Eastman Chemical's Monthly Returns Have a High Correlation with the Vanguard S&P 500 Index ETF

Here's the histogram of monthly returns for Eastman Chemical (EMN) between June 2019 and November 2022 (Exhibit 1). Please click on the image to see an enlarged version.  

Exhibit 1:

Eastman Chemical Histogram of Monthly Returns (Source: Data Provided by IEX Cloud, Author Calculations using Microsoft Excel)

  The average monthly returns of Eastman Chemical are slightly better than that of the Vanguard S&P 500 Index ETF (Exhibit 2 & 3). But Eastman Chemical has a much higher (nearly double) standard deviation (volatility) of monthly returns than the Vanguard S&P 500 Index ETF.       

Exhibit 2:

Eastman Chemical Average, First Quartile, Third Quartile, and Standard Deviation of Monthly Returns. (Data Provided by IEX Cloud, Author Calculations Using Microsoft Excel)

Exhibit 3:

Vanguard S&P 500 Index ETF Average, First Quartile, Third Quartile, and Standard Deviation of Monthly Returns. (Data Provided by IEX Cloud, Author Calculations Using Microsoft Excel)

Eastman Chemical moves closely with the market since it has a high positive correlation of 0.78.

> cor(VOOandEMN['EMN_Monthly_Return'], VOOandEMN['VOO_Monthly_Return'], method = c("pearson", "kendall", "spearman"))

                      VOO_Monthly_Return

EMN_Monthly_Return          0.7898654

A linear regression model of the monthly returns of Vanguard S&P 500 Index ETF as the independent variable and Eastman Chemical as the dependent variable yields a beta of 1.54.  

> # Conduct the Linear Regression of the Monthly Returns Between $VOO and $EMN

> lmVOOEMN = lm(EMN_Monthly_Return~VOO_Monthly_Return, data = VOOandEMN)

> # Present the summary of the results from the linear regression

> summary(lmVOOEMN)

Call:

lm(formula = EMN_Monthly_Return ~ VOO_Monthly_Return, data = VOOandEMN)

Residuals:

     Min       1Q   Median       3Q      Max 

-0.12433 -0.04969 -0.01148  0.05611  0.13701 

Coefficients:

                    Estimate Std. Error t value  Pr(>|t|)    

(Intercept)        -0.003992  0.010914   -0.366  0.716    

VOO_Monthly_Return  1.548548  0.190108    8.146  5.02e-10 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.06942 on 40 degrees of freedom

Multiple R-squared:  0.6239, Adjusted R-squared:  0.6145 

F-statistic: 66.35 on 1 and 40 DF,  p-value: 5.023e-10

The coefficient of VOO_Monthly_Return (slope of the regression line) is the stock's beta. This beta value means that for every 1% change in the monthly returns of the Vanguard S&P 500 Index ETF, Eastman Chemical, on average, changes by 1.54% (monthly). This relationship between the two companies is significant at the 95% confidence interval, given the p-value of 5.02e-10.

This close positive relationship between the two explains why Eastman Chemical has lost 25.6%, while the Vanguard S&P 500 Index ETF (VOO) has lost 14.5%.    

 

Monthly Return Analysis of Conagra Brands

Conagra Brands owns many iconic brands in the food business (Exhibit 1). The company is categorized as a consumer staple. 

Exhibit 1:

 

Here's the histogram of monthly returns of Conagra Brands between June 2019 and November 2022 (Exhibit 2). Please click on the image to see an enlarged version.  

Exhibit 2:

Conagra Brands Histogram of Monthly Returns (Source: Data Provided by IEX Cloud, Author Calculations using Excel)

The average monthly returns of Conagra Brands (Exhibit 3) are very similar to that of the Vanguard S&P 500 Index ETF (Exhibit 4).

Exhibit 3: 

(Source: Data Provided by IEX Cloud, Data Calculations Using Excel)

Exhibit 4:

(Source: Data Provided by IEX Cloud, Data Calculations Using Excel)

The monthly returns of Conagra Brands and the Vanguard S&P 500 Index ETF have a mild positive correlation of 0.27 (Exhibit 5). 

Exhibit 5:  

A 12-month rolling correlation of the monthly returns yielded a very high positive correlation of 0.8 between April 2020 and March 2021 (Exhibit 6).

Exhibit 6:

(Source: Data Provided by IEX Cloud, Correlation Calculations Using RStudio)

A 12-month rolling correlation of the monthly returns yielded the highest negative correlation of 0.37 between July 2021 and June 2022 (Exhibit 7).

Exhibit 7:

(Source: Data Provided by IEX Cloud, Correlation Calculations Using RStudio)

A linear regression model estimates Conagra's Beta at 0.34, which is not statistically significant at the 95% confidence interval. The p-value is 0.083, suggesting that the correlation is not statistically significant.

Here's the output of the linear model:

Call:

lm(formula = CAG_Monthly_Return ~ VOO_Monthly_Return, data = VOOandCAG)

Residuals:

      Min        1Q    Median        3Q       Max 

-0.168638  -0.044057  -0.004737   0.045175  0.170379 

Coefficients:

                   Estimate Std. Error t value Pr(>|t|)  

(Intercept)        0.007141   0.011079   0.645   0.5229  

VOO_Monthly_Return 0.342593   0.192981   1.775   0.0835 .

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.07047 on 40 degrees of freedom

Multiple R-squared:  0.07303, Adjusted R-squared:  0.04986 

F-statistic: 3.152 on 1 and 40 DF,  p-value: 0.08346

The adjusted R-squared is 0.049, meaning that just 4.9% of Conagra's monthly returns can be explained by the monthly returns of the Vanguard S&P 500 Index ETF.    

  

Reynolds Consumer Products Beta Included in the Latest List

Here's the beta list calculated using a linear regression model [Exhibit 1]. The beta is based on the monthly returns of the Vanguard S&P 500 Index ETF (Click on the image to see an enlarged version).  

Exhibit 1

(Source: Data Provided by IEX Cloud, Calculations Using, RStudio, Yahoo Finance)

Latest additions:

• Corning
• Reynolds Consumer Products

Mothly Return Volatility (Beta) of Reynolds Consumer Products

Reynolds Consumer Products (REYN) makes many iconic household products, such as Reynolds Wrap, Hefty waste bags, and FreshLock zipper bags [Exhibit 1]. 

Exhibit 1: Some of the Products Made by Reynolds Consumer Products Co.

Reynolds Consumer Products Source: Reynolds brands 

 I analyzed the monthly return of Reynolds (REYN) between February 2020 and November 2022. Here's the histogram of the monthly returns (click on the image to see an enlarged version) [Exhibit 2]:

Exhibit 2

Source: Data Provided by IEX Cloud, Author Calculations and Graphs Using Microsoft Excel 

Here's the graph of the monthly returns of the Vanguard S&P 500 Index ETF (VOO) on the x-axis and Reynold's monthly returns on the y-axis [Exhibit 3]:

Exhibit 3

Source: Data Provided by IEX Cloud, Graph Created using RStudio

The Pearson correlation of the monthly returns is a positive 0.46. This correlation value can be considered to have medium strength. This correlation is statistically significant at the 95% confidence interval with a p-value of 0.0057.  

A linear regression of the monthly returns of Reynolds and the Vanguard S&P 500 Index ETF yields a beta value of 0.44. This beta value means that for every 1% change in the value of the Vanguard ETF, on average, Reynolds' stock will change by 0.44%. Yahoo Finance also shows a beta of 0.44 [Exhibit 4]. 

Exhibit 4

Source: Yahoo Finance

The adjusted R-squared value provided by the linear regression is 0.19. This adjusted R-squared value indicates that about 19% of Reynold's monthly returns are explained by the monthly returns of the Vanguard S&P 500 Index ETF.  

Here's the output from the linear regression model constructed using RStudio:

Call:

lm(formula = REYN_Monthly_Return ~ VOO_Monthly_Return, data = VOOandREYN_MonthlyReturns)

Residuals:

      Min        1Q    Median        3Q       Max 

-0.092919 -0.037524 -0.003499  0.037494  0.137349 

Coefficients:

                   Estimate Std. Error t value Pr(>|t|)   

(Intercept)        0.001072   0.009234   0.116  0.90828   

VOO_Monthly_Return 0.440311   0.148653   2.962  0.00572 **

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.05329 on 32 degrees of freedom

Multiple R-squared:  0.2152, Adjusted R-squared:  0.1907 

F-statistic: 8.773 on 1 and 32 DF,  p-value: 0.005722

The p-value is significant at a 95% confidence interval with a value of 0.005722. 

Here's the residuals plot for the linear regression between Reynolds Consumer Products and the Vanguard S&P 500 Index ETF [Exhibit 5]:

Exhibit 5

Residuals Plot for Linear Regression of the monthly returns of the Vanguard S&P 500 Index as the independent variable and Reynold Consumer Products (Source: Data Provided by IEX Cloud, Graph Created using RStudio)

  Here are the average, first quartile, third quartile, and standard deviation of Reynold's monthly returns [Exhibit 6]:

Exhibit 6

Here are the average, first quartile, third quartile, and standard deviation of the Vanguard S&P 500 Index ETF [Exhibit 7]:

Exhibit 7

  

Corning's Volatility Compared to the Vanguard S&P 500 Index ETF

Here's the histogram of Corning's (GLW) monthly returns between June 2019 and October 2022 (Click on the image to see a larger version):

Exhibit: Corning's Monthly Returns Fell at or below 2.56% for the Majority of the Months

Data Provided by IEX Cloud, Author Calculations

There were 14 months between June 2019 and October 2022 when Corning's monthly returns were greater than 2.56%.  There were seven months when the monthly returns were greater than or equal to 11.5%.    

Corning's monthly returns have a high positive correlation of 0.66 with the monthly returns of the Vanguard S&P 500 Index ETF (VOO). 

Exhibit: The Vanguard S&P 500 Index and Corning Monthly Returns [June 2019 - October 2022]

Data Provided by IEX Cloud, Monthly Returns Calculated by the Author, Graph using RStudio 

A linear regression of the Vanguard S&P 500 Index ETF and Corning's monthly returns yields a beta of 1.03 for Corning. Corning's average monthly return will mirror the Vanguard S&P 500 Index ETF. Corning may not help diversify a portfolio and will not protect against the market's volatility.  

Here's the linear regression model:

> # Conduct the Linear Regression of the Monthly Returns Between $VOO and $GLW

> lmVOOGLW = lm(GLW_Monthly_Return~VOO_Monthly_Return, data = VOOandGLW)

> # Present the summary of the results from the linear regression

> summary(lmVOOGLW)

Call:

lm(formula = GLW_Monthly_Return ~ VOO_Monthly_Return, data = VOOandGLW)

Residuals:

      Min        1Q      Median     3Q       Max 

   -0.118363 -0.050928 -0.009998  0.041106  0.187435 

Coefficients:

                   Estimate     Std. Error   t value   Pr(>|t|)    

(Intercept)        -0.003778     0.010818    -0.349    0.729    

VOO_Monthly_Return  1.039148     0.188256     5.520    2.4e-06 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.06823 on 39 degrees of freedom

Multiple R-squared:  0.4386, Adjusted R-squared:  0.4242 

F-statistic: 30.47 on 1 and 39 DF,  p-value: 2.403e-06

The coefficient for VOO_Monthly_Return [1.039148] is the beta for Corning.  The p-value is significant at a 95% confidence interval. The adjusted R-squared is 0.42, which means about 42% of Corning's average monthly return is explained by the Vanguard S&P 500 Index ETF returns.     

Beta of Cummins Included in the List

 Here's the latest list of beta values. I have included Cummins on this list, and the returns for Cummins and the Vanguard S&P 500 Index are based on November 25, 2022, closing prices. Click on the image to see an enlarged version. 

Exhibit: Beta Values for Cummins Included in the list

Companies in this list:

• Cisco Systems
• Colgate-Palmolive
• Lennox International
• Sealed Air
• Boeing
• Newell Brands
• Timken
• Cummins

 

Monthly Return Comparison Between Cummins and Vanguard S&P 500 Index ETF

The following chart shows the Vanguard S&P 500 Index ETF (VOO) monthly returns on the x-axis and Cummins (CMI) on the y-axis. The regression line on the graph shows a steep slope, and the Pearson correlation value is 0.7. This value shows a very strong correlation between the monthly returns of the Vanguard S&P 500 Index ETF and Cummins. The p-value is significant at a 95% confidence interval. Cummins has returned 13.9% in the past year, while the Vanguard S&P 500 Index ETF has returned a -12.4%.  

Exhibit: Monthly Returns of Vanguard S&P 500 Index ETF and Cummins [June 2019 - October 2022]

   

The following command was used to create this graph:

> # Create a new Graph of $VOO and $CMI Monthly Returns as Percentages

> ggscatter(df1, x = 'VOO_Monthly_Return', y = 'CMI_Monthly_Return', 

+           add = "reg.line", conf.int = TRUE, 

+           cor.coef = TRUE, cor.method = "pearson",

+           xlab = "VOO ETF Monthly Returns (%)", ylab = "CMI Monthly +           Returns (%)")

A linear regression of the monthly returns of the Vanguard S&P 500 Index ETF and Cummins shows the beta (coefficient of Vanguard S&P 500 Index ETF) for Cummins' monthly returns compared to the Vanguard ETF. 

# Conduct the Linear Regression of the Monthly Returns Between $VOO and $CMI

lmVOOCMI = lm(CMI_Monthly_Return~VOO_Monthly_Return, data = VOOandCMI)

# Present the summary of the results from the linear regression

summary(lmVOOCMI)

Call:

lm(formula = CMI_Monthly_Return ~ VOO_Monthly_Return, data = VOOandCMI)

Residuals:

      Min        1Q    Median        3Q       Max 

-0.123268 -0.051037  0.004537  0.047062  0.115727 

Coefficients:

                   Estimate Std. Error t value Pr(>|t|)    

(Intercept)        0.005104   0.009226   0.553    0.583    

VOO_Monthly_Return 0.993327   0.160541   6.187 2.84e-07 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.05819 on 39 degrees of freedom

Multiple R-squared:  0.4954, Adjusted R-squared:  0.4824 

F-statistic: 38.28 on 1 and 39 DF,  p-value: 2.845e-07

Cummins has a beta of 0.99 (nearly 1). Given this beta, Cummins, on average, moves in line with the S&P 500 Index. The adjusted R-squared value of 0.48 shows that about 48% of Cummins' monthly returns can be attributed to the returns of the S&P 500 Index. The p-value of 2.84e-07 shows that the regression analysis results are significant at the 95% confidence interval.

The average monthly return for Cummins between June 2019 and October 2022 was 1.49%. A one-sample t-test shows that the monthly return falls between -1.05% and 4.04%. But, the p-value of 0.99 is much higher than 0.05. This t-test may not be significant in the 95% confidence interval.        

#

# One Sample t-test of $CMI average monthly returns.

# 

# Step 1: 

# Copy Dataframe Column CMI_Monthly_Return into a List 

#

CMI_Monthly_Return_Col <- c(VOOandCMI['CMI_Monthly_Return'])

# CMI_Monthly_Return_Col is a list object, but needs to be numeric

# for qqnorm to work.  

#

typeof(CMI_Monthly_Return_Col)

# Convert List Object into a Column of doubles as as.numeric and unlist

#

y_CMI_Monthly_Return_Col <- as.numeric(unlist(CMI_Monthly_Return_Col))

typeof(y_CMI_Monthly_Return_Col)

# Let’s check if the data comes from a normal distribution 

# using a normal quantile-quantile plot.

# Source: https://cran.r-project.org/web/packages/distributions3/vignettes/one-sample-t-test.html

Exhibit: Check if Cummins' Monthly Returns are Normally Distributed before doing a t-test

#

qqnorm(y_CMI_Monthly_Return_Col)

qqline(y_CMI_Monthly_Return_Col)

# Conduct a t-test to see if the population mean is 1.49% [0.0149]

#

t.test(y_CMI_Monthly_Return_Col, mu = .0149)

One Sample t-test

data:  y_CMI_Monthly_Return_Col

t = 0.0045069, df = 40, p-value = 0.9964

alternative hypothesis: true mean is not equal to 0.0149

95 percent confidence interval:

 -0.01057188  0.04048574

sample estimates:

 mean of x 

0.01495693 

    

Beta of Various Stocks Listed in the US

I have calculated the beta of a few more stocks. Here's the latest list as of November 22, 2022. The one-year returns of Timken and Newell Brands are based on closing prices as of November 22.  

Exhibit: Beta of Various Stocks Listed in the U.S. 

Click on the image to see beta values. 
(Source:  Data Provided by IEX Cloud, Author's Analysis Using RStudio, Yahoo! Finance)

Stocks in this list: 

• Cisco
• Colgate
• Lennox
• Sealed Air
• Boeing
• Newell Brands
• Timken

  

Volatility of Monthly Returns of Newell Brands Compared to the Vanguard S&P 500 Index ETF

The monthly returns of Newell Brands and the Vanguard S&P 500 ETF have a positive correlation of 0.44, as calculated using the Pearson method. The data used in this study is range from June 2019 to October 2022 (41 months of data). 

Newell Brands is a company that owns some very famous brands across multiple consumer and commercial product lines. 

Exhibit: The Brands Owned by Newell Brands

(Source: Newell Brands)

      

Here's the R command and the output from R-Studio

> # Calculate the Monthly Return Correlation between Newell Brands 

> # and Vanguard S&P 500 Index using the Pearson method 

> cor(VOOandNWL['NWL_Monthly_Return'], VOOandNWL['VOO_Monthly_Return'], method = c("person"))

                        VOO_Monthly_Return

NWL_Monthly_Return          0.4434957 

Here's the plot of the S&P 500 and the Newell Brands' monthly returns:

Exhibit: S&P 500 Index Monthly Returns VS. Newell Brands Monthly Returns

                       S&P 500 Index Monthly Returns against Newell Brands' Returns

                          (Source: Data Provided by IEX Cloud, Correlation and Graph on RStudio)

When the correlation is calculated for the months when the S&P 500 Index had positive returns, the correlation drops to 0.28. 

> # Calculate the Monthly Return Correlation between Newell Brands 

> # and Vanguard S&P 500 Index using the Pearson method

> # for only those months when the Vanguard S&P 500 Index ETF 

> # had positive returns.

> cor(VOOandNWLPositiveReturns['NWL_Monthly_Return'], VOOandNWLPositiveReturns['VOO_Monthly_Return'], method = c("person"))

                        VOO_Monthly_Return

NWL_Monthly_Return           0.284022

Here's the plot of the S&P 500 Index against Newell Brands' monthly returns for months when the S&P 500 index had a positive return. 

           Exhibit: S&P 500 Index Monthly Positive Returns VS. Newell Brands Monthly Returns

S&P 500 Index Monthly Returns (Positive Months) against Newell Brands' Returns

                          (Source: Data Provided by IEX Cloud, Correlation and Graph on RStudio)

The linear regression of the monthly returns of the S&P 500 index and Newell Brands is used to estimate the average change in the monthly return of Newell Brands for a 1% change in the S&P 500 index. The coefficient of the independent variable (VOO_Monthly_Return) is the beta of Newell Brands.  In this case Newell Brands has a beta of 0.79. For every 1% monthly change in the S&P 500 index, Newell Brands is estimated to change by 0.79%. Yahoo Finance has calculated a beta of 0.84 for Newell Brands.      

> # Conduct the Linear Regression of the Monthly Returns Between $VOO and $NWL

> lmVOONWL = lm(NWL_Monthly_Return~VOO_Monthly_Return, data = VOOandNWL)

> # Present the summary of the results from the linear regression

> summary(lmVOONWL)

Call:

lm(formula = NWL_Monthly_Return ~ VOO_Monthly_Return, data = VOOandNWL)

Residuals:

     Min       1Q     Median       3Q      Max 

  -0.14372  -0.06818 -0.01767    0.06086  0.19915 

Coefficients:

                      Estimate   Std. Error   t value  Pr(>|t|)   

(Intercept)          -0.001988   0.014756     -0.135   0.89352   

VOO_Monthly_Return    0.793454   0.256769      3.090   0.00368 **

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.09306 on 39 degrees of freedom

Multiple R-squared:  0.1967, Adjusted R-squared:  0.1761 

F-statistic: 9.549 on 1 and 39 DF,  p-value: 0.003681