Tuesday, November 22, 2011

Characteristics vs. Factors

the Low Volatility ETF LVOL, put out by Russell-Axioma, tries to capture the low volatility goodness via a circuitous route. First, it takes into account beta, and momentum in some unspecified way, which makes it a really hard thing to nail down. What most amused me, was that it calculates the return to the lowest volatility third of the Russel1000 index. It then selects a portfolio of about 100 stocks that track this index. The idea is that you find the target portfolio, and then, instead of using that portfolio, you use stocks correlated with it.

Downloading their current holdings, the equal weighted beta is 0.91--low, but not by much. The average 90-day volatility of their holdings is 39%. In contrast, the SPLV low volatility ETF simply takes the 100 stocks from the S&P500 with the lowest volatility over the past 12 months. It has an average beta of 0.6, and an average volatility of 28%. The Russel 1000 itself has a 90-day of vol of 50%, and a beta slightly above 1. In short the SPLV ETF delivers 'low vol' more simply, and more efficiently, by focusing on the characteristic, not the factor.

The idea that there exist risk premiums based on covariances with unidentified stochastic discount factors that are like the S&P500 return, but orthogonal to it, will be in the trash heap of bad ideas. As no one can articulate what such a factor might be, it seems absurd that millions of people are implicitly valuing companies, currencies, and futures this way. But a more tangible problem created by this theory is thinking that to get a certain return stream you should target the asset with the requisite factor mimicking beta, as LVOL has done.

Daniel and Titman documented that it was the characteristic, rather than the factor, that generated the value and size effects. They did an ingenious study in that they took all the small stocks, and then separated them into those stocks that were correlated with the statistical size factor Fama and French constructed, and those that weren’t. That is, of all the small stocks, some were merely small, and weren’t correlated with the size factor of Fama-French, and the same is true for some high book-to-market stocks.

Remember, in risk it is only the covariance of a stock to some factor that counts. Daniel and Titman found that the pure characteristic of being small, or having a high book-to-market ratio, was sufficient to generate the return anomaly, independent of their loading on the factor proxy. In the APT or SDF, the covariance in the return with something is what makes it risky. In practice, it is the mere characteristic that generates the return lift.

Davis, Fama and French shot back that their approach did work better on the early, smaller sample, and more survivorship biased 1933-to-1960 period, but that implies at best that size and value seem the essence of characteristics, not factors, over the more recent and better documented 1963-to-2000 period. Data in favor of Daniel and Titman's characteristics approach was found in France by Souad Ajili, and in Japan by Daniel, Titman and Wei.

In a similar vein, Todd Houge and Tim Loughran (2006) find mutual funds with the highest loadings on the value factor reported no return premium over the same 1975-to-2002 period, even though the value factor generated a 6.2 percent average annual return over the same period. Loading on the factor, per se, did not generate a return premium.

The standard equity groupings of size, value/growth, and now volatility, are best done directly, and not via an exposure to factor-mimicking portfolios.


Anonymous said...

There is nothing mysterious, circuitous or amusing in the way Axioma build the low vol ETF. It would have been very easy to pick the lowest vol stocks for R1000 and build an ETF off them. There are two problems with this approach. First it ignores transaction costs; second, the portfolio may have significant exposures to other factors. What Axioma does is take a low-vol portfolio (not unlike SPLV), and then replicates its vol characteristics taking into account transaction costs (the 200 stock limit is arguably part of this approach) and neutralizing exposures to predicted beta and momentum. There is nothing magic to this. Most definitely it is not, as you write in the end, done by having non-zero factor exposure to vol factor. In this respect you and Axioma seem to agree.

Moreover, your estimates of beta and vol are historical. This is OK as a first approximation, but if you use more accurate *predicted* vols and betas from commercial risk models, you'll get closer results: 20% and 22% for vols (annualized), and .69 and .81 for betas. The reason for the worse beta is that short-term momentum has negative beta, and by being neutral to it the resulting portfolio must have higher beta.

I also have to disagree with your interpretation of Daniel and Titman. Certainly their paper fundamentally criticized the Fama-McBeth approach to factor model construction, but is compatible with fundamental risk models and factor models in general. In the former, the characteristic does have an interpretation as an approximate beta of the (estimated) factor with with a stock.

Eric Falkenstein said...

Well, I concede that Daniel and Titman think their approach is consistent with risk factors, but that's a stretch.

I still don't know exactly how the beta and momentum factors are being neutralized, especially since 'low vol' is intrinsically related to 'low beta', and so orthogonalizing vol from beta seems to hit at one of the main reasons why people want low vol.

As for prospective vol and beta, the beta of the SPLV vs. LVOL is 0.68 vs. 0.76, and vol 20% vs 23%, so out of sample its generating more risk.

It's not just me...SPLV trades 100x as much as LVOL, I'm just explaining why.

Anonymous said...

"I still don't know exactly how the beta and momentum factors are being neutralized"

I don't know the details either, however keep in mind that both Barra and Axioma have a *historical* beta factor, and probably that a factor to which what the output portfolio is neutralized. Historical and predicted are different animals. And I already intuitively described how momentum will hurt beta. In general additional exposure constraints will hurt vol and beta (although the difference is not a big as you initially stated). So why to go through the circuitous route? The first one, lower tcost, benefits primarily the provider. Both ETFs have the same expense ratio (0.39%) but Russell has a more efficient execution. The second however benefits the client. If the client is interested in having a vol exposure, both for hedging and speculation, he'll probably won't like to have spurious exposures to other factors, esp. momentum.

Having said, this, we're talking minor differences anyway. The daily historical beta between SPLV and LVOL returns is 1.07, and their correlation is 96%. It seems that the historical betas of both ETF to a few style factors are close, although SPLV does indeed have lower beta to historical market sensitivity, as one would expect. Probably all these details are lost on the retail investor, who is not used to factor models and factor-based risk management.

As per trading volume, it seems to me that all the Russell/Axioma factor ETFs are not getting much traction. Coming after an establish product like LVOL doesn't help. Not having a clear product differentiation doesn't help either. And finally, it seems that Russell is not marketing these funds very aggressively.

Ken said...

I keep reading your blog cause it's one of the few financial blogs where I can learn something (that's not just politically related).

I've always been confused about how the concept of beta evolved into firm characteristics and then turned into a method for reversing engineering tracking factors and setting sensitivities.

I think it's not just me -- the theory is confused, at least the way it's normally taught.

People who learn it just view it as this statistical tool they can start running against any available data streams.

Then of course, ETFs come along and become the perfect vehicle for the masses to invest into any black box formula.