Exercise Solution file

Author: PyDataBlog

Tutorials/Exercise Solution.py

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+#  Import numpy
+import numpy as np
+
+#  store the variables in arrays
+prob = np.array([0.25, 0.5, 0.25])
+rate_1 = np.array([0.05, 0.075, 0.10])
+rate_2 = np.array([0.2, 0.15, 0.1])
+
+#  expected return of each investment
+expected_return1 = np.sum(prob * rate_1)
+expected_return2 = np.sum(prob * rate_2)
+
+#  expected return of the equally weighted portfolio
+weights = np.array([0.5, 0.5])
+individual_returns = np.array([expected_return1, expected_return2])
+portfolio_returns = np.dot(weights, individual_returns)
+
+#  covariance matrix given probabilities
+cov_matrix = np.cov(rate_1, rate_2, ddof=0, aweights=prob)
+
+#  variance and standard deviation of each investment
+var1 = cov_matrix[0,0]
+var2 = cov_matrix[1,1]
+std1 = np.sqrt(var1)
+std2 = np.sqrt(var2)
+
+#  correlation between Asset 1 & 2's returns
+cov = cov_matrix[0,1]
+corr = cov / (std1 * std2)
+
+#  variance of portfolio
+portfolio_var = np.dot(weights.T, np.dot(cov_matrix, weights))
+
+#  standard deviation (volatility of the portfolio)
+portfolio_vols = np.sqrt(portfolio_var)
+
+def percentage (number):
+    return str(round(number, 4) * 100) + '%'
+
+print('Expected Return of Investment 1 = {}'.format(percentage(expected_return1)))
+print('Expected Return of Investment 2 = {}'.format(percentage(expected_return2)))
+print('Expected Return of Portfolio = {}'.format(percentage(portfolio_returns)))
+print('Standard Deviation of Investment 1 = {}'.format(percentage(std1)))
+print('Standard Deviation of Investment 1 = {}'.format(percentage(std2)))
+print('Correlation between Returns of 1 & 2 = {}'.format(round(corr, 4)))
+print('Risk of Portfilio = {}'.format(percentage(portfolio_vols)))