# Data Exploratory Analysis: Hypothesis Test and Regression Analysis of Portfolios Containing Gaming and Department Store Stocks

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Data Exploratory Analysis: Hypothesis Test and Regression Analysis of Portfolios Containing Gaming and Department Store Stocks

Introduction        2

Hypothesis Test for Mean and Variance        2

Linear Regression and Goodness of Fit Tests        3

Volatility Comparison with Market Return        9

Model Assumption Test        9

Reference        11

Introduction

Ten companies from two industries were selected for analysis. From the Gaming industry, Taketwo Interactive (TTWO), Activision Blizzard (ATVI), Electronic Arts (EA), NetEase (NTES), and Changyou (CYOU) were selected. From the Department Stores industry, JC Penney (JCP), Macy’s (M), Target (TGT), Walmart (WMT), and Nordstrom (JWN) were selected. Equal weighted portfolios are formed for each industry. Analysis is performed on the equal weighted portfolios unless otherwise stated. First, the two industries’ mean weekly return and variance are analyzed. Then, the capital assets pricing model (CAPM) is applied and the fit is evaluated. Next, we will check if the return of a single stock has the same volatility of market. Finally, we comment on the efficacy of the CAPM model.

## Hypothesis Test for Mean and Variance

Mean

The mean of both industry portfolios is evaluated using hypothesis test. The null hypothesis will be that the mean returns from both industries are equal. Significance level is set at 95%. Result are show in Table A1

Table A1

[pic 1]

The p-value is larger than 0.05, thus we cannot reject the null hypothesis that the two industries have same return.

Variance

To test whether the two industry porfolios have differing variances, the null hypothesis is set to assume both industry variances are equal. Significance level is set at 95%, Results are showed in Table A2

Table A2

[pic 2]

The p-value is less than 0.05, we can reject the null hypothesis that two industries have same variance.

## Linear Regression and Goodness of Fit Tests

Regression analysis is performed to determine whether the return of the individual stock is predicted by the CAPM model. Results are displayed in the following table. ANOVA test are also run in building the model.

TTWO Results

[pic 3]

The p-value in ANOVA test and coefficient tests are both small enough to reject the null. The CAPM model’s two parameters are statistically significant and they explain 21.9% of TTWO’s returns.

ATVI Results

[pic 4]

The p-value in ANOVA test and risk premium coefficient are low enough to reject the null. The CAPM model’s market return coefficient is statistically significant and the model explains 21.4% of ATVI’s returns.

EA Results

[pic 5]

The p-value in ANOVA test and risk premium coefficient are low enough to reject the null. The CAPM model’s market return coefficient is statistically significant and the model explains 15.3% of EA’s returns.

NTES Results

[pic 6]

The p-value in ANOVA test and risk premium coefficient are low enough to reject the null. The CAPM model’s market return coefficient is statistically significant and the model explains 20% of ATVI’s returns.

CYOU Results

[pic 7]

The p-value from ANOVA table is larger than 0.05, we cannot reject the null hypothesis that all coefficients are zero.

JCP Results

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The p-value in ANOVA test and risk premium coefficient are low enough to reject the null. T The CAPM model’s market return coefficient is statistically significant and the model explains 8% of JCP’s returns.

JWN Results

[pic 9]

The p-value in ANOVA test and risk premium coefficient are low enough to reject the null. The CAPM model’s market return coefficient is statistically significant and the model explains 13.6% of JWN’s returns.

WMT Results

[pic 10]

The p-value in ANOVA test and risk premium coefficient are low enough to reject the null. The CAPM model’s market return coefficient is statistically significant and the model explains 20.8% of WMT’s returns.

TGT Results

[pic 11]

The p-value in ANOVA test and risk premium coefficient are low enough to reject the null. The CAPM model’s market return coefficient is statistically significant and the model explains 8.9% of TGT’s returns.

M Results

[pic 12]

The p-value in ANOVA test and risk premium coefficient are lower than 0.05. The CAPM model’s market return coefficient is statistically significant and the model explains 3.9% of M’s returns.

## Volatility Comparison with Market Return

Single stock volatility is compared with market return volatility. The single stock’s coefficient for risk premium is tested to be statistically non-equal to one.

A hypothesis test (t-test) is implemented with null hypothesis stating that the coefficient of risk premium is equal to one. The hypothesis rejection is at a confidence level of 95%. Results shown in Table C1.

Table C1

[pic 13]

The t-stat value of NTES, JCP and JWN do not meat the rejection threshold. The evidence suggests that these stocks have volatility equal to the market.

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