Over coffee at the workshop this morning I had some interesting conversations about the “three body problem in global finance”. So there is this idea that we are moving from a Dollar based system towards a system based on the triad of Dollar, Euro and “an Asian currency”. There was a time when the latter was likely to be the Yen, but given the long-lasting depression of Japan and the rise of China, it might well be the RMB. This development raises the problem whether such a system is stable, or what it would take to make it stable.

There may be an important relation with the Sonnenschein-Mantel-Debreu theorem in general equilibrium theory: with three or more goods, any kind of chaotic dynamics is possible. What we are to make out of this in view of a multiple reserve currency system, I don’t know, but forgetting about it does not look like a very sound approach.

Experience has shown that in a system with a single reserve currency, markets and central banks dealing with other major currencies tend to focus on the relation between those currencies and the reserve currency. (“Small” currencies may focus on a major currency of particular relevance to them, the way the Swiss Franc is related primarily to the Euro. Exchange rates with the reserve currency then show long swings – typically lasting a couple of years – around the trend of purchasing parity. Between the non-reserve currencies, this then leads to further random fluctuations. The latter are bounded, however, by the “anchor” provided by the reserve currency.

With several reserve currencies of similar weight, the anchor is missing, and the long swings between different currencies can amplify each other, resulting in chaotic dynamics that can include very large and fast swings – leading to major financial crises.

It is interesting to compare the situation with a famous problem of dynamics arising in physics. In the solar system, the sun is much larger than the planets, and these are sufficiently distant from each other not to start to circle around each other, while their moons in turn are small in comparison with the planets and again sufficiently distant from each other. As a result, the solar system is sufficiently stable to allow for life and human cultures to evolve on planet Earth.

Things are very different if one considers the dynamics of bodies of similar size moving through space. With three and more such bodies, chaotic dynamics is the norm. Anything to be learned about currency dynamics from this?