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4. You have observed the following returns for Market, Apple, and Microsoft for last 3 vearS: Period Market 0.12 0.10 0.09 0.15 0.10 0.13 Microsoft 0.07 0.05 0.03 a) Calculate the markets return and standard deviation. Write out all the setups for each calculation. Use sample standard deviation formula. b) Calculate both the sample covariance and correlation coefficient between the market and Apple, and between the market and Microsoft. Write out all the setups for each calculation Calculate the betas for Apple and Microsoft, respectively, using i) ơw, ii) piw, iii) using slope function, and iv) using regression function on Excel. c) ƠM FINC 323 FINANCIAL MANAGEMENT 2 d) Calculate portfolio beta of Apple and Microsoft with equal weight (0.5) for each

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Calculation of average return and standard deviation of market:Period Mark et Apple Microsoft 0.15 0.1 0.13 0.12 0.1 0.09 0.07 0.05 0.03 2 10 Year Market Return 12.0%) 10.0% 9.0% 12 13 14 15 16 17 Average return can be calculated as follows: (Sum of returns)/Number of periods -(12.0%+10%+9.0%)/3 Average return 10.33% Hence Average market return is 10.33% Standard deviation should be calculated using the sample standard deviation formula Sample standard deviation is given by 21 23 Standard Deviation (o)- 26 27 n- Given, n-3, average return (r-bar) of 10.33 and the following data: 31 32 Stock Returns 12.0%) 10.0% 9.0% Standard deviation can be calculated as below: 35 36 37 38 39 Standard Deviation () (12.09.0-10.33%),t(1000-10.33%+(9.000-10.33%)2 41 42 43 = 1.52890 Hence Standard Deviation of market is 1.528%

Calculation of Covariance and Beta:47 49 Period Market AppleMicrosc 51 52 53 12.00% | 10.00%) 9.00% | 10.33%) 15.00%) 10.00%) 13.00% | 12.67% 7.00% 5.00% 3.00% 5.00% 2 3| Average Return 57 59 Covariance (Market, Apple) 3(12%-10.33%)(15%-12.67%)+(10%-10.33%)(10%-12.67%)+(13%-10.33%) (13%-12.67%))/(3-1) 61 0.0283% 3(12%-10.33%)( 7%-5%)+(10%-10.33%)(5%-5%)+(13%-10.33%) (3%-5%))/(3-1) -0.0100% 63 Covariance (Market, Microsoft -Covariance (Market, Apple)/Variance of market :0.0283%/(1.5289602) Beta For Apple 1.21 71 72 73 74. 75 76 Covariance (Market, Microsoft)/Variance of market -0.0100%/( 1.528%2) Beta for Microsoft 0.43 Hence Beta for Apple Beta for Microsoft 1.21 -0.43 79Formula sheet

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