Momentum portfolio(trend following) quant simulation on pandas - python

I am trying to construct trend following momentum portfolio strategy based on S&P500 index (momthly data)
I used Kaufmann's fractal efficiency ratio to filter out whipsaw signal
(http://etfhq.com/blog/2011/02/07/kaufmans-efficiency-ratio/)
I succeeded in coding, but it's very clumsy, so I need advice for better code.
Strategy
Get data of S&P 500 index from yahoo finance
Calculate Kaufmann's efficiency ratio on lookback period X (1 , if close > close(n), 0)
Averages calculated value of 2, from 1 to 12 time period ---> Monthly asset allocation ratio, 1-asset allocation ratio = cash (3% per year)
I am having a difficulty in averaging 1 to 12 efficiency ratio. Of course I know that it can be simply implemented by for loop and it's very easy task, but I failed.
I need more concise and refined code, anybody can help me?
a['meanfractal'] bothers me in the code below..
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import pandas_datareader.data as web
def price(stock, start):
price = web.DataReader(name=stock, data_source='yahoo', start=start)['Adj Close']
return price.div(price.iat[0]).resample('M').last().to_frame('price')
a = price('SPY','2000-01-01')
def fractal(a,p):
a['direction'] = np.where(a['price'].diff(p)>0,1,0)
a['abs'] = a['price'].diff(p).abs()
a['volatility'] = a.price.diff().abs().rolling(p).sum()
a['fractal'] = a['abs'].values/a['volatility'].values*a['direction'].values
return a['fractal']
def meanfractal(a):
a['meanfractal']= (fractal(a,1).values+fractal(a,2).values+fractal(a,3).values+fractal(a,4).values+fractal(a,5).values+fractal(a,6).values+fractal(a,7).values+fractal(a,8).values+fractal(a,9).values+fractal(a,10).values+fractal(a,11).values+fractal(a,12).values)/12
a['portfolio1'] = (a.price/a.price.shift(1).values*a.meanfractal.shift(1).values+(1-a.meanfractal.shift(1).values)*1.03**(1/12)).cumprod()
a['portfolio2'] = ((a.price/a.price.shift(1).values*a.meanfractal.shift(1).values+1.03**(1/12))/(1+a.meanfractal.shift(1))).cumprod()
a=a.dropna()
a=a.div(a.ix[0])
return a[['price','portfolio1','portfolio2']].plot()
print(a)
plt.show()

You could simplify further by storing the values corresponding to p in a DF rather than computing for each series separately as shown:
def fractal(a, p):
df = pd.DataFrame()
for count in range(1,p+1):
a['direction'] = np.where(a['price'].diff(count)>0,1,0)
a['abs'] = a['price'].diff(count).abs()
a['volatility'] = a.price.diff().abs().rolling(count).sum()
a['fractal'] = a['abs']/a['volatility']*a['direction']
df = pd.concat([df, a['fractal']], axis=1)
return df
Then, you could assign the repeating operations to a variable which reduces the re-computation time.
def meanfractal(a, l=12):
a['meanfractal']= pd.DataFrame(fractal(a, l)).sum(1,skipna=False)/l
mean_shift = a['meanfractal'].shift(1)
price_shift = a['price'].shift(1)
factor = 1.03**(1/l)
a['portfolio1'] = (a['price']/price_shift*mean_shift+(1-mean_shift)*factor).cumprod()
a['portfolio2'] = ((a['price']/price_shift*mean_shift+factor)/(1+mean_shift)).cumprod()
a.dropna(inplace=True)
a = a.div(a.ix[0])
return a[['price','portfolio1','portfolio2']].plot()
Resulting plot obtained:
meanfractal(a)
Note: If speed is not a major concern, you could perform the operations via the built-in methods present in pandas instead of converting them into it's corresponding numpy array values.

Related

Error using Santiment sanpy library for cryptocurrency data analysis

I am using sanpy to gather crypto market data, compute alpha, beta and rsquared with statsmodels, and then create a crypto = input("Cryptocurrency: ") function with a while loop that allows me to ask the user for an specific crypto and output its respective statistics, followed by showing the input again.
With the following code I receive the error: ValueError: If using all scalar values, you must pass an index
import san
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import datetime
import statsmodels.api as sm
from statsmodels import regression
cryptos = ["bitcoin", "ethereum", "ripple", "bitcoin-cash", "tether",
"bitcoin-sv", "litecoin", "binance-coin", "eos", "chainlink",
"monero", "bitcoin-gold"]
def get_and_process_data(c):
raw_data = san.get("daily_closing_price_usd/" + c, from_date="2014-12-31", to_date="2019-12-31", interval="1d") # "query/slug"
return raw_data.pct_change()[1:]
df = pd.DataFrame({c: get_and_process_data(c) for c in cryptos})
df['MKT Return'] = df.mean(axis=1) # avg market return
#print(df) # show dataframe with all data
def model(x, y):
# Calculate r-squared
X = sm.add_constant(x) # artificially add intercept to x, as advised in the docs
model = sm.OLS(y,X).fit()
rsquared = model.rsquared
# Fit linear regression and calculate alpha and beta
X = sm.add_constant(x)
model = regression.linear_model.OLS(y,X).fit()
alpha = model.params[0]
beta = model.params[1]
return rsquared, alpha, beta
results = pd.DataFrame({c: model(df[df[c].notnull()]['MKT Return'], df[df[c].notnull()][c]) for c in cryptos}).transpose()
results.columns = ['rsquared', 'alpha', 'beta']
print(results)
The error is in the following line:
df = pd.DataFrame({c: get_and_process_data(c) for c in cryptos})
I tried solving the issue by changing it to:
df = {c: get_and_process_data(c) for c in cryptos}
df['MKT Return'] = df.mean(axis=1) # avg market return
print(df) # show dataframe with all data
But with that, it gave me a different error: AttributeError: 'dict' object has no attribute 'mean'.
The goal is to create a single DataFrame with the datatime column, columns for the cryptos and their pct.change data, an additional column for MKT Return with the daily mean from all cryptos' pct.change. Then, use all this data to calculate each crypto's statistics and finally create the input function mentioned at the beginning.
I hope I made myself clear and that someone is able to help me with this matter.
This is a great start, but I think that you are getting confused with the return from san. If you look at
import san
import pandas as pd
# List of data we are interested in
cryptos = ["bitcoin", "ethereum", "ripple", "bitcoin-cash", "tether",
"bitcoin-sv", "litecoin", "binance-coin", "eos", "chainlink",
"monero", "bitcoin-gold"]
# function to get the data from san into a dataframe and turn in into
# a daily percentage change
def get_and_process_data(c):
raw_data = san.get("daily_closing_price_usd/" + c, from_date="2014-12-31", to_date="2019-12-31", interval="1d") # "query/slug"
return raw_data.pct_change()[1:]
# now set up an empty dataframe to get all the data put into
df = pd.DataFrame()
# cycle through your list
for c in cryptos:
# get the data as percentage changes
dftemp = get_and_process_data(c)
# then add it to the output dataframe df
df[c] = dftemp['value']
# have a look at what you have
print(df)
And from that point on you know you have some good data and you can play with it as you go forward.
If I could suggest that you just get one currency and get the regressions working with that one then move forward to cycling through all of them.
You are passing scalar values, you need to pass lists so try the following:
data = {c: [get_and_process_data(c)] for c in cryptos}
df = pd.DataFrame(data)
Maybe try this first

How to implement a normality-check function in python?

I am building a Monte Carlo simulation in order to study the behaviour of a set of 1000 iterations. Every simulation has an output graph given by a Pandas dataframe converted into a png by matplotlib.pyplot. Since I am not sure that every output is a Normal ditribution, even if a read an article about this and it secures every output is, I'd like to understand how to check it.
I've found something in this link but I didn't understand which one is the best and how to implement it.
Here's the code:
import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
sns.set_style('whitegrid')
avg = 1
std_dev = .1
num_reps = 500
num_simulations = 1000
#generate a list of percentages that will replicate our historical normsal distribution
#two decimal places in order to make it very easy to see the boundaries
pct_to_target = np.random.normal(avg, std_dev, num_reps).round(2)
#input of historical datas
sales_target_values = [75_000, 100_000, 200_000, 300_000, 400_000, 500_000]
sales_target_prob = [.3, .3, .2, .1, .05, .05]
sales_target = np.random.choice(sales_target_values, num_reps, p=sales_target_prob)
#build up a pandas dataframe
df = pd.DataFrame(index=range(num_reps), data={'Pct_To_Target': pct_to_target,
'Sales_Target': sales_target})
df['Sales'] = df['Pct_To_Target'] * df['Sales_Target']
#Here is what our new dataframe looks like
print("how our dataframe looks like")
print(df)
#Return the commission rate based on the excell table
def calc_commission_rate(x):
if x <= .90:
return .02
if x <= .99:
return .03
else:
return .04
#create our commission rate and multiply it times sales
df['Commission_Rate'] = df['Pct_To_Target'].apply(calc_commission_rate)
df['Commission_Amount'] = df['Commission_Rate'] * df['Sales']
print(df)
# Define a list to keep all the results from each simulation that we want to analyze
all_stats = []
# Loop through many simulations
for i in range(num_simulations):
# Choose random inputs for the sales targets and percent to target
sales_target = np.random.choice(sales_target_values, num_reps, p=sales_target_prob)
pct_to_target = np.random.normal(avg, std_dev, num_reps).round(2)
# Build the dataframe based on the inputs and number of reps
df = pd.DataFrame(index=range(num_reps), data={'Pct_To_Target': pct_to_target,
'Sales_Target': sales_target})
# Back into the sales number using the percent to target rate
df['Sales'] = df['Pct_To_Target'] * df['Sales_Target']
# Determine the commissions rate and calculate it
df['Commission_Rate'] = df['Pct_To_Target'].apply(calc_commission_rate)
df['Commission_Amount'] = df['Commission_Rate'] * df['Sales']
#print(df)
# We want to track sales,commission amounts and sales targets over all the simulations
all_stats.append([df['Sales'].sum().round(0),
df['Commission_Amount'].sum().round(0),
df['Sales_Target'].sum().round(0)])
results_df = pd.DataFrame.from_records(all_stats, columns=['Sales',
'Commission_Amount',
'Sales_Target'])
results_df.describe().style.format('{:,}')
print(results_df)
results_df['Commission_Amount'].plot(kind='hist', title="Total Commission Amount")
plt.savefig('graph.png')
# results_df['Sales'].plot(kind='hist')
# plt.savefig('graph2.png')
print(results_df)
I'd like to add a function that checks if the output distribution is a Gaussian (normal) distribution , because I am not sure that it actually is at every running.

Pandas: How to detect the peak points (outliers) in a dataframe?

I am having a pandas dataframe with several of speed values which is continuously moving values, but its a sensor data, so we often get the errors in the middle at some points the moving average seems to be not helping also, so what methods can I use to remove these outliers or peak points from the data?
Example:
data points = {0.5,0.5,0.7,0.6,0.5,0.7,0.5,0.4,0.6,4,0.5,0.5,4,5,6,0.4,0.7,0.8,0.9}
in this data If I see the points 4, 4, 5, 6 are completely outlier values,
before I have used the rolling mean with 5 min of window frame to smooth these values but still I am getting these type of a lot of blip points, which I want to remove, can any one suggest me any technique to get rid of these points.
I have an image which is more clear view of data:
if you see here how the data is showing some outlier points which I have to remove?
any Idea whats the possible way to get rid of these points?
I really think z-score using scipy.stats.zscore() is the way to go here. Have a look at the related issue in this post. There they are focusing on which method to use before removing potential outliers. As I see it, your challenge is a bit simpler, since judging by the data provided, it would be pretty straight forward to identify potential outliers without having to transform the data. Below is a code snippet that does just that. Just remember though, that what does and does not look like outliers will depend entirely on your dataset. And after removing some outliers, what has not looked like an outlier before, suddenly will do so now. Have a look:
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
# your data (as a list)
data = [0.5,0.5,0.7,0.6,0.5,0.7,0.5,0.4,0.6,4,0.5,0.5,4,5,6,0.4,0.7,0.8,0.9]
# initial plot
df1 = pd.DataFrame(data = data)
df1.columns = ['data']
df1.plot(style = 'o')
# Function to identify and remove outliers
def outliers(df, level):
# 1. temporary dataframe
df = df1.copy(deep = True)
# 2. Select a level for a Z-score to identify and remove outliers
df_Z = df[(np.abs(stats.zscore(df)) < level).all(axis=1)]
ix_keep = df_Z.index
# 3. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df.loc[ix_keep]
return(df_keep)
Originial data:
Test run 1 : Z-score = 4:
As you can see, no data has been removed because the level was set too high.
Test run 2 : Z-score = 2:
Now we're getting somewhere. Two outliers have been removed, but there is still some dubious data left.
Test run 3 : Z-score = 1.2:
This is looking really good. The remaining data now seems to be a bit more evenly distributed than before. But now the data point highlighted by the original datapoint is starting to look a bit like a potential outlier. So where to stop? That's going to be entirely up to you!
EDIT: Here's the whole thing for an easy copy&paste:
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
# your data (as a list)
data = [0.5,0.5,0.7,0.6,0.5,0.7,0.5,0.4,0.6,4,0.5,0.5,4,5,6,0.4,0.7,0.8,0.9]
# initial plot
df1 = pd.DataFrame(data = data)
df1.columns = ['data']
df1.plot(style = 'o')
# Function to identify and remove outliers
def outliers(df, level):
# 1. temporary dataframe
df = df1.copy(deep = True)
# 2. Select a level for a Z-score to identify and remove outliers
df_Z = df[(np.abs(stats.zscore(df)) < level).all(axis=1)]
ix_keep = df_Z.index
# 3. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df.loc[ix_keep]
return(df_keep)
# remove outliers
level = 1.2
print("df_clean = outliers(df = df1, level = " + str(level)+')')
df_clean = outliers(df = df1, level = level)
# final plot
df_clean.plot(style = 'o')
You might cut values above a certain quantile as follows:
import numpy as np
clean_data=np.array(data_points)[(data_points<=np.percentile(data_points, 95))]
In pandas you would use df.quantile, you can find it here
Or you may use the Q3+1.5*IQR approach to eliminate the outliers, like you would do through a boxplot

How can I remove sharp jumps in data?

I have some skin temperature data (collected at 1Hz) which I intend to analyse.
However, the sensors were not always in contact with the skin. So I have a challenge of removing this non-skin temperature data, whilst preserving the actual skin temperature data. I have about 100 files to analyse, so I need to make this automated.
I'm aware that there is already this similar post, however I've not been able to use that to solve my problem.
My data roughly looks like this:
df =
timeStamp Temp
2018-05-04 10:08:00 28.63
. .
. .
2018-05-04 21:00:00 31.63
The first step I've taken is to simply apply a minimum threshold- this has got rid of the majority of the non-skin data. However, I'm left with the sharp jumps where the sensor was either removed or attached:
To remove these jumps, I was thinking about taking an approach where I use the first order differential of the temp and then use another set of thresholds to get rid of the data I'm not interested in.
e.g.
df_diff = df.diff(60) # period of about 60 makes jumps stick out
filter_index = np.nonzero((df.Temp <-1) | (df.Temp>0.5)) # when diff is less than -1 and greater than 0.5, most likely data jumps.
However, I find myself stuck here. The main problem is that:
1) I don't know how to now use this index list to delete the non-skin data in df. How is best to do this?
The more minor problem is that
2) I think I will still be left with some residual artefacts from the data jumps near the edges (e.g. where a tighter threshold would start to chuck away good data). Is there either a better filtering strategy or a way to then get rid of these artefacts?
*Edit as suggested I've also calculated the second order diff, but to be honest, I think the first order diff would allow for tighter thresholds (see below):
*Edit 2: Link to sample data
Try the code below (I used a tangent function to generate data). I used the second order difference idea from Mad Physicist in the comments.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
df = pd.DataFrame()
df[0] = np.arange(0,10,0.005)
df[1] = np.tan(df[0])
#the following line calculates the absolute value of a second order finite
#difference (derivative)
df[2] = 0.5*(df[1].diff()+df[1].diff(periods=-1)).abs()
df.loc[df[2] < .05][1].plot() #select out regions of a high rate-of-change
df[1].plot() #plot original data
plt.show()
Following is a zoom of the output showing what got filtered. Matplotlib plots a line from beginning to end of the removed data.
Your first question I believe is answered with the .loc selection above.
You second question will take some experimentation with your dataset. The code above only selects out high-derivative data. You'll also need your threshold selection to remove zeroes or the like. You can experiment with where to make the derivative selection. You can also plot a histogram of the derivative to give you a hint as to what to select out.
Also, higher order difference equations are possible to help with smoothing. This should help remove artifacts without having to trim around the cuts.
Edit:
A fourth-order finite difference can be applied using this:
df[2] = (df[1].diff(periods=1)-df[1].diff(periods=-1))*8/12 - \
(df[1].diff(periods=2)-df[1].diff(periods=-2))*1/12
df[2] = df[2].abs()
It's reasonable to think that it may help. The coefficients above can be worked out or derived from the following link for higher orders.
Finite Difference Coefficients Calculator
Note: The above second and fourth order central difference equations are not proper first derivatives. One must divide by the interval length (in this case 0.005) to get the actual derivative.
Here's a suggestion that targets your issues regarding
[...]an approach where I use the first order differential of the temp and then use another set of thresholds to get rid of the data I'm not interested in.
[..]I don't know how to now use this index list to delete the non-skin data in df. How is best to do this?
using stats.zscore() and pandas.merge()
As it is, it will still have a minor issue with your concerns regarding
[...]left with some residual artefacts from the data jumps near the edges[...]
But we'll get to that later.
First, here's a snippet to produce a dataframe that shares some of the challenges with your dataset:
# Imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
np.random.seed(22)
# A function for noisy data with a trend element
def sample():
base = 100
nsample = 50
sigma = 10
# Basic df with trend and sinus seasonality
trend1 = np.linspace(0,1, nsample)
y1 = np.sin(trend1)
dates = pd.date_range(pd.datetime(2016, 1, 1).strftime('%Y-%m-%d'), periods=nsample).tolist()
df = pd.DataFrame({'dates':dates, 'trend1':trend1, 'y1':y1})
df = df.set_index(['dates'])
df.index = pd.to_datetime(df.index)
# Gaussian Noise with amplitude sigma
df['y2'] = sigma * np.random.normal(size=nsample)
df['y3'] = df['y2'] + base + (np.sin(trend1))
df['trend2'] = 1/(np.cos(trend1)/1.05)
df['y4'] = df['y3'] * df['trend2']
df=df['y4'].to_frame()
df.columns = ['Temp']
df['Temp'][20:31] = np.nan
# Insert spikes and missing values
df['Temp'][19] = df['Temp'][39]/4000
df['Temp'][31] = df['Temp'][15]/4000
return(df)
# Dataframe with random data
df_raw = sample()
df_raw.plot()
As you can see, there are two distinct spikes with missing numbers between them. And it's really the missing numbers that are causing the problems here if you prefer to isolate values where the differences are large. The first spike is not a problem since you'll find the difference between a very small number and a number that is more similar to the rest of the data:
But for the second spike, you're going to get the (nonexisting) difference between a very small number and a non-existing number, so that the extreme data-point you'll end up removing is the difference between your outlier and the next observation:
This is not a huge problem for one single observation. You could just fill it right back in there. But for larger data sets that would not be a very viable soution. Anyway, if you can manage without that particular value, the below code should solve your problem. You will also have a similar problem with your very first observation, but I think it would be far more trivial to decide whether or not to keep that one value.
The steps:
# 1. Get some info about the original data:
firstVal = df_raw[:1]
colName = df_raw.columns
# 2. Take the first difference and
df_diff = df_raw.diff()
# 3. Remove missing values
df_clean = df_diff.dropna()
# 4. Select a level for a Z-score to identify and remove outliers
level = 3
df_Z = df_clean[(np.abs(stats.zscore(df_clean)) < level).all(axis=1)]
ix_keep = df_Z.index
# 5. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df_raw.loc[ix_keep]
# 6.
# df_keep will be missing some indexes.
# Do the following if you'd like to keep those indexes
# and, for example, fill missing values with the previous values
df_out = pd.merge(df_keep, df_raw, how='outer', left_index=True, right_index=True)
# 7. Keep only the first column
df_out = df_out.ix[:,0].to_frame()
# 8. Fill missing values
df_complete = df_out.fillna(axis=0, method='ffill')
# 9. Replace first value
df_complete.iloc[0] = firstVal.iloc[0]
# 10. Reset column names
df_complete.columns = colName
# Result
df_complete.plot()
Here's the whole thing for an easy copy-paste:
# Imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
np.random.seed(22)
# A function for noisy data with a trend element
def sample():
base = 100
nsample = 50
sigma = 10
# Basic df with trend and sinus seasonality
trend1 = np.linspace(0,1, nsample)
y1 = np.sin(trend1)
dates = pd.date_range(pd.datetime(2016, 1, 1).strftime('%Y-%m-%d'), periods=nsample).tolist()
df = pd.DataFrame({'dates':dates, 'trend1':trend1, 'y1':y1})
df = df.set_index(['dates'])
df.index = pd.to_datetime(df.index)
# Gaussian Noise with amplitude sigma
df['y2'] = sigma * np.random.normal(size=nsample)
df['y3'] = df['y2'] + base + (np.sin(trend1))
df['trend2'] = 1/(np.cos(trend1)/1.05)
df['y4'] = df['y3'] * df['trend2']
df=df['y4'].to_frame()
df.columns = ['Temp']
df['Temp'][20:31] = np.nan
# Insert spikes and missing values
df['Temp'][19] = df['Temp'][39]/4000
df['Temp'][31] = df['Temp'][15]/4000
return(df)
# A function for removing outliers
def noSpikes(df, level, keepFirst):
# 1. Get some info about the original data:
firstVal = df[:1]
colName = df.columns
# 2. Take the first difference and
df_diff = df.diff()
# 3. Remove missing values
df_clean = df_diff.dropna()
# 4. Select a level for a Z-score to identify and remove outliers
df_Z = df_clean[(np.abs(stats.zscore(df_clean)) < level).all(axis=1)]
ix_keep = df_Z.index
# 5. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df_raw.loc[ix_keep]
# 6.
# df_keep will be missing some indexes.
# Do the following if you'd like to keep those indexes
# and, for example, fill missing values with the previous values
df_out = pd.merge(df_keep, df_raw, how='outer', left_index=True, right_index=True)
# 7. Keep only the first column
df_out = df_out.ix[:,0].to_frame()
# 8. Fill missing values
df_complete = df_out.fillna(axis=0, method='ffill')
# 9. Reset column names
df_complete.columns = colName
# Keep the first value
if keepFirst:
df_complete.iloc[0] = firstVal.iloc[0]
return(df_complete)
# Dataframe with random data
df_raw = sample()
df_raw.plot()
# Remove outliers
df_cleaned = noSpikes(df=df_raw, level = 3, keepFirst = True)
df_cleaned.plot()

Questions on pandas moving average

I am a beginner of python and pandas. I am having difficulty with making volatility adjusted moving average, so I need your help.
Volatility adjusted moving average is a kind of moving average, of which moving average period is not static, but dynamically adjusted according to volatility.
What I'd like to code is,
Get stock data from yahoo finance (monthly close)
Calculate monthly volatility X some constant --> use variables of dynamic moving average period
Calculate dynamic moving average
I've tried this code, but only to fail. I don't know what the problem is. If you know the problem, or any better code suggestion, please let me know.
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import pandas_datareader.data as web
def price(stock, start):
price = web.DataReader(name=stock, data_source='yahoo', start=start)['Adj Close']
price = price / price[0]
a = price.resample('M').last().to_frame()
a.columns = ['price']
return a
a = price('SPY','2000-01-01')
a['volperiod'] = round(a.rolling(12).std()*100)*2
for i in range(len(a.index)):
k = a['price'].rolling(int(a['volperiod'][i])).mean()
a['ma'][i] = k[i]
print(a)
first of all: you need to calculate pct_change on price to calculate volatility of returns
my solution
def price(stock, start):
price = web.DataReader(name=stock, data_source='yahoo', start=start)['Adj Close']
return price.div(price.iat[0]).resample('M').last().to_frame('price')
a = price('SPY','2000-01-01')
v = a.pct_change().rolling(12).std().dropna().mul(200).astype(int)
def dyna_mean(x):
end = a.index.get_loc(x.name)
start = end - x.price
return a.price.iloc[start:end].mean()
pd.concat([a.price, v.price, v.apply(dyna_mean, axis=1)],
axis=1, keys=['price', 'vol', 'mean'])

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