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A VIX-ing Paradox

By Lawrence G. McMillan
Source: Barron's

Traders of volatility derivatives -- futures, options, or exchange-traded funds and notes -- often wonder why the VIX, or the Chicago Board Options Exchange Market Volatility Index, moves much more violently than do the derivative contracts that are based on it.

This particularly vexes derivative holders when the market plunges and the VIX (which rises as fear grows) climbs by far more than the futures do. I use the futures as a measuring stick, because the prices of the others -- options, ETFs, ETNs -- are based on the futures' prices.

Consider what happened on Aug. 8, when the Standard & Poor's 500 Index fell 6.7% and the VIX exploded to 48 -- 50% above its previous close. Near-term VIX futures didn't come close to that level. Instead, August futures settled at 36.55, up 25.3%, a huge discount of 11.45 points. September futures ended at 30.20, up 15.3% -- a stupendous 17.80-point discount.

Such differences prompt complaints about futures traders: "Why are they keeping the futures so low? Are they predicting a decrease in volatility? They must be crazy!"

But the discrepancy has nothing to do with the traders' opinions. Rather, it reflects a simple reality: The VIX and VIX futures don't have identical components.

Yes, the prices of both reflect the implied volatilities of SPX options, which are based on the S&P 500. But the VIX is a 30-day volatility estimate, using the two nearest-term strips of SPX options. On Aug. 8, it was a weighted calculation of the August and September SPX options.

The VIX futures, however, are based on just one strip of SPX options -- those that expire 30 days after the VIX futures do. Hence, the August futures were based on the SPX September options. And the September VIX futures were based on SPX October options.

The table nearby shows the implied volatilities of certain SPX options at the close of trading on Aug. 8. On that day, many traders were buying SPX puts, mostly August short-term options, for which they were willing to pay dearly. Those purchasing September options were paying far less. And October buyers were paying even less.

The out-of-the-money August SPX options' high volatility clearly influenced the price of the VIX. However, those options don't figure in the calculation of either the August or September VIX futures. Instead, the August futures (priced at $36.55) combined the implied volatilities listed under September in the table. And the September futures (priced at $30.20), reflected the volatilities listed under October. The price of the VIX itself ($48) reflected both the August and September columns.

Upshot: If you were long the VIX futures or the calls, you didn't come close to realizing profits commensurate with the big move in the VIX.

Eventually, at expiration, the VIX and its near-term futures converge in price. But anyone who expected them to move in lock step while the stock market was tanking on Aug. 8 was very mistaken.

Source: Barron's - A VIX-ing Paradox published 10/15/2011 

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