Lyxor Quants Ask: What Exactly Is A 'Risk Factor' Anyway?

by: AllAboutAlpha

Originally published July 6, 2016

Given the growing body of scholarly work over "risk factor" investing, especially the growing number of risks cited as factors, one has to wonder: what exactly is a "factor"? In terms that admirers of Rodgers and Hammerstein will remember: is a feature of an investment a risk factor because it's rewarded, or is it rewarded because it's a risk factor? In the former case, we may be calling any anomaly a risk factor. In the latter, only that which yields a risk premium is a risk factor.

Two quants from Lyxor Asset Management, in Paris, addressed this point two years ago, in a paper with the alliterative title "Facts and Fantasies about Factor Investing." It is worth a close re-examination.

Since Mark M. Carhart's publication of "On Persistence in Mutual Fund Performance," (1997), the literature has settled on a (somewhat) standard list of four core risk factors: company size, price to book ratio, market risk, and momentum. But other scholars are always putting forward proposals to lengthen the list to include, for example: volatility, low beta, or liquidity. Indeed, John H. Cochrane complained in a 2011 publication of the "zoo of new factors." It is difficult to assign any meaning to factor investing if it isn't clear what does or doesn't get into the bestiary.

The Lyxor Authors

Zélia Cazalet and Thierry Roncalli suggest that some of the proliferation of zoo denizens may be understood as the result of statistical methods that don't distinguish between true risk premia on the one hand and mere statistical anomalies on the other. Behavioral economists argue, for example, that the book to market effect, one of Carhart's four factors (and indeed one of the Fama/French three before that) isn't a risk premia at all, but an anomaly, an instance of investor overreaction.

Rafael La Porta, Joseph Lakonishok, Andrei Ahleifer, and Robert W. Vishny made this case in a 1997 paper, "Good news for value stocks," in the Journal of Finance. They studied earnings announcements, and the moves of stock prices around the dates of such announcements, over a five-year period and concluded "that a significant portion of the return difference between value and glamour stocks [defined by price to book] is attributable to earnings surprises that are systematically more positive for value stocks." This means that the results cannot "be reconciled with an entirely risk-based explanation of the return differential."

Cazalet and Roncalli observe this, and also understand that even if one does make the distinction between risk premia and anomalies, one might find that specific factors straddle the line.

Another complication: If a list is agreed upon, the authors say, it isn't obvious how to translate "academic risk factors into investable portfolios,' which requires study of the capacity, turnover and transaction costs of said portfolios.

Sorting Things Out

To try to sort out some of the confusion, Cazalet and Roncalli make the point that the presence of a "factor" on such a list should not be considered binary: either X is a risk factor or it isn't. Rather, what is a factor is time varying and mean-reverting (given a cycle of between 3 and 10 years). What is a factor in one region of the globe may not be a factor in another. As a related point, "the explanatory power of risk factors other than the market risk factor has declined over the last few years, because Beta has been back since 2003."

These authors also address some of the fictions, or as they say the "fantasies," that have clustered around the subject. For example, it is often thought that Carhart's momentum factor exhibits a CTA option profile. "This is wrong," they say, since a CTA option has a long straddle profile whereas momentum, a/k/a winners minus losers, "presents some similarities to a short call exposure."

Likewise, it is often thought that long-only risk factors are riskier than the L/S variety. This is also wrong. The risk of L/S momentum in particular is very high.

The authors refrain from making the claim that factor investing is merely another investing fad, and should be ignored until it goes away. There is a core of validity to it, as they acknowledge throughout. But it is "not as simple as it is sometimes presented by practitioners," and only a few of the "factors and anomalies" usually presented are reliable.