This paper describes material originally distributed but not discussed at Fraser Management’s Contrary Opinion Forum of 2009. It presents a contrarian view of the meaning embedded in option-implied volatility. The model is a work-in-progress. Comment and suggestion are welcome by the author who has allowed us to reprint his work here.
Is VIX Really a “Fear Index”?
The CBOE VIX index measures the S&P volatility implied in options prices. Given stock price, strike price, and time to expiration, implied volatility is the value of standard deviation that balances the Black-Scholes equation with actual option prices. It’s the volatility that “must be” expected by the market to justify actual observed option prices.
VIX values vary inversely with market prices. The VIX generally goes up when the market does down, and vice versa. As declining prices can be fearful, the VIX has come to be often referred to as a “fear index.” Here is a typical headline and passage from a recent Wall Street Journal:
“`Fear’ Fuels VIX’s Jump”
–WSJ Oct 2, 2009
“The stock market’s fear gauge jumped to its highest level since September 3 as stocks slipped lower for the third day in a row.”
“The VIX tracks prices investors are willing to pay to buy and sell options…often to protect against drops in the market. As a result, the index tends to move up when stocks move down, and vice versa.”
Although causality is not explicit, both tone and context clearly suggest the market decline, and resulting investor fear, caused the VIX to jump higher. In that view, the VIX would be plausible as an index of fear.
But the “fear” theory has three problems. First, the VIX is derived from call options as well as put options. If fear of decline were the essential driver of VIX levels, then receding call price should offset expanding put price. But even while the dollar price of calls declines with the market, implied call volatility generally rises along with the implied put volatility. That is, call prices expand relative to the contract terms; hardly a profile of “fear.”
The second problem is that the single most potent factor in implied volatility is recent actual volatility, not market direction. Over the past two years, for example, current actual volatility alone accounts for about 80% of VIX variance, while S&P alone accounts for less than 40%. The extreme influence of actual volatility is seen in the following graph. Actual and implied volatilities track closely throughout.
Blue “Sigma 500” path is a front-weighted actual S&P volatility.
The final problem with the market-driven-fear proposition is that the VIX leads the market (inversely) slightly more than the S&P leads the VIX. The lead-lag relationships go both ways, but based on lead-lag correlations, the VIX-leads-market relation is stronger. It’s not much of an edge, but it’s enough to undermine the idea of VIX primarily responding to market trend.
The chart below (page 3) shows correlation coefficients between 5-day VIX change and 5-day S&P change, at successive leads and lags out to 20 days each way. At left are correlations of S&P leading VIX; at right are correlations of VIX leading S&P. All the correlations are negative (as expected), but the correlations to the right are consistently larger (more negative) than those to the left. VIX says more about coming market change than market change says about coming VIX. The difference is modest, but clearly tilted toward VIX-then-market sequence, and hard to reconcile with VIX change as a result of declining prices.
For all of these reasons, we suggest an alternative understanding of the meaning of VIX….
An Alternative View of VIX
Suppose instead that expected volatility (embodied in VIX) is a factor in market price, in the same way that William Sharpe postulated over 40 years ago. Sharpe’s Capital Market Line portrays a simple risk-return relationship. The higher the risk of a security, the higher is the market’s required return for that security.
Sharpe’s model is cross-sectional. Risk and required return are assessed for each individual security (and for the market) all at one time. But the same kind of risk-return relationship should prevail through time for a given security or portfolio…so long as “everything else” is held constant. If perceived risk increases, the required return should increase; if perceived risk declines, the required return should decline.
The resulting risk-and-return scatter would create a Dynamic Market Line, as illustrated at the top of page 5. The hypothetical zig-zags through time align at or near investors’ risk-return preference line. That single line can only persist so long as “everything else” remains constant (which is to say, not terribly long). Then—when other factors have changed—a new dynamic line emerges.
Sequential Schematic: Risk and Required Return
Line Inversion. When required return rises, price falls. For a given level of fundamental value, the only way to get higher return is with lower price. This relation brings us to the negative relation between the VIX and the market fluctuation.
Sequential Schematic: Risk and Market Price
Actual Data. Below is a scatter plot of the VIX (horizontal) and S&P (vertical) for the bear market and bottom 2000-2003. The sequence starts at the red square near the top, at April 1, 2000. The color changes every calendar year (red-cyan-green-blue). The dominant zig-zags are all down-sloping to the right (north-west to south-east), as expected in our stylized price-and-volatility schematic above.
In addition to the NW-SE zig-zags, there are successive down-shifts of the broader bear market. In this risk-return framework, quasi-linear NW-SE zig-zags are taken as price adjustments to changing volatility, while the downshifts represent real change in market perception or expectation. And down-shifts to the left, in particular, indicates lowered expectations in spite of lower volatility.
Color changes with calendar years
So the connected-dot scatter distinguishes volatility effects (the zig-zags) from changing investor outlook. Much of the S&P fluctuation and loss of 2002 (green segment above) is driven by higher volatility. But the net loss of 2001 (cyan segment) shows net movement to lower left…indicating lower valuation in spite of lower volatility. (2001 cyan also had its own volatility spike, but by end of year the net change was NE-to-SW.)
The final segment in 2003 (dark blue) is also interesting in close-up. The scatter plot below focuses on the final 1½ years of the scatter above. In this chart (below), the color changes with each calendar quarter. The final segment (cyan) covers 2nd quarter of 2003. Our view is that the “drift” of this final leg indicates a sentiment change, as reduced volatility first fails to bring commensurate price gain…and then the final price gain is not driven by commensurate lower volatility.
Color changes at calendar quarters
Bull Market Scatter. The following plot (top of page 8) shows two years ending with the final bull market highs in 3rd quarter 2007. Here the clustered zig-zags still run NW-SE showing basic risk-to-price trade-offs. But the zig-zag clusters are punctuated by successive up-shifts in the valuation line.
Two notable exceptions punctuate the zig-zag behavior. Starting in the 4th quarter of 2006 (mid-range red segment below) the VIX-S&P scatter follows a much looser NW-SE drift, not the typically crisp risk-return zig-zag. Then following a 1st quarter zig-zag, the 2nd quarter of 2007 (upper green segment), shows advancing price in spite of increasing volatility. This gives an atypical SW-to-NE drift. This unusual NE drift suggests a general escalation of investor expectation. Unless specifically supported by external improvement, a drift to the upper right would represent a sign of sentiment inflation prior to the final top in the coming 3rd quarter (dark blue).
Final Bull Market Years
Color changes at calendar quarters
The Scatter Today. The sell-off in the 4th quarter of 2008 (red segment at right in chart below) is shown to be partly characterized by volatility-driven zig-zag and partly by down-shifting trade-off line. Then in 1st quarter 2009 (cyan segment) the path shifted clearly into a SW drift quite unlike the typical zig-zags. So as the March lows arrived, the price action (decline, then rebound) had become essentially independent of the volatility function.
12 Months Ending October 12, 2009
Color changes at calendar quarters.
Then in 2nd quarter of 2009 (green segment), “sentiment” stabilized for a while as the sharp price advance resumed zig-zagging along its new risk-return function closely.
Finally, in 3rd quarter 2009 (dark blue) and early days of Q4, we find the risk-return path drifting upward—up-shifting from the 2nd quarter NW-SE line, but also not quite giving any NE drift. So we find recent price escalation virtually dis-associated from volatility, but not quite defying it. The upward drift of Q3 is reminiscent of the 2nd quarter of 2006 (red segment in top chart on page 8), representing net upward valuation independent of the VIX function.
The net upward valuation is reason for caution. It can be argued—and many do argue—that currently improving fundamentals justify such revaluation. That is a separate issue; the VIX analysis at this point shows only that although up-trends are often driven by reduced volatility (zig-zagging SE-to-NW), the present up-trend is not. If and when we find the path drifting upward to the right, that drift will present more pointed warning of price escalation even in the face of higher volatility.
Work In Progress. In this revised view of VIX, investor outlook or “sentiment” is tracked not in the VIX itself, but in the market’s pricing relative to VIX. Growing optimism is found in upward movement not supported by reduced volatility…and especially when prices rise in spite of higher volatility. Pessimism is found in downward movement not related to higher volatility. Price movement along negative diagonals (NW-to-SE) is essentially silent on outlook or sentiment, as that risk-return function is normal.
The present model of VIX and S&P interaction is incomplete. In particular, while the model successfully distinguishes between volatility-driven and non-volatility components of market trend, it does not yet distinguish between “fundamental” and “sentimental” factors of the non-volatility component. For that, the model will need a third dimension addressing fundamental or economic reality.
Letter from the Editor
Figure 1: A valuation chart of XLF, the Financial Select Sector SPDR.
Figure 2: Parallax tools provided timely signals for HANS. (Editor’s note: This is not a well-selected example provided by the company. In discussing bubbles, I mentioned HANS as an example and Mr. Kaufman was unfamiliar with the company.)
