Exchange rates: the basic equations
4.5 y Big Mac purchasing power parity
We now turn to The Economist’s Big Mac index. Invented in 1986 as a light-hearted guide to whether currencies are at their right level, the index is based upon the price of a McDonald’s Big Mac burger around the world. The Big Mac is produced locally to roughly the same recipe in 118 countries. The Big Mac purchasing power parity methodology aims to calculate the exchange rate that would leave non-USA burgers costing the same as in the United States. The Economist’s burgernomics compares the Big Mac exchange rate with the actual exchange rate as a test of whether a currency is over- or undervalued. Take an example. It uses prices in April 2003. The price of the Big Mac averaged over New York and Chicago was US$2.71. The price in Britain was £1.99, giving an implied Big Mac PPP rate of £1 = US$1.36. At the time, the actual exchange rate was £1 = US$1.58. If the Big Mac were the only item in your shopping basket, this would imply an overvaluation of the £ against the US$ of 16 per cent.
Light-hearted burgernomics has become a matter of increasing academic interest and has spawned many articles and even a whole book by Ong (2003) of the International Monetary Fund. Little did McDonald’s and The Economist know what they were starting with the Big Mac the assumed sole constituent of the basket for PPP calculations. Continuing the good humour of this section, may we suggest that your shopping basket should be slightly more diversified.
4.6
y
Summary
n The direct quotation method means a rate of exchange quoted in terms of X units of home currency to one unit of foreign currency.
n The indirect quotation method means a rate of exchange quoted in terms of Y units of foreign currency per unit of home currency.
n The United Kingdom generally uses the indirect quotation method; most others usually employ direct quotation.
n The foreign exchange spot market is a currency market for immediate delivery. In practice, payment and delivery are usually two working days after the trans- action date.
n The forward market involves rates quoted today for delivery and payment at a future fixed date of a specified amount of one currency against another.
n Forward markets go out to ten years for major currencies, but not for all. Some currencies do not even have a forward market.
n The forward market enables companies and others to insure themselves against foreign exchange loss.
n In the absence of barriers to international capital movements, there is a theoret- ical relationship between exchange rates, inflation and fixed interest rates.
n Note how bankers quote interest rates. If the banker wants a 2 per cent return over three months, he or she quotes an annual rate of 8 per cent. In reality, based on compounding every quarter, 2 per cent every three months means an interest rate over a year of 8.24 per cent. But the banker does not quote 8.24 per cent; he or she quotes 8 per cent. Note too that bankers always quote annual rates – even though lending for a week or a month or whatever.
n Figure 4.1 is most important. Note that dollars and pounds are used in the figure. It can be used for any pair of currencies – simply substitute in the formulae. But remember that the formulae are based on a logic that uses New York direct quota- tions – that is London indirect. So when you substitute, remember to ensure consistency. Use the direct quote for both currencies as if you were in the centre substituted for dollars in the equations.
n Interest rate parity concludes that there is a relationship between spot and for- ward exchange rates which is underpinned by Eurocurrency interest rate differ- entials. These interest rate differentials are based on fixed – not floating – interest rates for the period concerned. With the notation of Table 4.1 in the text:
n Note that in the above formulation, the left-hand side is termed the forward pre- mium or forward discount. The right-hand side is termed the interest differential. n Note in the above formula, and indeed all formulae used in this section, that we are using precise relationships based on correct deductive reasoning. In the formulae above, we do not use (i$− i£) as the interest differential. We actually use this as the numerator in our calculation. There is an essential denominator – and this is given by (1+ i£).
n Remember also that if we do calculations connected with a three-month forward rate, we have to use corresponding interest rates – that is for three months. Thus, an 8 per cent rate as quoted by the banker becomes 2 per cent over three months. n In reality, in the market place, forward rates are based on numbers of days. In
this text, we approximate by using months.
n The logical proof of interest rate parity is based upon covered interest arbitrage. Note what is entailed in this process – see the text.
n Some courses on international financial management require you to be able to prove the four-way equivalence model; some do not require this facility. As a matter of information, courses that the author teaches do not demand such proof.
n Purchasing power parity is concerned with the relationship between movements in spot exchange rates and relative inflation rates. With the notation in the text:
L M M M t s s − = − + 0 0 1 $ £ £ f s s i i i 0 0 0 1 − = − + $ £ £
74 Chapter 4. Exchange rates: the basic equations
n This formula is clearly forward-looking since it uses expected movements in exchange rate and inflation rates.
n A currency whose value moved exactly in line with purchasing power parity would have a real effective exchange rate of 100 throughout the period concerned.
n If the exchange rate for a currency over time were exactly to reflect inflation dif- ferentials as defined above, one would say that its real effective exchange rate (sometimes abbreviated to real exchange rate) was constant.
n A formulation which is backward-looking (that is, based on historic data) would take the form:
In this form, rather than using expected data, past rates would be used.
n A currency would be overvalued if it were too strong compared with its pur- chasing power parity value. It would be undervalued if it were too weak com- pared with its purchasing power parity values.
n If purchasing power parity calculations are to reflect a currency’s strength against all of its trading partners, it is necessary to weight exchange rate movements and relative inflation rates in accordance with its trade patterns.
n Note that different purchasing power parity values will be obtained as different base years for calculation are used.
n The above difficulty may be overcome by using a base date when the exchange rate is in equilibrium. This is perhaps best taken as a time when the country’s cur- rent account in its balance of payments is zero.
n A real exchange rate of 100 implies correct valuation. A real effective exchange rate of 100 plus implies overvaluation and a real effective rate of less than 100 implies undervaluation.
n Note that inflation may be based on consumer prices, wholesale prices, the GDP deflator or export prices. The last of the above four gives the best purchasing power parity valuation. After all, this is the best definition of inflation for inter- national trade purposes.
n The Fisher effect is concerned with the relationship between interest rates and inflation. With the notation of Table 4.1 it suggests that:
n Expectations theory relates the forward discount and changes in spot rate. It sug- gests that: f s s s s t 0 0 0 0 0 − = L − i i i $ £ £ $ £ £ − + = − + 1 1 M M M s s s p p p t − = − + 0 0 1 $ £ £
n The international Fisher effect links interest rate differentials with expected changes in spot rates. It suggests that:
n The four-way equivalence model developed in this chapter is a deductive model. In terms of using it in the real world, we have to ask how will it stand up empir- ically. Findings are summarized in Chapter 7. In a nutshell, at the level of most corporate users of foreign exchange rate markets it is only interest rate parity that holds in the short term. The other relationships are found to stand up fairly well long term. But more of that later.
4.7
y
End of chapter questions
Question 1All other things being equal, assume that US interest rates fall relative to UK interest rates. Again with all other things being equal, how should this affect the:
(a) US demand for British pounds; (b) supply of pounds for sale; and (c) equilibrium value of the pound? Question 2
What is the expected relationship between the relative real interest rates of two coun- tries and the exchange rate of their currencies?
Question 3
Some Latin American currencies have depreciated against the US dollar on a daily basis. What is the major factor that places such a severe downward pressure on the value of these currencies? What obvious change in Latin American economic policy would prevent the regular depreciation of these currencies?
Notes
1. ‘Agio’ means the sum payable for the convenience of exchanging one kind of money for another. The term originally derived from Italian moneylending in the Middle Ages. 2. Some textbooks state the interest rate parity formula as:
This is perfectly correct and is merely an adaptation of the formulation used in this book. 3. Like all ‘laws’ in the social sciences, we should not give this one the status of immutability.
i i i s s t $ £ £ − + = − 1 0 0 L