A recent WSJ article titled “Four Things Sure to Happen in Markets During 2018” mentioned the fact that for equity investors, “the apparent lack of risk may be a risk in itself” and cited a study by David Le Bris, a finance professor at Toulouse Business School in France, who studies market crashes. His point is that “a fall has a stronger impact on a stable market than on a highly volatile one and therefore a crash is not a certain percentage decrease during a specific period but represents an important discrepancy compared with what was previously observed”.
In other words, you need to put the absolute size of a market downturn into its proper volatility context. The definition of a crash cannot simply be a constant percentage fall in prices. It must represent a severe departure from the expectation of the current environment. “In a highly volatile market, a fall of x % has more limited repercussions than on a market used to great stability.”
Using monthly data for the FTSE World Developed, Emerging, and Asia Pacific ex-Japan indices, we used Le Bris’ adjustment method to reclassify a 5% and 10% market fall (in a single month), in the context of the current low volatility regime to understand what would constitute a market crash in 2018. In our study, the ‘expected loss’ is defined as one standard deviation (per month) of the adverse future price movement predicted by Axioma’s relevant risk model. We used a 12-months rolling windows to calibrate the ‘current’ norm for investors. This period is a good representation of a ‘stable’ environment since it does not contain the Trump surprise win, Brexit, nor the China Crash.
The charts below represent the rolling Z-Score (left axis) of a 5% and 10% market fall respectively on each of the three regional indices mentioned above, against the volatility-implied expected one-standard deviation loss (right axis). As noted by Le Bris, when volatility is low, expectations for a market fall are equally low and even a 5% fall in quiet times can have big consequences on portfolios, especially leveraged ones.
A 5% monthly fall in the FTSE World Developed today would represent a two-standard deviation event compared to just a 1.14 one in June 2016, at the time of Brexit. A 10% fall would be a four-standard deviation event today! In all cases we looked at, today’s levels are at or near new highs for the history of the model (i.e. going back to 2001). By way of comparison, a 10% fall at the low volatility point in 2008 (August), was only a two-standard deviation event.
If your definition of a crash is a three-standard deviation event, then this translates into a 7.5%, 11.1%, and 9.9% monthly fall for the FTSE World Developed, FTSE EM, and FTSE APACxJP respectively. A steep discount to what it would have taken in the past! So even if you think the downside risk is only 10% from here on, in terms of market shock, this would still cause a lot of pain to a lot of people.
 Note that the link refers to a badly translated English version of the original study in French.
 To put these into perspective, Brexit caused an initial shock of -11% in the first two days, and (worst) -18% over the next four months. We also have data for a 15%, 20%, 25% and 30% fall.
 We also tested a 24-months and 36-months window which include those events – data available upon request.
 See WSJ article on investors abandoning hedges as stocks hit new highs.