By Christopher van Hoecke and Max Margenot
https://www.quantopian.com/lectures/means
This lecture corresponds to the Means lecture, which is part of the Quantopian lecture series. This homework expects you to rely heavily on the code presented in the corresponding lecture. Please copy and paste regularly from that lecture when starting to work on the problems, as trying to do them from scratch will likely be too difficult.
Part of the Quantopian Lecture Series:
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# Useful Functions
def mode(l):
# Count the number of times each element appears in the list
counts = {}
for e in l:
if e in counts:
counts[e] += 1
else:
counts[e] = 1
# Return the elements that appear the most times
maxcount = 0
modes = {}
for (key, value) in counts.items():
if value > maxcount:
maxcount = value
modes = {key}
elif value == maxcount:
modes.add(key)
if maxcount > 1 or len(l) == 1:
return list(modes)
return 'No mode'
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# Useful Libraries
import scipy.stats as stats
import numpy as np
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l=[]
for x in range(1,100):
x=np.random.randint(1,100)
l.append(x)
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## Your code goes here
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price = get_pricing('ITI', fields='price', start_date='2005-01-01', end_date='2010-01-01')
returns = price.pct_change()[1:]
## Your code goes here.
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## Your code goes here
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price = get_pricing('BAC', fields='open_price', start_date='2005-01-01', end_date='2010-01-01')
returns = price.pct_change()[1:]
## Your code goes here
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## Your code goes here
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start = '2014-01-01'
end = '2015-01-01'
pricing = get_pricing('GS', fields='price', start_date=start, end_date=end)
returns = pricing.pct_change()[1:]
## Your code goes here
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## Your code goes here
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price = get_pricing('C', fields='open_price', start_date='2005-01-01', end_date='2010-01-01')
## Your code goes here
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## Your code goes here
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## Your code goes here
Skewness in a probability distribution is the measure of asymmetry. Negative skew has fewer low values and a longer left tail, whereas positive skew has fewer high values and a longer right tail. In asset pricing, skewness is an important information, naimly in risk assessment. Knowledge that the market has a 60% chance of going down and a 40% chance of going up apears helpfull but only if we know the market is obeying a normal distrubtuion. If we are told that the market will go up 2% but down 18%, we can see how skewness would give us better information.
Determine if the returns of SPY from 2010 to 2017 is positivly or negativly skewed. Recall a data set is positivly skewed if the mode is smaller than the median, which is smaller than the mean. A data set is negativly skewed in the event of the reverse (i.e: the mean is greater than the median, which is greater than the mode)
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price = get_pricing('SPY', fields='volume', start_date='2010-01-01', end_date='2017-01-01')
returns = price.pct_change()[1:]
## Your code goes here
We can clearly see positive skewing from the histogram of the returns. We see fewer higher values and a longer right tail. Plot the histograms of the returns now.
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## Your code here
Congratulations on completing the Means exercises!
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