Does option-implied correlation, a measure of the expected average correlation between a stock index and its components over a specified horizon, predict stock market behavior? In their January 2017 paper entitled “Option-Implied Correlations, Factor Models, and Market Risk”, Adrian Buss, Lorenzo Schoenleber and Grigory Vilkov examine option-implied correlation as a stock market return predictor. They consider expected average correlations between:

- Major U.S. stock indexes (S&P 500, S&P 100 and Dow Jones Industrial Average) and their respective component stocks.
- Major U.S. stock indexes the nine Select Sector SPDR exchange-traded funds (ETF).
- The nine Select Sector SPDR ETFs and their respective component stocks.

They calculate a correlation risk premium (CRP) as the implied average correlation minus realized average correlation measured over the past month, quarter or year. For comparison, they also calculate variance risk premium (VRP) as the difference between option-implied and realized return variances. Using daily returns for the specified indexes and ETFs (and component stocks of all) and for associated near-the-money options with 30, 91 and 365 days to maturity since January 1996 for S&P 500 and S&P 100 index, since October 1997 for DJIA and since mid-December 1998 for sector ETFs, all through August 2015, *they find that:*

- There are significant CRPs for both stocks relative to major indexes and sectors relative to major indexes. These premiums generally increase with option maturity. In other words, investors tend to expect that future average correlations will be higher than recent past average correlations (diversification opportunity will decline).
- Both VRPs and CRPs vary considerably for stocks relative to their respective sectors. CRPs are largest for consumer staples, financial and technology and lowest for energy, health care and utilities.
- Implied correlation for any broad (multi-sector) stock index predicts future market returns for horizons up to a year. Also, the predictive power of implied correlation:
- Is consistently stronger than that of VRP, especially for horizons beyond one quarter, and remains significant in joint regressions with VRP.
- Depends more on broad sector coverage than on the number of stocks used to estimate implied correlation, such that using just the nine sector ETFs relative to the S&P 500 Index is sufficient.
- Derives not from predicting average correlation but from predicting the dispersion of market betas of component assets (a combination of both correlations and volatilities).
- Is much weaker when predicting equal-weighted rather than value-weighted market returns.

- Realized correlation is a better predictor of future realized correlation than is implied correlation at horizons greater than one quarter.

In summary, *evidence indicates that implied correlation for a broad stock market index relative to its components and the associated correlation risk premium may be useful for predicting equity market returns.*

Cautions regarding findings include:

- Reported predictive powers are gross, not net. Accounting for costs of exploitation may alter findings.
- Tests are statistical only. The authors do not test any investment strategies based on implied correlation or CRP.
- Testing multiple versions of implied correlation introduces data snooping bias, such the best-performing version overstates expectations. Moreover, the rules for calculating implied and realized variances and correlations offer further opportunities for snooping (such as time to maturity for options and lookback interval for past returns).
- The implied correlation and CRP estimation processes described above are complex and beyond the reach of most investors, who would bear fees for delegating the work. CBOE S&P 500 Implied Correlation Indexes are readily available to investors, but their specifications differ from those above. Per CBOE: “Using SPX [S&P 500 Index] options prices, together with the prices of options on the 50 largest stocks in the S&P 500 Index, the CBOE S&P 500 Implied Correlation Indexes offers insight into the relative cost of SPX options compared to the price of options on individual stocks that comprise the S&P 500.”