The Australian dollar has been going for a bit of a run over the last few weeks and many commentators are concerned that it has become over-valued. A widely quoted Bloomberg article published yesterday argued that the Aussie is 27% over fair value compared to the US dollar.

Australian Dollar vs US Dollar (Jun 2009 – Sep 2010)

Their case rests on the theory of “purchasing power parity” (PPP). According to this centuries-old idea, exchange rates should be such that identical goods in different countries should, in the long run at least, cost the same amount. If prevailing exchange rates make it cheaper to buy the same goods overseas than in Australia, then the buying power of the Australian dollar is too high and the currency is over-valued.

The rationale behind PPP is that if there is a big price difference, it becomes worthwhile for enterprising souls to export goods from the cheap country to Australia. Not only would this put upward pressure on prices in the cheap country, but the entrepreneurs would be buying the cheap country’s currency and selling the Australian dollar, thereby putting downward pressure on the Australian dollar. Both of these effects would tend to correct the over-valuation implied by PPP.

For years now The Economist has, famously, been publishing league tables of over- and under-valued currencies based on the price of a Big Mac at McDonalds. Their most recent report suggested that the Australian dollar was over-valued by almost 4%. At the time of publication, the Australian dollar was trading in currency markets at around US$0.88. Since then it has increased in value by another 9%, suggesting the over-valuation is now 13% (assuming Big Mac prices are about the same). However, the Big Mac index has come in for some criticism: last year various News Corporation organs broke the alarming story that Australian Big Macs are in fact smaller than Big Macs around the world, which suggests they are not as cheap in Australia as the Economist believes.

Perhaps aware of this problem, CBA economists have instead constructed an iPod index, based on the price of iPod Nanos around the world. Now I know that Apple only recently brought out their new Nano, but my Apple gadget of choice is the iPhone. Phone prices are tricky though, as they are distorted by the plethora of phone plan deals. So instead, I have constructed a PPP index based on the iPod Touch to illustrate the workings of PPP exchange rate indices. After all, the Touch is just an iPhone without the phone.

The table below has iPod Touch 32G prices from five countries around the world. For each of the non-US countries, the local price has been converted to an effective US dollar price using current currency market exchange rates. The PPP rate shows what the exchange rate would have to be to ensure that the local currency price would convert to the US dollar price of $299. Intriguingly, on this basis all four currencies appear to be over-valued relative to the US dollar. Indeed, the 13% over-valuation of the Australian dollar appears modest compared to a 23% over-valuation of the euro and the Pound. Even the Japanese Yen appears to be very slightly expensive.

iPod Touch (32G) PPP Index

There is another possibility here though. Perhaps it is not so much that these currencies are all over-valued (or that the US dollar is under-valued), but simply that Apple rips off all its non-US customers! Mind you, as most Australians would know, Apple are far from alone in charging us more for electronic consumer goods than they charge Americans (although Europeans seem to get an even worse deal). So, sadly, the iPod index may not be very useful. The analysis does, however, highlight the challenges of using PPP to assess fair value of currencies.

Economists would caution against using a single product and would instead use a “basket” of consumer goods to compare currencies, which is what most of those arguing that the Australian dollar is over-valued would have done. But the real problem with the PPP analysis is that prices of consumer goods are not nearly as relevant to currency markets at the moment as interest rates are. Compared to the rest of the world, investors see Australian interest rates as attractively high. Here is a comparison of the interest rates you would earn by buying government bonds rather than iPods in the same five countries.

Government Bond Rates (Sep 2010)

Depending on the “term” of the bond you buy (i.e. how many years before you get your money back), the rate you earn will differ. Typically, longer-dated bonds will generate higher returns, but regardless of the term an investor chooses, at the moment they can earn significantly more by investing in Australia than in any of the other four countries. Now Australia is certainly not the only country in the world with higher interest rates than the US, Europe or Japan, but most of the countries with high interest rates are developing countries which investors would consider a much riskier proposition than Australia. Furthemore, the noises coming from Australia’s central bankers suggest that interest rates here are only heading higher. In order to invest in Australia, offshore investors have to buy Australian dollars, and this goes a long way to explaining why the currency keeps getting stronger.

The practice of switching investments from low interest rate countries to high interest rate countries is known as the “carry trade” and it is not without risks. In fact, the Economist has compared the carry trade to picking up nickels in front of a steam roller. Where is the steam roller? It is the exchange rate. A US investor may be drawn to the extra 4.36% that a 2 year Australian government bond offers compared to a US government bond, but if the Australian dollar falls back as far as it has risen over recent months that investor would lose that 4.36% and more. On the other hand, if investors think that the Australian dollar is only going to keep going up as long as everyone is jumping on the carry trade, they may not see depreciation as much of a risk. Everybody wins, until the music stops… and Reserve Bank governor Glenn Stevens seems to be promising to keep that music playing.

So where does that leave the theory of Purchasing Power Parity? Most economists would take refuge in the caveat “in the long run”. It’s not that Purchasing Power Parity is wrong, it’s just taking a back seat to the carry trade for now. Eventually it will re-assert itself. Perhaps. In the meantime, Australians travelling abroad will be making the most of their buying power.

Data sources: exchange rates from OANDA, iPod Touch prices from Apple, bond rates from Bloomberg.

* The US price excludes tax, while the other countries include GST/VAT etc. To provide a fair comparison, the US price has been grossed up by 6%, a mid-range sales tax rate.

UPDATE: Thanks to Andrew for the comment about sales tax. The post has been updated accordingly.

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