Futures on Variance and Deviance

Variance futures have more drawbacks than advantages.
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"Don't look back. Something might be gaining on you." -- Satchel Paige
"Want to sell more window insurance? Learn how to throw rocks." -- Howard Simons

Economic decision-making has been compared to driving at 80 miles per hour while looking solely at the rearview mirror, and we economists certainly have the results to prove it. But historic data are far more available than future data, so what else are you going to use?

Risk and uncertainty enter into this equation as well. We are no longer at risk to past events, only to future developments. But as anyone who has ever bought insurance knows, actuarial tables have to be based on past events; they live in the rearview mirror too.

The insurance industry, particularly its reinsurance segment, revels in pricing esoteric risks. The spreads are richer than those available for mundane risks, and they also present intellectual challenges greater than those associated with driving the family chariot into the garage door.

Both futures and options have insurance components, and an over-the-counter market has grown around realized price variance, so it was only a matter of time before an exchange-traded futures contract on variance arose -- in this case at the Chicago Board of Options Futures Exchange. The specifications of these futures and the methodology behind them can be found

here.

Implied vs. Historic Volatility

The world of options trading is based on a market-derived assessment of future events. The standard Black-Scholes model contains five variables, four of which -- current price, strike price, time to expiration and the risk-free interest rate -- are known exactly at all times. The fifth, implied volatility, can be derived from the market price of options to allow for the model's solution.

Implied volatility and the historic variance of returns, or daily percentage price changes, measure different things -- the market's price of future uncertainty and a relative frequency distribution of events, respectively -- so we have no reason to expect them to be equal. Indeed, a long-term comparison of variance, the CBOE's new volatility index based on the

S&P 500

index and Parkinson's high-low-close volatility -- a measure that incorporates intraday range as well as interday change -- shows significant differences.

Different Measures, Different Concepts

Source: Howard Simons

Variance Drawbacks

The mechanics of constructing variance restrict its scope to the daily percentage changes of closing prices. A market environment wherein 20-point daily ranges on the S&P are common would be classified as having low variance if the settlement prices were close to one another. This is intuitively incomplete: We all know that the wider the daily range, the lower the probability of any one price in the range representing the fair value of the index. The closing price may be more important for cash-flow reasons -- positions are marked to this price for account valuation purposes -- but it has no greater economic importance than other points in the range, and indeed it may be subject to manipulation by index arbitrageurs, especially around expirations.

The Parkinson measure incorporates the effects of intraday range, and for this reason it will exceed variance in all but the most strongly trending markets, such as the bear market collapse in 2002. The Parkinson measure produces a lower volatility during strong trends, for the straightforward reason that such markets, while producing big price changes, are actually fairly certain about the direction in which they are moving.

Variance falls far below implied volatility as measured by the VIX during protracted trading ranges, such as January to March 2004. While the backward-looking measure is falling, uncertainty about the magnitude and even direction of the eventual breakout is increasing. To which measure do you feel more exposed?

Variance and Price

The relationship between the VIX and price has been discussed here previously; it is not as simple as the "price collapses, VIX surges" word association embedded in the public's mind. The relationship between price and variance is even less direct.

It is true variance rose quite sharply during the crises involving Asia, Russia and Long Term Capital Management of 1997 to 1998, and even more rapidly during 2002, but these were markets in obvious distress on all other measures. We could say that the low variance of the early and mid-1990s was associated with the general bull market, but it was also associated with the yearlong trading range of 1994. The big market top of 2000 saw an oscillating variance measure that, as in 1997 to 1998, added no further analytic value.

Does Variance Measure Price Risk?

Source: Howard Simons

Does the present upturn in variance from a low level presage an impending collapse, or is it more analogous to similar moves in the early 1990s? Finally, and most important, are we better off using forward-looking measures like the VIX than backward-looking variance? I will go with the VIX, and only on an either-or basis.

Self-Imposed Risk

If investors are not exposed to further damage from past events and if variance is poorly related to both price and to other measures of volatility, then what market do variance futures serve? The answer, as mentioned above, is those dealers who have entered into OTC derivatives on variance. This seems a little circular, but because it is hard to manipulate the underlying variance of the S&P 500 itself without using astronomical sums of trading capital for no other reason, this market is probably harmless to bystanders.

In a September 2003

column on the then-impending VIX futures, I noted a number of operational considerations I believed would make trading those instruments difficult if not impossible. These included an underlying index that switched composition eight days prior to expiration, no forward curve, no defined cost of carry, no way for market makers to offset their risks and the inability to hedge both price (gamma) and volatility (vega) risks simultaneously.

Many of the same considerations apply to variance futures, particularly the difficulty in making a market for which there is no actively trading underlying asset and no forward curve. Bid-ask spreads have been quite wide during the first few days of trading as a result.

Many consider volatility and variance to be a new asset class, and this may yet be true. For now, however, future hopes do not create present reality.

Howard L. Simons is a trading consultant and the author of

The Dynamic Option Selection System. Under no circumstances does the information in this column represent a recommendation to buy or sell securities. While Simons cannot provide investment advice or recommendations, he invites you to send your feedback to

howard.simons@thestreet.com.

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