A. Suppose that the daily simple returns of a stock in one week were -0.4%, 0.8%, 1.3%, -1.5%, and 0.9%. What are the corresponding daily log returns? What is the weekly simple return of the stock?

A. Suppose that the daily simple returns of a stock in one week were -0.4%, 0.8%, 1.3%, -1.5%, and 0.9%. What are the corresponding daily log returns? What is the weekly simple return of the stock?

B.  Please list out three types of Moments of a Random Variable and briefly explain why they are important for financial data.

C. The data file assignment_1.txt contains stock returns for “ge” (general electric), “vw” (value-weighted market returns), “ew” (equal-weighted market returns), and “sp” (Standard Poor composite index). The time span of the data ranges from Jan 1940 to Sept 2011. Please do following work within R/RStudio environment. 

(a) Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of each simple return series.

(b) Transform the simple returns to log returns and redo part (a).

(c) Test the null hypothesis that the mean of the log returns of “ge” stock is zero. Use 5% significance level to draw your conclusion.

date           ge            vw            ew            sp
19400131      -0.061920     -0.024020     -0.019978     -0.035228
19400229      -0.009901      0.013664      0.029733      0.006639
19400330       0.049333      0.018939      0.026168      0.009893
19400430      -0.041667      0.001196      0.013115     -0.004898
19400531      -0.197324     -0.220314     -0.269754     -0.239541
19400629       0.061667      0.066664      0.066550      0.076591
19400731       0.067460      0.032230      0.036805      0.031062
19400831       0.011152      0.023962      0.023221      0.026239
19400930       0.043382      0.023028      0.037207      0.009470
19401031       0.007117      0.029705      0.049218      0.039400
19401130      -0.048057     -0.016348     -0.001669     -0.042419
19401231       0.007605      0.006811     -0.018789     -0.002828
19410131      -0.003774     -0.040505     -0.007317     -0.048204
19410228      -0.003788     -0.014839     -0.019409     -0.014896
19410331      -0.008365      0.009599      0.014308      0.004032
19410430      -0.104651     -0.053065     -0.057382     -0.065261
19410531      -0.012987      0.013858      0.010105      0.004296
19410630       0.143860      0.058683      0.066908      0.053476
19410731      -0.015504      0.059519      0.130139      0.054822
19410830       0.031496     -0.000463     -0.007180     -0.008662
19410930      -0.016031     -0.007494     -0.020448     -0.009709
19411031      -0.133333     -0.051786     -0.062030     -0.068627
19411129      -0.032579     -0.019367     -0.034209     -0.042105
19411231       0.022749     -0.046728     -0.081886     -0.045055
19420131       0.018779      0.007158      0.130814      0.013809
19420228      -0.041475     -0.024149     -0.017579     -0.024972
19420331      -0.077885     -0.065655     -0.052240     -0.067520
19420430      -0.026455     -0.043145     -0.046260     -0.043695
19420529       0.086957      0.061047      0.028879      0.063969
19420630       0.049000      0.025482      0.025086      0.018405
19420731       0.014493      0.034877      0.046405      0.031325
19420831       0.009524      0.018656      0.028304      0.007009
19420930       0.050943      0.026300      0.047557      0.026682
19421031       0.068182      0.067688      0.101294      0.064407
19421130      -0.004255      0.002500     -0.013177     -0.013800
19421231       0.054701      0.050416      0.035554      0.051668
19430130       0.114754      0.073303      0.168551      0.071648
19430227       0.047794      0.059920      0.130930      0.050621
19430331       0.055439      0.062077      0.112136      0.052727
19430430      -0.023490      0.006903      0.035466      0.000864
19430529       0.044674      0.057158      0.084513      0.044866
19430630       0.055263      0.016911      0.010979      0.019818
19430731      -0.081761     -0.046205     -0.064335     -0.054251
19430831       0.013699      0.012986      0.003373      0.010274
19430930       0.056757      0.024527      0.034867      0.023729
19431030      -0.058065     -0.012218     -0.003943     -0.013245
19431130      -0.047945     -0.058529     -0.088584     -0.075503
19431231       0.071223      0.063623      0.098730      0.058984
19440131      -0.010169      0.018072      0.045949      0.015424
19440229      -0.041096      0.003686      0.013018     -0.002532
19440331       0.035000      0.024417      0.041526      0.016920
19440429      -0.003484     -0.016341     -0.029289     -0.012479
19440531       0.010490      0.050955      0.066135      0.040438
19440630       0.061592      0.056171      0.104935      0.051012
19440731      -0.016447     -0.015151     -0.012724     -0.020801
19440831       0.016722      0.015927      0.030082      0.008655
19440930      -0.010526      0.000191      0.000252     -0.003120
19441031       0.036913      0.002504      0.000953       .      
19441130       0.016181      0.016456      0.023183      0.003912
19441230       0.015287      0.041224      0.069303      0.035074
19450131      -0.018987      0.019194      0.043353      0.014307
19450228       0.096774      0.064282      0.086339      0.061618
19450331      -0.043529     -0.038728     -0.056802     -0.046154
19450430       0.086957      0.077474      0.088844      0.087977
19450531       0.011429      0.018630      0.030017      0.011456
19450630      -0.027684      0.003422      0.036565     -0.003331
19450731       0.020528     -0.022095     -0.035068     -0.020053
19450831       0.086207      0.061123      0.065928      0.057981
19450929       0.032275      0.048051      0.062646      0.041908
19451031      -0.023256      0.039018      0.064522      0.030322
19451130      -0.018519      0.054546      0.097574      0.032432
19451231       0.038275      0.011763      0.024073      0.009889
19460131       0.057592      0.063309      0.094677      0.069700
19460228      -0.051980     -0.057852     -0.066906     -0.069467
19460330      -0.009922      0.058716      0.057922      0.046296
19460430      -0.023936      0.042899      0.052109      0.037611
19460531       0.087193      0.039864      0.054749      0.022388
19460628      -0.039599     -0.039140     -0.048887     -0.039103
19460731      -0.015789     -0.025465     -0.040842     -0.025502
19460830      -0.080214     -0.063922     -0.075327     -0.072940
19460930      -0.077907     -0.100202     -0.135552     -0.101502
19461031      -0.057325     -0.014164     -0.011814     -0.008021
19461130      -0.054054      0.001200     -0.002634     -0.011456
19461231       0.036429      0.050925      0.046908      0.042945
19470131       0.090592      0.015128      0.030197      0.023529
19470228      -0.038339     -0.011577     -0.007105     -0.014687
19470331      -0.045847     -0.017058     -0.030425     -0.016850
19470430      -0.021127     -0.047868     -0.081680     -0.038893
19470529      -0.010791     -0.009997     -0.037321     -0.008916
19470630       0.044364      0.053652      0.057096      0.052595
19470731       0.073944      0.041240      0.061670      0.036160
19470829      -0.036066     -0.017509     -0.017166     -0.027919
19470930       0.004082     -0.004419      0.005783     -0.013708
19471031       0.000000      0.024614      0.033156      0.021178
19471129      -0.041096     -0.018306     -0.029305     -0.028516
19471231       0.032857      0.030189      0.023863      0.020680
19480131      -0.038462     -0.037266     -0.016276     -0.039869
19480228      -0.050909     -0.043439     -0.059451     -0.046971
19480331       0.115709      0.082763      0.095843      0.077143
19480430      -0.031250      0.037775      0.040151      0.026525
19480528       0.204301      0.074581      0.087630      0.078165
19480630      -0.011310     -0.000177     -0.012534      0.002996
19480730      -0.069909     -0.050421     -0.053733     -0.053166
19480831       0.032680      0.003854     -0.001818      0.007571
19480930       0.000000     -0.029544     -0.042785     -0.030056
19481030       0.083333      0.060056      0.053201      0.067786
19481130      -0.118343     -0.090626     -0.106320     -0.108223
19481231       0.057047      0.032202      0.013703      0.030508
19490131      -0.016077      0.003043      0.017749      0.001316
19490228      -0.058824     -0.029464     -0.041302     -0.039422
19490331       0.065972      0.041521      0.059309      0.030096
19490430      -0.023102     -0.017866     -0.031490     -0.021248
19490531      -0.050676     -0.027440     -0.043168     -0.037313
19490630       0.003559      0.003093     -0.007713     -0.002114
19490729       0.068345      0.055845      0.062022      0.062147
19490831       0.003367      0.026592      0.026020      0.011968
19490930       0.010067      0.031831      0.043249      0.023653
19491031       0.006734      0.031224      0.039025      0.029525
19491130       0.070234      0.018842      0.009400      0.001247
19491231       0.078125      0.052102      0.070120      0.043587
19500131       0.047478      0.017283      0.040293      0.017303
19500228       0.048159      0.014635      0.016102      0.009971
19500331       0.012973      0.012198     -0.001770      0.004065
19500429       0.045946      0.040257      0.047443      0.045113
19500531       0.018088      0.043689      0.033185      0.039292
19500630      -0.066497     -0.057935     -0.075737     -0.058040
19500731       0.013774      0.016118      0.050635      0.008479
19500831       0.038043      0.050699      0.051892      0.032511
19500929       0.007330      0.048804      0.055013      0.055917
19501031       0.023684     -0.001109     -0.005504      0.004113
19501130       0.000000      0.028518      0.031622     -0.001024
19501230       0.057218      0.057703      0.084545      0.046130
19510131       0.095477      0.058239      0.076248      0.061244
19510228       0.025229      0.014434      0.011586      0.006464
19510331      -0.008949     -0.020949     -0.033890     -0.018349
19510430       0.016018      0.049613      0.040814      0.048131
19510531      -0.033784     -0.022624     -0.024919     -0.040571
19510629      -0.002331     -0.025324     -0.044929     -0.026022
19510731       0.059242      0.071166      0.063332      0.068702
19510831       0.067114      0.045082      0.047438      0.039286
19510928       0.041929      0.009177      0.023631     -0.000859
19511031      -0.083503     -0.022397     -0.023609     -0.013758
19511130      -0.004444      0.005923      0.007185     -0.002616
19511231       0.075893      0.034898      0.015248      0.038899
19520131      -0.021008      0.016906      0.017491      0.015566
19520229      -0.053648     -0.024983     -0.020650     -0.036454
19520331       0.088435      0.045586      0.028864      0.047721
19520430      -0.037975     -0.048900     -0.044936     -0.043086
19520529       0.046053      0.032874      0.024515      0.023156
19520630       0.067086      0.039283      0.030728      0.046102
19520731       0.001988      0.011482      0.010652      0.017628
19520829       0.001984     -0.006584      0.000056     -0.014567
19520930       0.013861     -0.018991     -0.015160     -0.019577
19521031      -0.015810     -0.005456     -0.011717     -0.000815
19521128       0.128514      0.058795      0.055644      0.046493
19521231       0.046263      0.031210      0.022641      0.035464
19530130      -0.051546     -0.001342      0.024706     -0.007151
19530227       0.000000     -0.001711      0.012031     -0.018196
19530331       0.003623     -0.013417     -0.010486     -0.023552
19530430       0.027372     -0.027474     -0.024027     -0.026493
19530529       0.024867      0.007141      0.005896     -0.003249
19530630      -0.005199     -0.016655     -0.031671     -0.016300
19530731       0.031690      0.025329      0.017571      0.025269
19530831      -0.034130     -0.044092     -0.051874     -0.057778
19530930       0.045936      0.003053     -0.011005      0.001286
19531030       0.114334      0.047090      0.037834      0.050964
19531130       0.108729      0.028267      0.021317      0.008965
19531231      -0.011173      0.000768     -0.015444      0.002019
19540129       0.062857      0.052460      0.071683      0.051189
19540226       0.079301      0.017482      0.013576      0.002684
19540331       0.074720      0.037251      0.029150      0.030210
19540430       0.153216      0.042851      0.016373      0.048998
19540528      -0.047667      0.031569      0.043151      0.032909
19540630       0.185942      0.011477      0.012275      0.000685
19540730      -0.043478      0.050368      0.071989      0.057172
19540831      -0.056818     -0.022516     -0.009175     -0.034003
19540930       0.063855      0.064304      0.044308      0.083138
19541029      -0.037143     -0.016211     -0.006860     -0.019499
19541130       0.086053      0.095289      0.092199      0.080808
19541231       0.030601      0.055263      0.087724      0.050818
19550131       0.064171      0.006994      0.014124      0.018066
19550228       0.047739      0.031280      0.042781      0.003549
19550331      -0.042686     -0.001122      0.000530     -0.004897
19550429       0.065657      0.032281      0.022598      0.037726
19550531      -0.018957      0.011856      0.007814     -0.001317
19550630       0.034300      0.065800      0.034694      0.082300
19550729      -0.035294      0.020283      0.008001      0.060687
19550831       0.034146      0.004250      0.005764     -0.007813
19550930      -0.049057     -0.002034     -0.007751      0.011348
19551031      -0.065000     -0.025728     -0.017815     -0.030456
19551130       0.149733      0.071558      0.055257      0.074870
19551230       0.083721      0.016437      0.022836     -0.000659
19560131      -0.060606     -0.027987     -0.020746     -0.036500
19560229       0.073733      0.039532      0.033613      0.034687
19560329       0.100858      0.068175      0.051383      0.069255
19560430      -0.031434      0.005093      0.003827     -0.002063
19560531      -0.070994     -0.049186     -0.039964     -0.065730
19560629       0.074236      0.037157      0.021712      0.039159
19560731       0.047131      0.050753      0.039967      0.051522
19560831      -0.039139     -0.030342     -0.018161     -0.038064
19560928      -0.079430     -0.049677     -0.035938     -0.045464
19561031       0.066964      0.007221      0.007063      0.005072
19561130      -0.008368      0.004611      0.005277     -0.010970
19561231       0.025316      0.034934      0.023122      0.035271
19570131      -0.107884     -0.032051      0.003613     -0.041783
19570228       0.030233     -0.018698     -0.023299     -0.032648
19570329       0.060948      0.024087      0.022499      0.019649
19570430       0.087983      0.045059      0.025909      0.036953
19570531       0.053254      0.036599      0.022263      0.036948
19570628       0.033708     -0.005107     -0.006747     -0.001265
19570731       0.018248      0.008920      0.005610      0.011400
19570830      -0.064516     -0.050003     -0.050190     -0.056147
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