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# EQD Research: Seasonality In VOLQ And NDX Realized Volatility

Apr 12, 2021

A common rule of thumb is that option implied volatility is overpriced more often than it is not. Stated in a more direct fashion, over a long period of time option sellers will be expected to profit from this semi-consistent state of option pricing. However, there are also periods of time where case where option selling strategies do not offer returns as there are times where short option traders who are also short volatility will feel the pain of getting steamrolled by a dramatic move out of the underlying.

The specifics behind the overpricing of options is that implied volatility is an indication of a one standard deviation move in the underlying security. For those that need a quick brush up, an observation of a series of data would be expected to fall within up or down one standard deviation 68.2% of observations.

I always like to test out these common perceptions in the market and set out to do so by comparing the Nasdaq-100 Volatility Index (VOLQ) at the end of each month to the subsequent realized volatility over that month. Using VOLQ data from January 2014 through March 2021 we took a look at how often realized volatility was greater than the expectations for realized volatility as indicated by Nasdaq-100 option pricing. The initial result matched up pretty closely to the one standard deviation statistical assumption with 66.7% of monthly observations falling inside the one standard deviation threshold and the other 33.3% resulting in moves that were of greater magnitude than what was expected by the option market.

With that we began to slice and dice the data a bit. The first break down was to explore of there is any seasonality around NDX option pricing and realized volatility. We broke out the monthly observations that show up in the table below. Each monthly data point represents VOLQ – Realized Volatility.

The individual monthly results are color coded with the red representing the bottom 25% of months based on subtracting realized volatility from VOLQ. These red figures are the months where VOLQ understated the realized volatility over the following month. The green months are those where VOLQ greatly over stated the subsequent realized volatility while the blue represents the balance of months or the middle two quartiles and includes months where VOLQ both understated and overstated realized volatility by a small amount.

An interesting outcome of this testing was that April and July are two of the three months where there is only one observation with VOLQ understating the following month’s realized volatility. Both of these months are months where a good portion of Nasdaq-100 components report their earnings. The other month was November, which may be a function of VOLQ often being elevated coming out of October.

Since all implied volatility should be considered within some sort of context we compared the average VOLQ by month from 2014 through 2020 to the average VIX by month for each month from 2014 through 2020. Elevated volatility in the first three months of 2021 skewed the average monthly results a bit so we chose to narrow the observations a bit. The rankings appear below with the highest levels in green and lowest in red.

March is the highest average month for both VOLQ and VIX with April and October ranking in the top three for both measures. The March result is due to the market reaction to Covid last year and April may have been impacted as well. October just seems to be a month where the markets are on edge regardless of the environment. There is no real pattern here and what is very interesting is July, the other month where VOLQ was overpriced going into the month is at the bottom of both lists. That is definitely a nice anecdotal example of making sure volatility expectations are taken within context.

While looking at the side by side July numbers for VOLQ and VIX, we noticed there is a pretty wide spread between the two. That got us back on the earnings announcement path of running numbers. The final quick study we ran compared the average VOLQ in the four earnings months versus VIX and then the same figures for the eight non-earnings months.

The outcomes of this shows the following stats:

- VOLQ averages a premium of 1.01 to VIX during earnings months.
- This premium moves lower to an average premium of 0.37 during non-earnings months.
- During the months of February and March the average price for VOLQ is actually at a discount relative to VIX. The only two moths where this occurs.
- April is the only earnings month where the VOLQ premium to VIX is below the longer term average at 0.35.

The chart below shows the VOLQ minus VIX average by month with the earnings months highlighted in blue and non-earnings months in red.

There is a lot more work to do around this seasonality as well as the impact on certain strategies. We are hard at work running some numbers on straddles, strangles, and other strategies that rely on option selling to see if there is a good time to be these sorts of trades and maybe a time to reduce the size or even stay on the sidelines. The plan is to report back in the next few days with some more practical applications of the seasonal behavior of expected volatility for the NDX.