000042365 THE CORELATIONS BETWEEN VN-INDEX AND OTHER INDEXES: EXPLORING THE OPPORTUNITIES FOR INTERNATIONAL DIVERSIFICATION MỐI QUAN HỆ TƯƠNG QUAN GIỮA VN-INDEX VÀ CÁC CHỈ SỐ KHÁC: KHÁM PHÁ CƠ HỘI ĐA DẠNG HÓA QUỐC TẾ
In tro d u c tio n
B ack gro un d
In today’s highly volatile investment world, investors must balance risk control with the goal of preserving returns The old saying “don’t put all your eggs in one basket” captures a timeless principle—diversification—that predates formal investment theories and remains central to risk management By spreading investments across different assets, portfolios become less vulnerable to a single downturn, but the key question is which baskets to choose Some investors diversify by asset class, others by industry, and many expand their reach across various countries and regions worldwide to reduce concentration risk and pursue steadier, long‑term growth.
International investing can enhance portfolio returns while helping to manage risk, because different global markets tend to move independently rather than in lockstep By spreading investments across regions and asset classes, investors can capitalize on lower correlations and reduce overall volatility In other words, the core of diversification lies in the correlation patterns among assets, which determine how much risk is reduced when adding international investments to a portfolio.
International portfolio diversification was started since 1970s with the decision o f
M organ G uaranty to invest a part o f its pension fund outside the United State in 1974
At that tim e the US m arket had been decreasing for two successive years 1973 and
In 1974, returns outside the United States remained highly attractive (Fadhlaoui et al., 2009) Since that initial step, international diversification has been actively developed and has become a common practice in the investment world, guiding cross-border portfolio strategies and risk management.
In an era of globalization, nations are increasingly interdependent, causing markets to move together and reducing the benefits of international diversification Empirical studies document rising correlations among nations, especially in developed markets Yet this same process of integration also creates new investment opportunities with the rise of emerging economies The potential for international diversification depends on two key factors: imperfect positive correlations across markets and the number of available markets Global integration, on the one hand, diminishes diversification benefits by increasing market co-movement.
Introduction 10 correlations am ong m arkets, on the other hand, facilitates the international diversification by m aking a wide range o f oversea m arkets available to investors all over the world.
Vietnamese stock market is one of the most attractive markets for international investors today Having been established for only nine years, the Vietnamese stock market has experienced impressive growth, attracting a large number of foreign investors The market shows high potential, and it is expected that by 2015 the market capitalization of the Vietnamese stock market will continue to increase.
V ietnam ese stock m arket will be 65-70% o f GDP; by 2020, the figure will be 90-100% (V ovnew s, 2009).
Research significances
a Significance o f correlations and international diversification
Investors face a trade-off between risk and return in investments The familiar adage 'high risk, high return' is well understood in finance, but it doesn’t guarantee that every risk will be rewarded with higher returns Some risks can be eliminated or mitigated through risk management and diversification without depressing overall performance At the same level of risk, returns can differ across investors because the specific risk that is diversifiable is not compensated In practice, portfolios aim to minimize unsystematic risk while capturing the return associated with systematic risk, acknowledging that diversification reshapes the risk–return profile.
Diversification is powerful because it reduces risk while preserving potential returns, making it a cornerstone of sound investing This principle often earns diversification the nickname of the 'one free lunch in the investment world,' a distinction for smart investors who build portfolios that spread risk across multiple assets (Geoff, 2006) By balancing asset classes that don't move in perfect tandem, diversified portfolios can lower overall volatility without sacrificing growth, supporting a more resilient investment strategy.
Diversification in an investment portfolio depends on the correlations between its components, with lower correlations delivering more effective diversification These correlations reflect whether assets are driven by the same underlying factors—assets in the same country are typically exposed to similar forces such as economic growth, shifts in interest rates, inflation, and government policies, which can limit diversification International investing helps diversify away national market uncertainty, since different regions respond to different catalysts Markets in distinct parts of the world are less likely to be influenced by identical factors, leading to lower correlations and better diversification opportunities In practice, combining domestic and international assets across varied sectors and styles enhances diversification and can improve risk-adjusted returns.
Introduction 11 degree o f interrelation also varies across countries A s a result, studying the correlations am ong m arkets is critical in m axim izing the benefits o f international diversification.
Previous studies show both short-term and long-term relationships among markets In the short term, market correlations rise during crises, with events such as the 1997 Asia Crisis and the 1998 Russian Crisis offering empirical evidence of volatility transmission across markets and eroding diversification benefits when they are most needed In the long run, capital markets tend to move in tandem, which can lessen the gains from international diversification for long-term investors; however, diversification benefits may persist because returns often respond slowly to trends Therefore, accurate measurement of volatility and cross-market correlations remains a key focus for understanding risk across markets.
The dynamics of correlations have important implications for forecasting and investment decisions As correlations vary across different timeframes and in response to social, economic, and political conditions, they must be continually revised and monitored to generate accurate predictions and, consequently, optimal investment strategies The study of the Vietnamese stock market is significant because it reveals how correlations unfold in an emerging economy, informs diversification and risk management, and sheds light on investment opportunities within a rapidly evolving market.
Vietnam's market has become increasingly attractive to foreign investors thanks to solid government finances, low public debt, a positive trade balance, and a high, rising saving rate, all of which underpin a strong economic foundation More importantly, Vietnam offers substantial growth potential, making it a compelling opportunity for international investors seeking exposure to a dynamic emerging market.
Although the Vietnam stock market has surged to a market capitalization of up to USD 14 billion, it remains small compared with its regional neighbor as of Spring 2007 Therefore, it is worth investigating scientifically how investing in Vietnam can actually benefit international investors.
The research
This study analyzes the benefits of including Vietnamese securities in internationally diversified portfolios by examining the risk and return characteristics of the Vietnam stock market and, more importantly, the correlations between Vietnam and other major markets By assessing how Vietnamese equities behave in terms of risk and return and how tightly they are linked to global markets, the research evaluates the diversification benefits and portfolio implications for investors seeking exposure to Vietnam The results illuminate cross-market correlations, the degree of market integration, and how Vietnam's stock market can influence risk management and diversification strategies in a global investment portfolio.
The objectives o f this research can be sum m arized in the follow ing points:
Investigating the risk and return o f V ietnam ese stock market in com parison to foreign markets
C alculating and analyzing the correlations betw een V ietnam ese stock market and foreign markets
Illustrating how the international diversification opportunities can be obtained.
O verview o f the th e s is
This paper is organized into seven sections: Introduction, Literature Review, Methodology, Findings and Discussion, Implications, Limitations and Future Research, and Conclusion The Introduction sets out the background and significance of the issues addressed The Literature Review provides the theoretical framework that underpins the research The Methodology describes the research design, data processing of secondary data, and the statistical tests employed The Findings and Discussion present the results and offer interpretation and context The Implications address the practical and scholarly impact of the study The Limitations acknowledge study constraints and the Future Research section outlines opportunities for further study The Conclusion summarizes the main findings and conclusions of the research.
Literature re v ie w
C orrelations
C orrelation is one o f the most useful and popular statistics Correlation rho (p) is the statistical param eter that indicates how strong the linear relationship between pair o f
Literature review 13 v a r ia b le s is C o rre la tio n is o nly d efin ed if stan d ard d e v ia tio n s o f both v ariab les a re finite and d iffe re n t from zero.
The correlation p o f tw o data sets X and Y with expected values p.x and (iy and standard deviation o f o x and o y is defined as follow:
S in ce Hx = E(A ), o.v2 = E[(X- E(,Y))2] = E(^r2) - E 2(X) and E[(X - E(X))(Y-E(Y))} = E(XY) ~ E(X)E(Y ):
Correlation coefficients range from -1 to 1 and describe the strength and direction of the relationship between two variables The closer the coefficient is to 1 or -1, the stronger the relationship; a value of 1 means a perfect positive relationship where the variables move in the same direction, and a value of -1 means a perfect negative relationship where they move in opposite directions A coefficient of 0 indicates no linear relationship, though the variables may still be dependent through nonlinear relationships, since correlation measures only linear associations.
A pplications o f correlation in portfolio m anagem ent th eory
C orrelation is the foundation o f portfolio theory, w hich helps reducing portfolio volatility w ithout hurting the returns through diversification am ong assets with low correlations.
D iversification is an investing technique that aim s at m axim izing return w hile m inim izing risk by including a w ide variety o f investm ents in a portfolio.
Risks associated with an investment can be categorized into systematic (market) risk and unsystematic (idiosyncratic) risk Unsystematic risk can be reduced through diversification, while systematic risk cannot be eliminated by diversification alone Company-specific risk can be diversified away by investing in a range of different companies, and industry-specific risks affect particular sectors.
L iterature review 14 can be reduced by investing indifferent industries Similarly, country specific risk can be reduced by diversifying investm ent internationally.
The effectiveness o f diversification has been proved through num erous em pirical studies.
An investor may pursue naive diversification by building equally weighted portfolios of several securities to reduce unsystematic risk As more securities are added, exposure to idiosyncratic factors is spread more widely, reflecting the insurance principle that independent risk sources can be mitigated Yet, diversification benefits fade as the portfolio grows, and regardless of how many securities are included, a certain level of risk persists—systematic risk that affects all assets This relationship is commonly illustrated by a figure showing how diversification lowers risk up to a point, after which systematic risk sets a lower bound on portfolio risk.
Figure 1: Portfolio risk as a function o f the num ber o f stock in the portfolio
A diversification strategy can construct a portfolio with the lowest possible risk for any given expected return Consider a two-asset portfolio with investments A and B, where the portfolio’s expected return is the weighted average rP = wA rA + wB rB, with rA and rB denoting the expected returns of A and B and wA and wB their respective weights that satisfy wA + wB = 1 By selecting these weights, you trace the set of possible portfolios and identify the minimum‑variance portfolio for a target return, illustrating how diversification lowers overall risk by combining assets with different risk profiles and correlations.
L iterature review 15 the w eight o f A in the portfolio, wb be the weight o f B and n> be the expected return o f the portfolio We have: rP = w ArA + w Br B
Portfolio variance is not simply a weighted average of the individual variances; instead, it is a weighted sum of covariances across all pairs of assets, with each pair’s contribution determined by the product of their portfolio weights, w_i w_j, multiplied by Cov(r_i, r_j) This means Var(P) = sum_i sum_j w_i w_j Cov(r_i, r_j), where the diagonal terms (i = j) reduce to the asset variances Var(r_i), but the off-diagonal terms capture how asset returns co-move In short, portfolio variance aggregates all pairwise covariances weighted by the product of the corresponding asset weights, while the portfolio’s expected return remains a simple weighted average of individual asset means.
Covariance o f expected return o f A and B is defined as:
Cov(rA,rB) = pA,BoAoB
From the derivation above, when P_ab equals 1, the portfolio's standard deviation is the weighted average of the standard deviations of its component investments In other words, with perfect positive correlation, diversification does not reduce portfolio risk.
O n the other extrem e, w hen pAB = - L o j = w j o j + w j c r j - 2 w a w b o a o b
It is now possible to elim inate the risk:
A llocating to A and B w ith the calculated w eight above will drive the portfolio risk to zero, creating the position o f perfect hedged.
Sim ilarly, if the portfolio has m ore than two com ponents, the return and risk are calculated as follow:
Whenever asset returns are not perfectly correlated (correlation less than 1), the portfolio’s standard deviation is lower than the weighted average of the individual assets’ standard deviations If the assets in the portfolio are negatively correlated, diversification becomes especially effective at reducing portfolio risk While the portfolio’s expected return is the weighted average of the individual asset returns and is unaffected by inter-asset correlation, diversification reduces risk without altering returns In short, a portfolio of assets with less than perfect correlation offers better risk–return opportunities than any single asset, and the lower the correlation, the greater the diversification benefit (Bodie, 2005).
The effects o f correlations on the effectiveness o f a investm ent portfolio is illustrated as follow: n e M = 'Y j WiE (ri) n n i=1 7 = 1
Figure 2: Portfolio expected return as a function o f standard deviation w ith different correlations
Source: J Wang a n dJ Zhu, "Portfolio Theory o f Information Retrieval, " in SIGIR09 Full Paper, 2009
Portfolio expected return is the weighted average of the returns of the assets in the portfolio However, the portfolio's standard deviation is not simply the weighted average of the individual assets' standard deviations Diversification opportunities emerge when the correlations among the portfolio's constituent investments are less than perfectly positive; the lower the correlation, the greater the diversification benefits In the special case of perfectly negative correlation, a perfectly hedged position is possible, enabling the construction of a zero-variance portfolio while maintaining the portfolio’s expected return.
International diversification
Effective diversification seeks investments with low correlations to maximize the portfolio's diversification benefits Investors look for these low-correlation opportunities through different strategies, including diversification by asset classes (such as stocks, bonds, real estate, and commodities), by industries or sectors, and by geographic locations By spreading exposures across assets, sectors, and regions, a portfolio can reduce overall risk and improve risk-adjusted returns.
A diversified portfolio cannot eliminate macroeconomic risk, which stems from factors that affect the entire economy, such as inflation, economic growth, and unemployment To mitigate these risks, investors diversify across countries by allocating capital to foreign markets As global economic integration accelerates, accessing foreign markets becomes easier, making international diversification a practical way to broaden exposure and improve resilience.
Investing in foreign markets offers three key advantages First, it diversifies away country-specific shocks, reducing exposure to localized economic risks Second, it can provide higher returns by accessing growth opportunities overseas Third, foreign investment often benefits from an improved economic environment in destination markets, creating more favorable conditions for investors.
International diversification offers clear risk-reduction benefits for investors A study of US investors shows that constructing a portfolio of roughly 20 securities spread across the United States and major European stock markets can cut risk exposure by at least 50% compared with an all-US stock portfolio (Solnik, 1996).
The below figure is a visual illustration o f the benefit o f international diversification
Source: Solnik, Why N ot D iversify Internationally Rather than D om estically , Financial Analyst Journal,
International diversification: developed market vs em erging m a rk e t
Numerous studies show a persistent rise in correlations among developed financial markets From January 1988 through June 2009, the 60-month rolling correlation between the U.S and Japanese markets increased from 42% to 71% (Mallik, 2009).
Figure 4: Pair-wise C orrelations A m ong C ore C ountries
Source: G oetm ann W N , 2 0 0 2 , Long-term G lobal Market C orrelations , IMF
As can be seen from chart, although the pair-wise correlations o f developed markets fluctuated largely in different periods they have becom e highly positive for a few last decades.
Consequently, capital flows from developed countries to emerging markets in search of lower correlations, making the link between developed and emerging markets a well-documented research topic Overall, studies consistently find that correlations between emerging and developed markets are substantially lower than those observed among developed markets themselves.
Many scholars emphasize the importance of developing markets in international diversification The average correlation between developing markets and the US market is about 0.62, while the correlation between the US and emerging markets is around 0.22 This suggests that developing markets are less affected by global events or crises Their relative isolation offers an attractive diversification option, making emerging markets a favorable addition to an international portfolio due to their low correlations with other markets (Fowdar, 2008).
Vietnam stock market correlations with international markets attract close attention from financial analysts When the index is used as the input for correlation calculations, they find that the Vietnam stock market shows high correlations with global markets (Wall Street Securities, 2009) However, I argue that index correlations do not truly reflect market co-movements; monthly returns should be used to measure inter-market linkages Further explanation will be provided in the next section.
W ith a view to exam ine the im pact o f international stock market m ovem ents to
The Vietnamese stock market may be influenced by international market movements, creating potential for predicting Vietnamese market behavior from global trends Thinh (2007) explored this possibility by examining the co-movement between the VN-index and key foreign indices, including the Dow Jones Industrial Average, the S&P 500, the DAX, and the Nikkei He then ran regressions between the VN-index returns and the foreign index returns to quantify the strength and statistical significance of these links and to assess whether international market movements can help forecast Vietnamese stock performance.
An in-depth analysis of the VN-Index alongside major foreign indices examined the correlations and covariances between each pair The findings show that while the Vietnam stock market often moves in a similar direction to foreign markets, it does not exhibit meaningful correlations with most other markets.
Another study finds that the Vietnamese stock market exhibits low short-term correlations with foreign markets However, it supports the hypothesis that long-run correlations will increase as Vietnam becomes more integrated into the global economy (Biet Viet Securities, 2007).
M ethodology
R esearch objectives
This research aim s to explore opportunities for the international diversification by including V ietnam ese securities in an internationally diversified portfolio To investigate the benefits o f such opportunities, the first objective is to w ork out and analyze the risk-and-retum profiles o f V N -index and other indexes The second one is to observe the co-m ovem ents o f V N -index and indexes o f a num ber o f foreign markets by calculating the correlations The research also aims to com pare the co-m ovem ents o f tw o dom estic indexes (V N -index and H N X -index) and those o f VN-index and foreign m arkets’ indexes This research is supposed to provide guidance for investors w ishing to capitalize on diversifying their portfolios At the same time, it provides a supporting evidence o f portfolio theory fram ework.
R esearch questions
Based on the research objectives, the follow ing questions are to be addressed:
W hat is the level o f risk and return o f V ietnam ese stock m arket?
H ow is V ietnam ese stock m arket correlated w ith stock m arket in other countries?
Is it beneficial to include V ietnam stock m arket in an internationally diversified portfolio?
Secondary data an aly sis
The input for the calculation and analysis o f the correlations are secondary data, historical value o f the selected indexes The database is from reliable sources, collected from official or reputable w ebsites, including Y ahoo Finance and database o f a num ber o f V ietnam ese securities com panies The secondary data collected will be used to:
Investigate the risk-return features o f each market
Calculate the correlations am ong the markets
C onstruct diversified portfolios to capitalize on the low correlations
Five foreign stock market indices, together with the domestic VN-index, are used to analyze correlations with the VN-index These indices are carefully selected to serve as representative benchmarks for their markets, and the foreign indices span five countries across different continents to illustrate the benefits of international diversification The dataset covers August 2000—the date of the establishment of HOSE and the VN-index—through October 2009, the period of the study; the S&P/ASX 200, however, is available only from November 2001, so this data window represents the longest possible duration available for observation to date.
VN-Index is the benchmark for Vietnam's stock market, a market-capitalization-weighted index of all shares listed on the Ho Chi Minh City Stock Exchange (HOSE) It has served as HOSE's official market index since the establishment of the exchange, and remains the most popular indicator of Vietnam's equity market The Dow Jones Industrial Average (DJIA) is another well-known benchmark, commonly cited as a key indicator in the United States.
Created by Charles Dow and Edw ard Jones, D ow Jones Industrial Average (DJIA, also know n as Industrial A verage, Dow Jones, Dow 30 or sim ply Dow) is the second oldest
Dow Jones Industrial Average (DJIA) is a key US stock market index that tracks the performance of 30 large, publicly traded American companies listed on NASDAQ and the NYSE It is a price-weighted average, meaning the index level is driven by the stock prices of its components Notable companies include Coca-Cola, IBM, Boeing, Johnson & Johnson, Bank of America, and others, providing a concise snapshot of the overall health of the US equity market.
H istorically, the index was com piled to m easure the perform ance o f industrial sector
Although many of today’s 30 components diverge from the traditional idea of an ‘industry,’ the 30-component index remains a meaningful proxy for the broader stock market It moves not only in response to company earnings and macroeconomic data but also to political events, whether domestic or international, and to natural disasters Even with its 30 constituents, the index effectively reflects overall market trends and investor sentiment across the economy.
D ow Jones, in fact is am ong the m ost closely w atched benchm ark indexes o f stock m arket, not only in US but all over the world (W ikipedia)
The Nikkei 225 is the flagship stock market index of the Tokyo Stock Exchange It was established in 1950, with price data backdated to May 16, 1949, and is calculated on a price-weighted basis The index comprises constituents from a broad range of industries, with components revised every September to ensure it remains representative of the market Today, it is the most widely quoted index of Japanese equities.
SSE com posite index is the index o f all the stocks listed on Shanghai Stock Exchange
It w as first launch in 1991 It includes both A shares, w hich are denom inated in Chinese RM B, and B shares, w hich are denom inated in US dollar (W ikipedia) e F T S E 1 0 0
FTSE 100, commonly known as "Footsie," was established in 1984 as the London Stock Exchange's flagship share index It tracks the 100 most highly capitalized companies listed on the LSE, with its constituents accounting for about 81% of the market capitalization of the exchange The index is calculated using a value-weighted method with a base point of 1000, and its components are revised quarterly While the FTSE All-Share index offers a broader market view, the FTSE 100 remains the most widely used benchmark for the United Kingdom stock market.
S& P/A SX 200 is the stock index o f A ustralia Securities Exchange, calculated by Standard & Poor It started on 31 M arch 2000 The index is calculated based on value w eighted m ethod (W ikipedia) g H N X -index
HNX-Index, formerly known as HASTC-Index, is the market index of the Hanoi Stock Exchange (formerly the Hanoi Stock Trading Centre) It is a market value-weighted index that measures the performance of all listed shares on the exchange The HNX-Index was launched in 2005, aligning with the establishment of the Hanoi Stock Exchange.
D ata pro cessing
After the necessary data is collected, it is entered into an Excel spreadsheet for processing The program performs all calculations, including correlations, standard deviations, expected returns, and statistical tests, delivering a complete, data-driven analysis.
The database is processed to obtain the monthly values for each index From these monthly index values, the monthly returns for each index are calculated The co-movements of the selected markets are measured by analyzing the correlations among the monthly returns of the indexes.
Correlations of returns are used instead of correlations of index levels for several reasons Investors care more about returns—the percentage changes—than the absolute values of the indexes Moreover, correlating index values can distort the perceived co-movements of markets because index levels are large (hundreds or thousands of points, depending on the index) while the changes are often only a few points As a result, focusing on absolute levels makes the indexes appear to move marginally and become highly correlated, which masks the true co-movements of the markets.
The actual calculations are the em pirical evidence to the above argument:
Table 2: t-statistic for correlations o f daily index
T able 4: t-test for significance o f correlations o f m onthly indexes t-statistic
Across the two correlation matrices, the seven indices exhibit consistently high correlations, whether calculated on a monthly or daily basis All observed correlations are statistically significant, as indicated by t-statistics well above the benchmark of 2.
Monthly returns are used instead of daily returns to avoid misrepresenting correlations in Vietnam’s stock market, where government price controls and a trading band have served as instruments of intervention in the infant market The trading band, set by the State Securities Commission (SSC), started at 5% of the reference price for HOSE and 10% for HNX In early 2008, as the VN-Index fell sharply, the government lowered the bands to 1% on HOSE and 2% on HNX to slow price movements Once the market stabilized, the bands were gradually returned to their initial levels of 5% for HOSE and 10% for HNX (SSC, 2008).
V ietnam ’s a certain level o f intervention is necessary for long-term development
However, controlling for price movements comes at the expense of market liquidity and efficiency Because the trading band constrains daily prices, they may not fully reflect the actual supply and demand forces The true trend in supply and demand unfolds over a period of time, which is why monthly returns provide a more accurate measure of the underlying dynamics than daily movements.
M ethodology 27 a R is k -a n d -re tu rn c h a ra c te ristic s
T a b le 5: T h e r is k -re tu rn c h a ra c te ris tic s of th e indexes (m o n th ly )
A s can be seen from the table, V N-index has m uch higher standard deviation, indicating a higher risk com pared to other markets.
We are now testing whether the variance of the VN-index is greater than that of other market indices The results of these tests will, at the same time, determine which statistical approach to use when comparing the expected returns across markets, specifically whether to apply a two-sample t-test assuming equal variances or a test that accommodates unequal variances.
To test whether variances of each pair of indices are greater than, smaller than, or equal to each other, use the F-test for two-sample variances in Excel’s Data Analysis Toolpak The test output provides the F-statistic, P-value, and the critical value(s) of F As noted, at each level of significance there are two critical F-values, each the inverse of the other, with 1 lying between them A value of F close to 1 provides evidence that the underlying population variances are equal In the output, if F < 1, the F critical one-tail value is less than 1 for the chosen alpha; if F > 1, the corresponding upper-tail critical value is greater than 1, guiding the conclusion about variance equality.
F > 1, the “ F critical one-tail” gives the critical value greater than 1 for alpha.
• Test f o r variances o f returns o f VN-index and DJIA
• H ypotheses o Ho: a 2 VN-index / O ~DJIA ~ 1 o Ha 0 VN-index DJIA > 1
The test result is as follow:
Table 6: Test for variances o f returns o f VN-index and DJIA
F-Test Tw o-Sam ple for Variances
• F-statistic > greater-than-one critical value o f F W e reject H0, in favor o f the alternative hypothesis that cTvN-mdex > o2djia
In other w ords, there is enough statistical evidence to conclude that the variance o f returns o f VN-index is greater than that o f DJIA
• Test fo r variances o f returns o f VN-index and Nikkei 225
O Ho: a 2 VN-index / O 2Nikkei225 = 1 o H a greater-than-one critical value o f F W e reject Ho, in favor o f the alternative hypothesis that a : VN_mdcx > o 2Nikkei225
In other words, there is enough statistical evidence to conclude that the variances o f returns o f VN-index is greater than that o f Nikkei 225
• Test fo r variances o f returns o f VN-index and SSE Composite Index
• H ypotheses o H o : a " vN-index / o 2 s s e = 1 o H a : O 2VN-index /t^ S S E > 1
The test result is as follow:
T able 8: T est for variances o f returns o f VN-index and SSE C om posite Index
F-Test Two-Sample for Variances
• F-statistic > greater-than-one critical value o f F ^ W e reject H0, in favor o f the alternative hypothesis that a 2vN-mdex > o2sse
In other words, there is enough statistical evidence to conclude that the variances o f returns o f V N-index is greater than that o f SSE C om posite Index
• Test fo r variances o f returns o f VN-index and FTSE 100
O Ho! O2 VN-index/ greater-than-one critical value o f F ^ W e reject H0, in favor o f the alternative hypothesis that c 2vN-indcx > 1
The test result is as follow:
Table 10: Test for variances o f returns o f V N-index and S& P/A SX200
F-Test Tw o-Sam ple for Variances
• F-statistic > greater-than-one critical value o f F ^ W e reject H0, in favor o f the alternative hypothesis that o'vN-index -> ®~s&p/axs200
In other words, there is enough statistical evidence to conclude that the variances o f returns o f VN-index is greater than that o f S&P/ASX
• Test fo r variances o f returns o f VN-index and HNX-index
The test result is as follow:
T able 11: T est for variances o f returns o f V N -index and H N X -index
F-Test Tw o-Sam ple for V ariances
• F-statistic < sm aller-than-one critical value o f F ^ W e reject Ho in favor o f the hypothesis that o 2vN-mdex < o2hnx
In other words, there is enough statistical evidence to conclude that the variances o f returns o f VN-index is sm aller than that o f H NX -index
An analysis of the time series indicates that the VN-Index outperforms other markets in terms of returns The VN-Index records a monthly return of 2.42%, with an annualized return of 29.04% per year By comparison, the expected returns across other markets, particularly developed markets, are significantly lower.
Now we assess whether the VN-index returns are statistically significantly higher than the returns of other markets The tests are conducted using Excel’s Data Analysis Toolpak at a 5% level of significance The results are as follows.
• Test fo r returns o f VN-index and DJIA
O Ho: JiVN-mdex = (¿DJIA o Ha: JXvN-index > HDJIA
The test result is as follow:
T able 12: Test for returns o f V N -index and DJIA t-Test: Tw o-Sam ple A ssum ing Unequal V ariances
P(T HNikkei225 o H a ^ VN-index — HNikkei225
The test result is as follow:
T a b le 13: T est fo r r e tu r n o f V N -index a n d N ikkei 225 t-Test: Tw o-Sam ple A ssum ing Unequal V ariances
P (T |*SSE o H a H VN-index — USSE
The test result is as follow:
T able 14: Test for return o f V N -index and SSE t-Test: Tw o-Sam ple A ssum ing Unequal V ariances
P(T