Could you please explain how the returns were calculated?

Date 1/3/2012 2/1/2012 3/1/2012 4/2/2012 5/1/2012 6/1/2012 7/2/2012 8/1/2012 9/4/2012 10/1/2012 11/1/2012 12/3/2012 1/2/2013 2/1/2013 3/1/2013 4/1/2013 5/1/2013 6/3/2013 7/1/2013 8/1/2013 9/3/2013 10/1/2013 11/1/2013 12/2/2013 1/2/2014 2/3/2014 3/3/2014 4/1/2014 5/1/2014 6/2/2014 7/1/2014 8/1/2014 9/2/2014 10/1/2014 11/3/2014 12/1/2014 1/2/2015 2/2/2015 3/2/2015 4/1/2015 5/1/2015 6/1/2015 7/1/2015 8/3/2015 9/1/2015 10/1/2015 11/2/2015 12/1/2015 DATA MRK 24 NKE GSPC -0.00261305 0.01723943 0.02187488 -0.04230367 0.12310495 0.05796397 -0.02535652 0.05759411 0.01175166 -0.02914750 -0.06698228 0.05642416 -0.01202314 0.04437272 0.06334840 -0.00638294 0.00378164 0.03702901 -0.01826861 0.01584055 -0.05293005 0.10512309 0.01352535 0.05834168 0.07589199 0.00391506 0.03153075 -0.01195353 0.00736391 -0.01918748 0.05939369 -0.00661434 -0.02260459 0.04245774 -0.05266077 0.06145442 -0.02886523 -0.01016172 0.03618653 0.02233038 -0.05792355 0.03565778 -0.08666892 -0.07492646 0.10670171 -0.03018664 0.00502658 -0.0663200 -0.7902320 -0.1823810 -1.7938380 -5.8789750 0.3321510 0.0443040 -1.5881000 -1.8473450 0.4642520 0.4800090 0.1812800 -0.7004450 1.2023160 1.2216800 -1.8390830 -0.0189930 -1.3690930 -0.9471260 3.7849060 0.5202560 0.6469420 -1.1235730 -3.8300860 1.7813870 -3.1768790 -1.4461670 1.0605770 -0.6852230 -1.2065770 -0.1849290 4.2538680 0.8598250 2.1177910 -2.4126480 -2.9294850 1.5487440 0.5927200 -1.7393030 0.5419000 2.1593100 2.5822100 -2.7264250 4.7374190 3.0202520 -0.3765100 -4.4800570 0.04058946 0.03133231 -0.00749745 -0.06265073 0.03955498 0.01259757 0.01976337 0.02423615 -0.01978941 0.00284672 0.00706823 0.05042810 0.01106065 0.03598772 0.01808577 0.02076281 -0.01499930 0.04946208 -0.03129802 0.02974952 0.04459575 0.02804947 0.02356279 -0.03558291 0.04311703 0.00693217 0.00620079 0.02103028 0.01905833 -0.01507983 0.03765530 -0.01551384 0.02320146 0.02453359 -0.00418859 -0.03104081 0.05489251 -0.01739611 0.00852082 0.01049138 -0.02101167 0.01974203 -0.06258082 -0.02644283 0.08298312 0.00050487 -0.01753019 0.01100990 -0.1958658 0.00991478 0.0023080799 a. i AVERAGE ii VARIANCE 4.7058474264 0.0009106589 iii S.DEVIATION 0.0480424804 2.169296528 NKE is has the highest risk and the lowest returns. 0.0301771259 b. i ii COVARIANCE COR .COEFFICIENT MRK 24 &NKE MRK 24 & GSPC NKE & GSPC -0.0129644957 0.000706978 0.0179600747 -0.1243973948 0.4876436529 0.2743540287 Correration between MRK 24 & NKE show negative relationship while the rest have a postive relationship c i ii AVERAGE RETURN PORTFOLIO S.DEV MRK 24 & GSPC 0.0104623385 0.034031951 d. i ii AVERAGE RETURN PORTFOLIO S.DEV MRK 24, NKE &GSPC -0.0596892387 0.7386619463 iii No, nike is not a good addition because it has increased portfolio risk and lowered the prortfolio expected return e. MRK BETA 0.7763367094 f NKE BETA 19.7220651166 FIN 5130 Mini-Case Instructor: Dr. Palkar Late assignments will not be accepted so please plan accordingly. You need to show your working notes for credit. You must submit your work using excel files (with .xls or .xlsx for credit). You must upload your files on Blackboard under the Assignment Dropbox for credit. This assignment will require you to analyze time series of monthly returns. Start by retrieving MONTHLY data for the period of 1 January, 2012 - December 31, 2015 from Yahoo website for S&P 500 Index (ticker: ^GSPC) Merck & Co. Inc (ticker: MRK) Nike (ticker: NKE) Instructions for downloading the data from Yahoo!: To obtain the monthly data, click on \"Historical Prices\" on the left panel. Select Date Range. Make sure Monthly is selected and then click on \"Get Prices\". Scroll down and click on \"Download to Spreadsheet\". Instructions for sorting the data by DATE: Re-sort the data so that the most previous date is at the bottom of your spreadsheet (i.e. highlight DATE columns and click on SORT, make sure you \"Expand the selection\" is selected, then click on SORT and sort by Date and order by 'Oldest to Newest'). First Calculate Returns: Use the 'Adjusted Close' column to obtain returns for each period. Remember that the Adjusted Close column has already adjusted the prices for dividends and stock splits so you do not have to adjust for it again. Just use the adjusted close column to obtain the returns. Rt = Pt 1 Pt 1 Solve for the following: A. Calculate the average, variance and standard deviation for the returns of each series. Comment on the statistics. B. Calculate the covariance and the correlation coefficient between each of the return series (there should be a total of three correlations and three covariances). Comment on the statistics. C. If you were to form a portfolio that had 50% of the S&P 500 Index and 50% of Merck, what would be the average returns and the standard deviation of that portfolio? (Ignore the fact that both Merck may already be included in the S&P 500) D. If you were to add Nike to your portfolio so that you now had 33% S&P 500, 33% Merck, and 34% Nike, what would be the new average returns and standard Page 1 of 2 FIN 5130 Mini-Case Instructor: Dr. Palkar deviation? (Ignore the fact that both Nike and Merck may already be included in the S&P 500) Is Nike a good addition to your portfolio? Why do you think so? E. Determine MRK's beta. F. Determine Nike's beta. Page 2 of 2