Create RTNS by reading RTNS.cvs file using R or R Studio. The RTNS includes monthly log stock returns of 4 firms from January 2006 to December 2016. Use the packages as follows: install.packages("tseries") install.packages("xts") library(tseries) library(xts)

Convert RTNS to xts object and assign the name rtns to the new object as follows:

rtns <- as.xts(RTNS[, -1], order.by = as.Date(RTNS$Date, "%m/%d/%Y"))

Using rtns above, find mean-variance efficient portfolio with target return 0.5%, and answer the following questions #1 and #2.

1) What is the standard deviation of the mean-variance portfolio?

2) What are the weights of the mean-variance efficient portfolio?

Date	AAPL	BA	IBM	MSFT
1/31/2006	0.05035466	-0.027477229	-0.010948827	0.076481848
2/28/2006	-0.092967797	0.068600054	-0.010559962	-0.042236151
3/31/2006	-0.084245858	0.072086913	0.027791668	0.012653479
4/30/2006	0.12228963	0.07083275	-0.001576388	-0.112458643
5/31/2006	-0.150873826	0.001016347	-0.026124977	-0.058454549
6/30/2006	-0.041826858	-0.016096053	-0.038548207	0.028697558
7/31/2006	0.186659582	-0.054816327	0.007680331	0.032618026
8/31/2006	-0.001618618	-0.028821576	0.05016056	0.072096445
9/30/2006	0.134561532	0.052736932	0.011979752	0.06420235
10/31/2006	0.053260615	0.012809166	0.126800085	0.04972572
11/30/2006	0.130488423	0.112498449	-0.001210044	0.026136449
12/31/2006	-0.074405446	0.003501601	0.056897331	0.017029974
1/31/2007	0.010490367	0.008104479	0.020586722	0.03348962
2/28/2007	-0.013064246	-0.021918393	-0.059807537	-0.084002722
3/31/2007	0.098097031	0.018909018	0.014202714	-0.010649612
4/30/2007	0.074157836	0.046001541	0.084341146	0.074273412
5/31/2007	0.214328642	0.085646158	0.04701053	0.028370694
6/30/2007	0.007013861	-0.044040088	-0.012664154	-0.039752402
7/31/2007	0.079645944	0.075603126	0.051306425	-0.016287772
8/31/2007	0.051001896	-0.061887293	0.058315335	-0.005494917
9/30/2007	0.108246615	0.085729071	0.009512391	0.025408948
10/31/2007	0.237701173	-0.060958192	-0.014261464	0.24949091
11/30/2007	-0.040694874	-0.057990518	-0.091000025	-0.084186728
12/31/2007	0.087037572	-0.054895194	0.02776191	0.059523818
1/31/2008	-0.316639713	-0.048936646	-0.009158162	-0.084269639
2/29/2008	-0.076388878	0.000208909	0.067083566	-0.162402148
3/31/2008	0.147816303	-0.101703077	0.01124187	0.043382299
4/30/2008	0.212195158	0.141051465	0.048289022	0.004933096
5/31/2008	0.085081861	-0.020079002	0.076711356	-0.00335712
6/30/2008	-0.112900612	-0.205992458	-0.084215366	-0.028601704
7/31/2008	-0.050704684	-0.070146087	0.0797267	-0.065067247
8/31/2008	0.066561722	0.079441839	-0.045131007	0.065273905
9/30/2008	-0.329558176	-0.125228785	-0.039185114	-0.021986067
10/31/2008	-0.053404911	-0.085963401	-0.205112839	-0.163357064
11/30/2008	-0.13867459	-0.180648473	-0.117390866	-0.088357519
12/31/2008	-0.078989982	0.000938255	0.031372626	-0.038575606
1/31/2009	0.056004716	-0.008436773	0.088997114	-0.120370418
2/28/2009	-0.009097991	-0.249423566	0.009608836	-0.049079933
3/31/2009	0.177023871	0.131679447	0.052808878	0.137461408
4/30/2009	0.197012917	0.125632291	0.065228607	0.102885061
5/31/2009	0.079313378	0.130857413	0.035123743	0.037643969
6/30/2009	0.048744577	-0.052396857	-0.017500952	0.137865084
7/31/2009	0.147160013	0.009647058	0.129381372	-0.010517461
8/31/2009	0.029499987	0.168653886	0.005686444	0.053937093
9/30/2009	0.101896403	0.090195364	0.013214713	0.04340769
10/31/2009	0.016994908	-0.117266884	0.008360513	0.078149341
11/30/2009	0.060530481	0.106101773	0.052292951	0.065272296
12/31/2009	0.054124377	0.032818181	0.03601104	0.036382151
1/31/2010	-0.088596802	0.119527015	-0.065011422	-0.075459299
2/28/2010	0.0653962	0.04935973	0.043620765	0.022145787
3/31/2010	0.148470432	0.149620018	0.008571855	0.021625418
4/30/2010	0.111021236	-0.002478987	0.005847952	0.042676699
5/31/2010	-0.016124692	-0.108760623	-0.024015071	-0.151394375
6/30/2010	-0.02082688	-0.022281088	-0.014210434	-0.108139494
7/31/2010	0.022740819	0.085896404	0.039844431	0.121686211
8/31/2010	-0.05500482	-0.097425153	-0.036291882	-0.085811757
9/30/2010	0.167215077	0.088499912	0.089417705	0.043459748
10/31/2010	0.060722478	0.06161704	0.070523382	0.089015952
11/30/2010	0.03378966	-0.0917872	-0.010524941	-0.0470488
12/31/2010	0.036670426	0.023365239	0.037466331	0.104908941
1/31/2011	0.051959268	0.064664433	0.103843053	-0.006449333
2/28/2011	0.040934839	0.042434823	0.003215704	-0.035805821
3/31/2011	-0.013306536	0.026662938	0.007351138	-0.044770529
4/30/2011	0.004648327	0.079128897	0.046053808	0.020874363
5/31/2011	-0.006569	-0.016770149	-0.005244188	-0.028783478
6/30/2011	-0.034959556	-0.052543874	0.015509445	0.03958417
7/31/2011	0.163285319	-0.046801016	0.060040822	0.053846124
8/31/2011	-0.014469326	-0.044792	-0.050543842	-0.023069687
9/30/2011	-0.009120937	-0.094974606	0.017218264	-0.064285744
10/31/2011	0.061523129	0.087258354	0.055812944	0.069907609
11/30/2011	-0.055783399	0.050736954	0.022345982	-0.032195981
12/31/2011	0.05965467	0.067840951	-0.021914866	0.014855309
1/31/2012	0.127111049	0.011315634	0.047422236	0.137519345
2/29/2012	0.18831065	0.016326706	0.025420946	0.081915037
3/31/2012	0.105283507	-0.007738413	0.060590651	0.016383072
4/30/2012	-0.025969512	0.032674475	-0.007524524	-0.00743948
5/31/2012	-0.010702377	-0.088299543	-0.064573599	-0.082400512
6/30/2012	0.010852815	0.067375404	0.013893251	0.047961604
7/31/2012	0.045821877	-0.005248984	0.002045166	-0.036613296
8/31/2012	0.093876854	-0.028166927	-0.001520774	0.052737551
9/30/2012	0.00279601	-0.025210127	0.064665076	-0.034393252
10/31/2012	-0.10760008	0.012069024	-0.062280062	-0.040994602
11/30/2012	-0.012374561	0.060996513	-0.018650877	-0.059609605
12/31/2012	-0.090742889	0.014539606	0.007786582	0.00338084
1/31/2013	-0.144089281	-0.01977173	0.060140977	0.027705014
2/28/2013	-0.025285985	0.047704895	-0.00686796	0.02113536
3/31/2013	0.002854561	0.116384874	0.062092321	0.029136743
4/30/2013	0.000271036	0.064764185	-0.050445426	0.15693803
5/31/2013	0.022419293	0.088822244	0.031870423	0.061774321
6/30/2013	-0.118293232	0.034538541	-0.081290274	-0.010315202
7/31/2013	0.141225068	0.02596638	0.02056403	-0.078170267
8/31/2013	0.083766761	-0.006726887	-0.060802034	0.056386826
9/30/2013	-0.021489336	0.13067747	0.015965262	-0.003592884
10/31/2013	0.096381741	0.110638295	-0.032238827	0.06400242
11/30/2013	0.070052711	0.032484657	0.008006885	0.084981038
12/31/2013	0.008901793	0.016685327	0.043911485	-0.01888281
1/31/2014	-0.107696739	-0.08227711	-0.058058401	0.011494267
2/28/2014	0.05751083	0.035024099	0.053798581	0.020012505
3/31/2014	0.019952875	-0.02660565	0.039531282	0.069955642
4/30/2014	0.099396369	0.028129788	0.020676376	-0.014393748
5/31/2014	0.078709291	0.05416904	-0.056174558	0.020515239
6/30/2014	0.0276619	-0.059297568	-0.016760664	0.018563806
7/31/2014	0.028731292	-0.053053524	0.057372943	0.035011976
8/31/2014	0.077508844	0.058830588	0.009220405	0.059169284
9/30/2014	-0.017073171	0.00457408	-0.012844521	0.020471057
10/31/2014	0.071960302	-0.019390747	-0.133962009	0.01272649
11/30/2014	0.105978719	0.081930723	-0.006813085	0.024740135
12/31/2014	-0.071891052	-0.032599025	-0.010667793	-0.028445934
1/31/2015	0.061424232	0.118402828	-0.044440318	-0.130247558
2/28/2015	0.100776612	0.044115187	0.063700889	0.09312029
3/31/2015	-0.031371685	-0.005104436	-0.008892196	-0.072747967
4/30/2015	0.005786394	-0.044909417	0.067227372	0.196261656
5/31/2015	0.045339013	-0.013391102	-0.002079009	-0.030334235
6/30/2015	-0.037227501	-0.012809585	-0.04120242	-0.057831828
7/31/2015	-0.032926713	0.039287756	-0.004119012	0.057757633
8/31/2015	-0.066196163	-0.087786955	-0.079463642	-0.061948911
9/30/2015	-0.02181624	0.002066143	-0.019744391	0.017003615
10/31/2015	0.083408853	0.130737004	-0.033731112	0.189335785
11/30/2015	-0.005804233	-0.011620913	0.0046244	0.039444073
12/31/2015	-0.110228234	-0.005912687	-0.012910653	0.020791177
1/31/2016	0.060722478	0.06161704	0.070523382	0.089015952
2/29/2016	0.03378966	-0.0917872	-0.010524941	-0.0470488
3/31/2016	0.036670426	0.023365239	0.037466331	0.104908941
4/30/2016	0.051959268	0.064664433	0.103843053	-0.006449333
5/31/2016	0.040934839	0.042434823	0.003215704	-0.035805821
6/30/2016	-0.013306536	0.026662938	0.007351138	-0.044770529
7/31/2016	0.004648327	0.079128897	0.046053808	0.020874363
8/31/2016	-0.006569	-0.016770149	-0.005244188	-0.028783478
9/30/2016	-0.034959556	-0.052543874	0.015509445	0.03958417
10/31/2016	0.163285319	-0.046801016	0.060040822	0.053846124
11/30/2016	-0.014469326	-0.044792	-0.050543842	-0.023069687
12/31/2016	-0.009120937	-0.094974606	0.017218264	-0.064285744