Question: This problem, similar to problem 7-3 from the text, extends that problem to illustrate the impact of different weights, and correlations on the standard deviation
This problem, similar to problem 7-3 from the text, extends that problem to illustrate the impact of different weights, and correlations on the standard deviation of two-security portfolios. Assignment: You are provided with multiple year return information for four scenarios in parts a) through d). Please calculate the expected returns, variances, standard deviations, covariances, and correlations for each part. The answers are provide for your guidance but you must replace the raw numbers with the appropriate equations or Excel functions. Please note that when you assign weights for a two-security portfolio, one weight will be "x" and the other will be "1-x". Graph the results for each each part placing the standard deviations on the horizontal axis and returns on verticle axis. Part a) Zenon Dynamics Year Zenon Returns Dynamics Returns 0.0989 -0.4767 2019 -0.1234 0.3079 2018 0.1356 0.2478 2017 0.3456 0.0789 2016 -0.1523 0.2442 2015 0.2009 0.3456 2014 0.0756 0.6756 2013 0.1647 0.4467 2012 0.1834 0.7856 2011 0.1556 0.51 2010 Expected Return 10.85% 31.66% Variance 2.22% 12.22% 14.89% 34.96% Standard Deviation 14.89% 34.96% Covarianace 0.14% Correlation 0.027 Weight Zenon 0.5 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Weight Dynamics 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Expected Portfolio Return 0.21251 0.10846 0.12927 0.15008 0.17089 0.1917 0.21251 0.23332 0.25413 0.27494 0.29575 Portfolio Variance 0.036798681 0.022160472 0.019426268 0.019523 0.022451 0.028209 0.036799 0.048219 0.06247 0.079553 0.099466 Portfolio Standard Deviation 0.191829823 0.148863936 0.139378148 0.139725 0.149835 0.167956 0.19183 0.219588 0.249941 0.282051 0.315382 Part b) Sunglasses Umbrellas Year Returns Returns 0.05 1 2019 0.1 0.9 2018 0.15 0.8 2017 0.2 0.7 2016 0.25 0.6 2015 0.3 0.5 2014 0.35 0.4 2013 0.4 0.3 2012 0.45 0.2 2011 0.5 0.1 2010 Expected Return 27.50% 55.00% Variance 2.29% 9.17% Standard Deviation 15.14% 30.28% Covarianace -4.58% Correlation -1 Weight Sunglasses 0.5 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -1E-15 Weight Umbrella 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Expected Portfolio Return 0.4125 0.275 0.3025 0.33 0.3575 0.385 0.4125 0.44 0.4675 0.495 0.5225 0.55 Portfolio Variance 0.005729167 0.022916667 0.011229167 0.003667 0.000229 0.000917 0.005729 0.014667 0.027729 0.044917 0.066229 0.091667 Portfolio Standard Deviation 0.075691259 0.151382518 0.105967762 0.060553 0.015138 0.030277 0.075691 0.121106 0.166521 0.211936 0.25735 0.302765 Part c) Rain Coats Umbrellas Year Returns Returns 0.5 0.5 2019 0.45 0.45 2018 0.4 0.4 2017 0.35 0.35 2016 0.3 0.3 2015 0.25 0.25 2014 0.2 0.2 2013 0.15 0.15 2012 0.1 0.1 2011 0.05 0.05 2010 Expected Return 27.50% 27.50% Variance 2.29% 2.29% Standard Deviation 15.14% 15.14% Covarianace 2.29% Correlation 1 Weight Rain Coats 0.5 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -1E-15 Weight Umbrella 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Expected Portfolio Return 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 Portfolio Variance 0.022916667 0.022916667 0.022916667 0.022917 0.022917 0.022917 0.022917 0.022917 0.022917 0.022917 0.022917 0.022917 Portfolio Standard Deviation 0.151382518 0.151382518 0.151382518 0.151383 0.151383 0.151383 0.151383 0.151383 0.151383 0.151383 0.151383 0.151383 Part d) Vacumn Umbrellas Year Returns Returns 0.275 0.5 2019 0.275 0.45 2018 0.275 0.4 2017 0.275 0.35 2016 0.275 0.3 2015 0.275 0.25 2014 0.275 0.2 2013 0.275 0.15 2012 0.275 0.1 2011 0.275 0.05 2010 Expected Return 27.50% 27.50% Variance 0.00% 2.29% Standard Deviation 0.00% 15.14% Covarianace 0.00% Correlation 0.00% Weight Vacumn 0.5 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -1E-15 Weight Umbrella 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Expected Portfolio Return 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 0.275 Portfolio Variance 0.005729167 3.42388E-33 0.000229167 0.000917 0.002063 0.003667 0.005729 0.00825 0.011229 0.014667 0.018563 0.022917 Portfolio Standard Deviation 0.075691259 5.85139E-17 0.015138252 0.030277 0.045415 0.060553 0.075691 0.09083 0.105968 0.121106 0.136244 0.151383
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