Investment

FIN 683 Style betas from multifactor models

Regress returns of portfolio i on the four return premia (four X variables and four different betas).

ri = rf + β M i (rm − rf )︸ ︷︷ ︸

market premium

+βSi SMB︸ ︷︷ ︸ size

premium

+βHi HML︸ ︷︷ ︸ BE/ME premium

+βUi UMD︸ ︷︷ ︸ momentum premium

+�

Style betas can indicate a tilt in the portfolio toward a particular characteristic. For example, suppose the portfolio contains all big (large-cap) stocks. That portfolio’s returns should behave like the ’B’ in the SMB portfolio, where the ’B’ is the return of a benchmark portfolio of big stocks. The ’B’ portfolio has a negative weight in SMB; so the portfolio’s beta on SMB should be negative.

Style betas

positive negative zero βS small-cap large-cap neither βH value growth neither βU momentum contrarian neither