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Nathan S. and Mary P. Sharp Professor of Finance

Oleg Bondarenko was previously a Visiting Scholar at Kellogg

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Finance & Accounting Sep 1, 2008

# The VIX, CIV, and MFIV

## Measuring up the accuracy of option-based predictors of volatility

Beyond growth and leverage, a key factor in the value of a given stock, and the broader market, is volatility, or the magnitude of variation in prices over time. Especially in today’s uncertainty-ridden market including a major credit crisis and declining dollar, investors pay sizeable premiums to be hedged against increases in volatility, which typically represent bad market conditions. So it is no surprise that there has been growing market and academic interest in equity-index volatility measures. The best-known volatility measure is the volatility index, or VIX, established by the Chicago Board of Options Exchange (CBOE) in 1993. Practitioners and business scholars have established that the VIX, which is based on real-time option market prices for the S&P 500 stock index, correlates significantly with future equity market volatility as well as global risk factors embedded in credit and sovereign debt spreads. Thus the VIX has also become known as the “global fear index”—the higher the VIX, the greater the concern about global markets. In response, multiple public and over-the-counter markets have emerged to enable direct trading of volatility for different assets—using the methodology behind the VIX—rather than more traditional volatility measures based on the Black-Scholes options pricing model.

The great practical interest in forecasting volatility raises two key questions: How accurate is the VIX as a predictor of actual future return volatility? And, are there more accurate alternative predictors based on option market prices?

To answer these questions, Torben G. Andersen, professor of finance at Northwestern’s Kellogg School of Management, and co-author Oleg Bondarenko conducted a study of the construction, interpretation, and predictive value of the VIX and several other option-based volatility measures using over fifteen years of data on option pricing, VIX, and U.S. Treasury bill rates. Andersen and Bondarenko, who present their study in a 2007 National Bureau of Economic Research working paper, find that the VIX is closely related to the concept of so-called corridor implied volatility (CIV); both volatility measures are related to the concept of “model-free implied volatility” (MFIV), which provides another specific volatility index. Further, as part of this empirical study of the CIV, the authors demonstrate that while the VIX is strongly correlated to the MFIV and the broadest CIV measure, it is inferior to the narrowest CIV measures and those based on the traditional Black-Scholes model as The best possible market-based implied volatility measure for volatility prediction may take the form of a corridor implied volatility (CIV) measure.a predictor of actual future market volatility. This result, which runs counter to earlier academic findings, has significant implications for business scholars and investors alike. First, VIX style volatility indices are biased predictors of future volatility. Second, the forecast bias is likely to fluctuate systematically over time. Third, more precise and robust option-based volatility forecasts can be constructed and they are related to the narrow CIV style measure. Fourth, using both the VIX measure and an alternative CIV measure one may obtain information regarding the current market price of volatility insurance, or volatility risk premium, and hence learn about the degree of “fear” priced into the market.

**MFIV, VIX, and CIV: The Basics**

CBOE’s VIX grew out of the development of a “model-free” implied volatility (MFIV) measure which can, in principle, be derived directly from a cross-section of European put and call option prices with strikes spanning the full range of possible values for the underlying asset at the option’s expiration date. This contrasts sharply with the traditional Black-Scholes implied volatility (BSIV) measure, which relies on a specific, counterfactual assumption about return dynamics. In fact, according to Andersen, the “new volatility measurements—both from the underlying asset and options markets—are not tied to a particular, and invariably faulty, model of the price dynamics but are instead designed to provide correct answers under general conditions , thus spurring a large increase in over-the-counter markets for volatility and variance swaps and the like.” Though the VIX has replaced the BSIV measure, researchers have suggested that the CBOE measure contains both random noise and systematic errors, in part because the MFIV bundles a pure volatility forecast with market pricing of the uncertainty associated with the forecast. Nonetheless, implied volatility forecasts generally correlate quite well with future realized volatility, and they are often deemed superior to most alternate methods for volatility prediction.

Andersen and Bondarenko point out that because the VIX is based on an abbreviated range of strike prices, thus representing a scaled down MFIV, it can more accurately be considered a variant of what is known as the model-free “corridor implied volatility” (CIV) measure, which can be constructed in broader or narrower versions and has never before been explored empirically. In this context, the authors assess implied volatility indices including the VIX, MFIV, CIV, and BSIV on multiple dimensions including how similar or distinct they are in terms of their mutual correlation values as well as their usefulness in predicting actual future market volatility.

**How They Studied Volatility Measures**

To assess the volatility measures, Andersen and Bondarenko obtained market data for the period covering January 1990 to December 2006. Their data included daily prices of options on the S&P 500 futures and tick-by-tick data for the S&P 500 futures themselves obtained from the Chicago Mercantile Exchange (CME); daily levels of the VIX index (computed according to the redesign of the measure in 2003) during that period from the CBOE; and Treasury bill rates from the U.S. Federal Reserve (as a proxy for the risk-free interest rate).

The authors note that the CME data have some advantages over the same data from the CBOE. First, there is a 15-minute difference between the close of the CBOE markets and the NYSE, AMEX, and NASDAQ markets where the S&P 500 components are traded; the CME options and futures close at the same time (3:15 PM CST). Second, because CME futures and futures options are traded in pits side by side, it facilitates hedging, arbitrage, and speculation—along with greater market efficiency. Finally, whereas the S&P 500 index pays dividends, the futures contracts do not, requiring no assumptions regarding the index dividend stream.

**What They Found**

Andersen and Bondarenko present key findings in multiple domains.

*Basic Features of the Volatility Measures.*While there was good coherence between the VIX and realized volatility (RVH), the VIX almost uniformly exceeded realized volatility, consistent with earlier work establishing the presence of a substantial negative variance risk premium in the VIX. As the authors put it, “investors are on average willing to pay a sizeable premium to acquire a positive exposure to future equity-index volatility.” To ensure that this finding was not the result of a mismatch between measures (VIX was computed on the basis of options written on the S&P cash index; RVH was computed from authors’ S&P 500 futures sample), the authors analyzed several model-free volatility measures computed directly from options on S&P futures contracts. They found that the VIX was compatible with the MFIV extracted from the futures options, and that both exceeded realized volatility levels by more than 23 percent. Further, as predicted, the VIX was highly correlated with both the MFIV and the broadest CIV measure. The traditional BSIV measure, in contrast, was highly correlated with the intermediate CIV measures. Andersen and Bondarenko conclude that “the various implied volatility measures are all highly correlated although clearly not identical,” and that they all embed a sizeable variable risk premium.

*The Predictive Value of Implied Volatility Measures.* Andersen and Bondarenko used a well-documented criterion and the statistical approach of regression to rank volatility forecasts by their ability to predict realized volatility within the data sample. They found that while all volatility measures outperformed lagged realized volatility measures including RVH as predictors of actual volatility, the VIX provided the worst in-sample prediction of realized volatility, though its performance was close to that of the MFIV and the broadest CIV measure included. BSIV and the two most narrow corridor measures had the best predictive ability. On a different note, because the implied volatility measures are highly correlated, Andersen and Bondarenko hypothesize and demonstrate that combining them to improve volatility forecasts is of limited value. In contrast, the combination of the narrowest CIV measure and RVH had significantly greater predictive ability than either measure alone. Similar analyses using out-of-sample data confirmed the authors’ findings: the narrowest CIV and the BSIV provided the most superior forecasts, with the broader CIV measures, MFIV, and VIX offering progressively inferior predictions. When Andersen and Bondarenko created data sub-samples based on the level of volatility, “the VIX and MFIV [were] the clear losers among the implied volatility measures for the higher volatility scenarios.” Finally, RVH (i.e., realized volatility history) continued to supplement the narrowest CIV measure’s predictive ability better than the VIX.

**Implications and Future Research Directions**

The study by Andersen and Bondarenko, the first empirical investigation of corridor implied volatility, suggests that “the best possible market-based implied volatility measure for volatility prediction may take the form of a CIV measure,” especially when combined with a measure of historical realized volatility, though the specific combination of these indices that would provide the best forecast remains for future research to determine. That is not to suggest that the MFIV measure is of low value. Rather, it should be interpreted strictly for what it aims to represent: the market price of volatility exposure consistent with observed option prices. In this context it is theoretically superior to the BSIV measure. But as a direct indicator of future volatility, the MFIV is more limited because it combines volatility forecasting with the pricing of the risk associated with volatility. Similarly, the predictive content of the VIX is clearly overshadowed by the information provided by the narrower CIV measure here, a finding that is not only new to the literature, but also provided by an empirical study using longer time series and more carefully constructed volatility measures than existing research. In light of these findings, Andersen notes that it is important to bear in mind the dual function of the VIX—conveying how the equity market is pricing risk *and* predicting market volatility—and separating these out as needed.

Andersen and Bondarenko suggest that combining complementary CIV measures in the future may enable more detailed studies of the interaction between equity volatility pricing and financial market conditions, shedding light on the documented but poorly understood links between the VIX, pricing in global equity, credit, and debt markets, and the overall functioning and liquidity of the financial system. The authors close by noting that model-free and corridor implied volatility, rather than being tied to equity-index volatility pricing and forecasting over a monthly horizon only, provide “useful tools for quantifying and interpreting corresponding dynamic market features across diverse asset categories and maturities.”

Investors and others viewing the VIX as the optimal predictor of realized volatility would do well to take note of the illuminating findings of Andersen and Bondarenko.

Featured Faculty

About the Writer

Sachin Waikar is a freelance business writer living in Evanston, IL.

About the Research

Andersen, Torben G. and Oleg Bondarenko, “Construction and Interpretation of Model-Free Implied Volatility,” in Israel Nelken (ed.): *Volatility as an Asset Class*, Risk Books, London (2007), 141-181.

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