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Trading Differences in Skewness and Tail Risk Across Regimes

Article Quant Q&A · Author: Chris
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Summary

The document asks whether differences in higher moments of returns can support relative-value trades. It proposes dividing observations into groups using an external variable, such as volatility regimes, and comparing the return distributions. If one group has different skewness or kurtosis, the question is how to express a trade that isolates that feature rather than simply taking a view on its average return.

It offers no proposed strategy, empirical results, or evidence that these distribution differences are stable or tradable. The volatility example is only an analogy: selling options after realized volatility rises assumes it will revert, while option prices also depend on other factors. Any higher-moment strategy would likewise need to distinguish a persistent, forecastable distributional difference from sampling noise and account for the instrument’s exposure to other risks. The document frames an open research question rather than providing a tested method.

Key ideas

  • The document asks whether return-distribution differences across groups can motivate relative-value trades.
  • It suggests sorting observations by an external factor, such as volatility regime, and comparing the resulting distributions.
  • A useful trade would need to isolate skewness or kurtosis exposure from differences in average returns.
  • The document proposes no specific instrument, strategy, or empirical validation.

Tags

StatisticsVolatilityOptionsRisk management
Full text
# Are there ways to trade differences in distribution between (or within) assets?


# Are there ways to trade differences in distribution between (or within) assets?












It's common enough to examine asset returns, or grouped subset asset returns, compare across them and make some investment decision, either directionally or via a spread/relative value trade.

Can do something similar with the second moment, whereby, for instance, like to like the options on an asset with higher vol will be more expensive than one with lower vol. More pointedly, if an asset has a LT volatility of 20% and we see it's 30d rolling SD spike to 30%, we could sell its volatility by writing call or put options with the expectation its premiums would revert lower once its vol returned to normal (again, ignoring the impacts of greeks, other inputs, etc).

Is there a corollary though for higher momemnts (eg, skew, kurtosis)?

For instance, for a given asset, say I quintile based on some exogenous factor (eg, v high/high/med/low/v low volatility regimes) and plot density functions for each subset's daily change in price. In a situation where there was no meaningful or impactful info represented in the exogenous var, I'd expect PDFs to look pretty similar, like this:

But say it looked like this--where density for the v high vol group had a distribution noticeably different from the others:

Taking as given the differences are meaningful, what would the trade be (trading based on the fact one group shows more 'skew' than the others and not just based on having a negative mean where others are close to 0)? Same question for the fourth moment--one subgroup shows higher peak/fatter tails (or the inverse) than the others, what's the trade?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.