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Regression on equally- and value-weighted returns for funds

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Hi there experts,

I received splendid help last time (thanks Nick Cox + Joseph Coveney) and was wondering regarding a regression I am trying to run on funds, before/after fees. I adjusted my data universe in Stata in accordance with below:
Date Fund Name Fund Return Net Fund Return Gross Fund Size Market risk premium
2001-01-31 Fund 1 4,2 4,32617 19716488006,0 X
2001-01-31 Fund 2 5,7 5,81227 194165768,0 X
2001-01-31 Fund 3 3,4 3,55422 422431153,0 X
2001-02-28 Fund 1 -5,3 -5,1255 19284833552,0 Z
2001-02-28 Fund 2 -13,3 -13,12707 198439370,0 Z
2001-02-28 Fund 3 -4,7 -4,56866 421806529,0 Z
2001-03-31 Fund 1 -10,8 -10,64289 20171831942,0 Y
2001-03-31 Fund 2 -13,1 -12,99907 204030245,0 Y
2001-03-31 Fund 3 -12,0 -11,86222 444887777,0 Y
2001-04-30 Fund 1 10,0 10,17476 20557372063,0 M
2001-04-30 Fund 2 12,2 12,35831 209740158,0 M
2001-04-30 Fund 3 10,7 10,81611 307815552,0 M
2001-05-31 Fund 1 2,6 2,70044 19919384588,0 N
2001-05-31 Fund 2 -1,3 -1,14742 200211325,0 N
2001-05-31 Fund 3 2,5 2,66869 299116102,0 N
2001-06-30 Fund 1 -3,6 -3,47347 20634754178,0 P
2001-06-30 Fund 2 -5,1 -4,99922 212068898,0 P
2001-06-30 Fund 3 -3,7 -3,56978 316508935,0 P

Now I am trying to regress the funds upon a market premium to test a model called CAPM within finance, trying to find pricing errors (alpha.) This market risk premium is on a monthly basis. My question is how I am to conduct this regression on both an equally- and value weighted level in relation to the fund sizes. The output should look something in accordance to the below illustration (arbitrary numbers.)
αlpha βm
Net Gross
Equally Weighted Returns -1,15 0,22 1,02
Value Weighted Returns -1,13 -0,19 0,99
Thanks in advance!

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