The term black swan refers to rare events that are unpredictable in nature. These events are mathematically difficult to compute and statistically insignificant. Black Monday on October 19, 1987, is a typical example. One may consider the COVID-19 pandemic a black swan as well.
CBOE launched the SKEW Index in 1990, and it has been considered the black-swan index in finance. Normally, SKEW above the 150 level is taken as a black-swan signal, indicating that a catastrophic event might happen during the next 30 days, with a nontrivial probability.
To dig a little deeper, the SKEW Index uses out-of-money options to track the S&P 500 tail risk. Tail risk rarely happens, but it hurts when it does happen. The circled area in Figure 1 points to those uncommon returns. Unless they are gamblers, most agents use those out-of-money options as a hedging position, particularly if they are deeply out-of-money. Hence, we can extrapolate key information on how the market perceives the forward-looking underlying risk through those options. SKEW ranges between 100 and 150 most of the time. At close to the 100 level, black-swan concern is negligible; at the 150 level there is over a 15% probability that a large downside return might happen.
Figure 1. S&P 500 One-Month Log Return & Normal Return, 1990–2009, Same Mean and Std. Deviation as S&P 500.
The SKEW didn’t hit 150 until June 28, 2016. In the two and half decades prior to that, it had had been above 146 level on only three occasions. (The probability of a black swan event is roughly 14.5% at 146.) The first occurrence was on October 16, 1998, one day after the Fed decreased the target fund rate and discount rate in the middle of the Russian financial crisis and Long-Term Capital Management collapse. The next one was on September 19, 2014, after the Fed pledged to keep interest rates near zero for “a considerable time.” The last one was on December 11, 2015, days before the anticipated Fed rate-hike meeting, as crude oil fell below $36 a barrel to a new seven-year low. On that occasion, we find that the one-month S&P 500 return was quite violent in both directions. But the market was less volatile and turned positive in the ensuing 6-month period. Interestingly, there was no black swan event after June 28, 2016, though the Brexit referendum occurred just five days prior. The SKEW index has hit above 150 14 times since then, although there were no black swan events within 30 days after each time. The latest 150 level was read on December 19, 2019. The post-150 returns are mixed in the short term, while positive in the long term.
The returns are not surprising, as the 15% probability of a black swan is still a low figure, after all. This is not to deny the efficacy of SKEW. However, SKEW has been unbelievably suppressed throughout the COVID-19 sell-off. It briefly touched the 140 level in mid-February and dropped to 110 afterwards. So is SKEW accurate? In our view, SKEW is merely a reflection of market perception through traders’ lenses; obviously, it cannot be a trading indicator from the absolute point of view.
Leo Chen, Ph.D.
Portfolio Manager & Quantitative Strategist
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