I'm hoping some of you guys can help me out. I am applying the paramametric portfolio optimisation of Brandt, Michael W., Pedro Santa-Clara, and Rossen Valkanov. in which the weights on specific assets are determined by historical characteristics. Brandt et al have use lagged FF3 and 1 year lagged momentum to explain asset returns. I extent this research by including option based characteristcs specificially, impplied volatilitty (iv), skewness (skew), and implied volatility spread(ivs.
I ran the optimisation multiple times, once with lagged option characteristics and also with comptemporanous (non lagged) characteristics. The coefficients/ sign on these optimisations changes sign 180 degrees (from + to - an vice versa) For example when using non lagged implied volatility the coefficient appears negative, implying that the portfolio tilts away from firms with high call iv, otherwise the lagged optimisation shows that the portfolio will tilt toward firms with high lagged call implied volatility.
What could explain this? Would there be a possibility of slow diffusion between the option market and stock market, so that implied volatility is negative untill it diffuses towards the stock market leading to higher returns?
What would be the main argument for not using non-lagged option based characteristis. Would there be a problem of look ahead bias?
For completeness: I am using optionmetrics to obtain implied volatilities, using 1 month call/put options with delta 50. Skewness is defined as difference in implied volatility between a 25 delta put (30 day exp) and a 50 delta call. Implied volatility spread is defined as the difference between a 30delta call and a 30 delta put (30 day exp).