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Irrational Numbers

  • By Karl Schamotta
  • Published: 9/8/2011

Amid the financial market turmoil in August, exchange rates shifted rapidly and substantially. As investors turned pessimistic on global economic prospects, they bought into safe havens such as the Japanese yen and the Swiss franc, while selling growth-oriented currencies such as the Australian and Canadian dollars.

As the plunge continued, something interesting occurred.

Both the aussie and the loonie ran into invisible barriers as they fell. After moving four or five hundred basis points with relative ease, they both ran into firm resistance as they approached par with the US dollar.

To the rational observer, this must seem rather odd—there is very little difference between 0.9921 and 1.0000 for example. Par is after all, an arbitrary number. If markets were truly efficient and traders were truly rational, trading activity would be randomly distributed along all price points, and par would simply be another point on the price continuum. Selling would drive the exchange rate smoothly through par as if it were any other number.

Not logical 

It has long been known that does not happen in reality. Beginning in the early sixties, researchers were able to show that price movement is not always purely logical.

Prior to the introduction of decimalization on financial markets, stock prices and market orders tended to cluster around whole numbers, followed by halves, quarters, and one-eighths (Osborne, 1962 and Niederhoffer, 1965).

A more recent study (Sonnemans, 2003) showed that when Dutch stock markets converted from the guilder to the euro in 1999, investors immediately switched from whole numbers expressed in guilders to whole numbers expressed in euros. Whole numbers in guilders became odd numbers in euros, and market orders and prices quickly gravitated toward the new whole numbers. Rational investors would not have made this switch—logically, appropriate price levels in guilders should have been appropriate in euros as well. Many studies have followed since, indicating that traders tend to highlight price points that end in zeros and fives.

An example of cultural preferences comes from China, where a study (Brown & Mitchell, 2004) tracked price behavior on two types of shares—“A” shares which were traded by Chinese investors only, and “B” shares which were mainly offered to international investors. Sure enough, prices ending in the lucky number 8 were far more sticky than those ending in the unlucky number 4 on the A shares, while the effect was negligible on the 'B' shares.

Market resistance 

All of this would be of purely academic interest if it were not for the fact that price clustering creates resistance in the market. When many orders are positioned close to a single price level, it makes it far more difficult for the market to smoothly transition through. Buyers and sellers enter the market at these levels, and their actions cause the market to resist the prevailing market trend, sapping its momentum. When market expectations finally do shift enough to force trading activity through these resistance levels, price trends often tend to accelerate towards the next resistance level.

Collectively, traders tend to focus on a limited set of price levels, and this phenomenon creates a number of opportunities for market participants who are more concerned with the economic value of their trades. A strong awareness of these “sticky levels” can be a substantial benefit within a corporate risk management program.

By avoiding these resistance points when placing market orders and establishing risk thresholds, treasurers can increase the odds of success while also increasing their exposures to favorable trends.

Avoiding par can help to drive above-par hedging performance.

Karl Schamotta is president of AFPC Calgary and a market strategist for Western Union Business Solutions 

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