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).

  • $\begingroup$ I am not sure what you mean by lagged and nonlagged. If you are trying to "explain" (in a statistical sense) the returns for 2018, it would be legitimate to use the IVs determined as of Dec 31, 2017. It would not be legitimate to use the average IV for all days in 2018 or the IV for December 31, 2018 (because, as you mention, of lookahead bias). $\endgroup$ – Alex C Aug 23 '19 at 18:13
  • $\begingroup$ For momentum, you could explain the returns of 2018 by the cumulative returns in 2017. Is that what you mean by "lagged"? I imagine that is what Brandt does, although I have not looked at the paper in a while. $\endgroup$ – Alex C Aug 23 '19 at 18:15
  • $\begingroup$ @AlexC Exactly. Okay to be more precise. Initially I constructed the matrices of characteristics using the end op the month option data, meaning I took call implied volatilities at the last trading day of the month. I matched these against returns from last month obtained from CRSP. These charactereristics are used to optimise/ set parameters for the the portfolio at t+1. As also explained in this thread (insightr.wordpress.com/2018/02/12/parametric-portfolio-policies) The momentum characteristic I indeed calculated as you described. $\endgroup$ – incognito Aug 23 '19 at 18:59

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