Short-term Mean-Reversion Between Implied and Realized Volatility

The VIX^{®} (CBOE Volatility Index) is an index that infers 30-day (calendar days, regularly between 20 and 22 trading days) expected (implied) market (S&P 500) volatility from S&P 500 index options (usually in the first and second month, and averaging the weighted prices of puts and calls over a range of strike prices). It closed at **41.04** last Friday.

The current 21-day **realized **(not implied) volatility closed at 49.15(%) last Friday. Thus the delta between the markets expectation of future (30-day = 21 trading days) volatility and the just experienced realized volatility during the last 21 trading days is currently at -8.11% (means the markets expectation of future volatility is trading (significantly) below the just experienced realized volatility), which could be regarded as some kind of complacency in the market (which regularly doesn’t bode well concerning the market’s short-term performance).

The table shows

- percentage wise (for those 46 session which fulfilled the conditions of w/Survey I since 01/03/2007),
- utilizing the
**VIX**(index data) itself and not any equity index, - and taking into account those sessions only after the VIX closed at least -8.00% below the then current rolling 21-day realized volatility the day before (‘
**w/Survey I**‘)

the historical probabilities (since 01/03/2007) for a higher and lower open, the average change between close and open (close -open), the average daily True Range (Wilder True Range), the historical probabilities for a higher high and lower low (than the last session’s high/low) and a higher or lower close as well as the respective sum of all profits and losses (theoretically, and for statistical purposes only due to the fact that the VIX is not a tradable asset) going long/short on open. But due to the fact that in the 2nd table probabilities significantly above or significantly below their respective at-any-time probabilities (in this case +/-15.00%, but this percentage is up to everyone’s decision what may be regarded as ’significant above’ or ‘below’) are marked by a **green **(for a probable bullish outcome) and **red **(for a probable bearish outcome) background color, one may be able to catch on a glimpse the impact of taking into account those sessions only after the VIX closed -8.00% or less below the then current rolling 21-day realized volatility on the respective probabilities and odds.

**Table I**

(click on image to enlarge)

**Bottom line:**

- On those 46 occurrences which fulfilled the conditions of
**w/Survey I**, the VIX closed -on average- the next session not only significantly above it’s opening quotation independently if it opened higher or lower, but additionally significantly above the respective at-any-time magnitudes of change. This may be regarded as some kind of a short-term mean-reversion tendency between implied and realized volatility. On those 16 sessions with a higher open the VIX’ True Range averaged**16.00%**(that would correspond to an approximately 6+ move today).

- Going long on open (that means theoretically ‘buying’ the VIX on open) would have yielded a high profit factor of above 4 (way above the at-any-time profit factor theoretically buying the VIX on open in the event the VIX opens higher), and going short the VIX on a lower open would have yielded a profit factor below 1 for a negative expectancy.
- Needless to say that on average (not to be mistaken for
*‘always*‘) -and due to the regularly inverse relationship between the VIX and the S&P 500- this didn’t bode well for the equity indexes (S&P 500, SPY) in the past (concerning the specific session after this setup had been triggered) …

Successful trading,

**Frank**

Filed under: Studies/Survey, Trading Strategies

Frank,

Really enjoy your new site. Fresh perspectives.

How do you calculate the “realized” volatility?

Thanks.

Russ,

thanks a lot.

A good step by step explanation concerning the calculation of ‘realized volatility’ can be found here: http://www.tradingacademy.com/lessons/lessons20080814.shtm

Best,

Frank