Exercises: Variance

By Christopher van Hoecke, Maxwell Margenot, and Delaney Mackenzie

Lecture Link :

https://www.quantopian.com/lectures/variance

IMPORTANT NOTE:

This lecture corresponds to the Variance 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 Libraries
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

Data:



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X = np.random.randint(100, size = 100)

Exercise 1:

Using the skills aquired in the lecture series, find the following parameters of the list X above:

Range
Mean Absolute Deviation
Variance and Standard Deviation
Semivariance and Semideviation
Target variance (with B = 60)



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# Range of X
range_X =

## Your code goes here
print 'Range of X: %s' %(range_X)



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# Mean Absolute Deviation
# First calculate the value of mu (the mean)

mu = np.mean(X)

## Your code goes here
print 'Mean absolute deviation of X:', MAD



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# Variance and standard deviation

## Your code goes here

print 'Variance of X:',
print 'Standard deviation of X:',



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# Semivariance and semideviation

## Your code goes here

print 'Semivariance of X:', 
print 'Semideviation of X:',



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# Target variance

## Your code goes here

print 'Target semivariance of X:',
print 'Target semideviation of X:',

Exercise 2:

Using the skills aquired in the lecture series, find the following parameters of prices for AT&T stock over a year:

30 days rolling variance
15 days rolling Standard Deviation



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att = get_pricing('T', fields='open_price', start_date='2016-01-01', end_date='2017-01-01')



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# Rolling mean

## Your code goes here



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# Rolling standard deviation

## Your code goes here

Exercise 3 :

The portfolio variance is calculated as

$$\text{VAR}_p = \text{VAR}_{s1} (w_1^2) + \text{VAR}_{s2}(w_2^2) + \text{COV}_{S_1, S_2} (2 w_1 w_2)$$

Where $w_1$ and $w_2$ are the weights of $S_1$ and $S_2$.

Find values of $w_1$ and $w_2$ to have a portfolio variance of 50.



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asset1 = get_pricing('AAPL', fields='open_price', start_date='2016-01-01', end_date='2017-01-01')
asset2 = get_pricing('XLF', fields='open_price', start_date='2016-01-01', end_date='2017-01-01')

cov = np.cov(asset1, asset2)[0,1]

w1 = ## Your code goes here.
w2 = 1 - w1

v1 = np.var(asset1)
v2 = np.var(asset2)

pvariance = (w1**2)*v1+(w2**2)*v2+(2*w1*w2)*cov

print 'Portfolio variance: ', pvariance

Congratulations on completing the Variance exercises!

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