https://www.quantopian.com/lectures/linear-correlation-analysis
This lecture corresponds to the Linear Correlation Analysis 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:
# Useful Functions
def find_most_correlated(data):
n = data.shape[1]
keys = data.keys()
pair = []
max_value = 0
for i in range(n):
for j in range(i+1, n):
S1 = data[keys[i]]
S2 = data[keys[j]]
result = np.corrcoef(S1, S2)[0,1]
if result > max_value:
pair = (keys[i], keys[j])
max_value = result
return pair, max_value
# Useful Libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
A = np.random.rand(100)
B = -3 * A + np.random.exponential(0.05, 100)
#Your code goes here
By reading the matrix output from the np.cov() and np.corrcoef() functions, find the variance of the variables $C$ and $D$ and the covariance and correlation of their relationship.
C = np.random.rand(100)
D = np.random.normal(0, 0.5, 100)
#Your code goes here
X = np.random.rand(100)
#Your code goes here
Construct a variable $W$ which has a weak, negative correlation with $Z$ $(-0.3 < Corr(Z,W) < 0)$, and plot their relationship.
Z = np.random.rand(100)
#Your code goes here
OKE = get_pricing('OKE', fields='price', start_date='2013-01-01', end_date='2015-01-01')
LAKE = get_pricing('LAKE', fields='price', start_date='2013-01-01', end_date='2015-01-01')
benchmark = get_pricing('SPY', fields='price', start_date='2013-01-01', end_date='2015-01-01')
#Your code goes here
Find the most correlated pair of stocks in the following portfolio using 2015 pricing data and the find_most_correlated function defined in the Helper Functions section above.
symbol_list = ['GSK', 'SNOW', 'FB', 'AZO', 'XEC', 'AMZN']
data = get_pricing(symbol_list, fields=['price']
, start_date='2015-01-01', end_date='2016-01-01')['price']
data.columns = symbol_list
#Your code goes here
FB_15 = get_pricing('FB', fields='price', start_date='2015-01-01', end_date='2016-01-01')
AMZN_15 = get_pricing('AMZN', fields='price', start_date='2015-01-01', end_date='2016-01-01')
FB_16 = get_pricing('FB', fields='price', start_date='2016-01-01', end_date='2016-07-01')
AMZN_16 = get_pricing('AMZN', fields='price', start_date='2016-01-01', end_date='2016-07-01')
#Your code goes here
Plot the 60-day rolling correlation coefficient between FB and AMZN to make a conclusion about the stability of their relationship.
FB = get_pricing('FB', fields='price', start_date='2015-01-01', end_date='2017-01-01')
AMZN = get_pricing('AMZN', fields='price', start_date='2015-01-01', end_date='2017-01-01')
#Your code goes here
Congratulations on completing the Linear Correlation Analysis exercises!
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