Generating CAPM Beta

[Sartaj Hussain]

I want to use below code to generate monthly CAPM beta which is equal to beta coefficient of mkt obtained each month by regressing rt on mkt using twelve months daily rt and mkt data from months beginning t-11 and ending month t. However, before i use the code, I want to confirm that whether it is correctly specified. The code and data set example is appended below.

* Example generated by -dataex-. For more info, type help dataex
clear
input int stock_id str10 month str52 stock float(pr mk rf)
1 "29-06-2001" "3M India Ltd."  380.1 1050.43 .000190118
1 "02-07-2001" "3M India Ltd."    380  1044.7 .000190118
1 "03-07-2001" "3M India Ltd."    382 1016.12 .000190118
1 "04-07-2001" "3M India Ltd."    373 1012.19 .000189043
1 "05-07-2001" "3M India Ltd."    370 1016.32 .000189043
1 "06-07-2001" "3M India Ltd."    363 1008.44 .000189043
1 "09-07-2001" "3M India Ltd."  370.1 1005.61 .000189043
1 "10-07-2001" "3M India Ltd."    365 1015.86 .000189043
1 "11-07-2001" "3M India Ltd."    365  1023.1 .000189043
1 "12-07-2001" "3M India Ltd."      . 1045.89 .000189043
1 "13-07-2001" "3M India Ltd."  379.8 1047.82 .000189043
1 "16-07-2001" "3M India Ltd."  374.5 1043.17 .000189043
1 "17-07-2001" "3M India Ltd."    384 1038.48 .000189043
1 "18-07-2001" "3M India Ltd."      . 1035.52 .000191194
1 "19-07-2001" "3M India Ltd."    380 1029.28 .000191194
1 "20-07-2001" "3M India Ltd."    367 1021.48 .000191194
1 "23-07-2001" "3M India Ltd."      . 1017.91 .000191194
1 "24-07-2001" "3M India Ltd."    364 1007.34 .000191194
1 "25-07-2001" "3M India Ltd."  362.1  992.87 .000190118
1 "26-07-2001" "3M India Ltd."    345  983.87 .000190118
1 "27-07-2001" "3M India Ltd."    335  985.08 .000190118
1 "30-07-2001" "3M India Ltd."      .  997.06 .000190118
1 "31-07-2001" "3M India Ltd."  325.1 1007.38 .000190118
1 "01-08-2001" "3M India Ltd." 321.35 1002.07 .000187969
1 "02-08-2001" "3M India Ltd."    318 1007.21 .000187969
1 "03-08-2001" "3M India Ltd."    323 1016.31 .000187969
1 "06-08-2001" "3M India Ltd."  332.5 1016.84 .000187969
1 "07-08-2001" "3M India Ltd."    332  1009.8 .000187969
1 "08-08-2001" "3M India Ltd."    330 1005.47 .000186894
1 "09-08-2001" "3M India Ltd."    330 1005.16 .000186894
1 "10-08-2001" "3M India Ltd."  325.9 1001.29 .000186894
1 "13-08-2001" "3M India Ltd."    330  991.02 .000186894
1 "14-08-2001" "3M India Ltd."    325 1004.51 .000184742
1 "16-08-2001" "3M India Ltd."    320 1006.83 .000184742
1 "17-08-2001" "3M India Ltd."    320  998.73 .000184742
1 "20-08-2001" "3M India Ltd."  301.3  993.36 .000184742
1 "21-08-2001" "3M India Ltd." 309.55  998.08 .000184742
1 "23-08-2001" "3M India Ltd."    305  998.48 .000184742
1 "24-08-2001" "3M India Ltd."  302.5 1001.45 .000184742
1 "27-08-2001" "3M India Ltd."    315 1005.27 .000184742
1 "28-08-2001" "3M India Ltd."    315 1003.13 .000184742
1 "29-08-2001" "3M India Ltd."      . 1001.18 .000183666
1 "30-08-2001" "3M India Ltd."    323  999.71 .000183666
1 "31-08-2001" "3M India Ltd."      .  986.25 .000183666
1 "03-09-2001" "3M India Ltd." 311.05  976.87 .000183666
1 "04-09-2001" "3M India Ltd."    324  980.81 .000183666
1 "05-09-2001" "3M India Ltd."    321  976.21 .000183666
1 "06-09-2001" "3M India Ltd."  316.9  967.46 .000183666
1 "07-09-2001" "3M India Ltd."    318  968.13 .000183666
1 "10-09-2001" "3M India Ltd."    317  965.93 .000183666
1 "11-09-2001" "3M India Ltd."    310  959.32 .000183666
1 "12-09-2001" "3M India Ltd." 303.85  924.96 .000187969
1 "13-09-2001" "3M India Ltd."  305.4  915.84 .000187969
1 "14-09-2001" "3M India Ltd."    290  861.02 .000187969
1 "17-09-2001" "3M India Ltd."  257.3  804.92 .000187969
1 "18-09-2001" "3M India Ltd."    280   836.2 .000187969
1 "19-09-2001" "3M India Ltd."    290  840.08 .000193344
1 "20-09-2001" "3M India Ltd." 278.95  826.37 .000193344
1 "21-09-2001" "3M India Ltd."    272  792.18 .000193344
1 "24-09-2001" "3M India Ltd."    271  815.18 .000193344
1 "25-09-2001" "3M India Ltd."    270  807.94 .000193344
1 "26-09-2001" "3M India Ltd."  261.5  821.67 .000187969
1 "27-09-2001" "3M India Ltd."    260  825.81 .000187969
1 "28-09-2001" "3M India Ltd."    266  850.56 .000187969
1 "01-10-2001" "3M India Ltd."  276.5   844.2 .000187969
1 "03-10-2001" "3M India Ltd."    270  832.46 .000184742
1 "04-10-2001" "3M India Ltd."  263.8  842.15 .000184742
1 "05-10-2001" "3M India Ltd."      .  844.87 .000184742
1 "08-10-2001" "3M India Ltd."  273.5  831.16 .000184742
1 "09-10-2001" "3M India Ltd."    270  842.27 .000184742
1 "10-10-2001" "3M India Ltd."    278  861.97 .000185818
1 "11-10-2001" "3M India Ltd."    270  875.14 .000185818
1 "12-10-2001" "3M India Ltd."  265.5  878.54 .000185818
1 "15-10-2001" "3M India Ltd."  262.2  880.39 .000185818
1 "16-10-2001" "3M India Ltd." 259.85  891.59 .000185818
1 "17-10-2001" "3M India Ltd."    260  906.58 .000187969
1 "18-10-2001" "3M India Ltd."  261.9  890.81 .000187969
1 "19-10-2001" "3M India Ltd."    260   899.6 .000187969
1 "22-10-2001" "3M India Ltd."    265  903.64 .000187969
1 "23-10-2001" "3M India Ltd."    265   916.9 .000187969
1 "24-10-2001" "3M India Ltd."  261.6  912.92 .000178282
1 "25-10-2001" "3M India Ltd." 263.25  909.88 .000178282
1 "29-10-2001" "3M India Ltd." 265.85  911.35 .000178282
1 "30-10-2001" "3M India Ltd."    265  895.86 .000178282
1 "31-10-2001" "3M India Ltd."    270  902.84 .000180436
1 "01-11-2001" "3M India Ltd."  274.9  916.37 .000180436
1 "02-11-2001" "3M India Ltd." 265.95  918.84 .000180436
1 "05-11-2001" "3M India Ltd."    270  919.12 .000180436
1 "06-11-2001" "3M India Ltd."    275  932.31 .000180436
1 "07-11-2001" "3M India Ltd." 270.25  920.84 .000180436
1 "08-11-2001" "3M India Ltd." 274.75  931.26 .000180436
1 "09-11-2001" "3M India Ltd."  271.5  934.92 .000180436
1 "12-11-2001" "3M India Ltd."    273  942.81 .000180436
1 "13-11-2001" "3M India Ltd."    285  937.24 .000180436
1 "14-11-2001" "3M India Ltd."  289.9  950.69 .000180436
1 "15-11-2001" "3M India Ltd."    290  968.45 .000180436
1 "19-11-2001" "3M India Ltd."  297.2   997.2 .000180436
1 "20-11-2001" "3M India Ltd."    288  986.23 .000180436
1 "21-11-2001" "3M India Ltd."    290  994.23 .000180436
1 "22-11-2001" "3M India Ltd."    288 1003.35 .000180436
end

gen date1=date(month,"DMY")
format date1 %td
drop month
rename date1 date
gen mdate= mofd(date)
format mdate %tm
bysort stock_id (date): gen rt_r =((pr[_n]-pr[_n-1])/pr[_n-1])
bysort stock_id (date):gen mkt_r =((mk[_n]-mk[_n-1])/mk[_n-1])
gen rt = rt_r-rf
gen mkt = mkt_r-rf
gen month = month(date)
gen year = year(date)
rangestat (reg) rt mkt, interval(mdate -11 0) by(stock_id) 
collapse(mean) mdate reg_nobs stock_id b_mkt, by(stock year month)
drop if mdate<ym(2002,6)
drop if mdate>ym(2003,5)
replace b_mkt =. if reg_nobs<200
rename b_mkt beta

[Clyde Schechter]

This looks fundamentally sound. The code appears to do what you seek.

I have one concern, which perhaps is not a real problem. There are gaps in the dates, most of which appear to relate to weekends. I suppose the others are holidays or other reasons that perhaps markets are closed or do not report prices. Anyway, becaues the returns of both the individual stocks and the market are calculated from the difference between consecutively reported prices, it means that sometimes the returns are for a 1 day period, often for a 3 day period, and occasionally for 2 or 4 days. So there may be a problem with pooling observations based on different time periods in the same regression. This could be a source of heteroskedasticity. I would also think that the returns would tend to be larger in magnitude over longer periods of time, though, presumably that is equally true of both the individual stocks and the market, so maybe this is not an issue. And although the number of calendar days between successive observations may vary, if these are due to weekend and holiday closures, then all observations may really reflect just one day's worth of trading, so maybe this isn't a problem at all. I don't work in finance, so I don't know the answer to this, nor, really, the best way to think about it. So I would check with somebody in your field about this if you do not feel confident making this determination yourself.

[Sartaj Hussain]

This is how stock market data is usually and hence returns are daily returns for days when markets trade.

[Clyde Schechter]

Thanks for clearing that up for me.