Statistical Methods & Capital Markets
Testing Random Walk Hypothesis
Nicolas Mancini
* Table of Content
Abstract
Theoretical background
Methodology
Data & Results
Comparison
Conclusion
References
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I. Abstract
The aim of this paper is to test the random walk hypothesis by applying the runs test on time series of several selected stocks. The random walk theory is the theory that stock prices changes have the same distribution and are independent of each other, so the past movement or trend of a stock price or market cannot be used to predict its future movement. Shortly said it is the idea that stocks take a random and unpredictable path.
The motivation
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More commonly and in a standardized output, we would rather use the p value in order to draw a conclusion about the hypothesis but as we don’t have one, we are forced to compare the absolute Z value to the quantile. In other words, an absolute value greater than 1.96, called the critical value, indicates non-randomness and disproves the random walk theory. The mathematical form of this statement is:
Z ≥Z1-α2=0.975
As the reader has got now all the information available about theory and methodology, it’s time to move on to the concrete part. Indeed, next header explains the extraction of data.
IV. Data
The data of the historical prices of the chosen stocks will be taken from the official source Yahoo! Finance. The R software uses this source by default and therefore the end user can simply assess this data by installing the package « quantmod » and using the library command.
In this paper three stocks have been chosen, Apple Inc. (NASDAQ: AAPL), IBM (NYSE: IBM) and
Refer to the financial reports of Apple, Inc. for the year ended September 25, 2010
The method of data analysis is clear, with deep explanation of colazzis approach. However, there are 3 points that making the
This report was done within Strategic Management course it consists on choosing a well known company that the public in general is familiar with and using the Hambrick/Fredrickson five element model describes how the strategy of a company can be seen. For this analysis I chose Apple Inc. because I think that it meets the requirements. Concluding the report, there is a summary where the soundness and successfulness of the company are evaluated.
The figure above shows Apple Inc, the Market cap lead, and Dell, the Market cap last, corporations and their market share compared to the industry and the technology sector. As you can see above Apple Inc. is almost as close to the market cap for the Personal Computers industry. Although, it does have a smaller P/E ratio compared to the industry it still is the highest among the top leaders within the industry. Compared to the industry Apple’s does not have a debt to equity ratio, which is excellent. Apple’s net profit is also the highest within the top competitors and the industry. The price to free cash flow exceeds the industry as well as the technology sector.
· Read the abstract and introduction at the beginning and the conclusion at the end of the article first. The topic and hypothesis will be provided in these sections. Then read the methodology and data/results sections. Reading the introduction, summary, and abstract will help you better understand and follow the data-heavy results section.
6. Using MS Excel make a summary line graph to show how each stock’s price per share changed through the period you owned it. These should be different colored lines on the same graph, each line representing one of the stocks.
The stock that I have analyzed is Apple (AAPPL), which it falls under the technology sector and trades under the NASDAQ. This sector holds the biggest companies around the world. A lot of these companies are well known such as: Amazon, Google, LinkedIn, and etc. The technology sector is an undeniably investment opportunity for every investor around the world. Lets face it technology keeps improving and we have only seen the beginning of it. These companies, such as Apple, are associated with constant innovation and invention. Our modern economy relies upon the technology sector to improve quality, productivity, and profitability.
Refer to the financial reports of Apple, Inc. for the year ended September 25, 2010
Our group decided to analyse the company Apple Inc., listed on Nasdaq Market as AAPL. The analysis was mainly based on the annual financial report of the company for the fiscal year ended on September 29th 2007. Apple Inc. is today one of the most
Our analysis of Apple Inc. will incorporate the general overview of the company and how it records it revenues. We will observe how they make an honest effort to be within compliance of all accounting standards according to the Financial Accounting Standards Board for recording and disclosure of its income. Apple’s leading competitor, Google Inc., will also be examined to see whether they are comparable to Apple and still within compliance of the Securities and Exchange Commission and FASB for revenue recognition. Apple takes on design, development and marketing of personal computers, portable digital music players, and media devices that exceed the reach of everyday needs. The company also
Since 3.27 the t statistic is in the rejection area to the right of =1.701, the level of
We chose to research Apple Incorporated, one of the most innovative companies of our generation. It is safe to say that nearly every one in the US and many foreign countries have used or at least heard of Apple products. We will be looking at the macroeconomic variables that impact Apple’s business as well as how the current developments in the industry have impacted Apple’s financials and we will also look at how Apple competes with other firms in the same industry.
5) From calculations, computed z value is more than -1.65 and falls within Ho not rejected region. Ho is not rejected at α = 0.05 & α = 0.01 significance levels.
Analyzing Apple’s stock price movement for the past three years, there has been a steady upward trend in the past one and a half years, from August 2007 to December 2008. The MACD began to move erratically from April 2008 onwards which suggests that the trading environment is growing more unpredictable with investors’ confidence changing momentum more drastically. This could be due to the looming global economic crisis. From the graphs below, one positive note is that Apple’s stock price consistently outperforms the market indices—the Dow Jones Industrial Average, S&P 500 and NASDAQ. In the long run, Apple’s stock is expected to rise tentatively in this volatile trading environment. Should this trend hold strong, we would recommend a buy option as the prices are on an upward sloping trend.
B) The estimated regression equation relating each of the individual stocks to the S&P 500 is shown below. The value of [pic]for each equation is also shown.