Data Interpretation for Apple Inc. (AAPL)

Cisco Systems, Inc. is an American corporation whose primary concern is networking devices. It offers services and goods to consumers all over the world, as well as advanced technologies for network construction and connection. The business was founded in the United States in 1984 by Leonard Bosack and Sandy Lerner, with headquarters initially in San Francisco and now in San Jose. The conglomerate is present in various technical sub-markets through a variety of subsidiaries, including WebEx, Jasper, OpenDNS, and others. In 2016, there were 71,883 workers working for the firm (wiki). The company is a public enterprise; its shares are listed on NASDAQ with a ticket CSCO. The stock price is included in all main stock exchange indexes: DJIA, NASDAQ-100, S&P 500, S&P 100, Russell 1000. The market capitalization of the company on August 2017 is about $156 bl (YF), its year revenue from last annual report (July 30, 2015 - July 30, 2016) is $49,247 mln (AR).
The purpose of this paper is to study statistical relationships between Cisco Systems stock price fluctuation and three other variables: the S&P500, the USD/EUR exchange rate, and the 10-year US T-Bond interest rate. In two series of regression models, I use data over a 2-year period – daily in the first case, and monthly in the second.
Around statistical methods applied to the data to understand the relationship between four variables is correlation, linear regression on one factor, multiple linear regression. Those methods allow evaluating the strength of the relationship between variables undependable on influence direction (correlation matrix). In addition, they provide a measure to evaluate an effect of independent variables (broad market, interest rates, exchange rates) on dependable one, that I study (Cisco stocks prices), in pairs (simple regression) and in combination (multiple regression). The second group of applied methods allows understanding better the nature of variables itself, the law of distribution matching them the best way. Around such methods, I use descriptive statistics and their graphical representation by histograms. An important part of the analysis is a testing of hypothesis about variables relations model quality and particular parameters evaluation quality with the application of such statistical instruments as T and F-tests.
The order of methods application is the next: first, the set of descriptive statistics that provide information if the distribution is normal and next parametric methods may be applied or should be replaced by nonparametric. Next evaluation of the correlation between time-series and finally testing of evaluated parameters significance. The relationships I study in this research are between:
• Cisco Systems stock price and broad American stock market (S&P 500), that allows to figure out what type of stocks it is (going with economic cycle or against it);
• Cisco Systems stock price and currency exchange rate (USD/EUR), that allow understanding how to export/import operations affects Cisco production;
• Cisco Systems stock price and riskless bond market instrument interest rate (US T-Bond), that allow evaluating how investors see risks related to operations with this stocks.
• And all four parameters in combination, that usually gives a more objective picture of price formation and possible prediction, as every of independent variables (interest and exchange rates, broad market index) affect not only dependent one (stock price), but each other in some degree.
The source of data I used for this research is Yahoo Finance for historical stock market data (daily, monthly). However, another forex market data source has been used for currency exchange rates (as yahoo finance and Morningstar web sites do not provide historical data sets for that variable). The data I use for all four variables is attributed to the same period: 21/08/2015 - 21/08/2017, close prices, not adjusted for dividends, two sets with daily and monthly periods of measurement. To make figures comparable (there are presented prices, interest rates, and index points) I have counted returns on different actives. Also, the time-series for currency and securities have had a different size due to differences in trading sessions schedule, the data would be cut by the shortest variant to make series comparable. That problem has been actual only for daily data, monthly time-series have had the same size. As result, I used daily data only for analysis of variables itself and in regression building and their relation study the monthly data been chosen for statistical processing. Also, I have done a comparison of daily and monthly data analysis results for variables description to show the importance of measurement periods.
First, based on daily and monthly data I have built diagrams showing variables distribution. The form of the histogram is matching such purpose the best, results presented in Appendix A. As the histograms show the form of returns distribution is close to the normal, bell-shaped one, therefore it is possible to apply to data sets parametric statistical methods. The daily diagrams seem better adjustable for distribution details representing, however, monthly diagram allows to catch misbalances between right and left tails faster.
In particular, for Cisco Systems stock return the daily histogram shows a symmetrical distribution with short tails and high concentration of returns around the mean, therefore I can describe this investment instrument like having low risks, and the relatively equal probability of growth and fall on the daily basis. Analysis of monthly data, however, shows that on longer periods that stock has tendency to grow more often than fall, the distribution is clearly asymmetrical with more values on the right from central tendency side, the right tail is very hard.
For other variables I see the same kind of daily-monthly visual changes in histograms, however, some of them looks more suitable each other (GSPC), while other shows serious asymmetry monthly, that is not clear on the daily graph (EUROUSD).
To be more particular in distribution attributes I have applied to data descriptive statistics function of Excel, the result is presented in Appendix B. Main distribution characteristic I need for variable nature understanding are Mean, Mode and Median for central tendency division and Standard deviation/ Variance, Kurtosis, Skewness for “about normal” distribution form specification. On the daily basis, the highest average return (mean) shows broad market index, the lowest - currency. The Median may be also a good measure of the central tendency and in a case of prices and returns, it is even more adequate and precise. By this characteristic, the most profitable on the daily basis active is Cisco stock, when the currency has a negative return, loss. The third central tendency measure, Mode for daily return data is not applicable as all prices in the time-series are individual. On the monthly basis the same measures tell that the most profitable in average is a broad market index, then Cisco stocks, bonds, and currency are less profitable instruments. Median values, however, gives the other picture: it is lower than average for stocks and higher for currency and bonds. Daily statistics look more precise, as more values/ information is used to count it.
The standard deviation of variances on the daily basis tells that Cisco stocks are riskier than the broad market, the lowest risk provides currency, as its variance and deviation are minimal. On the monthly basis currency as well has the lowest deviation, Cisco stocks are riskier than broad market again, but the dispersion has bonded. The specific form of distributions, "tallness" represented by kurtosis is the highest for Cisco on the daily basis and for bonds on the monthly basis, that means that variables have the highest concentration of values around central tendency (mean). The flattest and dispersed variables in the set are broad market daily and currency monthly, the last one has a negative kurtosis that means it is flatter than a normal distribution.
The skewness statistic tells if the distribution is misbalanced. By its negative or positive value is clear what tail is harder. Daily data shows that most of the stock returns are in the left tail, while for currency to the right. By monthly data, I see the opposite picture, the skewness of stock and bond market instruments is positive and for currency negative.
As the analysis of return, distributions shows they are close to normal one, therefore next I will apply parametric statistical methods, in particular in correlation and regression analysis. The correlation matrix for monthly data is presented in Appendix C. There is a relatively strong correlation between Cisco stocks return and broad market index return (0.7). A positive correlation between bond and broad stock market returns and a negative one between currency and bond market returns has average statistical significance (0.3 and -0.3). The other correlations are very weak and therefore not significant. By that results, I can expect good quality of regression of Cisco stock return on broad market and insignificant regressions for other factors.
For regression analysis, I have applied the simple linear model and automatic function embedded in Excel. The results of linear regression building are presented in Appendix D. The dependable variable for all three models is a Cisco stocks return. As an undependable variable, the first regression has a broad market index return. The evaluated coefficients are -0.00719 and 1.435193. The R-square statistic is 0.48 that is an average quality, the given regression does not fit well. For bond and currency market results are even worse, for linear regression with the bond market return as parameter R-square is 0.0003 and for regression with currency market return as a parameter, it is 0.003. Both results are showing that Cisco stock return does not dependent on currency and bond markets returns.
In multiple regression with three parameters, r-square is lower than the linear one with just broad market index return as the independent variable (0.5). That is predictable as the correlation between added variables and the dependent one is weak and significance of simple linear regressions with them is also low. So additional parameters, in this case, make the quality of regression worse.
To test the statistical significance of regressions above I use a t-test for the significance of particular coefficients evaluation and f-test for the significance of regression as a whole. The H0 hypothesis for the t-test is the coefficient really is equal to zero and insignificant, the H1 hypothesis is the coefficient is significantly different from zero. As a limit, I use 0.05 level of probability. In simple linear regressions, all evaluated coefficients but one for broad market index return is insignificant, as their p-values are higher than 0.05. In multiple regression also only evaluation of coefficient for broad market index return is statistically significant.
F-test for regressions above has as H0 hypothesis suggests that some regression model coefficients are not significant and the model as a whole as well, H1 hypothesis – all coefficients are significantly different from zero. With the level of significance 0.05 only first simple linear regression (on the broad market) and multiple regressions are significant.
 
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