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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Go Long or Short?
How does volatility affect returns of S&P 500 stocks?
Krupa Patel and Melanie Schnell
This Research Project was conducted at NYU Stern's DataBootcamp course.
For further inquireies please reach out to Krupa Patel at kp1524@nyu.edu and Melanie Schnell as ms7557@nyu.edu.
There is a common saying that states, "the higher the risk, the bigger the return." However, in the past volatile markets have yielded negative returns for many investors. This leads us to explore the question
Step1:  Step 2
Step2:  The path will vary based on what type of machine is processing the data, and where the file is saved on the computer. Be sure to update this code with your unique file path. The file path can be easily copied and pasted from file information page.
Step 3
Step3:  Step 4
Step4:  20 Day Return Calculation
This calculates the return over the course of 20 days. We calculated this by finding the difference between "close" values that are 20 days appart, before dividing that differnce by the older value.
Step5:  20 Day Volatility Calculaion
This applies a standard deviation to the volatility values over 20 days.
Step6:  Normalized 20 Day Return
We used a 250 day frame and normalized the data since it is a times series.
Step7:  Normalized 20 Day Volatility
This makes the volatility data comparable as well by making the data normalized.
Step8:  Step 5
Step9:  Table Formatting
First, we created a new Dataframe called zvol20ret20 by copying the normalized 20 day volatiliy and returns columns. We then renamed the columns "Volatility" and "Returns" to add clarity. Next, we eliminated the values that were nullified in the process of normalization, and sorted the rows by ascending order of volatility.
Step10:  Step 6
Step11:  Regression Results
The R-squared value (0.085) is very close to 0, showing that there is a weak association between volatility and return. However, the negative slope coefficient (-0.33) of the regression indicates that as volatility increases, returns tend to decrease. Also, while there is a cluster of positive returns between volatility levels of -3 and 4, there are no points that indicate a positive return after a volatility level of 6. This means that it is very unlikely to recieve a positive return during times of high market volatility.
Step12:  Negative Correlation
We calculated that the correlation between volatility and returns is -0.291. Because the value is negative, we see that high volatility yeilds low returns.
Step13:  Step 7
Step14:  Quintile Plot
We used seaborn to create a scatter plot with a regression line of the quintile data. The graph shows a clearer association between increasing volatility and decreasing returns.
Step15:  Quintile Regression Results
When we break the data into quintiles, there is a much higher R-squared value (0.88), demonstrating a stronger association between volatility and returns. We are aware that five points are not enough to run an accurate regression; however, because of the strong correlation value (-0.937) and the negative coefficient (-5) we are reassured that on average high volatility does lead to lower returns.
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Python Code:
import pandas as pd                        #Data Management Package
import pandas_datareader as pd_rd          #Data Reader Package
import numpy as np                         #Numerical Computing Package
import matplotlib.pyplot as plt            #Graphics Package
%matplotlib inline
import seaborn as sns                      #Graphics Package to Complement Matplotlib
import statsmodels.formula.api as smf      #Statistical Computing Package
Explanation: Go Long or Short?
How does volatility affect returns of S&P 500 stocks?
Krupa Patel and Melanie Schnell
This Research Project was conducted at NYU Stern's DataBootcamp course.
For further inquireies please reach out to Krupa Patel at kp1524@nyu.edu and Melanie Schnell as ms7557@nyu.edu.
There is a common saying that states, "the higher the risk, the bigger the return." However, in the past volatile markets have yielded negative returns for many investors. This leads us to explore the question: Is it profitable to go long or short when volatility is high?
We will use 57 years of S&P index to find the returns and volatilty. Then, we will normalize this times series, plot the data in a scatterplot, and run a regression to see if we get a positive or negative correlation between increasing volatility and returns.
If there is a positive slope it signifies that when volatility is high the returns are also high. However, if we get a negative slope it signifies that when volatility is high, returns are low.
Our data can easily be accessed here.
Step 1: Install Packages
To begin, we installed the necessary packages to read, manipulate, and plot our dataframe.
End of explanation
path= "/Users/MelanieSchnellAccount/Desktop/Senior_Year/Data_Bootcamp/S&P_data.csv"
df=pd.read_csv(path)
Explanation: Step 2: Import Data
We found our data on Yahoo Finance and click the download button to save a csv file. The file is named S&P_data.csv and saved to a Databootcamp folder. Our data did not need any changes. Next, we just needed to read in the data with the code below.
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df = df.rename(columns={'Adj Close': 'close'})
reversed_df = df.loc[::-1]
rdf=pd.DataFrame(reversed_df)
Explanation: The path will vary based on what type of machine is processing the data, and where the file is saved on the computer. Be sure to update this code with your unique file path. The file path can be easily copied and pasted from file information page.
Step 3: Arrange the Data
Next we reversed the dataframe to put the date in order by index, old to new. We also renamed the column "Adj Close" to "close" to make it better for slicing.
End of explanation
return1 = (rdf.close[1:].values - rdf.close[:-1].values) / rdf.close[:-1].values
return1 = pd.Series(return1, index=rdf.index[1:])
rdf["return1"]=return1
# calculates the return for the close column
Explanation: Step 4: Calculations
1 Day Return Calculation
This calculates the return after the close of one day. We calculated this by finding the difference between consecutive "close" column values, before dividing that difference by the newer value.
End of explanation
ret20 = (rdf.close[20:].values - rdf.close[:-20].values)/rdf.close[:-20].values
ret20 = pd.Series(ret20, index=rdf.index[20:])
rdf["ret20"]=ret20
Explanation: 20 Day Return Calculation
This calculates the return over the course of 20 days. We calculated this by finding the difference between "close" values that are 20 days appart, before dividing that differnce by the older value.
End of explanation
vol20= rdf["return1"].rolling(window=20).apply(np.std)
rdf["vol20"]=vol20
#Apply standard deviation to the volitility over 20 days
Explanation: 20 Day Volatility Calculaion
This applies a standard deviation to the volatility values over 20 days.
End of explanation
zret20=((rdf.ret20[270:].values)-(rdf.ret20[270:].rolling(window=250).apply(np.mean)))/(rdf.ret20[270:].rolling(window=250).apply(np.std))
zret20=pd.Series(zret20, index=rdf.index[270:])
rdf["zret20"]=zret20
# Remove the effects of imflation, make the data comparable
Explanation: Normalized 20 Day Return
We used a 250 day frame and normalized the data since it is a times series.
End of explanation
zvol20=((rdf.vol20[270:].values)-(rdf.vol20[270:].rolling(window=250).apply(np.mean)))/(rdf.vol20[270:].rolling(window=250).apply(np.std))
zvol20=pd.Series(zvol20, index=rdf.index[270:])
rdf["zvol20"]=zvol20
Explanation: Normalized 20 Day Volatility
This makes the volatility data comparable as well by making the data normalized.
End of explanation
rdf.shape
Explanation: Step 5: Create the Data Table
Table Dimensions
End of explanation
zvol20ret20=rdf[["zvol20", "zret20"]].copy()
zvol20ret20 = zvol20ret20.rename(columns={'zvol20' : 'Volatility', 'zret20' : 'Returns'})
zvol20ret20 = zvol20ret20[zvol20ret20.Volatility.notnull()]
zvol20ret20 = zvol20ret20[zvol20ret20.Returns.notnull()] 
Explanation: Table Formatting
First, we created a new Dataframe called zvol20ret20 by copying the normalized 20 day volatiliy and returns columns. We then renamed the columns "Volatility" and "Returns" to add clarity. Next, we eliminated the values that were nullified in the process of normalization, and sorted the rows by ascending order of volatility.
End of explanation
sns.lmplot(x='Volatility',y='Returns',data=zvol20ret20,fit_reg=True)
Explanation: Step 6: Plot the Data
Scatter Plot
We used seaborn to plot the data in a scatter plot to visually display the relationship between volatility and returns. The regression line demonstrates that (while points tend to cluster between -2 and 3 Volatility, and -3 and 2 Returns) there is a general trend towards lower returns during high market volatility.
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reg = smf.ols(formula='Volatility ~ Returns', data=zvol20ret20).fit()
reg.params
reg.summary()
Explanation: Regression Results
The R-squared value (0.085) is very close to 0, showing that there is a weak association between volatility and return. However, the negative slope coefficient (-0.33) of the regression indicates that as volatility increases, returns tend to decrease. Also, while there is a cluster of positive returns between volatility levels of -3 and 4, there are no points that indicate a positive return after a volatility level of 6. This means that it is very unlikely to recieve a positive return during times of high market volatility.
End of explanation
zvol20ret20.corr()
Explanation: Negative Correlation
We calculated that the correlation between volatility and returns is -0.291. Because the value is negative, we see that high volatility yeilds low returns.
End of explanation
zvol20ret20=zvol20ret20.sort_values('Volatility', ascending=True)
zvol20ret20 = zvol20ret20.reset_index(drop=True)
Ret=zvol20ret20.Returns.groupby(np.arange(len(zvol20ret20.Returns))//3283).mean().tolist()
Return= pd.Series(Ret)
quintileframe= pd.DataFrame({"Volatility":[1,2,3,4,5]})
quintileframe['Return'] = Return.values
quintileframe
Explanation: Step 7: Quintiles
Quintile Table
Because the points were clustered in the scatter plot, and the results showed a weak R-squared value, we grouped the data by quintiles. This showed a much clearer result with a stronger R-squared value. To accomplish this, we sorted the rows by volatility, from low to high. Because there are 16,411 rows in the dataframe, we took the mean of Returns in groups of 3,283 (one fifth of the total number of rows) and created a new dataframe with these values. In the new dataframe we assigned the volatiliy values one through five (one being the lowest volatility and five being the highest).
End of explanation
sns.lmplot(x='Volatility',y='Return',data=quintileframe,fit_reg=True)
Explanation: Quintile Plot
We used seaborn to create a scatter plot with a regression line of the quintile data. The graph shows a clearer association between increasing volatility and decreasing returns.
End of explanation
quintilereg=smf.ols(formula='Volatility ~ Return', data=quintileframe).fit()
quintilereg.params
quintilereg.summary()
quintileframe.corr()
Explanation: Quintile Regression Results
When we break the data into quintiles, there is a much higher R-squared value (0.88), demonstrating a stronger association between volatility and returns. We are aware that five points are not enough to run an accurate regression; however, because of the strong correlation value (-0.937) and the negative coefficient (-5) we are reassured that on average high volatility does lead to lower returns.
End of explanation
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