How do I calculate annual stock beta from daily returns?

[omars92]

Hello,

I have a time series sample of 4000 firms over 18 years period (2000-2017). I am trying to find a way to use the daily returns in order to estimate the annual beta for each stock. I am unsure of what code to use. Any advice or guidance on how to structure my SAS code is highly appreciated. (SAS version 9.4)

My data is structured as follows:

PERMCO           DATE         COMPANY_NAME            RETURN        MARKET_RETURN       YEAR         PERMCO&YEAR

153                  2000-02-01                                               -0.15                                                    2000            1532000 

153                  2000-02-02                                                0.1                                                       2000

153                  2000-02-03                                                 0.2                                                       2000

153

.

.

.

153                  2017-12-28 

674

674

674

.

.

.

2114

2114

211

etc...

I would like the output to look something like shown below: (1 beta for each stock per year)

PERMCO             YEAR            BETA

153                      2000              

153                      2001

153                      2002          

674                      2015

2114                    2017 

etc...

Thank you

[Ksharp]

@Rick_SAS wrote a blog about how to run thousands of Regression before.

proc reg data=have outest=want;

by PERMCO             YEAR ;

model  RETURN = date;

quit;

[omars92]

Sorry, I should have specified that I’m trying to estimate each stock’s annual CAPM beta (ideosyncratic risk). I have thought of estimating the covariance of RETURN with MARKET_RETURN by PERMCO YEAR and divide by the variance of MARKET return but cannot find a way to get the covariance value without the covariance matrix

[Ksharp · Accepted solution]

model RETURN = MARKET_RETURN; CAPM beta is just the regression coefficient you can find at OUT=WANT table. beta(correlation ) is covariance of RETURN with MARKET_RETURN when both RETURN and MARKET_RETURN have 0 mean ,1 std .

[omars92]

Thank you Ksharp. The code worked perfectly.