As we showed earlier today, last Thursday's unexpected, historic VIX explosion, driven by a surge of geopolitical worries about North Korea, and subsequent collapse was remarkable in both how fast and furious it was both on the way up and then, on the way down.As Bank of America said "*both the spike in vol and the speed of its retracement were almost unmatched*."

The move was also unprecedented in the sheer volume of VIX-related products - futures, options and ETFs - that participated in the surge higher as thousands of vol sellers suddenly scrambled to cover their positions (even if they were ultimately replaced with a new set of vol sellers). As BofA calculated, "volume in VIX-linked products reached an all-time high" with volume in VIX call and put options reaching a $250M

vega. VIX futures also had a record volume day with $850M while VIX ETP volumes hit $830M.

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In retrospect, the biggest surprise about last week's move - especially considering the loud warnings by famous Wall Street names such as Jeff Gundlach and Howard Marks predicted such a move - is how many people were taken by surprise by it. Or maybe they were not surprised, but just did not want or know how to hedge.

As Bank of America's Benjamin Bowler writes, "**most people ignore extreme risk as it’s simply too hard to price." **One possible reason is because deciding whether to hedge tail risks is difficult not only because of the challenge of estimating the probability of a “rare event”, but it’s also compounded by the difficulty of gauging the size of the shock, **if the event occurs. **This is likely why a majority of cross-asset volatilities remain near historical lows despite the threat of a nuclear conflict becoming most acute perhaps since the Cuban missile crisis in 1962, according to Bank of America.

And yet, if the events from last week demonstrated something, it is that just when there appears to be virtually no risk, is when the likelihood of a historic surge in volatility is greatest, as many experienced first hand last Thursday. Hence the need to hedge.

**But what? And using which product? **

Because, as Bowler also shows when it comes to discounting the probability of the next severe market shock, virtually every derviative product has a different perspective. As the strategist notes, "the decision about whether it’s rationale to hedge is really a matter of looking at the price of tail insurance embedded into option markets and asking if the probabilities they assign are “fair” or not." As he further writes, when it comes to predicting what the next "severe tail event" could look like, **"we find that not only are some markets like Gold pricing in a very low probability of Korean risk escalation, there are significant differences across assets in terms of what they imply about potential risks.**"

The chart below shows how historical worst 3M drawdowns since 2006 are priced by 3M 25- delta options across asset classes; hedges that are most underpricing their historical drawdowns are at the top and those most overpricing their tails are at the bottom. What the chart shows is that **gold call options still imply less than a 1 in 100 chance of a severe tail event over the next month, **despite being among the most reactive assets to rising Korean tensions last week. With record low Gold vol slaved to record low real rates vol, this represents a loose anchor which likely won’t hold in any significant geopolitical risk escalation. In contrast to gold, **Nikkei is at the other end of the spectrum with options assigning over a 5% chance of a near term tail-event.**

Looking at 3M 25-delta options, however, may not be the best measure of the price of “rare event” risk priced into options.

As BofA suggests, "*to get a better understanding of this implied risk for six assets – Gold, S&P 500, NKY (Japan equity), KOSPI2 (Korean equity), UKX (UK equity) and SX5E (European equity) – we estimate what options are pricing into their extreme tails using the following methodology:*"

- For each asset across its entire sample history, we identify the ten largest “vol-adjusted” drawdowns within 1-month periods. The reason for normalizing by volatility is that we have shown that while nominal asset drawdowns can significantly vary historically, vol-adjusted drawdowns are more evenly distributed. In other words, the probability of a 1-day drop in the S&P 500 equivalent in magnitude to the 1987 US stock market crash (-21%) is virtually zero at today’s low vol levels. So for each historical drawdown, we adjust for the prevailing vol level and assume we were to see a similar “sigma-drawdown” today.
- We then compute the probability that options are assigning to markets falling to (i) their 10th worst historical drawdown and (ii) the average of their 10 worst drawdowns in each asset (as shown in Chart 10).

BofA's analysis confirms that Gold is indeed pricing in the smallest probability of a “tail event”. The implication also is that should a "tail event" occur, the return from a gold-based hedge would be the one with the highest return. Here are the details:

- As implied from Gold (GLD ETF) options, the probability that Gold rallies over the next month by 10.3% (equivalent to the 10th largest vol-adjusted rally in Gold’s history) is 1.7%. The probability that Gold rallies by 14.6% (equivalent to the average of the 10 largest vol-adjusted rallies) is a mere 0.7%.
**This suggests GLD calls are implying less than a 1 in 100 chance (1 out of 143) of its average historical tail event occurring in the next month**. - At the other end of the spectrum is NKY,
**where options imply the probability that Japanese equities fall by 8.2% (10th largest drawdown) over the next month is 6.1% and the probability they fall by 10.4% (average of 10 largest****drawdowns) is 5.1% (1 in 20 chance).**

In other words, just between gold and Nikkei options, the "priced in" probability of a crash is either ~1% in the case of gold, or 5% in the case of the Japanese Nikkei.

What about S&P 500 puts? As the chart above shows, they are currently pricing in the second-highest level of tail risk after NKY, following the strong rise in S&P skew last week. **The probability that US equities fall by 7% (10th largest drawdown) over the next month is 4.5% and the probability they fall by 8.65% (average of 10 largest drawdowns) is 3.1%**.

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Why is gold such a great hedge to future volatility? One possible explanation for the relative attractiveness of gold-based hedges hinges on gold’s optionality being historically depressed. This has primarily been driven by realized volatility which has been steadily declining since the gold rally in Q1-16 and is now at multi-year lows (Chart 11). An important force behind gold’s declining volatility is real rates volatility. Indeed, real rates have a traditional relationship with gold through the channel of rational investment decisions, whereby investors measure the relative attractiveness of gold by how much they can earn elsewhere. As interest rates rise, so does the opportunity cost of holding a non-interest bearing asset such as gold.

While the relationship is not linear as not all real rate environments are created equal, and other important factors – such as the USD – impact underlying price dynamics, never before has this relationship has been so strong (see Chart 12). Importantly, real rates volatility itself has fallen to levels unseen since the start of the 2000s. This in turn has caused gold volatility to fall to ultra-low levels as correlation between gold/rates volatilities recently climbed to multi-year highs (see Chart 13).

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What are the conclusion? BofA's analysis reveals that for **those "hedging" an imminent market crash (over the next month) should be aware that the payout ratios of “tail options” is highest for Gold, and lowest for NKY and SPX. **

*So, for those who believe the above implied probabilities are too low relative to the potential geopolitical risks at hand, buying far out of the money “tail options” may be the best trade. *While there is more art than science to deciding on precise strikes and maturities, however, Table 2 below illustrates payout ratios for these six markets assuming 1M options are struck at the 10th worst vol-adjusted drawdown, but that markets fall to the average of their 10 worst drawdowns. In other words, if we get a shock that is worse than the 10th worst historical event but equal to the average of the 10 worst, what is the payout relative to cost of the tail insurance purchased today?

As shown in the table above, **deep out of the money GLD calls would offer 56 to 1 payout ratios with this methodology, far more than any other asset, followed by UKX (35 to 1), SX5E (25 to 1), KOSPI2 (9 to 1), SPX (6 to 1), and NKY (5 to 1).**

Finally, some parting words from BofA:

We see the escalation of ongoing geopolitical tensions as a very plausible candidate for

propelling both rates and gold volatilityhigher as investors flee to Treasuries and gold (both perceived as ‘safe haven’ assets). Indeed our rates strategistsrecently recommended accumulating US rate volatility in anticipation of a potential political risk-induced risk-off in September.