Is the skewness of returns bigger in FX or equities? I guessed equities. I think that most academics, options traders and other market participants would guess the same. I finally had time to do the analysis and I found some interesting results.
First, the realised skewness in equities has not been particularly big relative to FX. The data set from 1980 until 2014 reveals a skewness of -0.6 in US equities, whereas AUD-USD is -0.8 and USD-JPY is -0.44.
Second, and more interesting, that there is any negative skew at all in equities rests heavily on just one observation: 19 October 1987, also known as Black Monday. If we take this one, single observation out of our sample, the realised skewness of equities drops to just -0.15. Fascinating.
The charts below contain a full set of results. The first shows realised skewness by decade across several currencies and equities, all plotted in XXX-USD. The second chart is the same, but it filters out Black Monday.
Third, the bottom chart shows a positive skewness in USD-CHF (negative in CHF-USD) in the 2010s data set. That result also lies heavily on one single observation: the SNB's 6 September 2011 intervention to weaken the CHF during the European sovereign debt crisis. Without this observation, the realised skewness of USD-CHF is close to 0 for the 2010s.
The fact that single observations in data sets spanning several decades can affect our realised skewness statistics so dramatically poses a challenge for options pricing. A significant proportion of the price of skew in options depends on one of the hardest things for a trader to properly quantify: the conditional probability of an extreme event.
