A proof as in to test rather than a proof as in, my word this is absolutely and everywhere correct, of the efficient markets hypothesis that is. And the EMH, just for those who don't know, does not say that markets are always and everywhere the efficient way of doing things. We ourselves are quite keen that we don't have a free market in private armies. The history books are quite plain that the Wars of the Roses weren't a fun time for us run of the mill people even if the people wielding the broadswords enjoyed themselves immensely. 

All the EMH does state is that markets are efficient at processing the information about what prices should be in a market. Just about all economists sign on to this idea at some level - it's how strong the effect is which is muttered about. And a useful proof, in that sense of test, is to go and look at minor, very minor perhaps, issues which should affect prices and then see, well, have they affected prices? 

Which brings us to this paper here:

As of this writing in June 2016, the markets are predicting Venezuela to be on the brink of default. On June 1, 2015, the 6 month CDS contract traded at about 7000bps which translates into a likelihood of default of over 90%. Our interest in the Venezuelan crisis is that its outstanding sovereign bonds have a unique set of contractual features that, in combination with its near-default status, have created a natural experiment. This experiment has the potential to shed light on one of the long standing questions that sits at the intersection of the fields of law and finance, the question of the degree to which financial markets price contract terms. We find evidence to suggest that at least within the confines of a near-default scenario, the markets are highly sensitive to even small differences in contract language.

This is all about those collective action clauses. Argentine debt did not contain any and thus those holdouts, after default, were able to campaign and sue and then get paid fully. A CAC being a clause which states that if 75%, or 85% or whatever %, of all bond holders agree to change the terms of the bond, accept a haircut, then the others, those potential holdouts, can be forced to accept. This sort of thing is entirely normal in takeover law for example, if 90% of shareholders agree to accept an offer then the other 10% can be forced to sell at that offer price.

Argentina had no CAC clause. Thus the holdouts won. In Greece, Greek law bonds were changed by the Greek Parliament to have a CAC. Greek English law bonds were not - thus the differential payouts to the two classes of Greek bonds. Here, the point is that Venezuela has a series of bonds outstanding, some with no CAC, some with one of 85%, others with ones of 75%. 

So, if there's truth to the EMH then even these minor changes in contractual language should lead to differences in current prices. For the lower the percentage in a CAC the more likely it is that a bondholder will be forced into a cramdown in the event of a default. And the finding is that yes, the bonds are trading at different prices. Same maturities (as far as is possible to measure of course), same coupon, different CACs and different prices.

We have not here proved that the EMH is correct - that's not the way this sciencey stuff works. Rather, science works by having a hypothesis, testing that against reality, and as long as the evidence doesn't disprove the idea we can proceed with it as a working description of the universe until some aspect of that reality does disprove it. Scientific theories are thus true only in the sense that no one or no thing has yet disproved them. 

So it is with our efficient markets hypothesis. We know of times when it is not true or at least less than wholly so, like when markets are not complete (Shiller's part of the Nobel is largely for this). But in complete markets like sovereign bond ones we at least haven't any evidence against the idea that the EMH is true. And thus our working assumption has to be that the EMH is true in such complete markets.