## All

### Pablo Aznar

#### 01/09/2021

Purchasing Power Parity (PPP) is a well-known measure used to compare the currencies of different countries in terms of price levels. So, in this post, we are going to explain PPP and study, through an example, its relation with the currency pairs.

PPP is based on the law of one price (LOOP). For that reason, in order to understand PPP, first, we are going to explain the LOOP.

This law states that the same goods will have the same price in different countries, assuming that the price is not manipulated by individual buyers and sellers, and there are no transaction costs, transport costs, or legal restrictions.

The main rationale of this law is that if there exists a price difference, there would be arbitrage. So, one could buy the good where it is cheaper and sell it where it is more expensive in order to make profit. Therefore, in the end, prices would be equalized and the arbitrage opportunity would disappear.

So, once explained the LOOP, let’s see what PPP is.

## PPP

Purchasing power parity is the currency exchange rate that eliminates price differences between countries and tries to level their purchasing power. Hence the name, because if the PPP were the actual exchange rate, consumers would have the same purchasing power.

And, how is it calculated?

First, the price of a basket of goods and services in two countries with two different currencies is calculated. Then, as the LOOP states, those two prices should be equal (when brought to the same currency) in absence of transaction and transport costs. Therefore, the theoretical currency exchange rate can be calculated by dividing those two prices, and that resulting value is the PPP.

The OECD (Organization for Economic Co-operation and Development) is the organization that publishes the data every year. As the PPP is an annual value, the value published this year is the one that corresponds to the previous year. These data are relative to the USD and always in local currency. Therefore, the PPP of the USA will be 1.

Moreover, the basket of goods and services used by the OECD to calculate the PPP is a representative sample of those covered by GDP. Specifically, final consumption of households and government, fixed capital formation, and net exports. The final product list covers around 3,000 consumer goods and services, 30 occupations in government, 200 types of equipment goods, and about 15 construction projects. The basket is very large because, in this way, it is more representative and will be more accurate.

Therefore, an increase (or decrease) in the value of PPP in a country results in a corresponding strengthening (weakening) of the associated currency.

### Harrod-Balassa-Samuelson effect

However, the difference between the value of the PPP and the currency exchange rate is often very large and this may be due to the so-called Harrod-Balassa-Samuelson (HBS) effect.

The HBS effect states that the prices in more developed countries will be higher than in less developed countries. This is because more developed countries are more productive than less developed ones (due to the former having better technology) and that difference is more noticeable in tradable goods than in non-tradable ones.

As explained before in the LOOP, tradable goods should have equal prices in different countries but not non-tradable ones. This leads to higher salaries to workers in the sector of tradable goods and that originates higher prices in the non-tradable goods that they purchase.

Thus, this price difference will result in a difference between the PPP and the value of the currency pair.

## Big Mac Index

There also exist other versions which are simplifications of the PPP. One of the most famous is the Big Mac Index, published by The Economist in 1986. Other posts on this blog also discuss the Big Mac Index.

This index is not calculated using a basket of goods, but it only uses one, hamburgers. So, it measures the PPP comparing the price of a McDonald’s burger in two different countries.

The main limitations of this index are listed below:

• It is not very representative because it only uses one good in order to calculate it. That can lead to a large error.
• It is affected by the HBS effect because the good selected to calculate it (burgers) is non-tradable. This means that the price can diverge.
• It has geographical limitations, as McDonald’s is not present in all countries of the world. In consequence, there will be countries where there is no available information.

Although these limitations will make the difference between the index and the currency pair bigger than the one calculated by the OECD, it is a good simplification that helps to understand the PPP. As The Economist says: “Burgernomics was never intended as a precise gauge of currency misalignment, merely a tool to make exchange-rate theory more digestible”.

Other simplifications of the PPP similar to the Big Mac Index are KFC Index (Kentucky Fried Chicken), Ipod (Ipad) Index, and Chai Latte Index (Starbucks).

## Example

Therefore, let’s see an example based on the fact that, in the long term, the value of the currency pair will tend to the value of the PPP. The PPP data used is the one published by the OECD.

The two images show the EURUSD and USDJPY currency pairs in 2000, as well as their PPP. As can be seen, there are periods in which both time series are very distant. Nevertheless, it can be observed that in the long term, they converge to the same value, although later they diverge again.

For this reason, we are going to see if it is possible to make an investment strategy based on this concept.

Therefore, we first calculate the difference between the PPP and the currency pair every day. The PPP value will be the one of the previous year, as it is the one available at that time. Once we have calculated the difference, we can obtain the position. If the difference is positive, our position is long. On the contrary, if the difference is negative, our position is short. The following formulas summarize all this:

$$diff = PPP – CurrencyPair,$$

$$LONG \; if \; sign(diff) = 1,$$

$$SHORT \; if \; sign(diff) = -1,$$

Consequently, calculating the positions as explained, we obtain the following PnL.

On one hand, in the EURUSD, after 20 years there is no benefit at all. It is true that, for example, from 2001 to 2004 there are periods with large benefits, but they are followed by large drawdowns.

On the other hand, in the USDJPY the final result is much better. However, there are very big drawdowns, like the one from 2007 to 2012, where the strategy only generates losses.

## Conclusions

In this post, we have explained the law of one price, the purchasing power parity, and the Harrod-Balassa-Samuelson effect.

In conclusion, the value of a currency pair, in the long term, should tend to the value of the PPP. Nevertheless, there exists the HBS effect which states that the two values can diverge. In addition, we have implemented a simple strategy, which has not been very successful.

## References

[1] OECD (2021), Purchasing power parities (PPP) (indicator). doi: 10.1787/1290ee5a-en (Accessed on 16 August 2021)