a study about the correlation between vietnam and the us stock market

Vietnam National University International University Project Report Course: Statistics A STUDY ABOUT THE CORRELATION BETWEEN VIETNAM AND THE US STOCK MARKET Lecture: Dr... As the Vi

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Vietnam National University International University

Project Report Course: Statistics

A STUDY ABOUT THE CORRELATION BETWEEN VIETNAM AND THE US STOCK MARKET

Lecture: Dr Nguyen Minh Quan

December 26, 2022

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Contents

2.1 Dataanalysis 2 s“n“nhn.<ắ «a 4

2.3 Confidence interval for correlation coefficient 2 0.0 0 en 10

E9 vo on en ằ 11

A study about the correlation between Vietnam and the US stock market 2

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1 Introduction

Nowadays, the stock market is considered an attractive investment not only for professional investors but also for young people who do not have much experience in this area As the Vietnam stock market

is a frontier market, it is affected by other markets One of the most important ones is the US stock market Because of that, many investors keep an eye on the US stock market to predict the movement

of VNIndex In this project, we conduct a test to see whether there is a positive correlation between

those two markets For the Vietnam stock market, we take the VNIndex as a representative, and for the

US stock market, we take S&P 500, and Dow Jones Industrial Average (DJIA) as representatives From the internet, we have collected the data set which is the monthly basis of closed prices over years from

2018 to 2022

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2 Analysis

2.1 Data analysis

From those raw data sets, we are to analyze into 2 pairs, DJIA with VNIndex, S&P 500 with VNIndex

to take each correlation

Utilizing the Analysis ToolPak in Excel, and our understanding of Statistics, we have produced some values that show the distribution of three samples of stock markets: VNIndex sample, S&P 500 sample, DJIA sample

Deviation

Variance

Kurtosis

Maximum Maximum

Overall, these figures show a significant change in the three stock market’s average monthly returns With 0.78%, the median VNIndex score is the lowest of these samples The S&P 500 and DJIA are the largest and middle, at 1.82% and 1.24%, respectively And similarly for the means

On the other hand, the standard deviation of VNIndex sample is greater than that of the S&P 500 and DJIA indicating a higher volatility in Vietnam stock market However, with lower returns in 5 years’ time, we can see that the Vietnam stock market is still not interesting for foreign investors

A line chart that shows the percentage change for the three stock markets demonstrates that the pattern

of changes for 3 indexes is similar, the percentage increase and decrease differs depending on whether favorable or unfavorable events were taking place in Vietnam and the US at that time

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Percentage change of VNI

20,00%

15,00%

10,00%

5,00%

0,00%

-5, -10,00%

-15,00%

-20,00%

-25,00%

-30,00%

Date

Percentage change of S&P 500 15,00%

10,00%

5,00%

-5,00%

-10,00%

Date

Percentage change of DJIA

20,00%

15,00%

10,00%

5,00%

0,00%

-5,00%

-10,00%

-15,00%

-20,00%

Date

A study about the correlation between Vietnam and the US stock market

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According to the charts above showing the percentage change in the stock market, the number of times the percentage change in cash flow occurs is shown by their return frequency All three histograms are

shown in the form of left-skewed distribution

Frequency of return of VNI

30

25

20

Ễ 10

5

Percent

Frequency of return of S&P 500

25

Percent

Frequency of return of DJIA

22

Percent

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Moreover, the box plot charts show the IQR and amplitude of oscillation of the changes in the US and Vietnam stock markets While the US market does not have any outliers, the Vietnam stock market has

2 outliers with a high outlier of 16.09% and a low outlier -of 24.09%

15%

10%

0%

5%

-10%

-15%

20%

15%

10%

0%

-5%

-10%

~20%

Return of VNI

®16,09%

12,81%

,B8%

3,13%

~11,59%

®-24,90%

1

Return of S&P 500

—————T 12,68%

,16%

1,82%

-2,75%

Return of DJIA

71%

1,24%

3,48%

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2.2 Hypothesis Test

We realized from the last part that the three samples are not presumed to have a normal distribution and the 2 samples have positive correlations Therefore, moving on to the following stage, we will compare the two groups as specified, because we are unsure of the correlation between the two pairings of two markets Therefore, it is essential to calculate it using the t-Test for the Correlation Coefficient

t-Test for the Correlation Coefficient

For correlation coefficients, under the null hypothesis that the population correlation coefficient equals

0, the sample correlation is approximately Normally distributed with standard error ø„=\/ = and the standard error is y?-distributed Thus, the t-statistic is obtained by dividing the sample correlation coefficient r by this standard error:

TS =—=

Or 1—r2

n—2

follows a t-distribution with d.f =n — 2

The null hypothesis is that the linear correlation coefficient between 2 variables is greater or equal to 0, that is p > 0 The alternative hypothesis is

Linear correlation coefficient between the 2 variables is less than zero, p < 0

State the null hypothesis: (p is the population correlation coefficient)

Aly: p > 0 (The linear correlation coefficient is not negative in the population)

Al, : p <0 (The linear correlation coefficient is negative in the population)

Test correlation of two pairs:

p20] p<0

The correlation matrix of VNIndex stock, S&P500 stock, DJIA stock

VNIndex S&P500 | DJIA VNIndex 1

S&P500 | 0.578426365 1 DJIA 0.534672309 | 0.956636 1

Choosing the specific level of significance is 0.05 With 60—2 = 58 degrees of freedom and a one-sided test with a 5% level of significance, the critical value is t-Test =1.672 We do not reject the null hypothesis

if the calculated t-statistic is greater than 1.672

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Calculate the value of the test statistic | m——— = 5.3999 | —— = 4.8189

ic — 0.5784263657 [1 —0.5346723092 -

Do not reject the null hypothesis since the calculated TS is greater than 1.672 There is sufficient evidence

to conclude that the correlation between the monthly returns of these two markets is positive

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2.3 Confidence interval for correlation coefficient

Since we select a fixed period of time for the return of the two markets, there is no guarantee that the correlation coefficient between US and Vietnam stocks market will exactly match the correlation coefficient in the larger population in other words, for a longer, different period of time So, to capture this uncertainty we can create a confidence interval that contains a range of values that are likely to

contain the true correlation coefficient

We use the following steps to calculate a confidence interval for a population correlation coefficient, based

on sample size n and sample correlation coefficient r

Step 1: Transform the correlation with Fisher’s transformation

1+r

In +

Step 2: Calculate the standard deviation of the transformed correlation

1

n—3

S=

Step 3: Find log upper and lower bounds

“2

2

With z is the normal distribution value

Step 4: Find confidence interval

The final confidence interval can be found using the following formula:

e2U—1 3U _—]

(1 — a)Confidence interval = (TT: au] )

Following the algorithm, here is the 95% confidence interval for the population correlation coefficient

between S&P 500 and VNIndex:

1+ 0.5784

ln ——

(= 1= 05784 _ 9.6601

1

S = —— = 0.1325

V60—3

+ = 0.0601 — 0.1325 + 1.96 = 0.4004

U = 0.6601 + 0.1325 + 1.96 = 0.9198

e2+0.4004 —1 e2x0.9198 —1 95% Confidence interval = e2*0.4004 +1 } ø2+0.9198 + TL (0.3803; 0.7258)

Similarly, the 95% confidence interval for the population correlation coefficient between DJIA and

VNIndex:

95% Confidence interval = (0.3249; 0.6944)

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3.1 Linear regression

Because the correlation between S&P 500 sample and VNIndex sample seems to be higher than that

of DJIA sample and VNIndex, we will use S&P 500 to draw a regression line to predict the return of 'VNIndex

Regression line of VNI and S&P 500:

The R squared number, which is represented by the portion that the regression line explains the model,

is relatively small In the other words, by linear regression, we cannot get the data with high accuracy 3.2 Cubic equation regression

A cubic regression is a process of finding the third-degree equation of the curve that best fits a set of data As a result, we get an equation of the form: f(a) = ax* + bx? + cr +d where a 4 0 The best way to find this equation manually is by using the least squares method The purpose is to minimize the sum of the squares of the residuals between the measured y and the ?ÿ calculated with the cubic model

We will present a technique for determining the values of a, b, c, and d that minimize the sum of the squares of the residuals Given the data set (;,y;) with i=1,2, ,n and the function f(a;)=ax? + ba? + cx; +d Let g{a,b,c,d) = S*(y; — ax? — ba? — ex; — d)? with i=1,2, ,n and a,b,c,d € R,a 4 0 Take the

derivative of the function g{a,b,c,d) with respect to each coefficient a,b,c,d:

Ga —2a3 My, — ax} — bx? — ca, — đ) =

Ga 2? yi — ax", — bx? — cx; — d) =

G1 2x; S(y; — ax? — ba? — ex; —d) =

ae #—= —2Ề 6N — ax} — ba? — cx; —d) =

Equivalently, we have a set of equations that are called normal equations:

nd + (nae + 33(z2)b + V(e})a = 320)

Llwid + Meee + Va)b + Vw )a = Vwis

3/74 + Va e+ VG ¬" a = Se?

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Solving the set of normal equations, we obtain a = 92.084, b = —3.8483, c = 0.0225, d = 0.0131 Use the

cubic function f(x) = 92.0842" — 3.8483x? + 0.0225 + 0.0131 to sketch the regression and now we can see that the R-squared increases to 0.4804 which is better than the straight line regression (R-squared

=0.33458)

Linear regression of VNI and S&P 500

20,00%

` a e

5

Đ

œ

z

3.3 Removing outliers

To obtain a higher R-squared representing the regression model’s accuracy, we try to delete some outliers and redraw a new regression curve for better prediction To remove some outliers, we will use the following technique:

- Calculate the distance between the actual value and the estimated value error=|y; — yi

- Calculate the mean of all the distance y—->-0:=91),

- Calculate the standard deviation of the distance s= — 3 ` — error)2

- Remove errors which are bigger than 7+ 2s

- Redraw a regression model to see if the R-squared is increased or not

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3.54%+2*3.36%=10.26%

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So, after trimming some extreme data, we will solve the normal equation and obtain a new cubic regression equation f(x) = 102.41x° — 3.7394a? + 0.0609x + 0.0138 with a higher R-squared=0.6095

Linear regression of VNI and S&P 500

y = 102,41x3 - 3,7394x? - 0,0609x+0,0138 » R? = 0,6095

S&P 500 Return

The 2 pairs correlation between VNIndex and S&P 500 and VNIndex and DJIA are both positive This indicates that there is a positive relationship between Vietnam and US stock market One should remember that the correlation do not tell which variable depends on which However, using practical financial knowledge, the size and power of the US market indeed has an effect on the Vietnam market

So it is safe to say that the Vietnam financial market partially depends on the US financial market Therefore, the regression model should use S&P 500 as X (independent variable) and VNIndex as Y (dependent variable)

Although the regression model is quite good (with R-squared=0.6095 after trimming) means- it can explain nearly 61% of the variance for VNIndex that’s explained by S&P 500 in a regression model, one should not rely solely on this model because this is based entirely on the statistical past return There

is no certainty to ensure that the future of the stock movement depends on the past Moreover, this is just a simple model with 1 independent variable while in reality, the stock market is influenced by many

other factors So, if investors want to earn more return on the Vietnam stock market, they should use

more analytic methods such as top-down approach, tracking the movement of interest rate or exchange rate between VND/USD

Tiêu đề	A Study About The Correlation Between Vietnam And The US Stock Market
Tác giả	Tran Chau Thanh An, Le Minh Hoang, Le Yen Nhi
Người hướng dẫn	Dr. Nguyen Minh Quan
Trường học	Vietnam National University
Chuyên ngành	Statistics
Thể loại	Project Report
Năm xuất bản	2022

Định dạng
Số trang	16
Dung lượng	2,3 MB