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How are ADRs priced?
Academic research into ADRs seems to suggest that pairs-trading ADRs and their underlying shares reveals that there certainly are arbitrage opportunities, but that in most (but not all cases) such opportunities are quickly taken care of by the market. (See this article for the mexican case, the introduction has a list of other articles you could read on the subject). In some cases parity doesn't seem to be reached, which may have to do with transaction costs, the risk of transacting in a foreign market, as well as administrative & legal concerns that can affect the direct holder of a foreign share but don't impact the ADR holder (since those risks and costs are borne by the institution, which presumably has a better idea of how to manage such risks and costs). It's also worth pointing out that there are almost always arbitrage opportunities that get snapped up quickly: the law of one price doesn't apply for very short time-frames, just that if you're not an expert in that particular domain of the market, it might as well be a law since you won't see the arbitrage opportunities fast enough. That is to say, there are always opportunities for arbitrage with ADRs but chances are YOU won't be able to take advantage of it (In the Mexican case, the price divergence seems to have an average half-life of ~3 days). Some price divergence might be expected: ADR holders shouldn't be expected to know as much about the foreign market as the typical foreign share holder, and that uncertainty may also cause some divergence. There does seem to be some opportunity for arbitrage doing what you suggest in markets where it is not legally possible to short shares, but that likely is the value added from being able to short a share that belongs to a market where you can't do that.