Wednesday, February 20, 2013

Correlations in Down Markets Aren't That Different

Many people assert that correlations totally break down in down markets.  I created a bunch of portfolios from the Russell 2000 going back to July 1962 using the prior 36 months of data up to 1999, and the prior year's daily data from 1999 onward. I extrapolated backward the bottom market cap, relative to the SP500 index, to get a replica of this grouping back to 1962. This insured I only had real stocks that could be traded.

I then created 5 portfolios, each with 100 stocks.  First, those with the highest and lowest betas. Then, those with the betas nearest 0.5, 1.0, and 1.5.  These are all freely available, without any registration or any work, here.  

Here are the betas in the up and down months.  There's a tendency for betas for low beta stocks do move towards one, but then, high beta stocks move away from one.  In any case, the effect is not huge.

Correlations, which are measures of how linear a relationship is, are higher in down markets, but again, they aren't game changers.  Correlations certainly do not 'go to one', or 'go to zero.' 

A lot of quants have the very a strong opinion on the meaningless of correlations, and I hear from a lot of them via that Black Swan guy's acolytes.  These people are simply letting the perfect be the enemy of the good. Correlations, and betas, vary over time. Yet they are broadly consistent in up and down markets: stocks grouped by prior high betas have higher betas in future up and down markets, while lower beta stocks have lower betas in up and down markets.  It's all relative, but it's very meaningful, and has powerful implications.  You can design a portfolio with lower than average volatility or beta. Sure, you won't create a portfolio that has no basis risk, no downside risk, but that's an absurd objective. 


John said...

This is interesting, but sometimes I think when people are talking about correlations going to 1 they are more often talking about asset classes that typically have lower correlations during normal time periods.

Alon David Honig said...
This comment has been removed by the author.
honeyoak said...

in defense of the correlation haters out there I have a few points:
1) The impact of time on simple correlation models (i.e. pearson's correlation) can be substantial at a point in time while netting out on average (think of a white noise model with a sigma of one half of the mean vs twice the mean)
2) The vast majority of non-quant people act as if correlations are set in stone and trade on those values (i.e. CDO's, JPM whale)
3) many correlations are not actually that informative in terms of generating tradable ideas
4) In terms of generating profit, how the correlation measure is generated is as important as the sign of the coefficent

ssh said...

Sorry, just an actuary not an investment guy....

By correlation, do you mean correlation of the stocks within each portfolio? Or the correlation of the expected excess return of the portfolio with the market's? Wouldn't the latter just be the beta with standardized excess returns? If the latter, both charts are just a restatement, right? Thx

Corey Hoffstein said...

How did you measure correlations? Was it average cross-asset correlation?

Also, how did you measure "down" versus "up"? Was it "up months" and "down months"?

If you are just averaging across monthly periods (e.g. averaging cross-asset correlations in all down months), you might just be getting an averaging effect. It might be more interesting to break those up and down moves into quantiles based on size (or, size relative to the past 36 months) -- people refer to correlations going to 1 in extreme down moves, not every down move. In other words, if the market has a 1% loss in a month, I don't expect an increase in correlations; if it has a 15% loss, I do.

And that is almost by definition based on diversification. To have such a large magnitude loss in a 100 stock portfolio, all the stocks will have to move in the same direction.

Eric Falkenstein said...

up and down were just months in which the S&P500 was up or down. I just took the average beta in those two subsamples, where I looked at the various portfolio returns.

Steven said...

It's been a while since I looked at this, but I seem to remember that aggregate volatilities move a lot more than idiosyncratic volatilities, so correlations go up when aggregate volatilities go up, but pretty much only because of common correlations with the market.