Convert monthly volatility to annual volatility

[Miral Ayan]

Dear all,
I have calculated the monthly volatility from the market model and now want to annualise it. May I seek your guidance on how to annualise the total volatility? Below is the data:


dataex PERMNO DATE RET tvol ivol exret

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* Example generated by -dataex-. To install: ssc install dataex
clear
input double PERMNO long DATE double(RET tvol ivol exret)
10001 18109   -.04708201438188553  .08289202070028498  .08188363281432942   -.06270162926807615
10001 18017    .04462098702788353   .1165001737347956  .11257741083653544   .014912350178509903
10001 17955    .05622203275561333  .11517802925164382  .10871759094349727      .126415342178361
10001 17927   .034140389412641525   .1141635610631263  .10520607004808531    .09546376416506384
10001 18078   .019445838406682014  .08321462265398194  .08148416004406007   .018561529255079184
10001 18046   .002941122744232416  .08266560779063693  .08118362845119823  -.015858538120206933
10001 17897     .1559889167547226   .1136977485686472  .10332962475355326    .14597400888946818
10001 17987   -.08053683489561081  .11664023970774141  .11451353232322233    -.1322164159203304
10001 18231    .00709455506876111  .05795523530342138 .052898662816276185   .009207247501119273
10001 18170   .012283406220376492  .07342032358738194  .07328719277023761   .004850228450360757
10001 18200    .03780274838209152  .07330058087707882  .07325366394323743   .039122224642664565
10001 18140     .0533742792904377  .08477966107314294  .08324501990084149    .04843238760493684
10001 18319 -.0006561087793670595 .059749323306738975 .057981231378127114   .010027587362489293
10001 18443  -.043421052396297455  .06261712982112598  .06198158835495011   -.04395890704090459
10001 18291   -.01893201656639576 .060551878363260994  .05773897184654667  -.030368002035141298
10001 18382    .12438547611236572  .05885882165854039  .05801381610235683     .1258308009388172
10001 18410   .004828733392059803 .058783283484517036 .058782221570570226   -.01849752487861112
10001 18352    .02064267173409462  .05141156467371459 .051320740393985945    .04229408010446295
10001 18262    .16262087225914001   .0593159067218374  .05518665686938645    .17271220760797004
10001 20697   .036619752645492554 .059716673400645556 .059336787679531905    .03557238378777417
10001 19964     -.121411994099617  .10542461923600302  .06236612931320194  -.028101137070330934
10001 20269   .030000019818544388  .08909625762471526  .08677311320472317   .020008521284799182
10001 19904    .00905626267194748  .07341608385390458  .06406026806216793    .03913781475709113
10001 18837   -.02813851833343506  .06450380494534641 .051789281370344165 -.0034856871262632094
10001 18596   -.11843638122081757   .0858788769342062  .07278326429049418    -.1229909466823498
10001 20300   -.01310683973133564   .0549859493688872 .054979916237431384  -.002048189403000028
10001 20544  -.006361347157508135  .06435631761685391   .0642459258205094  -.011800982327738227
10001 19570    .01601940579712391 .026360504128852998 .023285515301973363  -.017970038273898398
10001 19173  -.027325015515089035 .035850883858485345 .033676654369881896   -.03692281271592435
10001 18658    .02899232506752014  .07372658527618116  .05984864664237741    .01360129944580023
10001 19782   .025626998394727707  .06482983647364668 .060213093247420815    .07019120625367473
10001 19754     .1475716531276703  .06448261306717097 .058437340708629104    .15713440495232664
10001 20605  -.021917851641774178  .06471995000594091   .0646807761590783  -.023141033312999527
10001 20422  -.009070286527276039  .04866411056667872 .038773047671773364  -.013496538998663285
10001 19873  -.033486224710941315  .07342015345273656  .06502158449860612   -.01015954387510595
10001 18535    .07655959576368332  .07474438218515314  .06291122973239247   .009291848056484475
10001 19113  -.015000010840594769 .025601569517845396    .025304503241687   -.01474304547737851
10001 19023   -.01970231719315052 .032471739341617054 .032468890277517454    -.0235475442719068
10001 20482    .11677850782871246  .06447936598274827  .06380058172760082    .16842559531753612
10001 20635  -.021008417010307312  .06269466457478907  .06255683165004529  -.021182106760081098
10001 18931   .005004570819437504 .049269454951454454  .04865511226898758   -.02635315785110723
10001 19205   .009405865333974361  .03542638109968229   .0335508723161782   .007645763337734478
10001 18746  -.038789428770542145  .06922086716198117  .05564522244529798   -.06246557070116639
10001 18778   .028049908578395844  .06953681448654252  .05163619616283711   .037842834511068756
10001 18627   .052290886640548706  .07404677369686652  .05972254061897235  -.004670706511056277
10001 20208   .011044141836464405    .089353234447125   .0872757329653507   .015686597395023608
10001 18717    .07240437716245651   .0755444541601926  .06178291364544361    .06865029157466232
10001 20178 -.0004950829315930605  .09285777033895848  .09017561824068883  -.010641635651274045
10001 20453    -.1321510225534439 .058794285262147035  .04733414018552459   -.11556778419877738
10001 20391  .0016778658609837294  .04966688312703281  .03905220180633302   -.07483562745470657
10001 20027   -.03513971343636513  .10643490119838803  .06362620653403493   .041589581332912504
10001 18991    .05183490738272667  .03182295685081616  .03160886462864912   .050733917812853156
10001 18870  -.013864110223948956  .05424725757474078 .048671739293090176   .043160846311068396
10001 19445   .030684128403663635  .03740332628933982 .026499008001385868  -.005130687662898481
10001 18473    .08333339542150497 .060022407752283666  .05504253620430069    .07082768535319311
10001 19297   .012676090002059937  .03554938785362936 .031986324078941884   .018812641482170128
10001 19264  .0005010060267522931 .035314340552280006  .03208358378656931  -.005400313299616395
10001 18808   .008260886184871197  .06769755678520212  .05237094861335776    .02612258786252615
10001 20664   .026466401293873787  .06440649439737332  .06396076049158068   .022404349501927507
10001 20118    -.1152450442314148  .09494467215145609  .09020913965550155   -.19835195481010373
10001 19082   .048759933561086655 .028155923896831817 .028113035971459033     .0491048383587052
10001 19631   .004411764908581972 .026621917649172724  .02232909257331326  -.016259344588718284
10001 19478   .017156874760985374  .03785379850759561 .027035024784125467   .004002496960035001
10001 20727    .04211955517530441   .0615017031944498  .06111054416804355    .04235299252544003
10001 20513    -.0552884116768837  .06444691182200389   .0643880615613229  -.055331146780704964
10001 18564    .03281479328870773  .07470133362914774  .06202548398538237   .005121924318808098
10001 20758     .6199479103088379  .19117817189776432  .18347833069875502     .6159467735297098
10001 19662  -.018137210980057716 .027493196305337125  .02337733240570769   -.04024754764189022
10001 20088    -.0378260463476181  .09299592173083271  .06313603067202733   -.03958973643854727
10001 20331   -.11166499555110931  .05332485598570385  .04373926882759861   -.10983829379325886
10001 19537   .006323002278804779 .026222954351896793   .0231641967059385   .012769119986490385
10001 19600  -.016794651746749878  .02668168783694074 .022246710460061943 -.0023115757818769796
10001 19509 -.0004840453912038356 .027974959116018838  .02602101614382176   -.02484477615205327
10001 18686   .022727256640791893  .07365768243393905 .059357114302998226  -.004752057381225212
10001 19691   -.13490474224090576   .0472444575124007 .046517669896701926    -.1524486117861972
10001 20788    .01214571762830019  .19073304906734334    .183052377995879     .0950413037866816
10001 19358  -.015231147408485413 .032878857505729754 .028026153424314977  -.021414450605082888
10001 19935    .22722963988780975  .09683352063865444  .07503423397384806     .2013944571996909
10001 19996   .050975240767002106  .10573993166792336  .06523388505777993  -.013633735754786463
10001 20361  .0033669734839349985  .04964576328862792  .03811865599222282    .03317385886029737
10001 19144   -.08436109870672226  .03544097166370442  .03280331300087826   -.07974699118488246
10001 18900   .005009128712117672  .05007057202311355 .048734388913781145    .04810259700133391
10001 18961  -.005000034347176552  .03186427551737327 .030906288110561682  -.004582708504840722
10001 19843    .08797208219766617  .07230268081533073  .06396590469929168    .08604307765619414
10001 20146   .035897474735975266  .09511618962800593  .09180521103908236    .10782130801490158
10001 20573  -.055697791278362274  .06484836640633422  .06479249561054741   -.05660262567211502
10001 19327  -.045504387468099594  .03762931802057508 .033974628568261965   -.04942401842210585
10001 19813    .07959409803152084  .06827390997712601  .06150310994012547    .08309675951796748
10001 19417   .011651438660919666  .03933186950585774 .028550596804665613  .0008837268275411325
10001 19723   -.05885783210396767  .04987026522879985   .0493392904218954   -.06795592832019327
10001 19236  -.012315278872847557 .035387072128742036  .03372988890061648  -.017738966400599326
10001 20818    .01000001560896635  .18286898406025245   .1679057500203045   .038228368071874005
10001 19389    .06270096451044083 .039129191387695855  .02864769592802455   .032143286686207924
10001 19052   .005004517268389463 .032111613815859266  .03210666737161573   .004626025157123079
10001 20237   -.00695131067186594   .0887580574274477   .0868822423498433  .0023675376922927278
10001 20055   .017180582508444786  .09467174834369847 .056452436577817414    .10027874776377907
10001 18505   -.11126279085874558  .07328516691441833  .06379637287463269    -.0879783111064351
10002 18627    .06374505162239075  .19051750311029206  .18772159349539244    .02681226799160523
10002 18046   -.36626139283180237    .284759017422604    .282845782890377   -.40519700859424757
10002 18017    .03949446976184845    .265230578100853  .25786188865315574   -.04292068612693625
end
format %td DATE

Thanks in advance

[Attaullah Shah]

The general formula of converting monthly volatility to annual is

sqrt(12)*monthly volatility

Though you have not specified the variable name that has the monthly volatility values, let me assume that the variable tvol has monthly volatility, then

gen vol_yearly = sqrt(12) * tvol