This paper explores the application of probability and statistics to real-world stock market decision-making, using automotive industry companies as a case study. The author identifies relevant financial data — including market share, profit, and sales revenue over ten years — and applies basic probability concepts to assess each company's likelihood of future market leadership. The paper also examines whether stock price charts resemble standard statistical distributions. It discusses the trade-off between accuracy and precision in statistical measurement and concludes that while quantitative analysis is a valuable tool, qualitative factors must also be considered before making investment decisions.
Many students at various levels of mathematics find themselves asking: why do I need to learn this? It is admittedly true that many people will never really use algebra in their daily lives, and the complex world of statistics and probability also goes unutilized by many. In actuality, however, algebra, probability, and statistics can all be useful to everyone — and more importantly, there are specific instances where these areas of mathematics prove absolutely invaluable.
When it comes to the stock market, many people try to use statistical models to predict when certain stocks represent good values or when they are poised to generate significant returns for investors. There are also more sensible, grounded applications of probability and statistics concepts that serve as reasonable tools for influencing stock-buying decisions. Applying a few basic methods of analysis to elements of business and stock performance can yield probabilities for future success.
With a specific interest in buying the stock of an automotive company, the first step was to assess what relevant information was available to which probability and statistics concepts could be applied. This information was identified as current financial data on several automotive companies, past performance of these companies, and historical data regarding the relationship between these companies' financial standing and their stock performance in terms of sales and revenues.
It quickly became clear how statistics could be applied in a more extensive manner — specifically, by measuring the degree of correlation between sales records and stock performance in the automotive industry in order to determine whether the former is a reliable predictor of the latter.
Such a correlation analysis would be quite extensive, and while the results could prove highly useful, it falls somewhat beyond the scope of what is practical here. The probability and statistics concepts selected for application are highly relevant, if somewhat simpler to apply.
The relative strength of several automotive companies over each of the past ten years was determined in terms of market share, profit, and sales revenue. From this data, the probability of each company potentially becoming the leader in each of these areas over the next several years was calculated as a simple probability. The common graphs created by charting each stock's daily price were also examined for any relationship to standard statistical distributions, both in shorter and longer time segments. Any such similarity would have suggested a definite statistical relationship among stock prices.
The outcome of the probability assessment is relatively straightforward. Each company's data for the past ten years was compiled and organized into charts, making a visual comparison of the data clearly visible. From this data, it was fairly easy to establish probabilities for repetitions of the observed performance records. For instance, one company had the largest sales revenue by a wide margin in seven out of the past ten years; it therefore seems probable that this same company would be the sales leader in the industry over the next several years as well. Similar results were obtained for the other identified criteria.
The statistical analysis, on the other hand, did not yield any particularly useful results. No regular patterns emerged in any of the companies' stock price graphs, nor did the graphs appear to relate meaningfully to one another. The stock market data, in this respect, resisted classification within standard statistical distributions.
"Trade-off between accurate and precise stock metrics"
Based on the data obtained, the conclusion reached was that more research is needed before actually selecting a stock to buy. While several automotive companies emerged as rather promising investments based on the probability data acquired and analyzed, there are entirely non-statistical elements of various companies that must also be assessed. There is no magic method for crunching stock numbers in order to pick a winner. Qualitative issues and leadership changes at these companies are ongoing, and they make the investment decision considerably more complex than any single statistical model can fully capture.
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