The 
“low-volatility anomaly” looms rather large in CAPM literature. A new paper suggests that it has a lot to do with another phenomenon, generally discussed in a very different body of literature, known as “keeping up with the Jones’” or the KUJ effect. The KUJ effect is easier to appreciate when discussing consumer goods, such as the haircut underway in this bit of clipart.
But this is AllAboutAlpha! Let discuss the low-vol anomaly and work our way back to the haircut.
The anomaly is simply the fact that low-volatility equities produce higher returns than they “should” under that model. Further, this is no fleeting oddity, but a lasting characteristic of markets. In econo-speak, not only the existence but the persistence of the anomaly requires explanation.
After all, an anomaly that exists for only a short period and then is arbitraged away isn’t really a threat to the CAPM model. That is exactly what is supposed to happen, the arbs are supposed to enforce the relationship of risk to return.
Yet the low-vol anomaly does persist, at least within the world of equities. Taking “equities” as one class, and ranking risk by classes, there is no such anomaly, the classes of investment “behave.” But that just means that the anomaly disappears if you look elsewhere.
Miller and Banner Make Non-Heroic Assumptions
Naturally, if you find the CAPM model to be in any sense appealing, you’ll be curious how this anomaly may be explained with the fewest possible, and the least heroic, assumptions.
Almost forty years ago Edward Miller made an attempt at this, arguing (1977) that in a market with restricted short selling, with significant divergences of opinion about the value of particular stocks, over-performance of the low-vol stock is to be expected. Actually, Miller put it the other way around, focusing on underperformance of the high-vol stocks.
I’ll mention here only one other of the many efforts in that direction over the years , a 2012 article published in Institutional Investor, by Adrian Banner et al. The authors said that the secret sauce wasn’t in the low-vol stocks themselves, but in what managers or indexers did with them while maintaining low-vol portfolios. It was in the compounding and rebalancing effects that come with that maintenance.
“When multiple stocks are combined in a long-only portfolio, their interaction actually causes the portfolio to have a higher compound growth rate than the weighted average compound growth rate of the stocks in that portfolio,” they wrote.
Eric G. Falkenstein, of Pine River Asset Management, has been a student of this matter since his 1994 Ph.D. thesis, which focused on the analogous anomaly among mutual funds.
Falkenstein and Heroic Assumptions
He expressed his disbelief in the Banner theory almost immediately, in his blog. The specter of arbitrage hangs over this explanation. After all if the sauce is in the PM, then any arb could simply go long broad indexes (where presumably this benefit is captured) while shorting the underlying stocks (where by definition it isn’t). If anyone is making billions that way, the fact should be empirically observable.
In a new paper, “Requisite Assumptions for the Persistence of the Low Volatility Anomaly,” a little more than two years after the Banner theory and the reactions thereto, Falkenstein now takes another look at the anomaly, and confirms what a knotty problem this is: knotty enough to take him to the neighboring Jones’ of an old adage.
He dismisses such explanations as Edward Miller’s on the ground that they are informally presented and rely on partial equilibrium reasoning. Also, Miller’s view in particular involves the predictive consequence that “rational and unconstrained investors, surely an identifiable and sizeable subset, should be avoiding and shorting high-beta stocks, which is rare.”
Falkenstein contends that a better explanation requires the following assumptions:
- Hybrid relative utility;
- A delusional subset of investors; and
- Residual systematic risk across betas.
The first of those assumptions is the biggie. Falkenstein postulates that people define risk as a deviation from a benchmark. Deviation from that benchmark may “increase a Sharpe ratio” while at the same time decreasing the “particular Information Ratio used by investors.” In simpler words, portfolio vol goes one way while benchmark vol goes the other way, like the hands of a magician performing some misdirection. The eyes of unmodified CAPM theory are fooled by this theory, they follow the wrong hand.
The consequence of making these assumptions, and in particular that first assumption, go far beyond the sense of intellectual relief that a certain anomaly is no longer so … anomalous. For if we understand that utility is relative, we’ll have a deeper sense of what people who’ve never taken an economics course already know, and that “keeping up with the Jones’” is a ubiquitous motive in human social existence, everywhere from equity investments to lakefront residential property purchases to stylish labor-intensive haircuts.
Since you aren’t Robinson Crusoe, your behavior will always depend largely on your benchmarks, on who are your Jones’.