USD-EUR currency exchange rate and the Ellsberg paradox.

USD-EUR currency exchange rate and the Ellsberg paradox.
David R. Kotok
December 4, 2011


“Suppose you have an urn containing 30 red balls and 60 other balls that are either black or yellow. You don’t know how many black or how many yellow balls there are, but that the total number of black balls plus the total number of yellow equals 60. The balls are well mixed so that each individual ball is as likely to be drawn as any other. You are now given a choice between two gambles.” For the rest see: For historical reference see: Ellsberg, Daniel, “Risk, Ambiguity, and the Savage Axioms,” The Quarterly Journal of Economics (Nov., 1961).

A variation of the Ellsberg paradox now drives the euro-dollar currency exchange rate. Here is the outline and the options with regard to certainty, the likely outcomes that may be forecast, and also Knightian uncertainty (the unknown unknowns). For information about Frank Knight’s theory see: Knight, F.H. (1921) Risk, Uncertainty, and Profit. Boston, MA: Hart, Schaffner & Marx; Houghton Mifflin Company. Thank you to Wikipedia.

What is certain? If you take 1350 US dollars today, you may exchange them for 1000 euros. Actually you need a million in a round-lot trade to get close to the exact market exchange rate, but the pricing of the USD-EUR is pretty transparent in the spot market.

Nearly certain is the USD-EUR price tomorrow, which is most likely going to be very close to the price today. Less certain but still estimable is the price next week. And as time goes by, the estimation has a wider margin for error. That said, we can still forecast the USD-EUR with some degree of probability. We can estimate the outcome, bearing in mind the Ellsberg paradox with regard to drawing a red ball from the urn. Under Ellsberg the odds that you will draw a red ball in the initial draw from the urn are 1 out of 3. Once you draw a ball, the odds change for the next draw, since only 89 balls are left.

In the USD-EUR currency exchange-rate estimate for today, the assumption is that the euro survives until tomorrow. As time horizon extends, that assumption becomes increasingly problematic. We cannot obtain a probability distribution on the eventual outcome of the Eurozone crisis. We can list the various outcomes, which range from Eurozone is preserved and strengthened to full dismemberment.

Many pundits project that the euro will dismember. Others say that Greece will be out and that this or that other country may also be out. They suggest that a smaller Eurozone can survive. They offer one- and two-year timeframes. They believe that a core Eurozone will continue. All these scenarios are speculation.

Part of the estimation of the USD-EUR exchange rate includes the probabilities of euro dismemberment or partial dismemberment. Erwan Mahé noted as much in the research piece we quoted a few days ago. See for reference the piece is entitled “Measuring Europe’s Contagion.”

The Ellsberg problem of estimation with Knightian uncertainty in play comes about when you need to find a break-up value for the euro. I get many emails forecasting a decline in the value of the euro. I’m not so sure. Others forecast all types of doom if and when Greece defaults. I’m not so sure. Let’s look at this issue.

Under the euro dismemberment scenario, Greece defaults and reverts to a new drachma. The devaluation is fierce. The country then experiences high, dislocating inflation and low capital formation. The banking system has been undermined. Government instability is coupled with destruction of remaining wealth and capital. Greece suffers for a generation. They brought it on themselves, and they pay the ultimate economic price of policy failure.

Italy is the next suspect. My friend and co-author of our book on Europe, Vincenzo Sciarretta, wrote me about the growing burden upon Italy. “Taxes in Italy will be 125 billion euro higher than before the crisis (on an economy of some 1600 bn). Starting next year and the following one, public spending before interest rises from some 39% in 2000 to 46% of GDP in 2010. Then there’s another large part of the economy which is formally private, but the management is chosen in Rome, ENI, ENEL, Finmeccanica and the like. All politicians of all parties have shared the idea that higher taxes are ‘necessary’. The idea of cutting spending has not emerged yet. When Italy was known as the ‘Italian Miracle back in the ’50s and ’60s, the tax burden was about 25% and the country was a locomotive.”

Greece is a small part of the Eurozone, so small that it will barely be missed. Italy is 18%, exceeded only by France (20%) and Germany (27%). Spain is fourth at 12%.

Now let’s think about what a post-euro dismemberment looks like. The new German deutschmark soars. I have seen estimates of a 20%, 30%, or even 50% gain in strength. The Swiss franc would no longer be linked, and soar as well. Netherlands, Finland, Austria, and others would be much more valuable in the FX market, while the peripheral south would go the other way. Greece would certainly set the low point. And the new Italian lira is an unknown unknown.

We could try to estimate what the exchange rates would be. We could use debt-to-GDP and/or income levels and/or labor productivity measures. GDP per Capita, External debt to GDP, inflation, government fiscal performance, ratios of fiscal performance—all these have statistical problems when used to forecast things like Eurozone credit spreads. My thanks to Kasper Bartholdy and Saad Skiddiqui, Credit Suisse, December 1.

Conclusion: we could use a whole variety of methods to guess. But the effort to be precise is a futile one. This is uncertainty as Frank Knight envisioned it. This is the application of the yellow-black ball decision in the Ellsberg paradox: we do not know the probability of drawing either yellow or black as an outcome when making a single draw from the urn.

But we do know that the USD-EUR currency exchange rate now carries some amount of Ellsberg paradox risk premium in its pricing. We do not know how much. We disagree with those who argue there is no premium. When we look at the monetary dynamics that ultimately influence the foreign exchange rates, we see the USD-EUR rate fairly consistent during this crisis. The yen has strengthened against both. Over longer time periods, currency exchange rate changes are partially explained by comparisons with central bank actions. So far this is not fully applicable to the USD-EUR. To compare, consider that the proportional change of the Federal Reserve’s balance sheet (It tripled) is much larger than that of the European Central Bank (It doubled). See the charts at the bottom of the homepage on to compare them.

Ellsberg’s paradox is at work. It is not transparent but it does exist. That is why we are underweighting Europe today and waiting for this to play out. We are investment advisers. We are willing to take risk when we can make educated guesses at the probabilities attached to the various outcomes.

In the Ellsberg paradox we know there is an initial one in three chance to draw a red ball. We know it is two out of three to draw a non-red ball. If the market misprices that risk, we know what to do. But in the unknown unknown Knightian realm, it is more dangerous to play. That is why we are underweight Europe. That is why we are avoiding the periphery.

We will leave for a quick trip to Europe on Thursday night. The trip follows our Thursday morning (8:30) panel at the ETF conference hosted by IndexUniverse at the New York Stock Exchange. In Paris, five private meetings on the status of events will include Europe-based money managers, consultants on Europe and central bankers. It is a fast trip but absolutely necessary. Avec nos amis, we hope to find a good French meal (et le bon vin) along the way.

One postscript is in order. Several Eurozone countries are now using the Emergency Lending Assistance (ELA) programs. This is very hard to track since the reporting is by each national central bank and has a time lag. ELA is an obligation of the National Central Bank and, hence, the country behind it. It is not a liability of the ECB. This a monetary variation of the Ellsberg paradox. The latest estimate I’ve seen is 130 bn euro; Greece alone is 40 bn. This form of credit is expanded nation-by-nation without timely transparency. In some cases, the recipient may be an insolvent domestic commercial bank. In this model, we have no Ellsberg paradox red balls; there are 17 separate national yellow and black balls. Hence, forecasts of monetary policy outcomes are in the Knightian realm. For details see:


David R. Kotok, Chairman and Chief Investment Officer

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