Why aren't skew and kurtosis traded like volatility?

This post was inspired by a recent post on low volatility here that got me thinking.

Why aren’t skew and kurtosis traded with contracts similar to the VIX? Maybe you could have “SIX” and “KIX” contracts or whatever. I know that some people say that you can get tangential exposure to skewness by trading VIX contracts (i.e., when the market drops, it drops by more than when it goes up, hence you can get second-order exposure to skewness by trading VIX), but it seems to me to be a pain in the @$$ to trade VIX contracts and get exposed to basis risk since you won’t be able to map to the skewness exposure you would like with a VIX contract than you would with our hypothetical “SIX” contract. Same thing with kurtosis.

You could make the calculation similar to VIX, based on some set of rules looking back, and users of the contract would utilize hedges accordingly to get their specific exposures.

Maybe these specific markets wouldn’t be deep enough to support SIX and KIX buyers and sellers? But I have to imagine that with all the talk being done in the markets today about skew and kurtosis, that surely there would be enough interested counterparties?

My guess is that they are too expensive or costly to hedge dynamically for there to be much demand.

I do know that some models of CAPM have used skew and kurtosis in utility functions, but found that it didn’t help much. This may have led banks to conclude that there is not much to gain by making markets in them.

My thought is that some have found that it would be too costly as well, but I am doubtful of the explanation of minimal impacts on “utility curves.” The continued discussion of utility functions to support the validity of CAPM is comical. Most people that put together portfolios for a living have no clue that utility curves are supposed to be part of the traditional optimization process, and traders definitely don’t care about any of that stuff.

So some non-practitioners put together some research showing that utility curves didn’t change much. What does that really say if nobody is monitoring portfolio outcomes by way of utility curves?

My guess is that on the one hand VIX was originally a byproduct of the BSM that no one cared about until some smart guy built products around it. Skewness and kurtosis are no inputs for any major asset pricing model and the underlying statistical principles are elusive at best to most people in the industry. The real question should be why volatility is such a dominant parameter and why it should be the only proxy for risk.

I think that this is correct, about VIX contracts being a byproduct of BSM. Clearly, BSM has many flaws, including a “volatility smile” at different strike prices which implies that actual traders of these products sense greater tail risk at distant strike prices versus the at-the-money option and are trying to bake in this risk by way of greater implied vols.

Wouldn’t it make sense to be able to directly target the offending risk parameter, if different from volatility, for this purpose? I have to imagine that some braniac number-cruncher has modeled out differences in term structure of skewness and term structure of excess kurtosis for various assets, similar to how the term structure of volatility is currently modeled out now. Granted, these would be very esoteric instruments and strategies to explain to retail and even some average institutional investors, but I have to imagine that there would be demand for these things through prop desks and highly-sophisticated institutional investors.

Here’s another item to ponder…what if “SIX” and “KIX” contracts don’t exist because structurally (since fat tails and negative skew seem to be chronic conditions in major markets), the overall market would be systemically net long excess kurtosis contracts and net short skewness contracts, and the exchanges know it would be difficult to continually find counterparties that would offset these bets? Unlike volatility, which (historically, anyways) is a very mean reversion-resistant time series?

If I could research whatever I want in my PhD program that would interest me very much. However, I’m bound to more subtle subjects. :frowning:

I’m not saying that CAPM should work with skew and volatility factors added to it. I’m just saying that people tried and didn’t find any substantial results in how the factors affected optimization and historical back tests. I don’t remember many details of the article because it’s not a result that affects my day to day work.

Nassim Taleb’s fund basically shoots for big kurtosis payoffs, but the problem is that it takes small losses, day after day, in the hopes that kurtosis-stretching outlier events make for big payoffs. But it is very very difficult to get people to withstand constant daily losses in the hopes of one day striking it big (though lottery tickets seem to work). My guess (like yours) is that it is too difficult to find counter parties for something like a kurtosis future. One could probably get this by dynamically hedging an underlying of options or double dynamically hedging a portfolio of index ETF’s but the transaction costs are likely to rise with the (I’m guessing) square of the kurtosis, though perhaps the math would make it the fourth power of kurtosis.

If you were to simply continually sell at the money straddles and buy at least 2:1 ratio of way out of the money puts and calls on the underlier would you not effectively be long kurtosis? And if you bought a different number of long puts/calls for skew?

And the whole package could be priced and traded monthly as the kurtosis/skew vehicle in one transaction?

^That would be too inaccurate. Technically there is the Corrado & Su expansion to the BSM, that takes into account skew and kurtosis. I don’t know if you could reverse that model. Probably you could arrive at conditional SIX/KIX. I guess with enough brainwork you could derive an index from such an expanded BSM.

Furthermore I don’t think making a market for such derivatives is impossible due to lack of short interest. It is all just a matter of price and expectations. I guess in 1900 nobody believed there would be somebody willing to short a call and therefore Bachelier’s work was shunned.