## Friday, March 14, 2008

### Internal Exchange Rates

In finance, there is a concept called internal rate of return. The internal rate of return is the interest rate which
equalizes the present value of the payments received from an investment to the initial investment amount. To use a very simplified example, if you say invest €10 million today and get €11 million back a year later, the internal rate of return would have been 10%. If you would have gotten back €10 million, the internal rate of return would have been zero, if you would have gotten back €10.5 million the internal rate of return would have been 5% and so on. The same principle applies for income received during more than one year, and so if you would have gotten back €5.5 million a year later and €6.05 million, the internal rate of return would have also been 10%.

The higher the internal rate of return, the better is the investment object. And as long as the internal rate of return is higher than the prevailing interest rate plus perhaps a few extra percentage points as a risk premium, the investment is worth making.

Why do I bring up this concept in finance. Not so much for its own sake, but rather because I have come up with a similar concept-internal exchange rates. The internal exchange rate is the exchange rate which equalizes GDP or GDP per capita for different countries or areas. For example, the internal exchange rate with regard to GDP per capita in the US and Sweden was during 2007 was exactly \$1.5675 per euro as the US had a GDP per capita of \$45,813 as GDP was \$13,843.8 billion and the mid-year population was 302.178 million. Sweden on its hand had a GDP of SEK 3073.8 billion and had a mid year population of 9.15 million, giving it a GDP per capita of SEK 335,934. This creates a GDP per capita internal exchange rate of 7.33 SEK/USD and a GDP internal exchange rate of 0.22 SEK/USD. The actual SEK/USD exchange rate is 6.04, implying that at current exchange rates Sweden has a higher GDP/capita than the U.S., but a much smaller GDP. The internal GDP per capita exchange rate is also lower than the estimated PPP calculated by the OECD, implying that after adjusting for price differences Swedish GDP per capita is lower after all. PPP measures are in principle better when comparing standard of living -but not economic influence-, yet they are on the other hand have significant measurement problems as was illustrated by the recent massive revision of Chinese and Indian PPP.

In most countries, the internal GDP exchange rate relative to the U.S. dollar is as in Sweden, much higher than the internal GDP per capita exchange rate because most countries have much smaller populations than the United States. The big exceptions are of course China and India, and to a lesser extent also the euro area.

The perhaps most interesting internal exchange rate is the one equalizing GDP in the United States and the euro area. In the United States, GDP was \$14,084.1 billion at an annual rate during the fourth quarter of 2007, while euro area GDP was €8986.4 billion, creating an internal GDP exchange rate of \$1.5673/€. Compare this to the exchange rate which I now see at Bloomberg, 1.5637, only 0.24% lower. This implies that at current exchange rate fourth quarter GDP was only 0.24% lower. And there are in fact two good reasons for suspecting that the actual internal exchange rate is even lower during this quarter. First, because this euro area number was based on the then 13 member states, but now Malta and Cyprus is also part of the euro area, which adds 0.2% to euro area GDP. Secondly, because U.S. GDP probably shrank during the first quarter, while euro area GDP probably grew, albeit only slightly. That means that the internal GDP exchange rate for this quarter is likely below \$1.56/€, implying in turn that the euro area has probably already overtaken the U.S. as the worlds largest currency area.

It will probably take a while before the financial journalists figure that out, but when they do, remember where you read about it first.