In theory skewness should decay with time since for long enough periods the distribution should become closer to normal. There is also an empirical law of skewness decay by sqrt(T). There's a lot more interesting and juicy stuff on this but way over my head. So I am testing this on SPX data taking as skewness measure PUT(95)-Call(ATM) for 30days up to 1y. (The data is from ivol and from their interpolation but should be OK for this purpose? ) The results seem to be varying a lot. A lot of days not only the power law is not holding but it seems that the decay is inversed at 180/360days ie skewness starts to increase at around 180 days (you get a U curve) Does this show some risk premium that would be possible to trade, eg with a calendar - sell the 1year RR buy the 3month?