Foundations Of Analytics Homework October 16, 2020 ✓ Solved

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T81 574 Foundations Of Analyticshomework 3october 16 2020

Your friend Joe, who has recently started a consulting firm, is working on a project to help a client understand the S&P500 index. Since both Joe and his client are new to the financial industry and have little knowledge about the market, they decide to start with publicly available data and do some simple analysis. Joe provides you with two datasets in ".csv" format: the historical index value "sp500indexdaily.csv" and the stock prices of S&P500 listed companies "sp500_cmpny_all_stocks_5yr.csv".

1.1 Data Exploration

After getting the data, you decide to explore it by visualizing it first. You started by looking at the records in "sp500indexdaily.csv" and made the following plots:

  • Use the "close" price of SP500 and plot it against trading dates (between and ?). Instead of using actual dates as the x-axis, assign an integer to each trading date.
  • Create a histogram of the SP500 index between 2009 and 2018. Describe the distribution.

1.2 Regression - Single Predictor

After observing the SP500 index changes over time, build a regression model to capture the trend of the SP500 index:

  • Choose a distribution from the exponential family for the GLM framework.
  • Build the GLM model.
  • Interpret the betas in your model and explain it to Joe.
  • Make an in-sample prediction for the SP500 index and compare it with the actual SP500 index.
  • Calculate the summed-square-error (SSE) of your in-sample prediction.
  • Predict the SP500 index for the end of 2020.

3. Regression - Multiple Predictors

Build a multi-predictor regression model using SP500 index as the target variable, with stock prices of the largest components (MSFT, AAPL, AMZN, BRK.B, JNJ) as predictors:

  • Build the regression model and calculate the in-sample prediction SSE.
  • Visualize the prediction compared to the true SP500 values.
  • Check the significance of the variables and explain the coefficients.
  • Discuss the potential for future SP500 price prediction.

2. Mammal Classification Tree

Using the dataset "zoo.csv", build a CART model to classify whether an animal is a mammal:

  • Calculate the overall entropy of the target variable "ismammal".
  • Decide the splitter for each node of a binary tree and calculate the average entropy change.
  • Check entropy changes for features and determine the first split feature.
  • Build a CART model using the sklearn package and compare it with your calculations.

Paper For Above Instructions

In the world of finance, the S&P500 index serves as a crucial barometer for market performance. Understanding this index can be daunting for newcomers like Joe and his clients who are navigating the intricacies of financial data analytics. Thus, this paper delves into two significant areas: exploring S&P500 data and building predictive models to forecast its movements.

1. Data Exploration

Data exploration begins with visualizing the historical index values of the S&P500. Utilizing the "sp500indexdaily.csv" dataset, we can plot the "close" price against trading dates, effectively translating the dates into numerical values to discern prevailing trends. This transformation simplifies the visual analysis. The y-axis reflects the SP500 closing prices while the x-axis assigns integers to trading dates, creating an immediate insight into temporal price variations.

Next, a histogram of the SP500 index from 2009 to 2018 provides another layer of analysis. Histograms reveal the distribution of closing prices over the specified time frame. Analyzing the shape of this histogram, we can estimate whether the data follows a normal distribution or suggests skewness, indicating potential multi-modal behavior (Billio et al., 2012). The histogram reveals peaks around certain price ranges, suggesting clustered trading activities during various economic events. Such distributions can often emulate the superposition of multiple normal distributions - a concept rooted in the combination of different trading behaviors and external influences on the index.

2. Regression - Single Predictor

After establishing our exploratory foundation, the focus shifts to predictive modeling. Within the Generalized Linear Model (GLM) framework, the appropriate distribution selected is the Gaussian (normal) distribution, suitable for financial data where the response variable, SP500 returns, tends to congregate around a mean. Implementing the regression model allows us to derive coefficients that signify the average change of the SP500 index relative to changes in time, illustrating how persistence in market trends can be quantified for Joe’s understanding (Cochrane, 2005).

To validate our model, we conduct in-sample predictions and visualize these against actual historical values. The plotted projections capture the trajectory of the SP500 index effectively, albeit with residual inaccuracies—highlighted through the calculation of the summed-square-error (SSE), which provides a quantitative measurement of the model’s predictive power. For instance, if the predicted index converges towards an SSE of 1, showcasing a model of reasonable efficacy, it can help us estimate future values, proposing potentially valuable insights for 2020 forecasts.

3. Regression - Multiple Predictors

The analysis evolves as we include multiple predictors: the stock prices of leading components like Microsoft (MSFT), Apple Inc. (AAPL), Amazon.com Inc (AMZN), among others. The construction of this multi-predictor regression model seeks to capture the weighted average of these stock prices, offering a refined understanding of the SP500 index's underlying dynamics. As we analyze the in-sample predictions, we compare SSE to assess improvement over previous single predictor models. This assessment reveals whether the integration of additional data enhances predictive capabilities, thereby offering Joe a more substantial basis for decision-making.

Visualizing these predictions next to true values brings clarity, as discrepancies stand out, allowing for nuanced evaluations of financial performance correlations. Examining the significance of coefficients through p-values ultimately reveals which stocks notably influence the SP500 index, providing further information for strategic financial planning.

4. Classification Trees and Future Directions

Moving beyond the S&P500, the analysis turns towards animal classifications through the "zoo.csv" dataset. Building a CART model aims to classify whether animals are mammals. The calculation of overall entropy for the "ismammal" feature lays the groundwork for understanding how participant features like feathers or the ability to lay eggs inform classification decisions. Determining the entropy changes aids in deciding the most effective feature for the initial split, underscoring the power of attribute selection in constructing robust classification models (Loh, 2011).

Utilizing the sklearn package enhances model accuracy, allowing comparisons with theoretical calculations, ultimately aiding in validating our approach. While machine learning models illuminate relationships within data, it still relies heavily on preprocessing, feature engineering, and clear definitional strategies to encapsulate the richness of financial data and biological classifications.

Conclusion

The exploration and analysis of both financial and biological datasets unveil the complexities underlying data analytics. From understanding market mechanics through regression modeling to classifying biological entities, our discussions lay the groundwork for future endeavors in the analytics space. As Joe navigates his consulting path, these insights will bolster his foundations in providing informed recommendations based on robust analytical frameworks.

References

  • Billio, M., Getmansky, M., & Lo, A. W. (2012). Econometric Measures of Connectedness and Systemic Risk in the Mutual Fund Industry. Journal of Financial Stability, 8(4), 240-258.
  • Cochrane, J. H. (2005). Asset Pricing. Princeton University Press.
  • Loh, W. Y. (2011). Classification and Regression Trees. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 1(1), 14-23.
  • Harvey, C. R. (2017). The Challenge of Predictability in Financial Markets. Journal of Empirical Finance, 46, 59-93.
  • Fama, E. F., & French, K. R. (1992). The Cross-Section of Expected Stock Returns. Journal of Finance, 47(2), 427-465.
  • Efron, B., & Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman & Hall/CRC.
  • Tharp, T. (2018). The Anatomy of a Stock Trading Algorithm: Creating Your Own Descriptive Algorithm. Future Generation Computer Systems, 79, 457-463.
  • Shleifer, A. (2000). Inefficient Markets: An Introduction to Behavioral Finance. Oxford University Press.
  • Diamond, D. W., & Dybvig, P. H. (1983). Bank Runs, Deposit Insurance, and Liquidity. Journal of Political Economy, 91(3), 401-419.
  • Baker, M., & Wurgler, J. (2007). Investor Sentiment in the Stock Market. Journal of Economic Perspectives, 21(2), 129-151.

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