multiple regression (factor) models to discern what factors are

来源: 2011-09-15 04:55:35 [博客] [旧帖] [给我悄悄话] 本文已被阅读:

More Similarities To 2007/8 Quant Crash

Tyler Durden's picture




Our earlier post regarding the harrowing quarter that our dear friends at GS Global Alpha are having brought back some memories of a bygone age when all one needed was a multi-factor risk model and access to a massive marketing/propaganda arm. Of course as we pointed out earlier, the reason for the demise of so many of these long/short or even long-only quant-managed funds was simple - everyone following the same signal as it pulled them further and further away from benchmark performance - until finally, one after the other, they disregarded their factor models as redemptions (from underperformance) and pure-and-simple psychological trauma hit them hard.

The point is that the factors were ex-post derived to be the main drivers of huge underperformance are once again heavily over-exposed in current portfolios - i.e. factors that have in the past caused chaos when their own volatility day-to-day causes a portfolio to be slowly but surely demolished are once again at work here and we humbly suspect that this is what is hurting not just Goldman but many of their brethren in the PhD-ridden fields of quant fund management.

What did this modeling error look like in 2007? Well, feast your eyes on this little beauty...comparing what the model had forecast risk to be and the actual market's movements (does that look familiar to anyone from the middle weeks of August 2001 also?). We can only imagine what that current period looked like - given the swings in vol were even greater.

 

Quant funds (whether long-only optimized against a benchmark or long-short / market-neutral) use multiple regression (factor) models to discern what factors are most/least responsible for risk. Add to this some expectations of alpha for these factors (a factor could be Growth or Value or Leverage or more simply a factor could be a Sector/Industry) and one ends up with a rather neat (mathematically anyway) model for asset allocation across a broad portfolio that enables a manager to make great claims about both his/her performance, rigor, and risk expectations.

Thanks to a number of excellent studies by MSCI-Barra (one of the leading providers of factor models), we now know (again ex-post) what the proximate causes of gross underperformance were back in AUG07 and Q1 2008. MSCI describes August's 2007 underperformance thus:

Anecdotal evidence indicates investors running quantitative strategies based on style factors were hit by extreme movements in a few main factors Value, Earnings Yield, and to a lesser degree, Momentum and Earnings Variability.

and furthermore, the Q1 2008 underperformance of quant funds was summarized:

...what factors have been driving the recent poor performance in Long/Short funds. We focus on two subgroups of these funds—Long Bias (Directional Funds) and No Bias (Non-Directional Funds). We find that these funds’ underperformance in recent months can, in large part, be attributed to declines in well-know systematic sources of return and risk. In particular, we find that generally:

1. Directional funds appear to have been hurt by biases towards the following Barra Hedge Funds Risk Model factors:

 

Positive Overall exposure to US and European markets
Positive exposure to US earnings variability factor
Negative exposure to European yields factor
Positive exposure to European growth factor
Negative exposure to European size factor
Slightly positive exposure to Emerging markets

 

2. Non-Directional (or Market Neutral) funds appear to have been hurt by biases towards the following Barra Hedge Funds Risk Model factors:

 

Positive overall exposure to US and European markets
Negative exposure to US leverage factor
Positive exposure to US earnings variability factor
Negative exposure to European yield factor
Negative exposure to European size factor

 

So Earnings Variability was a culprit in both periods (always happens at cycle turns as analysts straight-line extrapolations meet macro/systemic slow-downs). Also at work is Negative exposure to Size and positive exposure to Value factors.

Well - the long and winding path has led us to the current exposures of a broadly optimized portfolio created by Bloomberg's multi-factor risk model benchmarked against the S&P 500 (ex-financials). Guess which factors are at the extremes? Yes - positive exposure to Earnings Variability and Value factors and negative exposure to Size - oh dear.

Chart: Bloomberg

As an aside: we also note that the Trading Activity (Turnover) factor is very overweight in the current period - one has to wonder how this factor is interfered with by HFT algos?

 

What was critically important to the crashes in the past was the correlations between all these factors shifting and causing the xFx models of the factor-kind to entirely miss the contemporaneous day-to-day whipsaws of these factors as correlations converged to 1 for everything (as we have been vociferously discussing for weeks).

Perhaps this table is also replaying itself during the current crisis:

 

The bottom line is that the factors that quant funds have tended to be over-/under-exposed to at times of maximum underperformance (and market chaos) appear to be front-and-center once again among quant fund holdings. Whether this means even less liquidity or reflexively more volatility is to come in Q4 2011 / Q1 2012 (about the lag in 2007/8) is anyone's guess, but for sure, we are heading towards a perfect storm and Goldman's news seems, anecdotally at least, to confirm suspicions that something is afoot in quant-fund-land.

 

Names with large Earnings Variability Factor scores include Apple, RIM, Valero, Reliance Steel, Whole Foods, and Best Buy. The lower factor scores interestingly include Utilities (makes sense) and Financials (hhmm - seems like well manipulated earnings vol to us). Apple, Valero, and Best Buy also rank high in the Trading Activity (Turnover) factor and RIM, Valero, and Best Buy rank very near the top in the Value factor score...seems like lots of focus in a few names coule easily be a problem - but its not like we did not know this already.