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David Kotok | USD-EUR currency exchange rate and the Ellsberg paradox
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USD-EUR currency exchange rate and the Ellsberg paradox
David Kotok <david.kotok@cumber.com>
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: http://en.wikipedia.org/wiki/Ellsberg_paradox. For historical reference see: Ellsberg, Daniel, “Risk, Ambiguity, and the Savage Axioms,” The Quarterly Journal of Economics (Nov., 1961).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 www.cumber.com 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 www.cumber.com 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: http://www.nber.org/~wbuiter/sonofela.pdf.
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In this scenario however, the balls are not in a bag, they are in a glass-bottomed box *
Unfortunately most of us are only allowed to look down from the top...........
* with a secret hatch allowing color-swaps whenever it randomly goes against the house.
European central banks sitting down with big wigs for a bit,... of the common man. Sounds like insider information and trading to me. More RICO Act violations. I don't know how they phrase it in Europe, but in the United States it is illegal,... we just don't enforce the laws,... unless its someone who pisses on the government. These people are then dog meat. But the rest of the crooks can go free to steal some more,... until?, whose day is coming. Welcome to the newamericanrevolution.co
BTW : this guy was one of my heroes : the pentagon papers, what a true blue he was. Ellsberg, pride of free speech and warrior against MIC BS.
Ellsberg the brilliant game theory researcher became the brilliant free speech polemist.
Technical analysis seems so silly now that we have centrally driven markets. The entire purpose of market manipulation is to make the markets do what they would not otherwise do. That gets to the very definition of technical analysis to figure out what the market will do. It is now a failure, even when manipulation is not overwhelmingly in play, the trained response that 'support' is coming stops the market from behaving as it historically should.
It seems to me that technical analysis is now a waste of time. The only real answer is to be part of the club in the "know".
Beyond that, at 12ish% inflation for the year, what is the point of 3% bonds or anything else? It eats at your principal and demands you make so much that the risk vs return is ridiculous in the things you have to do to achieve it. Even when you make money in a high inflation era, you lose it in real value, and pay taxes on it to boot.
Good luck with those charts, I believe I will pass.
rc whalen the copy and paste troll
whit nary a thought in his own head .. just throwing mostly crap on the board see what sticks ..
the suck up to the guys beer drinking back slapping I am a regular guy trying to be the lizard of profound nothing .
Go gephart the come from behind in a race for sleaze person.
RC whalen sucks up to be on the same page with conformity and looking for a home in the muck
Another pseudo scientist trying to use some stuff he read to give a veneer of respectability. Finance is so full of them, makes me laugh.
Very well said and oh so true.
I think the paradox loses validity when you are dealing with 4 standard deviations on a regular basis. Roulette is designed for the house to win, if you want to add to house winnings you rig the game. The key is not to cheat so much that you are outside of the realm of chance. 00 is coming up way too often and the players are getting suspicious and leaving the table. Then the house needs 00 to come up more often to make the same amount of money.
I guess the paradox would work if you relabel your balls fraud and corruption and proceed from there with your analysis.
Couldn't this have been said much more simply:
"Better the devil you know..."
A Paradox usually means that we are ignorant of something.
http://neweconomicperspectives.blogspot.com/2011/12/there-will-be-blood.html#more
The Ellsberg paradox is idealized as an application to the EU/USD structure as Ellsberg provides for known states exclusively (color of the balls & size are distinct/homogenenic) whereby the components that underlie the EUR are subject to impairment & thereby, technically speaking, the balls can change color, size & value ratio - the fact that when Greece 'creates' the New Drachma it must be accepted by the ECB which must realize its loss of Greek debt that was denominated in Euros & converted into the newly re-issued drachma based debt which will not have a credit rating sufficient to be pledged at the ECB notwithstanding the negative cascading affect that would occur throughout public/private capital structures as this transition occurs
What is not known is, what the insiders know. A part of the game is rigged, so with out knowing how big the part is there is no probabilities.
One wonders, as well, which nation will hold which balls at the end of the day. Ireland, e.g., will likely seek some 'ball relief' in return for an affirmative vote on any treaty modification. Their ELA and bank bond debts have been mentioned. On a bigger scale will France have to guarantee its banks as Ireland was forced to do or will Sarkozy manage to shed that obligation onto the EFSF or some other multilateral agency. While the total number of balls may not change in whose 'urn' they end up is not certain either.
In the news photos, Sarkozy and Merkel are always holding each other's balls.
Just an observation.
Unworthy of ZH.
This seems like a silly use of a simple application of uncertainty and probability. For example, the number of balls and the possible colors is know in the example. There is no equivalent certaintly about magnitudes, shades of color, or much else in the eurozone endgame.
Also, the Ellsberg paradox's simple formulation in the link gives only alternate profit opportunities, when in the real world you have a profit-loss calculation, which itself is more complex and engages cognitive biases.
Finally, the Ellsberg paradox has a fixed and known number of balls. The Eurozone (and worldwide) crisis will end in credit failure, but the route and timing depend on political decisions that have yet to be made.
So how is this a helpful tool of analysis?
The intent here is not to offer a literal analogy between balls and currency choices, but an insight into the irrational nature of human behavior. Nassim Taleb does the same thing with observations about our preference for choices that suppress short-term volatility even at the expense of fostering exagerated medium and long-term instability. See: http://jamesshinn.net/wp-content/uploads/2011/04/The-Black-Swan-of-Cairo...
Thank you, Mr. Whalen and Mr. Kotok -- this was a superb post.
I think the author's intent was not to provide a "helpful tool of analysis" but to show rather why meaningful analysis is impossible more than a few days or weeks out.
Thus, they're staying out of the game, because playing is too dangerous when you don't know the rules and can't guage the risks.
Always good advice.
Thanks. What you say is fair enough, and maybe that was edited out. But ZH's excerpts should include that extra paragraph (like yours) that relates the simple concepts to the infinitely-complex reality that we're all trying to figure out.
This might be the bit you were looking for: " 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."
As you say, it's always tricky relating simple models to infinite complexity. Also known as "Predictions are always tough, especially about the future."
The challenge then is not to "save Europe." Instead it is to develop a new framework that cnrystallizes the losses which are now all but certain, and provides a predictable framework going forward. In short, an insolvency proceeding, or bankruptcy if I can use the word in polite company.
Standing in the way are the banks. Each in turn is latching on to well-hidden teats (except when their starvation has become obvious to all and they must be euthanized).
The public should demand transparency rather than particular capital ratios. The marketplace would then punish the laggards.
Suppose you have no balls at all and just take all the shit the banksters feed you?
Isn't that basically the Republican Party platform (with a middle finger)? Or the Democratic Party platform (with a smile) for that matter?