignificant from zero. The coefficient for the

U.S. stock market variable in the German equity purchase equation is negative and statistically

significant, which suggests increases in the U.S. stock market decreases U.S. investor purchases

of equities from German investors. The negative coefficient on the U.S. stock market index for

the regression of German equity purchases by U.S. investors was significant, which suggests

negative returns on the U.S. stock market increase purchases of German equities. The lack of

84

consistent significance of coefficients on stock market indices of non-host countries implies non-

host country indices do not appear to be a driver of purchasing foreign equities.

This result differs from Brennan and Cao (1997) where the coefficient on the U.S. stock

market index was insignificant, but this result indicates investors’ purchase decision of German

equities is driven from the U.S. stock market, not the German stock market. The overall results

indicate foreign investors’ forecasts of domestic stock market indices differ from domestic

investors in a more integrated global stock market. Increasingly correlated international stock

markets in recent time periods did not provide, according to this evidence, foreign investors with

the same ability to interpret information from foreign economies on foreign stock markets as

domestic investors.

Integrated markets imply that the return on any asset with relatively the same risk should

remain consistent across markets and investors, regardless of the location of the asset [Bekaert,

Harvey, and Lumsdaine (2002)]. Consequently, the statistically significant relationships in Panel

(b) of Table 19 suggest investors assess risk and assets differently across geographies, which

presents an inconsistent result with the theoretical implications of trading in integrated markets,

since several strands of literature state the post-2000 time period is an integrated international

market.

Foreign investors may choose, however, to not fully absorb all the necessary information

needed to assess the risk with the same thoroughness as domestic investors of domestic assets.

Nieuwerburgh and Veldkamp (2009) theoretically showed investors will refuse to learn about

foreign assets in order to specialize in more familiar assets in their home country. Dong (2009)

provided empirical evidence to support the theory of Nieuwerburgh and Veldkamp (2009) with

85

U.S. investors. These two studies explain the anomaly of trend-following behavior exhibited by

U.S. investors in Panel (b) of Table 19 in an integrated international equity market by showing

that investors may benefit from this behavior by specializing in domestic assets.

4.3.3 Additional Regressions

The results in Section 3, Part (b) above used a set of countries selected to compare with

the results of Brennan and Cao (1997). Supplemental regressions using data on additional

countries will provide robustness to the results seen in Part (b). The results seen in Table 20

below perform the same analysis in Part (b) above with the following countries: Australia,

Austria, Belgium, Denmark, France, Hong Kong, Ireland, Italy, the Netherlands, Singapore,

South Africa, and Switzerland. These countries contain the same number of data entries as the

countries in Part (b), which was the criterion for selecting these countries out of the data set used

in this study. The same regressions were run on this country set as in Part (b) above. Panel (a)

of Table 20 show the results for the three models for regressions before January 2000, and Panel

(b) of Table 20 displays the results for regressions conducted on data from January 2000 to

October 2010.

Panel (a) in Table 20 shows that all coefficients on the host country stock market indices

remain insignificant. The insignificance of the relationship implies investors in host countries do

not possess a forecasting difference with U.S. investors, or the insignificance suggests U.S.

investors do not exhibit a trend-following behavior.

However, a few coefficients of non-host country stock market index variables displayed

significance. The coefficients of the Swiss stock market index variable in the regression of

Australian equity purchases, the Austrian stock market index in the Belgium equity purchase

86

equation, the Irish stock market index in the Italian equity purchase equation, and the Australian

stock market index in the Dutch equity purchase equation showed statistical significance. This

suggests that returns of non-host stock market indices affected purchases of foreign equities by

U.S. investors for these specific instances. With only a few significant coefficients of non-host

country stock market indices, no pattern emerges, though, to suggest non-host country indices

systematically impact foreign equity purchasing.

Panel (b) of Table 20 shows the results over the time period of January 2000 to October

2010. All of the coefficients on the host countries’ stock market indices were insignificant,

except the coefficient on the Danish stock market index in the Denmark equation was negative

and statistically significant. The significance of Danish stock market coefficient remains

consistent with the theory laid out in Brennan and Cao (1997), but the negative sign differs from

the results seen in Table 19 and Brennan and Cao (1997). The negative coefficient suggest a

decrease in purchases of Danish equities by U.S. investors with increases in the returns of the

Danish stock market index, which could stem from domestic investors in Denmark purchasing

more equities from U.S. investors when the Danish stock market increases.

A few of the non-host country stock market index return coefficients displayed statistical

significance, which indicates returns on stock markets other than the host country drives

purchasing of equity purchases in specific instances. Only 11 out of the 144 non-host country

indices showed statistical significance, and the signs of the coefficients varied between positive

and negative values. Subsequently, a consistent relationship between non-host country index

returns and equity purchases does not surface from these results.

87

Tab

le 2

0 U

.S. P

urc

hase

s of

Sto

cks

in F

ore

ign

Mark

ets

Pre-2

000 –

Ad

dit

ion

al

Reg

ress

ion

s -

Pan

el (

a)

Pre

-200

0

Co

nst

an

t 𝜸𝑼

.𝑺.

𝜸𝑨𝒖𝒔𝒕𝒓𝒂𝒍𝒊𝒂

𝜸𝑨𝒖𝒔𝒕𝒓𝒊𝒂

𝜸𝑩𝒆𝒍𝒈𝒊𝒖𝒎

𝜸𝑫𝒆𝒏𝒎𝒂𝒓𝒌

𝜸𝑭𝒓𝒂𝒏𝒄𝒆

Au

stra

lia

38

.10

*

-0.6

8

0.2

7

2.1

8

-3.5

9

-0.6

7

-0.0

9

(4.1

1)

-(0.4

3)

(0.1

7)

(0.8

8)

-(1

.69

) -(

0.3

5)

-(0

.07

)

Au

stri

a

-2.3

8

0.1

2

-0.1

3

0.3

9

-0.0

3

-0.3

5

0.1

5

-(1

.38

) (0

.41)

-(0.4

6)

(0.8

5)

-(0

.06

) -(

0.9

9)

(0.6

7)

Bel

giu

m

-20

.88

*

0.4

7

0.9

5

4.5

3*

1.0

4

-1.3

1

-0.6

1

-(2

.70

) (0

.36)

(0.7

3)

(2.1

9)

(0.5

9)

-(0

.82

) -(

0.5

9)

Den

ma

rk

9.4

1

0.8

7

0.3

2

0.5

5

-1.2

6

-0.6

1

0.5

7

(1.6

8)

(0.9

2)

(0.3

4)

(0.3

7)

-(0

.99

) -(

0.5

3)

(0.7

6)

Fra

nce

6

0.0

4*

-0.7

2

-0.5

6

1.3

7

2.7

3

-2.5

5

0.3

6

(3.7

4)

-(0.2

6)

-(0.2

1)

(0.3

2)

(0.7

4)

-(0

.77

) (0

.17)

Ho

ng

Ko

ng

50.8

9*

-2.0

4

-0.2

9

0.3

1

-4.4

9

-1.1

3

1.8

0

(2.7

8)

-(0.6

6)

-(0.1

0)

(0.0

6)

-(1

.07

) -(

0.3

0)

(0.7

4)

Irel

an

d

21

.18

*

0.1

9

-0.8

1

1.7

4

-1.1

8

0.8

0

-0.5

8

(4.3

1)

(0.2

3)

-(0.9

9)

(1.3

3)

-(1

.05

) (0

.79)

-(0

.88

)

Ita

ly

4.2

4

1.9

9

-0.1

2

3.3

0

0.2

1

-4.4

8

-1.9

3

(0.3

3)

(0.9

0)

-(0.0

5)

(0.9

5)

(0.0

7)

-(1

.67

) -(

1.1

1)

Net

her

lan

ds

-19

.35

-0

.12

4.3

3*

-0.4

8

-0.1

1

-3.3

6

1.3

9

-(1

.52

) -(

0.0

6)

(2.0

4)

-(0.1

4)

-(0

.04

) -(

1.2

8)

(0.8

2)

Sin

ga

po

re

24

.58

*

1.1

3

-1.1

1

2.3

0

0.9

5

-1.0

4

0.9

1

(2.5

3)

(0.6

9)

-(0.6

8)

(0.8

9)

(0.4

3)

-(0

.52

) (0

.70)

Sou

th A

fric

a

11.6

6*

0.0

7

-0.2

6

0.1

8

-0.4

4

-0.3

9

-0.2

7

(4.9

9)

(0.1

8)

-(0.6

8)

(0.2

9)

-(0

.83

) -(

0.8

1)

-(0

.87

)

Sw

itze

rla

nd

3

.48

0.7

4

-0.1

3

-3.2

2

-3.2

3

-0.2

5

0.0

4

(0.2

4)

(0.2

9)

-(0.0

5)

-(0.8

2)

-(0

.95

) -(

0.0

8)

(0.0

2)

N =

276 f

or

each

var

iable

in e

ach e

quat

ion

*-

sign

ific

ant

at t

he

5%

lev

el;

t-st

atis

tics

are

rep

ort

ed i

n p

aren

thes

is

8888

T

ab

le 2

1 U

.S. P

urc

hase

s of

Sto

cks

in F

ore

ign

Mark

ets

Pre-2

000

– A

dd

itio

nal

Reg

ress

ion

s -

Pan

el (

a)

- C

on

tin

ued

Pre

-200

0

𝜸𝑯𝒐𝒏𝒈

𝑲𝒏𝒐𝒏𝒈

𝜸𝑰𝒓𝒆𝒍𝒂𝒏𝒅

𝜸𝑰𝒕𝒂𝒍𝒚

𝜸𝑵𝒆𝒕𝒉𝒆𝒓𝒍𝒂𝒏𝒅𝒔

𝜸𝑺𝒊𝒏𝒈𝒂𝒑𝒐𝒓𝒆

𝜸𝑺𝒐𝒖𝒕𝒉

𝑨𝒇𝒓𝒊𝒄𝒂

𝜸𝑺𝒘𝒊𝒕𝒛𝒆𝒓𝒍𝒂𝒏𝒅

Au

stra

lia

-0.2

0

0.2

5

-0.9

6

-0.5

9

-2.2

6

-0.4

7

6.2

2*

-(0

.11

) (0

.19)

-(0.2

8)

-(0.3

8)

-(1

.79

) -(

0.1

7)

(2.2

5)

Au

stri

a

0.1

7

-0.4

6

-0.4

3

-0.0

2

-0.1

0

0.4

0

0.5

1

(0.5

3)

-(1.9

0)

-(0.6

7)

-(0.0

7)

-(0

.41

) (0

.79)

(1.0

0)

Bel

giu

m

-0.1

1

-0.5

8

-1.4

9

-2.3

5

-1.2

6

-0.3

8

0.2

4

-(0

.08

) -(

0.5

3)

-(0.5

2)

-(1.8

1)

-(1

.20

) -(

0.1

7)

(0.1

0)

Den

ma

rk

-0.3

6

-0.2

4

-1.3

3

-0.3

6

-0.0

7

0.5

4

0.4

5

-(0

.35

) -(

0.3

1)

-(0.6

4)

-(0.3

8)

-(0

.09

) (0

.33)

(0.2

7)

Fra

nce

0

.38

0.8

7

-0.5

7

-2.5

3

-1.2

0

1.2

7

7.7

1

(0.1

3)

(0.3

8)

-(0.0

9)

-(0.9

4)

-(0

.55

) (0

.27)

(1.6

1)

Hon

g K

on

g

2.7

5

-0.8

8

2.3

6

-1.3

0

1.4

2

7.8

6

2.4

4

(0.8

0)

-(0.3

4)

(0.3

5)

-(0.4

2)

(0.5

7)

(1.4

7)

(0.4

5)

Irel

an

d

-1.2

4

-0.0

4

1.0

3

-0.5

6

-0.4

8

0.9

9

-1.0

6

-(1

.34

) -(

0.0

6)

(0.5

6)

-(0.6

7)

-(0

.72

) (0

.68)

-(0

.72

)

Ita

ly

1.4

6

4.3

0*

-2.7

4

-3.4

0

-1.8

8

6.0

8

1.4

5

(0.6

0)

(2.3

3)

-(0.5

7)

-(1.5

6)

-(1

.07

) (1

.60)

(0.3

7)

Net

her

lan

ds

-1.8

9

-2.0

6

4.9

9

0.1

6

1.6

3

1.5

0

-2.9

9

-(0

.79

) -(

1.1

5)

(1.0

6)

(0.0

7)

(0.9

4)

(0.4

0)

-(0

.79

)

Sin

ga

po

re

-1.3

2

-1.2

8

-4.2

6

1.3

4

-1.5

5

1.5

7

-0.1

2

-(0

.73

) -(

0.9

3)

-(1.1

8)

(0.8

2)

-(1

.17

) (0

.55)

-(0

.04

)

Sou

th A

fric

a

0.1

6

0.3

1

-0.2

0

-0.5

0

-0.5

3

1.2

8

0.7

5

(0.3

6)

(0.9

4)

-(0.2

3)

-(1.2

6)

-(1

.67

) (1

.87)

(1.0

8)

Sw

itze

rla

nd

0

.43

0.7

9

5.5

1

-2.0

2

-2.3

3

7.5

1

0.2

3

(0.1

6)

(0.3

8)

(1.0

0)

-(0.8

1)

-(1

.16

) (1

.74)

(0.0

5)

N =

276 f

or

each

var

iable

in e

ach e

quat

ion

*-

signif

ican

t at

the

5%

lev

el;

t-st

atis

tics

are

rep

ort

ed i

n p

aren

thes

is

88

89

Tab

le 2

2 U

.S. P

urc

hase

s of

Sto

cks

in F

ore

ign

Mark

ets

Pre-2

000 –

Ad

dit

ion

al

Reg

ress

ion

s -

Pan

el (

b)

Po

st-2

00

0

Co

nst

an

t 𝜸𝑼

.𝑺.

𝜸𝑨𝒖𝒔𝒕𝒓𝒂𝒍𝒊𝒂

𝜸𝑨𝒖𝒔𝒕𝒓𝒊𝒂

𝜸𝑩𝒆𝒍𝒈𝒊𝒖𝒎

𝜸𝑫𝒆𝒏𝒎𝒂𝒓𝒌

𝜸𝑭𝒓𝒂𝒏𝒄𝒆

Au

stra

lia

12

7.3

7*

55.3

*

-15.3

5

32.0

0

13

.58

14

.20

-22

.63

(2.5

0)

(3.1

0)

-(0

.95

) (1

.49)

(0.9

2)

(0.4

2)

-(1.5

7)

Au

stri

a

10

.92

0.4

1

-2.1

6

1.4

5

-0.5

6

-1.7

0

-1.2

8

(1.4

6)

(0.1

6)

-(0.9

1)

(0.4

6)

-(0

.26

) -(

0.3

4)

-(0

.60

)

Bel

giu

m

-58

.30

4.4

3

-7.5

1

-3.3

7

7.2

5

2.6

8

-8.0

8

-(1

.34

) (0

.29)

-(0.5

4)

-(0.1

8)

(0.5

7)

(0.0

9)

-(0

.65

)

Den

ma

rk

12

.79

2.3

3

-3.0

2

-1.4

4

12

.86

*

-17

.82

*

-4.9

9

(1.0

1)

(0.5

2)

-(0.7

5)

-(0.2

7)

(3.5

0)

-(2

.14

) -(

1.3

9)

Fra

nce

5

5.5

9

-45.8

2

27.0

5

-20.7

5

15

.51

45

.64

4.3

5

(0.8

3)

-(1.9

5)

(1.2

7)

-(0.7

3)

(0.8

0)

(1.0

3)

(0.2

3)

Ho

ng

Ko

ng

22

8.8

1

46.5

0

-2.8

3

13.7

0

36

.20

-47

.29

4

3.1

2

(1.3

2)

(0.7

6)

-(0.0

5)

(0.1

9)

(0.7

2)

-(0

.41

) (0

.88)

Irel

an

d

-21

.15

-1

9.2

6

14.3

9

-31.6

*

-1.3

0

11

.31

-15

.47

-(0

.57

) -(

1.4

7)

(1.2

2)

-(2.0

2)

-(0

.12

) (0

.46)

-(1

.47

)

Ita

ly

28

.02

2.3

5

4.6

4

22.9

1*

3.6

7

-22

.70

1

2.6

1

(1.0

3)

(0.2

5)

(0.5

4)

(2.0

0)

(0.4

6)

-(1

.27

) (1

.64)

Net

her

lan

ds

-76

.16

-1

.16

-1

9.4

1

-9.6

2

7.4

3

-59

.18

-3

4.5

*

-(1

.48

) -(

0.0

6)

-(1.1

9)

-(0.4

4)

(0.5

0)

-(1

.74

) -(

2.3

7)

Sin

ga

po

re

-73

.40

-3

4.0

4

20.3

8

16.5

3

34

.48

*

42

.28

2.7

4

-(1

.42

) -(

1.8

7)

(1.2

4)

(0.7

6)

(2.3

0)

(1.2

4)

(0.1

9)

So

uth

Afr

ica

26

.06

4.2

3

1.0

5

1.4

2

-1.4

7

-3.3

9

3.1

0

(1.5

9)

(0.7

3)

(0.2

0)

(0.2

1)

-(0

.31

) -(

0.3

1)

(0.6

7)

Sw

itze

rlan

d

37.6

8

-20.2

9

9.6

9

7.6

5

-13.1

6

77.3

6*

21.2

8

(0.6

9)

-(1.0

6)

(0.5

6)

(0.3

3)

-(0

.83

) (2

.15)

(1.3

8)

N =

130 f

or

each

var

iable

in e

ach e

quat

ion

*-

sign

ific

ant

at t

he

5%

lev

el;

t-st

atis

tics

are

rep

ort

ed i

n p

aren

thes

is

90

Tab

le 2

3 U

.S. P

urc

hase

s of

Sto

cks

in F

ore

ign

Mark

ets

Pre-2

000 –

Ad

dit

ion

al

Reg

ress

ion

s -

Pan

el (

b)

- C

on

tin

ued

Post

-20

00

𝜸𝑯𝒐𝒏𝒈

𝑲𝒏𝒐𝒏𝒈

𝜸𝑰𝒓𝒆𝒍𝒂𝒏𝒅

𝜸𝑰𝒕𝒂𝒍𝒚

𝜸𝑵𝒆𝒕𝒉𝒆𝒓𝒍𝒂𝒏𝒅𝒔

𝜸𝑺𝒊𝒏𝒈𝒂𝒑𝒐𝒓𝒆

𝜸𝑺𝒐𝒖𝒕𝒉

𝑨𝒇𝒓𝒊𝒄𝒂

𝜸𝑺𝒘𝒊𝒕𝒛𝒆𝒓𝒍𝒂𝒏𝒅

Au

stra

lia

-10

.26

-3

4.2

8

30.4

6

-6.5

3

-5.2

2

-13

.34

-4

8.1

6*

-(0

.75

) -(

1.4

6)

(1.1

2)

-(0.4

6)

-(0

.50

) -(

0.6

1)

-(2

.04

)

Au

stri

a

-0.8

6

2.1

4

2.3

9

-0.3

4

0.0

0

1.6

5

0.5

8

-(0

.43

) (0

.62)

(0.6

0)

-(0.1

6)

(0.0

0)

(0.5

2)

(0.1

7)

Bel

giu

m

28

.34

-11.6

5

-14.8

0

12.6

3

2.2

9

42

.3*

-61

.23

*

(2.4

2)

-(0.5

8)

-(0.6

4)

(1.0

4)

(0.2

6)

(2.2

8)

-(3

.03

)

Den

ma

rk

-3.0

4

6.4

5

2.9

9

-2.9

8

-2.2

7

6.5

0

5.7

8

-(0

.89

) (1

.11)

(0.4

4)

-(0.8

4)

-(0

.87

) (1

.20)

(0.9

9)

Fra

nce

-6

.44

-2

0.6

9

-8.6

8

7.7

9

8.6

7

-11.4

9

10.5

8

-(0

.36

) -(

0.6

7)

-(0.2

4)

(0.4

2)

(0.6

3)

-(0

.40

) (0

.34)

Hon

g K

on

g

61

.67

56.5

1

-94.4

5

62.4

6

-19

.70

-3

3.2

9

26

.83

(1.3

3)

(0.7

1)

-(1.0

2)

(1.2

9)

-(0

.55

) -(

0.4

5)

(0.3

3)

Irel

an

d

12

.01

-16.5

3

21.0

9

-4.0

2

7.8

8

-0.8

8

2.9

0

(1.2

0)

-(0.9

6)

(1.0

6)

-(0.3

9)

(1.0

3)

-(0

.06

) (0

.17)

Italy

-1

.49

5.9

4

-5.3

3

-8.6

0

-3.1

5

-26

.1*

2

0.1

9

-(0

.20

) (0

.47)

-(0.3

7)

-(1.1

3)

-(0

.56

) -(

2.2

5)

(1.6

0)

Net

her

lan

ds

3.3

3

20.2

0

45.7

9

18.8

4

7.3

3

22

.17

-8.9

5

(0.2

4)

(0.8

5)

(1.6

7)

(1.3

1)

(0.6

9)

(1.0

1)

-(0

.38

)

Sin

gap

ore

-2

.80

-1

6.1

1

-57.1

9

17.3

9

-2.5

3

-8.4

6

16.9

9

-(0

.20

) -(

0.6

8)

-(2.0

7)

(1.2

0)

-(0

.24

) -(

0.3

8)

(0.7

1)

Sou

th A

fric

a

-2.0

1

-3.3

6

1.4

0

0.9

7

3.9

2

3.9

8

-5.7

5

-(0

.46

) -(

0.4

4)

(0.1

6)

(0.2

1)

(1.1

6)

(0.5

7)

-(0

.76

)

Sw

itze

rla

nd

5

.17

-34.4

0

-69.9

3

3.5

5

-7.2

5

22

.45

12

.32

(0.3

5)

-(1.3

7)

-(2.4

1)

(0.2

3)

-(0

.65

) (0

.97)

(0.4

9)

N =

130 f

or

each

var

iable

in e

ach e

quat

ion

*-

signif

ican

t at

th

e 5%

lev

el;

t-st

atis

tics

are

rep

ort

ed i

n p

aren

thes

is

91

The consistent results seen in Panel (b) with all of the other coefficients, though, imply

that international market integration did not significantly affect the information interpretation of

investors across these countries. Consequently, the results of the regressions with this subsample

of countries suggest that forecasting agreements between foreign and domestic investors did not

change with differing international stock market integration investing environments.

4.4 Conclusion

This paper examines the affect of international stock market integration on the informational

advantage of host country investors on purchases of U.S. investors of foreign equities. Previous

literature theoretically and empirically shows that investors will possess an advantage in

interpreting information regarding their country’s stock market over foreigners, and foreigners

will form overly optimistic forecasts of foreign stock market indices compared to domestic

investors. Foreigners will demand equities from investors in a host country when the stock

market in the host country increases in value, consistent with trend-following behavior. This

paper observes the existence of this relationship when moving from a segmented international

stock market to an integrated international market. Integrated international stock market returns

will vary based on variation of a world risk factor, implying that interpretation of information

will not vary across investors residing in different countries. Therefore, the integration of

international stock markets should eliminate any evidence of differing interpretation across

investors based on where they live.

Purchases of foreign equities by U.S. investors were regressed on the stock market

returns of the host countries, and these regressions were tested from 1977 to 1999 and from 2000

to 2010. Overall, the significance of the coefficients remained consistent across the two different

92

time periods. The results provide no clear support that integration of international stock markets

affected the relationship between U.S. purchases of foreign equities and foreign equity stock

market returns. This implies that the integration of international stock markets did not cause any

changes in the purchasing behavior of U.S. investors. Previous literature states, however, that

investors may choose to not learn more about foreign markets because the expected cost of

learning exceeds the expected gains, even if the foreign stock market varies with global-wide

risk factors. This, coupled with the evidence seen in this investigation, suggests that the

integration of international stock markets did not affect the purchasing behavior of U.S.

investors.

93

CHAPTER 5

CONCLUSION

The stock market crashes of 1987 and 2007 erased massive amounts of wealth in a very

short time period, and these financial crises crippled stock markets throughout the entire world.

Both of these incidents illuminated the interconnectedness of international financial markets

during these large adjustments to equities valuations. For example, Datastream Global Index

data [Thomson Reuters (2016)] shows that 21 out of 23 countries with available data saw

negative returns on October 19, 1987, and the indices in the two countries with positive returns

on October 19th

later observed negative returns the following day. However, this insight

naturally leads to the question of whether international financial markets vary in unison during

non-crisis environments.

Investors seek to understand the relationship between international stock markets in order

to assess the current and future value of risk of assets in their respective domestic countries and

foreign markets they choose to invest. Segmented international stock markets vary without a

global-wide risk factor, which indicates assets with similar risks observe different returns based

on their geographic location. Alternatively, integrated international markets fluctuate with such

a global-wide risk factor, and assets achieve similar returns regardless of their geographic

position. Investors, therefore, should assess current and future values of assets based on whether

country-level risks or global-wide risk factors affect those asset values. This dissertation seeks

to bring this information to investors.

The first paper of the dissertation observes changes in the risk and skewness profile of

portfolios built with international stock market indices. Several pieces of literature [e.g. - You

94

and Daigler (2010)] document increasing correlations among country-level indices in recent time

periods, suggesting a diminished ability of investors to diversify across international markets.

At the same time, increasing cross-country correlations of stock markets reduce losses in positive

skewness occurring from diversification. This paper seeks to observe the changes in risks,

measured as standard deviations of portfolio returns, and skewness of increasingly more diverse

portfolios built with country-level indices.

The portfolios were constructed using data from Datastream Global Indices by

sequentially adding indices to portfolios to create increasingly more diverse holdings. The

standard deviation of the portfolios decreases as diversification increases, and the positive

skewness of the portfolios also reduces with more diversification. The standard deviation and

skewness measures were regressed on diversification to observe how much risk decreased at

differing levels of diversification. This allows for an estimate of how much risk is diminished

through diversification. This process was performed within each decade from the 1970s to the

2000s.

The results show the percentage of standard deviation and positive skewness reduces

more quickly and at lower levels of diversification in the most recent time period. The result

stems from increasing correlations among international stock markets, implying investors do not

reduce risks in their portfolios with the same magnitude in the current time period. However, the

results from observations made using skewness of portfolios also show that positive skewness is

also reduced at a lower rate currently than in the more distant past, which benefits investors.

Robustness checks, though, illustrate that an investor building portfolios by adding indices with

the highest possible returns will see a decrease in the amount of diversification reduced in recent

95

time periods instead of an increase. Consequently, the results are contingent upon the investment

strategy of the individual.

The second paper of the dissertation studies the relationship between international index

returns and systematic and idiosyncratic risks. A significant relationship between returns and

systematic risk indicates integrated international financial markets, but insignificant relationships

between country-level index returns and global-wide risks with significant relationships to

country-level risks imply segmented international markets. Previous literature provides evidence

of segmented markets, but increasing correlations among international index returns suggests

global-wide risks should affect index-level returns in recent time periods. The second paper,

therefore, observes the effect of systematic and idiosyncratic risk on index level returns in more

recent time periods compared to the more distant past.

The results of the investigation show that systematic risk did not affect country-level

index returns in either older or recent time periods when conducting the analysis across all

countries in the data set. The results stay robust to a segment of developing countries. However,

systematic risks significantly impact index returns after the year 2000 for a segment of advanced

economies. This suggests investors need to incorporate global-wide risk factors in their future

outlooks of returns in developed economies, but they should leave these factors out of their

forecasts when considering investment into emerging markets.

The third paper of the dissertation examines the effect returns on equity purchasing

behavior of U.S. investors of foreign securities. Previous literature built a theoretical model that

indicates foreign investors with an information disadvantage to domestic investors will purchase

foreign equities at a faster rate than domestic investors during positive stock market

96

environments, and foreign investors will sell securities to domestic investors at a faster rate

during negative stock market environments. This suggests foreign investors exhibit trend-

following behavior of investing.

Increasingly more integrated markets suggest both foreign and domestic investors will

forecast equity returns through global-wide risks, negating any differences between the outlooks

of the two groups. Therefore, the relationship between equity purchasing and index returns

should breakdown as a result of international stock market integration. The third paper observes

the index return and equity purchasing relationship in two different time periods: segmented

markets in the distant past and integrated international stock markets in recent time periods.

The results show the relationship between equity purchasing and index-level return trends

does not change across the two time periods. This implies that foreign and domestic investors

differ in their future outlooks of equity returns, even in a more integrated market. Alternative

literature [Nieuwerburgh and Veldkamp (2009)] proposes that investors may see a benefit to

specializing in investing in domestic markets, and they will chose not to invest in foreign

securities, though they may achieve diversification benefits through international investing.

Consequently, outlooks of equity assets differ across investors regardless of whether

international stock markets have become more integrated.

Overall, this dissertation observes international asset return behavior over time to

investigate the impact of increasing correlations of worldwide stock markets. The first paper

observes the impact of increasing correlations on the ability of diversification to reduce risk and

skewness of portfolios. The second paper examines whether global-wide or country-level risk

factors affect asset returns, and, finally, the third paper explores if integration of international

97

markets changed the purchasing behavior of investors of foreign equities. All three of these

analyses provide market participants with information on how increasing correlations of stock

markets affect asset returns.

The results in this dissertation implicate more highly correlated global stock markets do

not change asset return behavior across all economies. For example, the second paper of the

dissertation shows global-wide risk factors affect index-level returns in developed economies,

but these world-wide factors do not affect returns in emerging markets. Also, the first paper of

the dissertation shows that an investor needs less diversification to reduce risk in their portfolio

by adding indices with the lowest historical risk when building a portfolio. However, another

result in the first paper of the dissertation indicates that investors need more diversification in the

2000s decade than in previous decades when building portfolios by adding indices with the

highest historical return. This most likely stems from the fact that the indices with the lowest

risk come from developed economies, where emerging markets tend earn the largest historical

returns. Finally, increased correlations among international stock markets do not affect equity

purchasing behavior of foreign investors, possibly extending from investors specializing in

domestic market investments instead of diversifying with assets across borders. This

specialization could precipitate from investors seeing global-wide risks affecting some segments

of stock markets and not others. Investors may use the information in this dissertation for

additional insight into how they might diversify across international stock markets.

98

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examining international stock market integration: effects

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