Abstract
This report is a detailed summary of a stock market analysis. A sample of stock price indices in the year 2012 have been selected from Amsterdam, Frankfurt, London, Hong Kong, Japan, Singapore and New York stock markets. The inspiration for this project is to provide a statistical analysis on the performance of stock prices in these markets by assessing their trends and performance in a period of one year.
In general, the findings on market trends shall enable investors to predict future strong economies among the seven selected markets. This project shall major on regression analysis and Microsoft Excel, as basic tools for trend analysis and R-Programming for Advanced Statistics for testing various hypotheses related to the main objective of project.
Problem Statement
The problem that this project is addressing is the assessment of the performance, relationships and trends the selected stock markets. The reason why this project is appropriate is because previous statistics indicated extremely random and complex stock indices for these markets which exhibited complex graphs, difficult to analyze and draw conclusions.
The volume of stocks traded in the Japan has been conspicuous since 2010. Surprisingly, many investors have been losing their money on the Japanese financial Markets over the last three years. Inadequacy of periodic information on the performance of this market could be the main reason that inconvenienced the investors in mitigating their contingent financial risks. Therefore, this project is geared towards provision of a clearly sufficient analysis, so as to provide information on the stock market performance by the use of advanced statistical tools.
Procedures
We shall obtain the stock market price indices for the seven Financial Markets from Massey University Stock Market dataset. This dataset shall be imported to R-Software for inferential statistics, where advanced statistical analyses like regression modeling and hypothesis testing shall be performed. From R-Software, this data shall be exported to an excel spreadsheet, where further analyses shall follow. Converting our data into an excel spreadsheet shall enable us to perform simple descriptive statistics like plotting graphs.
Results
Tool for analysis: R-Software for advanced statistics
Regression Modelling
The following are the linear model equations for the seven stock markets’ price indices:
x.Amsterdam=0.1541 t +127.2803
x.Frankfurt=0.6327 t + 897.7938
x.London=0.9158 t + 1304.6411
x.HongKong=3.975 t -103.148
x.Japan=-2.322 t + 26004.867
x.Singapore=0.1031 t + 253.0322
x.NewYork=0.1809 t + 153.5884
The analysis of correlation of the stock prices between the seven markets
According to the correlation analysis shown in appendix 2, it is conspicuously notable that all stock price indices for Japan are negatively correlated to the rest of stock price indices in all other markets. The stock prices in Amsterdam and Frankfurt has the highest positive correlation of 0.99.
One Sample t-test Analysis for means
Statement of hypotheses (For a two-tailed test):
Ho: True mean =0
H1: True mean ≠0
In the hypothesis test, the p-value for all prices in the seven markets in less than 2.2*10-16. Testing at 5% significance level, we reject the null hypothesis in favor of the alternative. The true mean for all the stock prices in the seven markets is not equal to zero.
The confidence interval of the tocks prices in the seven markets is:
362.3519<x.Amsterdam<374.4171, 1863.285 <x.Frankfurt<1911.902
, 2706.484<x.London<2768.353, 5981.009<x.HongKong<6251.341
, 22175.58 <x.Japan<22568.98, 410.6102 <x.Singapore<418.1576
, 430.2920 <x.Singapore<442.9017
F-test for variance ratios
Hypotheses statement:
Ho: True variance ratio =1
H1: True variance ratio ≠1
The p-value for the two-tailed f-test for the variance ration between the stock prices in all the seven markets is always less than 2.2*10-16. Therefore we reject the null hypothesis and conclude that the true variance ratio is never equal to one, at 5% significance level.
Welch Two Sample t-test
Hypothesis statement:
Ho: True difference in means is not equal =0
H1: True difference in means is not equal ≠0
The p-value in the Welch two sample two-tailed t-test, for the difference of means is always less than 2.2*10-16. Thus, testing at 95% confidence interval we reject the null hypothesis and conclude that the true difference in the mean of stock prices in all seven markets in not equal to zero.
Independence test between Stock prices in Amsterdam and Frankfurt
Ho: Stock prices in Amsterdam and Frankfurt are independent
H1: Stock prices in Amsterdam and Frankfurt are related
Using the Pearson's Chi-squared test, to investigate the independence between Stock prices in Amsterdam and Frankfurt, since these markets are geographically near, the p-value of the test is less than 2.2*10-16. Thus we reject the null hypothesis in favor of the alternative hypothesis, and conclude that the stock prices in these two markets are generically dependent.
Conclusions
In conclusion, it is more risky to invest in Japanese stock markets since the analysis shows a general decline in performance. In addition to this, all stock markets seem to have a positive gradual improvement in performance, except Japan.
Discussion
While carrying out this research, there was a challenge of analyzing a large number of variables. To overcome this, I imported the data into the R-statistical software, which made analysis simpler.
APENDICES
Appendix 1: A graph showing the plot of the seven stock market price indices and their linear regression models.
Appendix 2: A table for the r-correlation coefficients between the stock market price indices
Appendix 3: A Combined ANOVA Table For all stock market price indices
REFERENCES
R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.Retrieved on 7thAugust 2013 from
http://www.R-project.org/
Source of data:
Massey University (2012).Stock market data. Retrieved on 1st February 2013 from http://www.massey.ac.nz/~pscowper/ts/stockmarket.dat
