# Multiple regression on hedge fund returns

I have a data set of long/short equity hedge funds returns and their associated benchmarks (market indices). I need to form multiple regression on the fund returns using the benchmarks returns as independent variables (i am allowed to form linear combination or manipulation of the indices or even non-linear combinations). Of course, I do not know which independent variables to choose. Are techniques such as subset selection, Lasso, and Ridge supposed to be used in situation like this?

• Can I ask, is this for a professional or academic project? Also, are you restricted to only using fund returns as your independent variables? – David Addison Feb 14 '18 at 6:07
• From your own question, it sounds like you are being asked to regress the hedge fund returns (dependent variable) against the benchmarks (independent variables). It further sounds like you can use ordinary least squares, and/or some using some non-linear function and/or transform your variable such that you can use OLS. – AlRacoon Feb 14 '18 at 14:58
• @DavidAddison Hi David. Good to see you again. I would say it is a professional project. Well, fund returns are 'dependent' variables and their indices should be independent variables. – Jun Jang Feb 14 '18 at 15:21
• @AlRacoon Hi AIRacoon, you are correct. I am asked to regress the hedge fund returns (DV) against indices returns (IV). I can use OLS and/or some using non-linear function and/or transform my variable such that I can use OLS. You are right. From my understanding, there have been many academic studies where they regress hedge fund returns (dependent variables) against market variables such as S&P500, Treasury yield spread, credit spread, etc. (independent variables) but not against only benchmarks and their combinations/manipulations. – Jun Jang Feb 14 '18 at 15:23
• @JunJang. My only thought is that it depends on what you're trying to do. If it were me, and I was trying to simply "describe" each fund's style through its exposure to various international benchmarks, then any number curve fitting techniques may work. If, however, I was to trying to "predict" the funds' returns, then I would inform my supervisor that this is not possible with the data given. – David Addison Feb 14 '18 at 18:51