Exercises: Linear Correlation Analysis

Lecture Link :

https://www.quantopian.com/lectures/linear-correlation-analysis

IMPORTANT NOTE:

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:

Key Concepts



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# 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



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# Useful Libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

Exercise 1: Dependence of Artificial Variables

a. Finding Variance, Covariance, and Correlation I

By reading the matrix output from the np.cov() and np.corrcoef() functions, find the variance of the variables $A$ and $B$ and the covariance and correlation of their relationship.



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A = np.random.rand(100)
B = -3 * A + np.random.exponential(0.05, 100)

#Your code goes here

b. Finding Variance, Covariance, and Correlation II

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.



In [ ]:

    
C = np.random.rand(100)
D = np.random.normal(0, 0.5, 100)

#Your code goes here

Exercise 2: Constructing Example Relationships

a. Positive Correlation Example

Construct a variable $Y$ which has a strong, but not perfect, positive correlation with $X$ $(0.9 < Corr(X,Y) < 1)$, and plot their relationship.



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X = np.random.rand(100)

#Your code goes here

b. Negative Correlation Example

Construct a variable $W$ which has a weak, negative correlation with $Z$ $(-0.3 < Corr(Z,W) < 0)$, and plot their relationship.



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Z = np.random.rand(100)

#Your code goes here

Exercise 3: Correlation of Real Assets

a. Finding Correlation of Real Assets

Find the correlation between the stocks OKE and LAKE. Also check how they correlate with the provided benchmark.



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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

b. Finding Correlated Pairs

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.



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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

Exercise 4: Limitations of Correlation

a. Out of Sample Tests

Using pricing data from the first half of 2016, find the correlation coefficient between FB and AMZN and compare it to the strong positive relationship predicted from the 2015 correlation coefficient to see if that result holds.



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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

b. Rolling Correlation

Plot the 60-day rolling correlation coefficient between FB and AMZN to make a conclusion about the stability of their relationship.



In [ ]:

    
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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