A more elegant measure of tail risk

April 23, 2017 09:00 AM

In recent years, some market participants have noted the the fact that the CBOE Volatility Index® (VIX®) has often been was several points below its long-term average of around 19.8, and they asked if there still continued to be strong interest in the hedging of equity portfolios. A response I give to this inquiry is to suggest that investors examine the values of a number of additional metrics, including VIX futures prices, the CBOE VIX of VIX Index (VVIX), and the CBOE SKEW Index (SKEW), in order to gain a fuller picture of trends in investor sentiment and interest in hedging.

The 200-day rolling averages in “One market, two fear gauges” (below) show that since 2008 the VIX Index generally has fallen, but the CBOE SKEW Index generally has risen. The price movements of the SKEW Index — which measures the perceived tail risk of the distribution of S&P 500 — show that there has continued to be strong interest in hedging severe left tail risk for U.S. equity portfolios in recent years.

CBOE SKEW Index values are calculated from weighted strips of out-of-the-money (OTM) S&P 500 options, and often rise to higher levels as investors become more fearful of a “black swan” event. The value of SKEW increases with the expected tail risk of S&P 500 returns. If there were no tail risk expectations and concerns, and if implied volatility for both at-the-money (ATM) and OTM SPX put options were equal, the SKEW Index would be close to 100. During the 27-year period from 1990 through 2016, the SKEW Index daily values ranged from a low of 101.23 to a high of 153.66, with an average value of 118.4.

In describing SKEW, CBOE notes, “The price of S&P 500 skewness is inconvenient to use directly as an index because it is typically a small negative number, for example -.8, -2.3 or -4.3. SKEW converts this price as follows: SKEW = 100 – 10 * price of skewness. With this definition, a price of -2.1 translates to a SKEW value of 121. S&P 500 options with 30 days to expiration are generally unavailable. SKEW is therefore interpolated from two “SKEW” values at the maturities of nearby and second nearby options with at least 8 days left to expiration.”

Options skew and hedging tail risk

Prior to October 1987, volatility skew charts often had the shape of a “smile” in that the implied volatility for the ATM options often was equally lower than the implied volatilities for both the OTM puts and calls. However, the S&P 500 (SPX) Index fell a breathtaking 24.6% over two trading days in October 1987, and the drop for the S&P 500 on Oct. 19, 1987 was more than 20 standard deviations away from the average single-day change in the S&P 500. After October 1987 investor demand for protection from extreme events with OTM index put options increased, and the implied volatilities for OTM index puts generally were higher than the implied volatilities for OTM index calls. SPX index options volatility skew charts now generally show a volatility “smirk” rather than a volatility “smile.”

“Breaking down returns” (below) shows that for a period of more than three decades, the S&P 500 Index did have more left tail risk than one might expect in a normal distribution. As shown in the histogram, the S&P 500 Index experienced three months with losses of worse than 12%, while a benchmark index that regularly purchases SPX protective puts — the CBOE S&P 500 5% Put Protection Index (PPUT) — did not have any months with losses of worse than 12%. The PPUT Index is a benchmark designed to reflect a strategy that holds a long position indexed to the S&P 500 Index, and buys a monthly 5% OTM SPX put as a hedge.

Why higher skew?

The average daily levels for the SKEW Index were from 116.9 in the 23-year period from 1990 through 2012, and a much higher 126.8 in the four-year period from 2013 through 2016. The past three years produced the highest average daily SKEW levels: 129.8 in 2014, 127.5 in 2015 and 127.6 in 2016. Why? 

A December 2015 Bloomberg story, “Who’s the Bear Driving Up the Price of U.S. Stock Options,” provides a clue. It notes, “For more than a year dealers in the U.S. equity derivatives market have noted a widening gap in the price of certain options. If you want to buy a put to protect against losses in the S&P 500 Index, often you’ll pay twice as much as you would for a bullish call betting on gains. New research suggests the divergence is a consequence of financial institutions hoarding insurance against declines in stocks.”

At a December 2015 presentation in Hong Kong, Krag (Buzz) Gregory of Goldman Sachs stated: The skew for the S&P 500 is the highest of any major market in the world, and the S&P 500 skew may remain high because of regulatory pressure on big banks to hedge big downside risks. Regulatory initiatives include: Comprehensive Capital Analysis Review (CCAR), an annual exercise by the Federal Reserve to assess whether the largest bank holding companies operating in the United States have sufficient capital to continue operations throughout times of economic and financial stress; [and the] Dodd-Frank Act stress testing, a forward-looking analysis conducted by the Federal Reserve and financial companies supervised by the Fed to help assess whether institutions have sufficient capital to absorb losses and support operations during adverse economic conditions.

Implied volatility & moneyness 

Moneyness is the relative position of the current or future price of an underlying asset with respect to the strike price of a derivative. “Measuring SKEW” (below) has volatility skew graphs with Bloomberg estimates for different slopes for the volatility skews for 30-trading day implied volatilities for SPX options on the following three dates that had different levels for the SKEW Index:

  • Aug. 24, 2015: Markets were concerned about falling prices in the Chinese stock market. The daily closing levels of both the VIX (40.74) and the SKEW (129.46) were higher than their long-term averages. The Bloomberg estimates for 30-trading day implied volatilities for SPX options were 55.1 at 80% moneyness (for the deep OTM index puts) and 32.2 for ATM SPX options.
  • Sept. 30, 2015: The SKEW Index was at 113.9, well below its average of 127.5 for the year. The Bloomberg estimates for 30-trading day implied volatilities for SPX options were 38.2 at 80% moneyness (for the deep OTM index puts) and 21.4 for ATM SPX options. The implied volatility estimate for the options at 80% moneyness was 78% higher than the implied volatility for the ATM options at 100% moneyness.
  • Jan. 20, 2017: President Donald Trump is inaugurated. The SKEW Index hit 146.33 — the third highest level dating back to 1990 — while the VIX Index closed at 11.54, well below its long-term average of 19.8. The Bloomberg estimates for 30-trading day implied volatilities for SPX options were 31.2 at 80% moneyness (for the deep OTM index puts) and only 8.6 for ATM SPX options. The implied volatility estimate for the options at 80% moneyness was 283% higher than the implied volatility for the ATM options at 100% moneyness. The Federal Reserve in its meeting minutes released on Jan. 22, “expressed concern that the low level of implied volatility in equity markets appeared inconsistent with the considerable uncertainty attending the outlook for such policy initiatives.” It is useful to examine both the VIX and SKEW indexes and the volatility skew charts to gain more robust insights on overall implied volatility and investor sentiment.

“Skewing options” (below) shows a volatility skew chart for SPX options, mid-day on Nov. 21, 2016, when the S&P 500 price was 2196.66. Many expiration dates for SPX options are shown on the left side. According to Livevol, the estimated implied volatility for the SPXW (weekly) 2085 put options that expired on Nov. 23 was 26.56. The implied volatilities for OTM puts often were higher than the implied volatilities for the similar OTM calls. The information provided in the skew chart can be helpful to traders who are considering various strike prices, maturities and tenors for their possible long and short options positions.  

Trading strategies

The CBOE SKEW Index and the volatility skew graph can provide valuable information and signals to investors above and beyond the information supplied by the VIX Index. The SKEW Index and volatility skew graph provide information helpful to both hedgers and traders in identifying times in which OTM SPX puts are relatively expensive compared to ATM options. At times when the OTM SPX puts are relatively expensive, one strategy that could be considered is to sell the OTM cash-secured SPX put options. Indexes that sell ATM cash secured SPX options include the CBOE S&P 500 PutWrite Index (PUT) and the CBOE S&P 500 One-Week PutWrite Index (WPUT). Over a period of more than three decades beginning in mid-1986, the PUT Index had higher returns and lower volatility than the S&P 500 and S&P GSCI indexes; a key factor in the strong risk-adjusted performance of the PUT index was the fact that there usually was a volatility risk premium that rewarded index options sellers; the implied volatility for the S&P 500 options usually was higher than the subsequent realized volatility.

It is also valuable to investors who are considering engaging in the vertical spread strategy, an options trading strategy with which a trader makes a simultaneous purchase and sale of two options that have the same expiration dates and same underlying security but different strike prices.

Hedgers who contemplate the purchase of SPX OTM protective puts can use the SKEW. The SKEW Index and volatility skew graph can help hedgers to gain a better idea of the relative cost of the strategy. Investors could consider the put spread collar strategy.

Trading signals?

Technical analysts often study sentiment indicators such as put/call ratios, bull/bear ratios, short interest and implied volatility to gain a better idea of changes in investor sentiment. “Skewing returns” (below) has two tables that show select days with very high or very low values for the SKEW and VIX indexes, and the subsequent percentage changes for the S&P 500 Index during the next five and 30 days. The tables are presented to stimulate ideas for more analysis, and are not designed to provide a robust and exhaustive analysis of the topic of whether the SKEW and VIX indexes can serve as useful trading signals. Some analysts believe that the VIX can serve as a contrarian indicator, and that when the VIX is at relatively low levels there can be much complacency in stocks and that low levels of the VIX might be a bearish indicator. The bottom half of the table shows the S&P 500 went up on the five days after VIX hit its yearly high levels. In doing your analysis of extreme values of VIX and SKEW, it would be useful to determine whether the indexes are leading market moves or merely coincident indicators in relation to market moves. There will be occasions when either is the case, which is important in determining what the index is indicating. 

The SKEW can serve as a good complement to the VIX for analysts and traders who are trying to gain insights on investor sentiment and potentially better options strategies. It is another tool for your toolbox.

The views expressed here are those of the author and do not necessarily reflect the views of Chicago Board Options Exchange Inc. (CBOE). 

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