Why Currencies Aren't Going Where They Should Be

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Having broken through the 100 mark, U.S. dollar/yen has just kept on going. The recent Group of Seven (G-7) meeting gave no reason to sell as the group accepted the idea that a weaker currency is inevitable collateral damage from the monetary policy.

Of course, given that Japan's monetary policy is no different from the U.S. or Britain's, how can any of them complain?

Furthermore, it looks like Prime Minister Shinzo Abe's policies are already starting to bear fruit. Money supply growth has picked up a bit, bank lending is increasing, some prices are rising, the stock market is soaring…You can't argue with success.

The question now is how high can U.S. dollar/yen go? Fundamental value for a currency is set by purchasing power parity (PPP). Purchasing power parity is a simple idea: two currencies are at parity when a basket of goods and services costs the same in both countries.

If a Big Mac costs $3 in the U.S. and 300 yen in Japan, then purchasing power parity is 100 yen to the dollar. (And by the way, people do study the price of Big Macs for just that purpose, because they're widely available and the same everywhere.)

There are several ways to figure out PPP. The Organization for Economic Cooperation and Development (OECD) does it as described above. They calculate that purchasing power parity for U.S. dollar/yen is now around 106, meaning the yen is still a bit overvalued. Normally, though it's much more overvalued.

On this methodology the yen has been overvalued by around 40 percent on average since 1985 (ranging from 1.4 percent to 113 percent on a monthly basis).There's nothing to say that couldn't turn around, though. Currencies often fluctuate between over- and under-valued according to economic fundamentals and market sentiment.

(Read More: Here's One Sector Suffering From Abenomics)

Fundamentals push currencies towards fair value over time, but the market usually overshoots fair value, because people tend to move in herds.

In any case, the situation with the yen has changed dramatically from the days when it was overvalued. Japan used to have a trade surplus; now it has a trade deficit. The current account surplus is narrowing too.

The consensus forecast is that Japan's current account surplus will stabilize over the next several years, but I wonder. The current account surplus is the difference between a country's savings and its investment.

(Read More: Japan's Economy Boosted by Consumption, Exports)

The reason Japan has a current account surplus is because it's been saving more than it's been investing. But those days are coming to an end. Savings, which peaked in 1991, seem likely to decrease further as the country's population ages and the government continues to run a huge deficit.

Retired people spend their savings, while "austerity" doesn't seem to be in the Japanese government's dictionary. On the other hand, I would expect investment to pick up as the yen weakens and Japan becomes a much better place to export from. Lower savings plus higher investment would mean an even smaller current account surplus or even a deficit.

(Read More: Hold On, Japan Still Missing Key Pillar of Growth )

Moreover, until recently the Japanese were selling off their foreign assets and bringing the money back home. But as they get used to the idea of the yen being weak and as inflation gains a foothold, I expect them to move more money abroad in search of higher returns. That should weaken the yen.

If the yen averaged 40 percent overvalued before, why couldn't it now be 40 percent undervalued under these conditions? That would be quite a turnaround, but nonetheless U.S. dollar/yen has sustained such a mis-evaluation before. (Euro/yen has been as much as 20 percent undervalued on this metric.) That would take U.S. dollar/yen to around 140.

Another way of calculating PPP is to take a time when trade between the two countries was largely in balance – neither side had a big deficit or surplus with the other – and assume that the prevailing rate then was the correct level to balance trade. Then you use the difference in prices in the two countries since then to calculate what the exchange rate should have been to keep the trade balanced.

Using that method, yen is currently about 9 percent undervalued versus the dollar. In the 2000s, the yen went to around 15 percent undervalued on this measure before reversing. That would be 105.

However, if we go back to the 1980s and 1990s, the undervaluation went to 25 percent before being corrected. That would be equivalent to 120. I think given the deterioration in Japan's trade account and budget situation, we could easily see the more extreme valuation.

(Read More: Yen to Weaken to 120 by Next Year: Economist)

So on one PPP measure U.S. dollar/yen could potentially go to 140, and on another it could go to 120. Taking the average of the two, I think 130 would be a reasonable first estimate for where U.S. dollar/yen could go on a fundamental basis.

Technically, the limit could come around there too. There is strong longer-term resistance at 125, a high that has been tested 10 times, as well as the resistance level of the downward-sloping trendline that extends from 1986.

Of course, this is a very rough back-of-the-envelope type of calculation and one could do much more sophisticated econometric modelling to come up with a more rigorous estimate of where the pair "should" trade. But as the graphs show currencies rarely trade where they "should."

Value is in the eye of the beholder; someone was willing to pay $511,000 for a pair of Dorothy's ruby slippers from the movie "The Wizard of Oz" a few years ago. By comparison, 130 yen for a dollar seems quite reasonable. I've paid that much myself back in 2002.

The author is the Head of Global FX Strategy at IronFX, an on-line trading firm specializing in Forex, CFDs on U.S. and U.K. stocks, and commodities. He was previously Head of the Forex Committee at Deutsche Bank Private Wealth Management.