# BofA: “There Is Something Historically Unusual About Today's Market”

As one would expect, last week’s report by Bank of America’s Benjamin Bowler, in which the strategist stated that **“these markets are very weird**“…

… and in which Bank of America warned that “**US equities continue to set long-term records for instability**“, prompted many questions from traders and investors.

For those who missed our take on the BofA report last week, what Bowler noted was that the -1.8% drop in the S&P 500 on 17-May represented a five standard deviation (5-sigma) event relative to trailing volatility, the third such outsized drawdown in stocks in less than a year, but only the 18th since 1928. Moreover, it was followed by the second-fastest retracement of a 5-sigma drop since 1928, illustrating the power of today’s “buy-the-dip” mentality.

So, in a follow up note released overnight, Bowler writes that he received a number of follow-up questions from investors sceptical that either the 17-May drawdown or the subsequent reversal were as striking as we suggested, given that the nominal decline in the S&P was “only” -1.8%.

But before we give Bowler the podium, here is the one observation that drew the greatest market response. When asked if prior low vol periods also saw frequent high-sigma SPX drawdowns, Bowler notes comparable periods to 2017 of ultra-low S&P realized volatility which include the early 1950s, mid-1960s, mid-1990s, and mid-2000s. What he finds is that while 3 sigma (or greater) daily SPX drawdowns were as or more frequent in these historical periods as they are today, the past year stands out for having generated an unprecedented number of 5 sigma (or greater) daily declines.

In other words, Bowler says “**there is a certain “nonlinearity” to today’s market instability such that if US equities do jump from a state of calm to stress, such a jump is unusually large by historical standards**.”

One could almost make the argument that the market is broken…

* * *

With that said, here is BofA’s vol expert addressing the most frequently asked questions that resulted from his report, and shows that “**the capacity today for US equities to jump quickly from calm to sudden stress and back (“fragility”) is indeed historically unusual.”**

Yes, US equities really are historically unstable

1. Aren’t high-sigma SPX drawdowns more likely when volatility is low?This was by far the most commonly asked question, as intuition suggests that a 5? drop (for example) in the S&P 500 should be “easier” to achieve when prevailing realized volatility is low, as stocks need to fall by a smaller nominal amount. However, while this is the case for sufficiently elevated levels of volatility, it is in fact not true empirically for low to moderate levels of volatility. Indeed, Chart 12 shows no discernible bias towards high-sigma moves when S&P realized volatility has been 20% or lower, which encompasses the bulk (~80%) of realized volatility levels observed since 1928.

2. Did prior low vol periods also see frequent high-sigma SPX drawdowns?Comparable periods to 2017 of ultra-low S&P realized volatility include the early 1950s, mid-1960s, mid-1990s, and mid-2000s. While 3-sigma (or greater) daily SPX drawdowns were as or more frequent in these historical periods as they are today (Chart 13),

the past year stands out for having generated an unprecedented number of 5-sigma (or greater) daily declines (Chart 14).In other words,there is a certain “nonlinearity” to today’s market instability such that if US equities do jump from a state of calm to stress, such a jump is unusually large by historical standards.

3. Isn’t a high-sigma drawdown that’s small in magnitude easier to retrace?Intuition again suggests that the smaller the size of a high-sigma SPX drawdown, the “easier” it should be to recoup the loss quickly. In other words, perhaps the S&P 500 recording the second-fastest (3 days) 85% retracement of a 5-sigma drop in history following 17-May is not that impressive since the nominal drop was “only” -1.8%. However, as seen from Chart 15, there is little historical relationship between the size of the 5-sigma 1-day SPX drawdown and the length of time it takes to recoup the bulk of this drawdown. For example, the Feb-94 5 sigma drop in the S&P was -2.3% and took 252 days to recoup, whereas the Jun-16 Brexit-induced drop was -2.45% but took only 9 days to recover. Moreover, the only retracement since 1928 that was faster (2 days) than the recent recovery occurred in 1962 following a much larger (-6.7%) nominal decline in the S&P.

4. Is there a “limit” to how much the S&P can fall in a day when vol is low?The distribution of 1-day sigma (i.e., vol-adjusted) returns of the S&P is well-bounded in the sense that since 1928 we have never observed a drawdown larger than ~11-sigma. This occurred on three separate occasions (Chart 16) – in Sep 1955 (when realized vol was 9.5% prior to a 1-day drop in the S&P of -6.6%), in Oct 1987 (when realized vol was 29.7% prior to a 1-day drop in the S&P of -20.5%), and in Oct 1989 (when realized vol was 9.2% prior to a 1-day drop in the S&P of -6.1%).

Put differently, with realized vol around 5.7% prior to the 17-May sell-off, the most US equities could have fallen that day if history is any guide was -3.96% (= 11 * (5.7% / ?252); see Chart 17). For context, the last time the S&P 500 fell that much on a single day (on a close-to-close basis) was on 24-Aug-15, although that represented only a 3.5-sigma event at the time when measured relative to trailing EWMA volatility. With realized vol closer to 8% today, an 11-sigma drop would amount to a -5.5% decline in the S&P 500 (Chart 17); the last comparable drop occurred on 8-Aug-11, when the S&P fell -6.7% or 4.4-sigma.

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