Tuesday 29 November 2011

Gambler's Ruin. EU's Gambler's Fallacy.

Leonardo, the 6 year old son of a  colleague of mine when asked what kind of a Christmas present he wants answered "Dada I want a money printing machine so I don't have to ask you for money again". The kid's understanding of money creation is not far off from what most esteemed economists, politicians and journalists have. Many of us have pondered; if it so easy to print money to get out of a financial mess why doesn't everybody doing it? The USA is doing it to the tune of few trillions and Her Majesty's government engaged in quantitative easing (Fancy word for money printing). According to this idea the ECB can print two trillion Euros in order to buy all Greek and Italian debt and bob's your uncle. No more austerity measures, no more hardship or reliance to market forces.

In fact, this is exactly what the central banks of the most advanced countries are doing the past 10 years. They have been doing it in a number of ways not often seen as money printing. In fact the expression money printing is a misnomer as there is no real printing of currency notes in the traditional sense but just the practice of adding few more zeros on the accounts the commercial banks have with the central bank.

Gambler's Ruin

If you have done statistics and probability in college, you have probably come across the example known as Gambler's ruin. If on the other hand, you are a trader or a simple betting man or woman you would have experienced this mathematical concept first hand. Let me explain it with a simple bet:

G.Neous, a gambler, and his friend, John Doe, play a simple coin toss game. G.Neous declares Heads or Tails and a coin is flipped. G.Neous starts with a bet of £100. If he guesses correctly he has won £200, since there is a 50/50 chance in a fair coin toss. If he loses however, he doubles  his bet, in order to recoup his losses and make up some profit.  This strategy is perfect! G.Neous is assured of a profit. As we all intuitively know, at one point in time G.Neous would guess correctly and make a handsome profit.In mathematical language this is expressed by saying that the probability (expectation) of winning is 100%. So where is the catch? The problem is that even though you have 100% probability of success (at some future time) you do not know or have a limit on when this is going to happen. In other words, it can come after 10 coin tosses or after 1000 or even after 1 million coin tosses. This means that you must have infinite amounts of money in order to play this strategy and infinite amounts of time (for biological beings). In mathematical language this is called infinite variance or unbound variance. How many times did a gambler say, "if I only had more money to bet". He knows that eventually he must win, but he runs out of money before that winning bet comes.

This is analogous to what central banks have done the past 11 years. When the internet bubble burst the Fed first and the ECB later lowered their intervention rates. This made the price of money even cheaper. Effectively, they indirectly threw trillions of dollars and euros into the system in order to avoid the recession. This created a real estate bubble. When the real estate and mortgage bubble burst they printed even more money to stop the collapsing and the recession. In the process, they moved the problem from the banks to the sovereigns and now politicians are asking for even more money printing in order to save the peripheral countries. Where is the catch in this case? Well obviously central banks have infinite amounts of money because money are not mined in some far away land but are computer generated. If something has infinite supply then standard logic says that it must have zero value. And modern fiat money does have zero intrinsic value. Its only value comes from the confidence people have in it. If that confidence is lost then the system collapses.  The more you print the less confidence you have that it may be worth anything.  And this is exactly the risk we are running which is analogous to the gambler's ruin.

So what is the bet that the central banks are taking when they print huge quantities of money. It is very simple. They bet that growth would kick in and inflation would lower the value of debt before people absolutely lose faith in the fiat currency they hold. As long as inflation is tamed then they can continue printing. Unfortunately, without realising they have engaged into the gambler's ruin strategy and suffer from the Gambler's Fallacy.

Gambler's Fallacy

Gambler's Fallacy is another great way that probabilities can fool you into thinking that you are a gambling genius. If for example, G.Neous plays the roulette and number 35 comes up 5 times in a row you may think that the probability of coming up again for the 6th time must be very very small. So you place your bet on everything else but 35. Or you may think that there is some hidden pattern and 35 would come up again for the 6th time. Wrong! Number 35 has exactly the same probability of coming up in a fair roulette (1 into 37 if there is only one zero in the roulette).
Policy makers have fallen into the gambler's fallacy trap. They believe that since inflation is mostly under control after two large doses of printing that would also be the case next time. They are running similar risks to our gambling friend G.Neous. Their thinking is not just wrong it is absolutely criminally dangerous. The more we print the closer we come to the abyss. Unfortunately as far as I know there is no direct measure or index  that captures the  faith on the fiat currency. Some people look at the price of gold or other physical assets in order to gauge it. My intuition tells me that if something appear to be too good to be true, then it is too good to be true.


There is growing evidence that policy makers on both sides of the Atlantic are committing the same mistakes our G.Neous gambler is making.They seem to engage the Gambler's ruin strategy as the best exit strategy out of the financial mess and their decision making process is based on a Gambler's fallacy. Let us hope (only thing we can do) that it works on this coin toss because there may be no more coin games later.