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Hi,

I am trying to analyse 100 funds' excess returns with classical factors by using the SUR model as a system which was relatively easy, except quite limited outputs for Wald's restriction tests where I set either alphas or betas as zeros.

Now, I would like to estimate how up-market and down-market or alternatively Recession dummy (1) and expansion dummy(0) as a refrence group have effects to the excess return. ( I have already created one-to-zero dummies (US recession add-in)

Could you provide advise how to write the following equation in a SUR system equation for 100 funds:

(Rit-Rft) = αi + βi (Rmt-Rft) - ciD(Rmt-Rft) + eit

where D = 0 if Rmt-Rft > or = an up market
=1 if Rmt-Rft < = Down market

βi is the up-market beta and (βi - ci) is the down-market beta and ci is the difference between the up-market beta and down-market beta.

+ would be Rit-Rft = αi + βi (Rmt-Rft) + eit
0 would be Rit-Rft = αi
- would be Rit-Rft = αi + (βi - ci) (Rmt-Rft) + eit

Hence, succesfull timing world have a positive ci, and if its statistically significat, it reflects manager talent.

I am thankfull to any advice, since I am new to this. :D