#### Implied Correlation

Among the CBOE Indexes, the Implied Correlation Index tend to spike around a market bottom and to drop around a short-term top. The cyclical swings in implied correlations may give clues on the market outlook and can enhance market timing strategy.

It can be reasonably held that an efficient options market could be able to produce superior forecasts because it employs a larger information set made of historical and expectational data. However, options are available on single firms (Apple, Cisco, Costco, etc.) and other few factors (gold, VIX, futures, etc.) but not on the co-movement between firms. Therefore, the available market information does not allow to build an implied risk-neutral forecast of such co-movement; in other terms, a measure similar for the VIX having as components options between firms. In portfolio terms, it is possible to build a covariance matrix with the elements on the diagonal constructed with data from options, but nothing can be said for the remaining elements. However, implied correlation measures can be built by assuming that each of the elements not on the diagonal is equally correlated with the others.

For instance, the VIX is a model-free estimate of the implied volatility of the S&P 500 Index for which the Cboe calculates and disseminates two correlation indexes tied to three different maturities, usually one year, two years, and three years out (JCJ, KCJ, and ICJ); all have been defined with such an assumption. Basically, the portfolio correlation formula has been modified by setting as the variance of the portfolio the implied standard deviation (i.e., the root of the VIX) and resolving to compute the average portfolio’s components correlations. Thus, the CBOE S&P 500 Implied Correlation Indexes are calculated using the index option implied volatilities and the implied volatilities of options on the 50 largest stocks comprising the S&P 500 Index.

Researchers have noted that by regressing the SPX and ICJ weekly return series against the future SPX multi-period return the estimation result suggests a relevant role for such information on the SPX and ICJ weekly changes; the model simply relates the expected weekly returns on the S&P500 with past ICJ with one and 6 lags (weeks) and one lag S&P returns interacted with ICJ. In general, the positive coefficient sign of the interacted term suggests that a trending stock market rally (positive or negative) with a strengthened average correlation should continue in the future 7 to 10 months. Specifically, the 6 weeks lag is significative to predict S&P volatility in the following 6 weeks. Similarly, a model based on daily returns suggests can predict volatility for the next two weeks.

#### Volatility of Volatility

The VVIX measures the volatility of the VIX, or the volatility of volatility; the ratio of the CBOE VVIX Index to the VIX Index can be considered a useful measure to gauge a change in volatility regimes whenever historical highs or lows are reached. Whenever correlations among equities are historically low, the low levels of index volatility are not derived from low levels of volatility in component stocks but in the historically low levels of correlation in the underlying stock returns processes. When correlations start to revert to historical averages, the index volatility will increase compounded by the non-linear interaction between the three maturities measures of implied correlations.

#### Skew

Finally, the SKEW Index is built similarly as the VIX but using the prices of S&P 500 out-of-the-money options. It is a gauge of tail risk hedging or the implied likelihood of a Black-Swan event; it tends to spike around macro events (like Brexit and the US 2016 election) and during selloff/correction. Indeed, demand for tail risk hedges rises as the market (and valuations) head higher and as the business cycle matures.

#### Variance and Volatility Futures

Variance futures on the EURO STOXX 50 stock index are based on standardized variance swaps augmenting transparency, liquidity (market depth), and tradability. Variance futures replicate the payoff of Over-the-Counter (OTC) variance swaps and are traded based on OTC conventions in vega notional and at volatility strikes.

A variance swap is a financial instrument that allows investors to trade future realized variance against current implied volatility (the strike); such a security is more similar to a forward contract than to a swap. Note that variance (instead of volatility) is additive over time (when a mean of about zero is assumed) simplifying the derivation of the present value of a variance swap at time t. In general, the value is driven from the time-weighted average of realized variance to time t and the implied variance for the remaining lifetime from t onwards. As a result, vega sensitivity diminishes over time and that it is proportional to the time-to-maturity. Specifically, implied volatility is only defined for a certain maturity and a certain strike determining changes in at-the-money implied volatility each time the spot changes. Instead, (implied) variance depends on all strikes for a given maturity.

VIX futures settle to the cash value of the VIX which cannot be statically replicated employing future pricing relationship based on cash and carry arbitrage. Instead, VIX futures are priced by assuming a model for the future evolution of implied volatility; however, there is no unique and established model because futures market prices do not respect the models’ predictions. For instance, rational expectations posits futures prices as unbiased predictors of the future value of the cash VIX. Instead, whenever the futures are trading over the cash VIX the futures will tend to fall and whenever the futures are trading below the cash VIX they will tend to rise. Studies have shown that when the VIX is high the futures curve will be downward sloping and when the VIX is low the curve will slope upward. However, this is subject to some form of regime-switching in the VIX. Indeed, a VIX ranging below 20 has a downward sloping (Backwardation) futures curve 22 percent of the time, whereas a VIX ranging between 40 and 50 has an upward sloping (Contango) future curve 46 percent of the time. As a result, a very steep contango may be the prelude to a rise in volatility unless the spread in the expected daily convergence suggests a reverse in the future prices; usually, such a threshold is set at 0.1 VIX points. Thus, Contango with expected daily convergence greater than 0.1 VIX points suggests a reversal in the future and a rise in the VIX; instead, a Backwardation with the expected daily convergence greater than 0.1 VIX points suggests an increasing VIX since Backawardation is a less expected event.

#### Conclusions

The VIX, VVIX/VIX ratio, the SKEW Index, and the Implied Correlation Indexes (JCJ, KCJ, and ICJ) are useful measure (although not independent) to forecast volatility in the near future.

#### References

Zhou, H. On the Predictive Power of the Implied Correlation Index

Da Costa, Ceretta, Muller (2015). Evidence of dependence between volume, returns and volatility: A correlation of distances approach, using intraday data for all Ibovespa stocks

Seeking Alpha (2017). Don’t Forget The VIX’s Siblings: SKEW And Implied Correlations

Hilpish, Y. (2014). Listed Volatility and Variance Derivatives.

Sincalir, E. (2016) Volatility Trading