Equity Market is Efficient – But on a Long Term

A new financial research paper sheds some light on a long debate abour market efficiency:

Authors: Bouchaud, Ciliberti, Lamperiere, Majewski, Seager, Ronia

Title: Black Was Right: Price Is Within a Factor 2 of Value

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3070850


We provide further evidence that markets trend on the medium term (months) and mean-revert on the long term (several years). Our results bolster Black’s intuition that prices tend to be off roughly by a factor of 2, and take years to equilibrate. The story behind these results fits well with the existence of two types of behaviour in financial markets: “chartists”, who act as trend followers, and “fundamentalists”, who set in when the price is clearly out of line. Mean-reversion is a self-correcting mechanism, tempering (albeit only weakly) the exuberance of financial markets.

Notable quotations from the academic research paper:

"In his remarkably insightful 1986 piece called “Noise”, Fisher Black famously wrote: An efficient market is one in which price is within a factor 2 of value, i.e. the price is more than half of value and less than twice value. He went on saying: The factor of 2 is arbitrary, of course. Intuitively, though, it seems reasonable to me, in the light of sources of uncertainty about value and the strength of the forces tending to cause price to return to value. By this definition, I think almost all markets are efficient almost all of the time.

As far as we are concerned, we always believed that Black was essentially right, precisely for the argument he sketched: humans are pretty much clueless about the “fundamental” value of anything traded on markets, except perhaps in relative terms. The myth that “informed” traders step in and arbitrage away any small discrepancies between value and prices does not make much sense. The wisdom of crowds is too easily distracted by trends and panic.

In Black’s view, prices evolve pretty much unbridled in response to uninformed supply and demand flows, until the difference with value is strong enough for some mean-reversion forces to drive prices back to more reasonable levels. If Black’s uncertainty band  was – say – 0.1%, the efficient market theory (EMT) would be a very accurate representation of reality for most purposes. But if  Black’s uncertainty band = 50% or so, as Black imagined, EMT would only make sense on time scale longer than the mean-reversion time TMR. For stock indices with volatility of 20%/year one finds TMR 6 years.

The dynamics of prices within Black’s uncertainty band is in fact not random but exhibits trends: in the absence of strong fundamental anchoring forces, investors tend to under-react to news and/or take cues from past price changes themselves. This induces positive autocorrelation of returns that have been documented in virtually all financial markets. The picture that emerges, and that we test in the present study, is therefore the following: market returns are positively correlated on time scales <<TMR and negatively correlated on long time scales ~ TMR, before eventually following the (very) long term fate of fundamental value – presumably a biased geometric random walk with a non-stationary drift.

We test this idea on a large set of instruments: indexes, bonds, FX and commodity futures since 1960 (using daily data) and spot prices since 1800 (using monthly data). Our results confirm, and make more precise, Black’s intuition. We find in particular that mean-reversion forces start cancelling trend following forces after a time around 2 years, and mean-reversion appears to peak for channel widths of Black’s uncertainty band on the order of 50 to 100%, which corresponds to Black’s “factor 2”.

In a way, our results are very intuitive: mean-reversion comes as a mitigating force against trend following that allows markets to become efficient on the very long run, as anticipated by many authors. However, even highly liquid markets only equilibrate on time scales of years – and not seconds, as market efficient enthusiasts would claim.


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