Dear statalisters,
I hope someone here is able to help me find out how to calculate a weighted standard deviation. I have included a datasample by Dataex at the end of this post, as it's rather long.
I've got panel data on stock performance, firms are identified with an id and have observations for each year. I've calculated Abnormal Returns (AR) and sorted stocks from low to high in quintiles by the variable CI (CI_quintile). My aim is to show the abnormal returns to an investment strategy that invests into all the stocks listed in a CI_quintile. The problem is, if I invest a single Dollar into the portfolio this dollar is divded over all these stocks according to their portfolio weight (varname = weight), because a large company makes up a larger share of the portfolio of course.
An individual stock's weighted Abnormal Return is weight * AR = wAR.
When doing descriptive statistics, I can do for example:
This will show me the unweighted mean, median and standard deviation for each CI_quintile.
If I want to look at the outcome of a portfolio strategy, I use the following code to calculate the yearly weighted return of an investment strategy into each CI_quintile and create the table below:
But, the standard deviation displayed in the second column is not the right one. This is calculated using the variance between the mean returns of the portfolios.
What I'm actually interested in is the weighted portfolio standard deviation. I can calculate this for each year's portfolio by hand, doing this:
In which 'w' is the weight of a stock in a portfolio, 'M' is equal to 'N' for me. and 'x' are means. The standard deviation of a group CI_quintile should then be the average those individual standard deviations calculated with that formula.
Doing it by hand is not an option for me, as I will need to do it for a lot of portfolios. Is the only option in Stata to calculate this weighted standard deviation by typing the formulas in by hand?
I'm hoping someone can help me find a quick way or trick to do this! I've searched the help pages for additional options in calculating standard deviations, etc. but I was unable to find what I'm looking for.
Data example below, I've made it this long so there's stocks of each quintile in it.
* Example generated by -dataex-. To install: ssc install dataex
clear
input float id int year float(CI_quintile weight AR wAR)
7458 1988 1 .003308191 .04755842 1.5733234e-06
7348 1988 1 .01979438 27.21212 .00538647
5423 1988 1 .006723564 -25.21848 -.0016955804
3706 1988 1 .005498273 -3.8384776 -.00021104998
7495 1988 1 .005953363 40.70152 .002423109
5709 1988 1 .006956758 26.44152 .0018394728
7683 1988 1 .002354228 43.05568 .0010136289
5940 1988 1 .004853771 -7.738739 -.0003756207
7496 1988 1 .00430986 -12.85874 -.0005541937
5533 1988 1 .001597837 -27.52244 -.0004397637
5821 1988 1 .006222964 1.7612606 .00010960262
5711 1988 1 .02864698 38.50694 .011031074
7209 1988 1 .007841516 -36.861877 -.00289053
6417 1988 1 .011576707 -25.737875 -.002979598
5486 1988 1 .014225017 -34.136192 -.004855879
5894 1988 1 .0027281865 -36.06244 -.0009838507
7097 1988 1 .0010399593 -25.13244 -.00026136715
6978 1988 1 .0019874882 -65.942444 -.0013105983
5840 1988 1 .00982461 12.952124 .0012724957
8354 1988 1 .02637184 31.396776 .008279908
5398 1988 1 .004116211 35.78768 .0014730964
6304 1988 1 .008858877 -9.938478 -.0008804376
5949 1988 1 .009482821 21.666206 .0020545677
5872 1988 1 .04225229 -5.378726 -.002272635
7206 1988 1 .02326138 -18.393063 -.00427848
7385 1988 1 .009919709 -18.677795 -.0018527828
6141 1988 1 .010994663 -21.157877 -.0023262373
6816 1988 1 .00971225 -34.093796 -.0033112746
5848 1988 1 .005435659 -11.66874 -.0006342728
7264 1988 1 .008940009 91.58195 .008187435
5501 1988 1 .02630546 -9.908727 -.002606536
8194 1988 1 .0015744547 116.97 .0018416398
7954 1988 1 .0006245719 -24.11289 -.00015060234
5524 1988 1 .0018336992 -42.28289 -.000775341
7757 1988 1 .012448753 59.1412 .007362343
6032 1988 1 .03246628 111.37627 .036159735
7085 1988 1 .005526206 -4.744877 -.00026221166
7083 1988 1 .00499736 18.115747 .000905309
6821 1988 1 .000877853 19.46686 .0001708904
7031 1988 1 .004767775 -64.56488 -.003078308
8037 1988 1 .0007281441 -20.45289 -.00014892654
3976 1988 1 .002622888 19.17756 .0005030059
6948 1988 1 .06607924 32.777126 .021658873
8446 1988 1 .0042028353 -63.46425 -.002667298
5475 1988 1 .004709554 -14.628477 -.0006889361
5418 1988 1 .010878066 .01212345 1.318797e-06
6138 1988 1 .0040314705 27.215406 .0010971811
6555 1988 1 .00775756 11.361523 .0008813769
5717 1988 1 .018076962 -16.627876 -.003005815
5496 1988 1 .03864232 -6.418726 -.002480345
7254 1988 1 .003252011 484.86795 .01576796
7145 1988 1 .07200812 -3.9270766 -.002827814
7294 1988 1 .003709455 -40.03103 -.001484933
6462 1988 1 .018823624 -1.3978765 -.00026313102
5870 1988 1 .008651262 -13.30874 -.001151374
6340 1988 1 .008757503 4.581522 .0004012269
7923 1988 1 .0027628676 -59.12244 -.001633475
7154 1988 1 .001613059 -40.30289 -.0006501094
6665 1988 1 .009262182 -24.833794 -.0023001512
5974 1988 1 .09308114 .786275 .0007318737
6946 1988 1 .032222416 47.52064 .015312297
5604 1988 1 .0037643795 -3.112319 -.0001171595
8504 1988 1 .004078392 15.433672 .0006294457
6836 1988 1 .0020328404 45.48768 .000924692
7217 1988 1 .013693974 32.054104 .004389481
6607 1988 1 .002903632 20.31768 .0005899506
6495 1988 1 .003260328 8.757681 .00028552912
6958 1988 1 .013698054 18.946796 .0025953425
5523 1988 1 .04979282 3.9112735 .0019475333
7184 1988 1 .003675088 65.49897 .002407145
5446 1988 1 .0123105 -19.09788 -.002351044
6859 1988 1 .003496818 -35.66232 -.0012470464
5397 1988 1 .0020494745 -46.04244 -.0009436281
5382 1988 1 .0031159546 45.20768 .001408651
5781 1988 1 .0020171476 -68.512436 -.001381997
7149 1988 1 .013541284 -3.033204 -.0004107348
6056 1988 1 .002672791 -43.60244 -.001165402
5655 1988 1 .05581209 -18.313065 -.010220904
5945 1988 2 .00463354 -1.204877 -.00005582845
6923 1988 2 .04139749 14.199373 .005878184
7144 1988 2 .0020478633 -57.57103 -.001178976
6309 1988 2 .0012699616 2.237681 .00002841769
7311 1988 2 .022528274 33.696278 .00759119
7204 1988 2 .0028297885 -48.55125 -.0013738978
5491 1988 2 .05930467 -13.633725 -.008085435
5824 1988 2 .002104283 -44.38244 -.0009339322
6362 1988 2 .0011264324 -8.682319 -.00009780045
6944 1988 2 .04139796 -7.973727 -.00330096
3869 1988 2 .0022640927 174.80896 .003957837
6647 1988 2 .03457022 46.43628 .016053123
6817 1988 2 .009060114 66.086205 .005987485
6921 1988 2 .02863818 70.34693 .02014608
5417 1988 2 .016566856 -14.123064 -.002339748
8473 1988 2 .00104213 -18.272894 -.0001904273
5412 1988 2 .004920411 -5.548478 -.0002730079
7151 1988 2 .0041635614 22.27852 .00092758
7386 1988 2 .002524859 40.87705 .0010320878
7192 1988 2 .004963919 26.25626 .0013033395
7405 1988 2 .007562788 -15.563204 -.001177012
5402 1988 2 .004635505 10.291522 .000477064
7328 1988 2 .00989378 53.80212 .005323063
6165 1988 2 .015527252 -31.34708 -.00486734
7734 1988 2 .002977996 10.388747 .00030937645
7243 1988 2 .0037797566 28.486946 .0010767372
5851 1988 2 .00394911 -25.584877 -.0010103749
8441 1988 2 .0039315196 3.245123 .00012758265
6970 1988 2 .017720142 -30.607077 -.005423618
7402 1988 2 .0024529074 -49.38103 -.001211271
5719 1988 2 .011361913 -31.06619 -.0035297135
5617 1988 2 .00308466 -37.54874 -.0011582511
7478 1988 2 .0035551065 -20.288477 -.000721277
7729 1988 2 .0033146436 -12.550977 -.0004160202
7413 1988 2 .002824081 -13.994253 -.000395209
6188 1988 2 .001548599 -11.94232 -.00018493863
5510 1988 2 .02763647 32.986275 .009116242
7349 1988 2 .0021389024 5.027107 .00010752492
6444 1988 2 .001595943 -17.962318 -.00028666836
8098 1988 2 .010091296 -46.3632 -.004678648
5858 1988 2 .00995357 -25.07619 -.002495976
6387 1988 2 .0017723136 -11.55232 -.00020474332
6047 1988 2 .011706795 -11.537877 -.0013507155
7228 1988 2 .0036947995 -32.694252 -.001207987
7444 1988 2 .004679574 -40.86488 -.0019123022
6818 1988 2 .028311545 -12.187077 -.00345035
6805 1988 2 .006330253 44.80099 .002836016
5707 1988 2 .25637916 -20.983725 -.0537979
7190 1988 2 .003115911 -16.884253 -.0005260983
5791 1988 2 .015835643 -57.34708 -.009081278
5845 1988 2 .0030567776 -51.24488 -.001566442
6648 1988 2 .008569831 -34.613205 -.002966293
6197 1988 2 .024474245 -26.30873 -.006438862
8041 1988 2 .005248919 99.51575 .0052235
7363 1988 2 .002289636 -33.84289 -.000774879
5442 1988 2 .01524141 -47.93306 -.007305675
6124 1988 2 .001596411 -24.57232 -.0003922752
6930 1988 2 .03641654 52.37858 .019074466
5482 1988 2 .033051092 -11.578727 -.003826896
8482 1988 2 .010423547 10.012124 .0010436184
5432 1988 2 .0018044064 -68.802895 -.001241484
7164 1988 2 .0009581085 -65.68103 -.0006292955
5495 1988 2 .004479999 -33.118477 -.0014837076
6919 1988 2 .01121801 5.850806 .000656344
6651 1988 2 .0021987841 48.70921 .0010710104
5995 1988 2 .003910561 -12.33874 -.00048251395
6971 1988 2 .001034832 -25.23244 -.00026111337
6205 1988 2 .0029855745 -24.16848 -.000721568
5461 1988 2 .00498731 -10.508478 -.00052409037
1571 1988 2 .00548985 -43.0032 -.002360811
8454 1988 2 .00383496 8.991261 .0003448113
7312 1988 2 .004747315 -10.678477 -.000506941
5399 1988 2 .02433521 65.471275 .015932571
6826 1988 2 .00601999 -31.88619 -.0019195458
7416 1988 2 .002490614 134.89755 .003359778
5613 1988 2 .0021592996 2.457681 .00005306869
6789 1988 2 .001412181 180.52898 .002549396
6012 1988 2 .006848043 -13.387877 -.0009168075
6913 1988 3 .04084988 31.08292 .012697336
6793 1988 3 .0042613777 54.11652 .0023061095
5769 1988 3 .0044555734 -26.13619 -.0011645172
8524 1988 3 .0017429963 -10.454877 -.0001822281
6201 1988 3 .05990786 -2.725325 -.0016326838
8097 1988 3 .004850253 -25.023205 -.001213689
5485 1988 3 .0787017 -29.518726 -.02323174
7202 1988 3 .003989745 -36.293793 -.0014480298
6800 1988 3 .0079699615 17.086206 .001361764
5756 1988 3 .00467556 -24.70619 -.0011551529
6949 1988 3 .008540733 9.826796 .0008392804
6035 1988 3 .023817774 -26.364063 -.006279333
7427 1988 3 .0014571343 -30.97289 -.0004513166
7628 1988 3 .0019216284 129.47617 .002488051
7166 1988 3 .0007566451 2.0971072 .00001586766
7730 1988 3 .001180102 9.018971 .00010643308
6017 1988 3 .06806776 2.056275 .0013996603
5827 1988 3 .0040634973 -1.8178765 -.00007386936
7428 1988 3 .0021379942 -68.524254 -.0014650446
6939 1988 3 .00689385 -.673204 -.00004640967
6979 1988 3 .034165345 -28.513723 -.009741812
5440 1988 3 .008331418 -17.436193 -.001452682
5629 1988 3 .007418692 -11.377876 -.0008440896
5690 1988 3 .0088299615 .6321235 .00005581626
7327 1988 3 .0013162995 9.077107 .00011948192
7643 1988 3 .02775778 -4.334364 -.001203123
5859 1988 3 .0011151162 -34.95232 -.000389759
8028 1988 3 .00950104 9.851274 .0009359733
7234 1988 3 .006829689 148.7038 .010156007
5839 1988 3 .07762425 -16.843725 -.013074816
6655 1988 3 .018472217 12.077623 .0022310049
6934 1988 3 .00785568 10.247707 .000805027
6894 1988 3 .016273174 10.152174 .001652081
5549 1988 3 .0021736952 6.731261 .0001463171
7261 1988 3 .010401885 35.372925 .003679451
7140 1988 3 .008885165 8.083205 .0007182062
8141 1988 3 .003636674 11.791522 .0004288192
5614 1988 3 .005748686 -45.30379 -.002604373
7293 1988 3 .0018526403 45.44512 .0008419346
7201 1988 3 .01150976 -25.298077 -.002911748
5721 1988 3 .009840135 -16.103064 -.001584563
5525 1988 3 .01986303 -6.538726 -.001298789
7393 1988 3 .06301429 48.50827 .030567145
6210 1988 3 .03263719 4.267936 .0013929345
7426 1988 3 .00049524015 -27.93103 -.00013832567
7373 1988 3 .008607878 33.675205 .002898721
7783 1988 3 .003173958 7.685747 .0002439424
7387 1988 3 .0029896726 44.89575 .001342236
5463 1988 3 .005716034 -19.73619 -.0011281276
5492 1988 3 .002470293 -29.96874 -.0007403156
7160 1988 3 .0006015808 -9.761028 -.00005872048
6943 1988 3 .0037111884 -9.274253 -.000344185
5826 1988 3 .011805595 -55.00306 -.006493439
7300 1988 3 .0010871016 -55.03102 -.0005982432
5855 1988 3 .017826866 -18.453724 -.003289721
5380 1988 3 .01225065 -12.247077 -.0015003466
6334 1988 3 .0014612634 7.787681 .00011379852
6051 1988 3 .002620656 -12.678477 -.0003322593
6796 1988 3 .003035093 19.335123 .000586839
5770 1988 3 .006713375 -5.326192 -.0003575673
6642 1988 3 .0609761 -.5287265 -.0003223968
6801 1988 3 .004390524 -25.653795 -.0011263359
5438 1988 3 .01051369 34.106937 .0035858974
7170 1988 3 .00054701295 -51.56103 -.0002820455
6156 1988 3 .05557616 -12.989727 -.007219191
6317 1988 3 .005031617 11.932123 .0006003787
6942 1988 3 .0015643643 -1.0210284 -.000015972604
7671 1988 3 .003283729 -50.82487 -.0016689514
5378 1988 3 .005568911 4.0938077 .0002279805
5853 1988 3 .0021910374 -11.92874 -.00026136314
5741 1988 3 .0015700816 -40.49244 -.0006357644
5554 1988 3 .004331509 -13.497877 -.0005846618
7171 1988 3 .006491927 -32.823204 -.0021308586
5610 1988 3 .008699799 -13.027877 -.0011333991
5416 1988 3 .01258314 -35.613064 -.0044812416
5720 1988 3 .0012657337 -10.532442 -.00013331267
8397 1988 3 .005552394 1.3897058 .00007716195
5624 1988 4 .05806098 -19.793724 -.01149243
3671 1988 4 .00607062 29.252125 .0017757853
8402 1988 4 .00122507 -4.913442 -.00006019309
7362 1988 4 .005687082 10.156796 .00057762535
7756 1988 4 .0012734267 37.337105 .0004754607
5708 1988 4 .013533988 -23.97708 -.003245055
5883 1988 4 .005295252 -50.66379 -.0026827755
7554 1988 4 .005735876 52.59091 .003016549
8444 1988 4 .0030944906 4.485123 .00013879171
7642 1988 4 .004470479 18.65236 .0008338499
7147 1988 4 .0007827005 -5.032893 -.00003939248
7289 1988 4 .011478996 29.783806 .003418882
7251 1988 4 .002458345 68.115746 .00167452
5654 1988 4 .003510936 -30.404877 -.0010674957
7457 1988 4 .0019048592 54.96897 .0010470815
6968 1988 4 .011513387 -36.653202 -.004220025
8363 1988 4 .004779474 22.485746 .0010747005
6037 1988 4 .015742868 28.75292 .0045265346
6558 1988 4 .0015354616 -46.53232 -.0007144859
6918 1988 4 .03322527 19.520636 .006485784
7484 1988 4 .0014729643 -16.942442 -.00024955612
5632 1988 4 .012606042 -8.817077 -.0011114845
7142 1988 4 .0021627042 18.535107 .0004008595
5778 1988 4 .0014651957 -22.92244 -.0003358586
5483 1988 4 .021556865 -24.233727 -.005224032
6000 1988 4 .0014881522 -17.212318 -.00025614552
5885 1988 4 .016856385 -4.5930634 -.0007742245
4063 1988 4 .0015768355 -22.65103 -.00035716945
7650 1988 4 .004959285 81.96282 .0040647704
5400 1988 4 .005623101 3.056206 .00017185355
7162 1988 4 .0018952576 -6.292893 -.00011926654
6950 1988 4 .018039556 14.067924 .002537791
7258 1988 4 .003267144 5.416422 .0001769623
6908 1988 4 .0034998504 2.175123 .00007612605
7146 1988 4 .011566631 -18.945793 -.0021913901
6786 1988 4 .002818141 -8.465753 -.0002385768
6962 1988 4 .00225357 66.50897 .0014988262
7477 1988 4 .008347234 22.487606 .001877093
6644 1988 4 .005800119 35.773808 .0020749234
5500 1988 4 .003786413 -20.97848 -.0007943318
5738 1988 4 .009033046 -30.967876 -.0027973424
6822 1988 4 .0043263687 -24.774254 -.0010718255
6183 1988 4 .0925658 -6.754726 -.006252565
7893 1988 4 .001762058 -11.462893 -.0002019828
7745 1988 4 .0018903696 48.33897 .0009137852
7397 1988 4 .015248388 -48.51708 -.007398072
6640 1988 4 .004762803 99.62362 .004744877
7137 1988 4 .009451935 11.291206 .0010672375
5474 1988 4 .014693768 -32.637077 -.004795616
8525 1988 4 .0005888366 -40.02603 -.0002356879
5684 1988 4 .0021408827 -13.76232 -.0002946351
7377 1988 4 .0032557966 -27.53425 -.0008964593
6814 1988 4 .05468481 86.95967 .04755374
5799 1988 4 .064684995 -35.643723 -.02305614
7181 1988 4 .001225768 -4.4424415 -.00005445403
7767 1988 4 .00953512 -35.522305 -.003387094
7390 1988 4 .005521063 -3.578204 -.0001975549
7431 1988 4 .001687777 -48.02103 -.0008104878
5546 1988 4 .0021170534 56.63768 .00119905
5384 1988 4 .00238869 -23.52488 -.0005619363
5642 1988 4 .02166475 -31.653065 -.006857558
7163 1988 4 .0025746105 -7.884253 -.0002029888
6872 1988 4 .008933888 5.572124 .0004978073
6175 1988 4 .01595096 -19.103064 -.003047122
5448 1988 4 .006448223 -11.646193 -.0007509724
7690 1988 4 .002955181 -42.90525 -.0012679278
6659 1988 4 .027012637 46.80002 .01264192
6906 1988 4 .006796322 81.7568 .005556455
6036 1988 4 .12919612 26.363274 .03406033
6662 1988 4 .05029769 21.634336 .010881572
6798 1988 4 .05231786 -19.916727 -.010420005
7352 1988 4 .0017966236 .8171072 .00001468034
5771 1988 4 .003273778 -22.57874 -.0007391777
7099 1988 4 .008245458 -41.44788 -.0034175673
6229 1988 4 .0027012636 13.57126 .00036659554
7237 1988 4 .007436484 11.206796 .0008333916
5698 1988 4 .0045691133 -10.80874 -.00049386354
6844 1988 4 .02384273 -31.42873 -.007493467
7169 1988 5 .008083384 14.363205 .0011610329
8531 1988 5 .0010763407 -61.34103 -.0006602384
7333 1988 5 .005559074 69.531265 .003865294
6657 1988 5 .015709555 -44.55708 -.006999718
8432 1988 5 .0019648154 -37.05244 -.000728012
6952 1988 5 .00607239 -5.656894 -.0003435086
5676 1988 5 .027412385 -1.4330636 -.0003928369
4891 1988 5 .01502965 -27.338726 -.0041089146
5457 1988 5 .016678939 -15.853064 -.002644123
5627 1988 5 .0045171767 -12.668477 -.0005722575
5414 1988 5 .019864453 -29.54306 -.005868568
5489 1988 5 .08767887 -12.523726 -.01098066
5652 1988 5 .00818786 9.773808 .0008002657
8516 1988 5 .0036292744 2.645123 .00009599878
7419 1988 5 .005822697 33.356796 .001942265
6458 1988 5 .0012275684 -20.79232 -.00025523992
7297 1988 5 .01499826 54.15762 .0081227
7183 1988 5 .002504942 49.89811 .0012499185
5543 1988 5 .002851382 23.08152 .0006581423
5394 1988 5 .003251825 -38.60488 -.001255363
6039 1988 5 .0265595 30.192924 .00801909
7205 1988 5 .006508993 -38.00619 -.0024738205
7213 1988 5 .0042424863 39.22912 .00166429
7105 1988 5 .0013341433 -58.99244 -.0007870437
8154 1988 5 .012183897 21.376205 .002604455
5646 1988 5 .020772774 -29.163063 -.006057977
7274 1988 5 .0020792142 -1.5557928 -.000032348264
5739 1988 5 .007919085 -19.38619 -.001535209
5479 1988 5 .005437042 -23.05874 -.0012537134
6652 1988 5 .022722894 -11.581077 -.002631556
6296 1988 5 .04706541 10.221273 .004810684
8343 1988 5 .003952148 -5.21874 -.0002062523
7392 1988 5 .007166286 50.9468 .003650993
5542 1988 5 .000838956 -32.272892 -.00027075538
5631 1988 5 .034742303 -34.213726 -.011886636
5638 1988 5 .010893262 -17.857876 -.0019453053
7006 1988 5 .00293544 -7.064253 -.0002073669
6489 1988 5 .005363766 -43.85488 -.002352273
6959 1988 5 .008517126 12.956797 .0011035466
5800 1988 5 .00273269 -36.61874 -.0010006765
8177 1988 5 .004422528 -60.13425 -.0026594545
5959 1988 5 .06709139 -6.583725 -.0044171126
5658 1988 5 .004046701 -53.54874 -.0021669574
5758 1988 5 .01260056 -60.70619 -.00764932
5498 1988 5 .019687654 -33.863728 -.006666973
5780 1988 5 .0025808895 2.2412605 .00005784446
7136 1988 5 .0021366521 19.97711 .0004268413
7936 1988 5 .017677996 -28.888725 -.005106948
7167 1988 5 .011817516 35.426796 .0041865674
7161 1988 5 .006111222 -4.203204 -.00025686712
7044 1988 5 .0012725074 -2.482319 -.000031587693
7070 1988 5 .0041681603 3.071522 .00012802597
8469 1988 5 .0009190065 -33.05103 -.0003037411
6220 1988 5 .003648357 -21.878477 -.000798205
6895 1988 5 .01134599 20.411106 .0023158423
7165 1988 5 .0009305514 -47.31603 -.0004403
7238 1988 5 .006276189 -50.9338 -.003196701
7888 1988 5 .002253436 -4.7310286 -.0001066107
5649 1988 5 .06367889 -22.983725 -.014635782
5616 1988 5 .01350955 10.573808 .0014284737
6176 1988 5 .04494316 23.071924 .010369252
6815 1988 5 .0026754425 11.98006 .0003205196
5383 1988 5 .05657749 4.3412733 .002456183
6206 1988 5 .007973183 -8.053204 -.0006420967
5518 1988 5 .0016337364 -41.03232 -.00067036
5626 1988 5 .02612137 -42.73373 -.011162634
6092 1988 5 .002454278 -20.61244 -.0005058866
5748 1988 5 .017545564 34.69292 .006087069
5944 1988 5 .012790716 2.6538076 .000339441
7266 1988 5 .013038692 14.093807 .001837648
5405 1988 5 .002873613 67.12152 .0019288127
7277 1988 5 .0226874 131.61694 .029860463
7672 1988 5 .0014592282 22.51768 .0003285844
7227 1988 5 .005988808 -20.276304 -.001214309
8509 1988 5 .003483581 137.14513 .004777561
6674 1988 5 .02666846 -25.893724 -.006905457
6810 1988 5 .008821299 33.444523 .0029502416
7169 1989 1 .026088715 44.665 .011652525
6304 1989 1 .00771959 -9.9 -.0007642394
6000 1989 1 .0017870337 -8.860001 -.0001583312
5461 1989 1 .009031327 -27.83375 -.002513757
7458 1989 1 .0038669384 20.1116 .0007777033
6816 1989 1 .010155418 -24.95973 -.002534765
7181 1989 1 .0023925565 -17.099154 -.0004091069
5652 1989 1 .01419654 -14.320545 -.002033022
6946 1989 1 .03730627 .9969214 .0003719142
7756 1989 1 .0039347988 48.33084 .0019017216
7650 1989 1 .011827474 -25.427935 -.003007482
8484 1989 1 .0040036207 -8.10708 -.00032457674
6821 1989 1 .0014844098 50.75104 .0007533535
7628 1989 1 .00632502 -18.197924 -.0011510223
5940 1989 1 .004935669 -26.048 -.0012856432
6607 1989 1 .0027870804 -7.667996 -.0002137132
5448 1989 1 .008897667 -18.288336 -.001627235
7683 1989 1 .003135448 -.55575687 -.00001742547
5756 1989 1 .012118147 15.621665 .0018930563
7164 1989 1 .002370715 47.18672 .0011186627
5738 1989 1 .0097543 -46.02949 -.0044898544
7433 1989 1 .007230282 1.5829195 .00011444953
8398 1989 1 .00128234 -13.59328 -.00017431207
6948 1989 1 .04039405 -57.38797 -.023181325
7426 1989 1 .0020418533 44.05125 .0008994618
7496 1989 1 .011042684 42.57 .004700871
6197 1989 1 .03762538 -5.613753 -.0021121958
7363 1989 1 .007087555 67.88555 .004811426
6138 1989 1 .0037527846 -21.775354 -.0008171821
6836 1989 1 .0025242935 11.338243 .00028621053
6796 1989 1 .011673208 19.600466 .0022880032
7312 1989 1 .011361793 5.616252 .0006381069
8482 1989 1 .017583923 -33.360004 -.005865998
7672 1989 1 .004710796 -18.657925 -.0008789368
5501 1989 1 .02730045 -16.98617 -.0046373
7757 1989 1 .00996049 -62.48813 -.006224125
7149 1989 1 .01364363 -16.285837 -.0022219792
5475 1989 1 .006492198 18.660002 .0012114443
6188 1989 1 .002455884 14.088 .00034598485
5974 1989 1 .12648721 2.762488 .003494194
6944 1989 1 .06907121 -9.85567 -.00680743
7085 1989 1 .003987686 -13.26534 -.00052898005
5720 1989 1 .002545036 -5.028398 -.00012797453
7217 1989 1 .015618722 -12.150582 -.0018977656
7254 1989 1 .005691749 62.25142 .003543194
8531 1989 1 .001857092 1.3467197 .000025009826
6640 1989 1 .008214256 -27.410284 -.0022515508
5862 1989 1 .002922389 -21.86833 -.0006390777
7416 1989 1 .004921658 .3537169 .000017408738
6872 1989 1 .019402415 6.389994 .001239813
8514 1989 1 .01400079 34.512966 .004832088
7006 1989 1 .0039931806 -46.7801 -.001868014
7144 1989 1 .005290769 -.3370806 -.000017834156
7209 1989 1 .0085446285 4.3580055 .0003723754
7745 1989 1 .005944782 48.72698 .002896713
7031 1989 1 .0013105005 -61.32054 -.000803606
5486 1989 1 .01510867 12.340512 .0018644874
8194 1989 1 .002485006 32.297443 .0008025934
6826 1989 1 .013000468 -12.513748 -.0016268458
5423 1989 1 .005128261 -23.965 -.0012289877
5920 1989 1 .005405746 8.400096 .0004540879
6383 1989 1 .003368426 7.151668 .00024089865
1571 1989 1 .008939565 -50.5573 -.0045196027
7767 1989 1 .015624766 -41.4489 -.006476294
5778 1989 1 .002501765 -1.1020019 -.000027569495
6286 1989 1 .002905767 -38.00328 -.0011042869
5848 1989 1 .0043545985 -17.061995 -.0007429814
7190 1989 1 .008908107 16.349094 .001456395
5949 1989 1 .006943043 -34.996284 -.002429807
7386 1989 1 .006954857 46.54272 .003236979
5432 1989 1 .0026918836 17.859463 .000480756
5546 1989 1 .0038483934 -18.571756 -.0007147143
5894 1989 1 .0014853714 -22.564 -.0003351592
6926 1989 1 .005381981 -27.289904 -.0014687375
4063 1989 1 .003162235 2.6484454 .00008375008
7154 1989 1 .0014550128 2.8294635 .00004116906
7293 1989 1 .007206242 28.92644 .0020845092
6651 1989 1 .004246764 -19.09472 -.0008109077
3706 1989 1 .003678743 -24.972 -.0009186557
7377 1989 1 .005867993 27.22292 .001597439
7690 1989 1 .0040071923 -47.93108 -.0019206906
5412 1989 1 .005992175 -26.92 -.0016130934
5709 1989 1 .010813965 38.9516 .0042122123
7643 1989 1 .09222806 5.089854 .004694274
3671 1989 1 .012384918 -22.748404 -.002817371
7206 1989 1 .031833626 28.65433 .009121712
7390 1989 2 .005273794 -12.060838 -.0006360637
7264 1989 2 .005712387 -25.24261 -.0014419556
6205 1989 2 .0021875934 -12.025 -.00026305811
5855 1989 2 .02129368 -33.009 -.00702883
7352 1989 2 .0023920285 7.119897 .00017030997
7431 1989 2 .0015024922 -13.252995 -.0001991252
6934 1989 2 .012313752 -15.43812 -.0019010116
7044 1989 2 .0006745656 -12.6 -.00008499526
7251 1989 2 .003100922 -30.682505 -.0009514406
7163 1989 2 .00337834 10.3735 .000350452
7328 1989 2 .007641471 -16.498404 -.0012607208
8524 1989 2 .002493548 11.125556 .00027742112
7642 1989 2 .004656721 7.383255 .0003438176
7671 1989 2 .00651066 .7762522 .00005053914
5405 1989 2 .0034687656 22.992077 .0007975412
6317 1989 2 .008145512 18.259995 .00148737
5870 1989 2 .004111515 3.3480055 .00013765374
5649 1989 2 .06085714 -1.4989974 -.000912247
8363 1989 2 .007868862 52.01782 .00409321
7213 1989 2 .002673004 -46.74128 -.0012493965
6950 1989 2 .02087567 -2.994668 -.000625157
8041 1989 2 .00554842 -27.315035 -.001515553
7151 1989 2 .0045993677 -22.624403 -.0010405795
8473 1989 2 .0018168894 52.158 .0009476531
5484 1989 2 .002844367 .1649995 4.693192e-06
5944 1989 2 .009971262 4.3994555 .00043868125
end
I hope someone here is able to help me find out how to calculate a weighted standard deviation. I have included a datasample by Dataex at the end of this post, as it's rather long.
I've got panel data on stock performance, firms are identified with an id and have observations for each year. I've calculated Abnormal Returns (AR) and sorted stocks from low to high in quintiles by the variable CI (CI_quintile). My aim is to show the abnormal returns to an investment strategy that invests into all the stocks listed in a CI_quintile. The problem is, if I invest a single Dollar into the portfolio this dollar is divded over all these stocks according to their portfolio weight (varname = weight), because a large company makes up a larger share of the portfolio of course.
An individual stock's weighted Abnormal Return is weight * AR = wAR.
When doing descriptive statistics, I can do for example:
Code:
tabstat AR, by(CI_quintile) statistics(count mean semean median max min) columns(statistics)
If I want to look at the outcome of a portfolio strategy, I use the following code to calculate the yearly weighted return of an investment strategy into each CI_quintile and create the table below:
Code:
gen wAR = weight * AR bysort year CI_quintile: egen weighted_total_AR = sum(wAR) tabstat weighted_total_AR, by(CI_quintile) statistics (mean semean median max min) //Because weighted_total_AR is an average, but egen generates observations for all. I just want to look at the first occurence of weighted_total in each year/group. bysort year CI_quintile: egen first = _n tabstat weighted_total_AR if first ==1, by(CI_quintile) statistics (mean semean median max min)
But, the standard deviation displayed in the second column is not the right one. This is calculated using the variance between the mean returns of the portfolios.
What I'm actually interested in is the weighted portfolio standard deviation. I can calculate this for each year's portfolio by hand, doing this:
In which 'w' is the weight of a stock in a portfolio, 'M' is equal to 'N' for me. and 'x' are means. The standard deviation of a group CI_quintile should then be the average those individual standard deviations calculated with that formula.
Doing it by hand is not an option for me, as I will need to do it for a lot of portfolios. Is the only option in Stata to calculate this weighted standard deviation by typing the formulas in by hand?
I'm hoping someone can help me find a quick way or trick to do this! I've searched the help pages for additional options in calculating standard deviations, etc. but I was unable to find what I'm looking for.
Data example below, I've made it this long so there's stocks of each quintile in it.
* Example generated by -dataex-. To install: ssc install dataex
clear
input float id int year float(CI_quintile weight AR wAR)
7458 1988 1 .003308191 .04755842 1.5733234e-06
7348 1988 1 .01979438 27.21212 .00538647
5423 1988 1 .006723564 -25.21848 -.0016955804
3706 1988 1 .005498273 -3.8384776 -.00021104998
7495 1988 1 .005953363 40.70152 .002423109
5709 1988 1 .006956758 26.44152 .0018394728
7683 1988 1 .002354228 43.05568 .0010136289
5940 1988 1 .004853771 -7.738739 -.0003756207
7496 1988 1 .00430986 -12.85874 -.0005541937
5533 1988 1 .001597837 -27.52244 -.0004397637
5821 1988 1 .006222964 1.7612606 .00010960262
5711 1988 1 .02864698 38.50694 .011031074
7209 1988 1 .007841516 -36.861877 -.00289053
6417 1988 1 .011576707 -25.737875 -.002979598
5486 1988 1 .014225017 -34.136192 -.004855879
5894 1988 1 .0027281865 -36.06244 -.0009838507
7097 1988 1 .0010399593 -25.13244 -.00026136715
6978 1988 1 .0019874882 -65.942444 -.0013105983
5840 1988 1 .00982461 12.952124 .0012724957
8354 1988 1 .02637184 31.396776 .008279908
5398 1988 1 .004116211 35.78768 .0014730964
6304 1988 1 .008858877 -9.938478 -.0008804376
5949 1988 1 .009482821 21.666206 .0020545677
5872 1988 1 .04225229 -5.378726 -.002272635
7206 1988 1 .02326138 -18.393063 -.00427848
7385 1988 1 .009919709 -18.677795 -.0018527828
6141 1988 1 .010994663 -21.157877 -.0023262373
6816 1988 1 .00971225 -34.093796 -.0033112746
5848 1988 1 .005435659 -11.66874 -.0006342728
7264 1988 1 .008940009 91.58195 .008187435
5501 1988 1 .02630546 -9.908727 -.002606536
8194 1988 1 .0015744547 116.97 .0018416398
7954 1988 1 .0006245719 -24.11289 -.00015060234
5524 1988 1 .0018336992 -42.28289 -.000775341
7757 1988 1 .012448753 59.1412 .007362343
6032 1988 1 .03246628 111.37627 .036159735
7085 1988 1 .005526206 -4.744877 -.00026221166
7083 1988 1 .00499736 18.115747 .000905309
6821 1988 1 .000877853 19.46686 .0001708904
7031 1988 1 .004767775 -64.56488 -.003078308
8037 1988 1 .0007281441 -20.45289 -.00014892654
3976 1988 1 .002622888 19.17756 .0005030059
6948 1988 1 .06607924 32.777126 .021658873
8446 1988 1 .0042028353 -63.46425 -.002667298
5475 1988 1 .004709554 -14.628477 -.0006889361
5418 1988 1 .010878066 .01212345 1.318797e-06
6138 1988 1 .0040314705 27.215406 .0010971811
6555 1988 1 .00775756 11.361523 .0008813769
5717 1988 1 .018076962 -16.627876 -.003005815
5496 1988 1 .03864232 -6.418726 -.002480345
7254 1988 1 .003252011 484.86795 .01576796
7145 1988 1 .07200812 -3.9270766 -.002827814
7294 1988 1 .003709455 -40.03103 -.001484933
6462 1988 1 .018823624 -1.3978765 -.00026313102
5870 1988 1 .008651262 -13.30874 -.001151374
6340 1988 1 .008757503 4.581522 .0004012269
7923 1988 1 .0027628676 -59.12244 -.001633475
7154 1988 1 .001613059 -40.30289 -.0006501094
6665 1988 1 .009262182 -24.833794 -.0023001512
5974 1988 1 .09308114 .786275 .0007318737
6946 1988 1 .032222416 47.52064 .015312297
5604 1988 1 .0037643795 -3.112319 -.0001171595
8504 1988 1 .004078392 15.433672 .0006294457
6836 1988 1 .0020328404 45.48768 .000924692
7217 1988 1 .013693974 32.054104 .004389481
6607 1988 1 .002903632 20.31768 .0005899506
6495 1988 1 .003260328 8.757681 .00028552912
6958 1988 1 .013698054 18.946796 .0025953425
5523 1988 1 .04979282 3.9112735 .0019475333
7184 1988 1 .003675088 65.49897 .002407145
5446 1988 1 .0123105 -19.09788 -.002351044
6859 1988 1 .003496818 -35.66232 -.0012470464
5397 1988 1 .0020494745 -46.04244 -.0009436281
5382 1988 1 .0031159546 45.20768 .001408651
5781 1988 1 .0020171476 -68.512436 -.001381997
7149 1988 1 .013541284 -3.033204 -.0004107348
6056 1988 1 .002672791 -43.60244 -.001165402
5655 1988 1 .05581209 -18.313065 -.010220904
5945 1988 2 .00463354 -1.204877 -.00005582845
6923 1988 2 .04139749 14.199373 .005878184
7144 1988 2 .0020478633 -57.57103 -.001178976
6309 1988 2 .0012699616 2.237681 .00002841769
7311 1988 2 .022528274 33.696278 .00759119
7204 1988 2 .0028297885 -48.55125 -.0013738978
5491 1988 2 .05930467 -13.633725 -.008085435
5824 1988 2 .002104283 -44.38244 -.0009339322
6362 1988 2 .0011264324 -8.682319 -.00009780045
6944 1988 2 .04139796 -7.973727 -.00330096
3869 1988 2 .0022640927 174.80896 .003957837
6647 1988 2 .03457022 46.43628 .016053123
6817 1988 2 .009060114 66.086205 .005987485
6921 1988 2 .02863818 70.34693 .02014608
5417 1988 2 .016566856 -14.123064 -.002339748
8473 1988 2 .00104213 -18.272894 -.0001904273
5412 1988 2 .004920411 -5.548478 -.0002730079
7151 1988 2 .0041635614 22.27852 .00092758
7386 1988 2 .002524859 40.87705 .0010320878
7192 1988 2 .004963919 26.25626 .0013033395
7405 1988 2 .007562788 -15.563204 -.001177012
5402 1988 2 .004635505 10.291522 .000477064
7328 1988 2 .00989378 53.80212 .005323063
6165 1988 2 .015527252 -31.34708 -.00486734
7734 1988 2 .002977996 10.388747 .00030937645
7243 1988 2 .0037797566 28.486946 .0010767372
5851 1988 2 .00394911 -25.584877 -.0010103749
8441 1988 2 .0039315196 3.245123 .00012758265
6970 1988 2 .017720142 -30.607077 -.005423618
7402 1988 2 .0024529074 -49.38103 -.001211271
5719 1988 2 .011361913 -31.06619 -.0035297135
5617 1988 2 .00308466 -37.54874 -.0011582511
7478 1988 2 .0035551065 -20.288477 -.000721277
7729 1988 2 .0033146436 -12.550977 -.0004160202
7413 1988 2 .002824081 -13.994253 -.000395209
6188 1988 2 .001548599 -11.94232 -.00018493863
5510 1988 2 .02763647 32.986275 .009116242
7349 1988 2 .0021389024 5.027107 .00010752492
6444 1988 2 .001595943 -17.962318 -.00028666836
8098 1988 2 .010091296 -46.3632 -.004678648
5858 1988 2 .00995357 -25.07619 -.002495976
6387 1988 2 .0017723136 -11.55232 -.00020474332
6047 1988 2 .011706795 -11.537877 -.0013507155
7228 1988 2 .0036947995 -32.694252 -.001207987
7444 1988 2 .004679574 -40.86488 -.0019123022
6818 1988 2 .028311545 -12.187077 -.00345035
6805 1988 2 .006330253 44.80099 .002836016
5707 1988 2 .25637916 -20.983725 -.0537979
7190 1988 2 .003115911 -16.884253 -.0005260983
5791 1988 2 .015835643 -57.34708 -.009081278
5845 1988 2 .0030567776 -51.24488 -.001566442
6648 1988 2 .008569831 -34.613205 -.002966293
6197 1988 2 .024474245 -26.30873 -.006438862
8041 1988 2 .005248919 99.51575 .0052235
7363 1988 2 .002289636 -33.84289 -.000774879
5442 1988 2 .01524141 -47.93306 -.007305675
6124 1988 2 .001596411 -24.57232 -.0003922752
6930 1988 2 .03641654 52.37858 .019074466
5482 1988 2 .033051092 -11.578727 -.003826896
8482 1988 2 .010423547 10.012124 .0010436184
5432 1988 2 .0018044064 -68.802895 -.001241484
7164 1988 2 .0009581085 -65.68103 -.0006292955
5495 1988 2 .004479999 -33.118477 -.0014837076
6919 1988 2 .01121801 5.850806 .000656344
6651 1988 2 .0021987841 48.70921 .0010710104
5995 1988 2 .003910561 -12.33874 -.00048251395
6971 1988 2 .001034832 -25.23244 -.00026111337
6205 1988 2 .0029855745 -24.16848 -.000721568
5461 1988 2 .00498731 -10.508478 -.00052409037
1571 1988 2 .00548985 -43.0032 -.002360811
8454 1988 2 .00383496 8.991261 .0003448113
7312 1988 2 .004747315 -10.678477 -.000506941
5399 1988 2 .02433521 65.471275 .015932571
6826 1988 2 .00601999 -31.88619 -.0019195458
7416 1988 2 .002490614 134.89755 .003359778
5613 1988 2 .0021592996 2.457681 .00005306869
6789 1988 2 .001412181 180.52898 .002549396
6012 1988 2 .006848043 -13.387877 -.0009168075
6913 1988 3 .04084988 31.08292 .012697336
6793 1988 3 .0042613777 54.11652 .0023061095
5769 1988 3 .0044555734 -26.13619 -.0011645172
8524 1988 3 .0017429963 -10.454877 -.0001822281
6201 1988 3 .05990786 -2.725325 -.0016326838
8097 1988 3 .004850253 -25.023205 -.001213689
5485 1988 3 .0787017 -29.518726 -.02323174
7202 1988 3 .003989745 -36.293793 -.0014480298
6800 1988 3 .0079699615 17.086206 .001361764
5756 1988 3 .00467556 -24.70619 -.0011551529
6949 1988 3 .008540733 9.826796 .0008392804
6035 1988 3 .023817774 -26.364063 -.006279333
7427 1988 3 .0014571343 -30.97289 -.0004513166
7628 1988 3 .0019216284 129.47617 .002488051
7166 1988 3 .0007566451 2.0971072 .00001586766
7730 1988 3 .001180102 9.018971 .00010643308
6017 1988 3 .06806776 2.056275 .0013996603
5827 1988 3 .0040634973 -1.8178765 -.00007386936
7428 1988 3 .0021379942 -68.524254 -.0014650446
6939 1988 3 .00689385 -.673204 -.00004640967
6979 1988 3 .034165345 -28.513723 -.009741812
5440 1988 3 .008331418 -17.436193 -.001452682
5629 1988 3 .007418692 -11.377876 -.0008440896
5690 1988 3 .0088299615 .6321235 .00005581626
7327 1988 3 .0013162995 9.077107 .00011948192
7643 1988 3 .02775778 -4.334364 -.001203123
5859 1988 3 .0011151162 -34.95232 -.000389759
8028 1988 3 .00950104 9.851274 .0009359733
7234 1988 3 .006829689 148.7038 .010156007
5839 1988 3 .07762425 -16.843725 -.013074816
6655 1988 3 .018472217 12.077623 .0022310049
6934 1988 3 .00785568 10.247707 .000805027
6894 1988 3 .016273174 10.152174 .001652081
5549 1988 3 .0021736952 6.731261 .0001463171
7261 1988 3 .010401885 35.372925 .003679451
7140 1988 3 .008885165 8.083205 .0007182062
8141 1988 3 .003636674 11.791522 .0004288192
5614 1988 3 .005748686 -45.30379 -.002604373
7293 1988 3 .0018526403 45.44512 .0008419346
7201 1988 3 .01150976 -25.298077 -.002911748
5721 1988 3 .009840135 -16.103064 -.001584563
5525 1988 3 .01986303 -6.538726 -.001298789
7393 1988 3 .06301429 48.50827 .030567145
6210 1988 3 .03263719 4.267936 .0013929345
7426 1988 3 .00049524015 -27.93103 -.00013832567
7373 1988 3 .008607878 33.675205 .002898721
7783 1988 3 .003173958 7.685747 .0002439424
7387 1988 3 .0029896726 44.89575 .001342236
5463 1988 3 .005716034 -19.73619 -.0011281276
5492 1988 3 .002470293 -29.96874 -.0007403156
7160 1988 3 .0006015808 -9.761028 -.00005872048
6943 1988 3 .0037111884 -9.274253 -.000344185
5826 1988 3 .011805595 -55.00306 -.006493439
7300 1988 3 .0010871016 -55.03102 -.0005982432
5855 1988 3 .017826866 -18.453724 -.003289721
5380 1988 3 .01225065 -12.247077 -.0015003466
6334 1988 3 .0014612634 7.787681 .00011379852
6051 1988 3 .002620656 -12.678477 -.0003322593
6796 1988 3 .003035093 19.335123 .000586839
5770 1988 3 .006713375 -5.326192 -.0003575673
6642 1988 3 .0609761 -.5287265 -.0003223968
6801 1988 3 .004390524 -25.653795 -.0011263359
5438 1988 3 .01051369 34.106937 .0035858974
7170 1988 3 .00054701295 -51.56103 -.0002820455
6156 1988 3 .05557616 -12.989727 -.007219191
6317 1988 3 .005031617 11.932123 .0006003787
6942 1988 3 .0015643643 -1.0210284 -.000015972604
7671 1988 3 .003283729 -50.82487 -.0016689514
5378 1988 3 .005568911 4.0938077 .0002279805
5853 1988 3 .0021910374 -11.92874 -.00026136314
5741 1988 3 .0015700816 -40.49244 -.0006357644
5554 1988 3 .004331509 -13.497877 -.0005846618
7171 1988 3 .006491927 -32.823204 -.0021308586
5610 1988 3 .008699799 -13.027877 -.0011333991
5416 1988 3 .01258314 -35.613064 -.0044812416
5720 1988 3 .0012657337 -10.532442 -.00013331267
8397 1988 3 .005552394 1.3897058 .00007716195
5624 1988 4 .05806098 -19.793724 -.01149243
3671 1988 4 .00607062 29.252125 .0017757853
8402 1988 4 .00122507 -4.913442 -.00006019309
7362 1988 4 .005687082 10.156796 .00057762535
7756 1988 4 .0012734267 37.337105 .0004754607
5708 1988 4 .013533988 -23.97708 -.003245055
5883 1988 4 .005295252 -50.66379 -.0026827755
7554 1988 4 .005735876 52.59091 .003016549
8444 1988 4 .0030944906 4.485123 .00013879171
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end
Comment