# Initial Conclusions On Correlation and Volatility

1) The variance of the index is approximately equal to average correlation between components times the average individual variance of its components.

2) Both variance and correlation drive index returns, and holding either one constant, the “surface volatility” of the index can change inexplicably.

3) If variance/volatility stays the same while correlation goes up, aggregate index volatility will increase. The reverse occurs when correlation goes down which drives low volatility in bull markets.

4) In a crisis, both correlations and component variance/volatility rise quickly creating an increase in index variance. The concurrent effect of both accounts for the tremendous increase in index volatility.

5) In the short-term increases in component correlation are negatively related to future index returns.

6) In the longer term (up to one quarter) a significant increase component correlation is positively related to future index returns.

7) Correlation is a superior forecasting tool to variance- variance has no significant forecasting power controlling for correlation. (Mungo and Wilson, 2006)

8) The risk premium initially thought to be related to higher volatility is thus primarily related to fear of increases in market correlation. The risk premium is “priced” as implied correlations are persistently higher than realized correlations. The index option premiums are higher relative to individual options of the components because they hedge correlation risk. (Driessen et al 2005). This accounts for the returns earned to those willing to engage in dispersion trading.

9) The correlation between index components is both stochastic and mean-reverting. Thus there is **incrementally more mean-reverting “surface volatility” in the index versus sectors or individual stocks**. This accounts for the large discrepancy in Sharpe Ratios between binary DV2 strategies on the index (SP500-SPY) versus its sector components (SPYDERS). A great visual and description was highlighted by Jeff Pietsch in his post on mean-reverters here : http://marketrewind.blogspot.com/2009/07/know-your-mean-reverters.html. This also accounts for why Country ETFs respond better to mean-reversion (RSI2, DV2 etc) strategies versus Commodity, Sector, and Fixed Income ETFs. This implies that relative strength strategies will be more profitable for the latter versus the former.

Thanks for your post, lots of things to test.

For your readers, a definition of implied correlation and some historical data is at the CBOE site: http://www.cboe.com/micro/impliedcorrelation/ .

thanks quant, im sure you will enjoy the research.

cheers

dv

David, this seems to refute the weak version of efficient markets – “The correlation between index components is both stochastic and mean-reverting”. It’s fine with me, but:

1. could you please share some studies on this?

2. It’s in the realm of possibilities that we haven’t had the tools to arbitrage this out of the markets, so this may disappear in 1 day – 100 years 🙂 “the $20 bill on the ground may or may not be there”. But that’s pure theory; empirical evidence is there until it isn’t, so i’m on board in practical and economic terms.

What’s the Mungo and Wilson, 2006 reference? Can’t find it.

DV should have referred to “Pollet and Wilson”, since the paper is by Joshua Matthew Pollet and Mungo Ivor Wilson, “Average Correlation and Stock Market Returns”, available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=965354 . SSRN is a great site for academic financial research.

hi, thanks very much for correcting the reference, sometimes I have so many author’s names its hard to keep things straight.

cheers

dv