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  • Interpreting CAAR Results

    Hi all,

    I have calculated AAR and CAAR and has resulted in the below. I am comparing the returns to the Fama-French 3 factor model, and have a very significant alpha. This seems like its a bit too good to be true (in showing that the fama-french model does not explain these returns). For clarity I am not concerned about each event on an individual basis per se, only their cumulative effect over the long run.

    Have I made an elementary mistake in the calculations, or does it look like it holds up?

    The actual calculations are based on equations 2,3,4 in this link, on the second slide: https://www.princeton.edu/~markus/te...escription.pdf

    Many thanks

    Code:
    sort event_window
    by event_window : egen cumulative_abnormal_return = sum(abnormal_return)
    
    gen AAR_all_eventdays = 1/241*sum(abnormal_return)
    gen CAAR_all_eventdays = sum(AAR_all_eventdays)
    
    reg CAAR_all_eventdays MktRF SMB HML if dif==0
    reg CAAR_all_eventdays MktRF SMB HML if dif==0 & Recession==1
    reg CAAR_all_eventdays MktRF SMB HML if dif==0 & Recession==0
    Code:
    reg CAAR_all_eventdays MktRF SMB HML if dif==0
    
          Source |       SS       df       MS              Number of obs =     241
    -------------+------------------------------           F(  3,   237) =    0.64
           Model |   4.9935795     3   1.6645265           Prob > F      =  0.5907
        Residual |  617.468913   237  2.60535406           R-squared     =  0.0080
    -------------+------------------------------           Adj R-squared = -0.0045
           Total |  622.462492   240  2.59359372           Root MSE      =  1.6141
    
    ------------------------------------------------------------------------------
    CAAR_all_e~s |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
           MktRF |    .119859   .0969136     1.24   0.217    -.0710632    .3107812
             SMB |   .0657994   .1834311     0.36   0.720    -.2955642     .427163
             HML |  -.0493991   .1709643    -0.29   0.773    -.3862029    .2874046
           _cons |  -1.411151   .1041861   -13.54   0.000    -1.616401   -1.205902
    ------------------------------------------------------------------------------
    
    . reg CAAR_all_eventdays MktRF SMB HML if dif==0 & Recession==1
    
          Source |       SS       df       MS              Number of obs =      97
    -------------+------------------------------           F(  3,    93) =    0.29
           Model |  .748732102     3  .249577367           Prob > F      =  0.8356
        Residual |  81.2323986    93  .873466652           R-squared     =  0.0091
    -------------+------------------------------           Adj R-squared = -0.0228
           Total |  81.9811307    96  .853970111           Root MSE      =  .93459
    
    ------------------------------------------------------------------------------
    CAAR_all_e~s |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
           MktRF |  -.0007622   .0785249    -0.01   0.992    -.1566971    .1551727
             SMB |   .0725492   .1440842     0.50   0.616    -.2135735    .3586718
             HML |   .1036188   .1669407     0.62   0.536    -.2278923    .4351299
           _cons |  -3.174789   .0958054   -33.14   0.000     -3.36504   -2.984538
    ------------------------------------------------------------------------------
    
    . reg CAAR_all_eventdays MktRF SMB HML if dif==0 & Recession==0
    
          Source |       SS       df       MS              Number of obs =     144
    -------------+------------------------------           F(  3,   140) =    1.03
           Model |  .933461494     3  .311153831           Prob > F      =  0.3822
        Residual |   42.365533   140   .30261095           R-squared     =  0.0216
    -------------+------------------------------           Adj R-squared =  0.0006
           Total |  43.2989945   143  .302790171           Root MSE      =   .5501
    
    ------------------------------------------------------------------------------
    CAAR_all_e~s |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
           MktRF |   .0560773   .0499722     1.12   0.264    -.0427204     .154875
             SMB |   .0699656   .0955959     0.73   0.465    -.1190326    .2589638
             HML |  -.0806837   .0748133    -1.08   0.283    -.2285937    .0672262
           _cons |  -.2366788   .0460216    -5.14   0.000    -.3276659   -.1456917
    ------------------------------------------------------------------------------
    Code:
    * Example generated by -dataex-. To install: ssc install dataex
    clear
    input byte(event_window estimation_window) float(abnormal_return cumulative_abnormal_return AAR_all_eventdays CAAR_all_eventdays)
    0 1           .         0            0            0
    1 0   .05959415 -7.760673 .00024727866 .00024727866
    1 0    .5421364 -7.760673   .002496807   .002744086
    1 0    .2576195 -7.760673   .003565768   .006309853
    1 0   .10945138 -7.760673   .004019923   .010329776
    1 0   .12240804 -7.760673    .00452784   .014857616
    1 0   .06451361 -7.760673   .004795531   .019653147
    1 0 -.030652797 -7.760673   .004668341    .02432149
    1 0    .3626951 -7.760673     .0061733    .03049479
    1 0     .227817 -7.760673   .007118599    .03761339
    1 0  -.14658122 -7.760673   .006510378    .04412377
    1 0   .10203883 -7.760673   .006933776    .05105754
    1 0   .21807218 -7.760673   .007838639    .05889618
    1 0   .09722055 -7.760673   .008242045   .067138225
    1 0  -.05101454 -7.760673   .008030366     .0751686
    1 0   .16639467 -7.760673     .0087208     .0838894
    1 0     -.22024 -7.760673   .007806941    .09169634
    1 0   .18104325 -7.760673   .008558158     .1002545
    1 0  -.18254925 -7.760673   .007800692    .10805518
    1 0    -.259024 -7.760673   .006725904     .1147811
    1 0   -.5607388 -7.760673   .004399187    .11918028
    1 0  -.09239985 -7.760673  .0040157847    .12319606
    1 0    .3072637 -7.760673   .005290738     .1284868
    1 0  -.53796405 -7.760673   .003058522    .13154532
    1 0  -.10400637 -7.760673    .00262696    .13417228
    1 0  -.24804254 -7.760673   .001597738    .13577002
    1 0  -.09729041 -7.760673  .0011940434    .13696407
    1 0   .12540217 -7.760673  .0017143844    .13867845
    1 0  -.10373652 -7.760673  .0012839424    .13996239
    1 0  -.05680742 -7.760673   .001048227    .14101061
    1 0   .04017539 -7.760673    .00121493    .14222555
    1 0 -.017416356 -7.760673  .0011426628    .14336821
    1 0    .4343492 -7.760673  .0029449416    .14631315
    1 0  -.13716766 -7.760673   .002375781    .14868893
    1 0  -.12441281 -7.760673  .0018595454    .15054847
    1 0  -.06934102 -7.760673  .0015718233     .1521203
    1 0    .2655262 -7.760673   .002673592     .1547939
    1 0    .0237745 -7.760673   .002772241    .15756613
    1 0    .1384742 -7.760673   .003346823    .16091296
    1 0   .18465085 -7.760673   .004113009    .16502596
    1 0    .3160078 -7.760673   .005424245     .1704502
    1 0   .28928107 -7.760673   .006624581     .1770748
    1 0   -.6030069 -7.760673   .004122478    .18119727
    1 0  -.06625619 -7.760673   .003847556    .18504483
    1 0  -.13191612 -7.760673   .003300186      .188345
    1 0   .16306625 -7.760673    .00397681     .1923218
    1 0    .2762084 -7.760673   .005122902     .1974447
    1 0  -.11553838 -7.760673    .00464349     .2020882
    1 0 -.022860376 -7.760673   .004548634    .20663685
    1 0   .25256503 -7.760673   .005596621    .21223347
    1 0    .1086689 -7.760673    .00604753      .218281
    1 0    .1841511 -7.760673   .006811642    .22509263
    1 0 -.014986612 -7.760673   .006749457     .2318421
    1 0   .01544381 -7.760673   .006813539    .23865564
    1 0  -.26508343 -7.760673   .005713608    .24436924
    1 0  -1.1647457 -7.760673  .0008806384     .2452499
    1 0   -.6206427 -7.760673 -.0016946424    .24355523
    1 0  -.11906217 -7.760673 -.0021886763    .24136657
    1 0   -.3064576 -7.760673  -.003460285    .23790628
    1 0  -.06030338 -7.760673  -.003710506    .23419577
    1 0  -.03715035 -7.760673  -.003864657     .2303311
    1 0     .208986 -7.760673  -.002997495     .2273336
    1 0   .12173986 -7.760673 -.0024923505    .22484127
    1 0  -.27226675 -7.760673  -.003622088     .2212192
    1 0  -.23810124 -7.760673 -.0046100602     .2166091
    1 0  -.19514324 -7.760673  -.005419783    .21118934
    1 0   .16322082 -7.760673  -.004742518    .20644683
    1 0   -.2799002 -7.760673   -.00590393     .2005429
    1 0  -.27891108 -7.760673  -.007061237    .19348165
    1 0  -.25054005 -7.760673  -.008100823    .18538083
    1 0   -.1664703 -7.760673  -.008791571    .17658927
    end
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