Tuesday, June 28, 2011

Negative SPX/VIX Correlation and Fu Result

Above is a chart of the monthly percent change for the VIX, an index approximately equal to the option volatility on the S&P500, and the return on the S&P500 itself. There's a clear negative pattern. This makes sense, and volatility increases when the market is falling and vice versa. If I told you the VIX, or its ETF the VXX, was up big, there's a strong chance the SPY was down big.

Move the date forward, however, so it's past volatility change and future return, and there's no correlation, and there's a slight negative correlation between volatility levels and stock returns. So, it seems mainly a contemporaneous pattern applied to changes in volatility, spilled milk as opposed to a predictor. Think about when volatility was rising in 2008, and prices were falling simultaneously. The rise in volatility was not predicting price moves, just reflecting them, and the high volatility correlated with both the big move down and the big rebound in the latter part of 2009.

Fangjian Fu has a well-cited paper in the 2009 JFE, Idiosyncratic Risk and the Cross-Section of Expected Stock Returns, that purports to show that contrary to earlier reports that idiosyncratic volatility and future returns are negatively correlated, they are actually positively related. He states that if you estimate idiosyncratic volatility using an EGARCH model, you reverse the results of Ang et al, and find a positive 1.75% return each month for the highest minus lowest idiosyncratic volatility deciles, which is basically flat except for a big jump upward in the highest expected volatility decile.

I've looked at this enough to believe he's made a mistake, but I don't know what, exactly. I don't see this in the data, and I doubt his specific EGARCH would change that, but it's difficult to recreate his methodology exactly. I presume it is in some sort of selection bias in his sample. He states that 'stocks with high idiosyncratic volatilities are contemporaneous with high returns, which tend to reverse in the following month. As a result, the returns of high-IVOL stocks are abnormally low in the next month', a finding I find bizarre because it's contrary to the pattern above, which hold not just for indices but stocks as well.

But, this is good news for low volatility traders. As long as the old guard can point to proof that their result is still viable, they will believe it, and that leaves more opportunity for those who see through this. To paraphrase Cicero, the function of wisdom is to discriminate between good and bad investments.


John said...

But who wants to take the time to fit an eGarch model to all the idiosyncratic returns? I've been looking at Random Matrix Theory and it basically says to just assume the idiosyncratic factors are random noise.

r2d2 said...

try the same in long dated USD/JPY vols (like 10y) against the change in same maturity forwards. correlation is much stronger. it's more than just the "spilled milk" effect, and more than implied by "constant normalized vol" or such. the forward drives vega exposure of some big derivatives books that are all the same way, and they all have to rebalance to stay within risk limits. there is no natural counterparty to take the other side, hence the "correlation" between the two markets (more llike cause and effect really).

that's about as deep as the philosophical part goes, yet I ocassionally see people that are unsatisfied with this explanation and try to find some much deeper meaning in all this, with the use of advanced quantitative tools. and, if you look hard enough, you will find some smart thing to say about what "the market" expects to happen to volatility in the long term future. but from what I see the market couldn't care less about the long term of anything. "the market" is an extremely busy person, and always has important things to take care of on the short term (like which way those derivatives books are coming from, in this case). the long term ends up being an unintended consequence of short term priorities. I wouldn't be surprised if a degree of this happened in most markets.

I find the effort that is put into finding what "the market" expects to be very similar to that joke with the indians that are preparing for winter. the more people try to find out what "the market" thinks and front run it, the less efficient markets get.

Anonymous said...

Since VIX is a function of both trailing realized vol on the index (30-60 day ATR divided by 30-60 moving day average of closes) and recent price changes (20-30 day ROC on the index), it follows that there's only one really useful way to look at VIX.

Calculate what the VIX "should be" based on vol and returns, the see what the VIX "is", and use the result as a sentiment indicator.

However, I've found that the VIX is pretty much irrelevent to me in the timeframes (2 weeks to 8 months) that I trade.