a. The exchange rates that are quoted on the foreign exchange markets are the nominal exchange rates.
b. A real exchange rate is the nominal exchange rate that has been adjusted for the relative purchasing power of the two currencies’ home countries. It is calculated by adjusting the exchange rates for the relative price levels of the countries in a pair.
c. If we assume the world with:
i. homogenous goods and services,
ii. no market frictions, and
iii. no trade barriers or capital restrictions.
In such a world if a good cost ₤ 1,000 in the UK and $ 1500 in the US, then the expected exchange rate would be USD/GBP = 1.5. This exchange rate is also called the purchasing power parity because at this rate people could buy the same basket of goods and services in both countries.
d. Purchasing power parity (PPP) is a condition in which identical goods and services are priced the same in different markets. It does not hold because of trade barriers, transaction costs, and limits to capital flows.
e. These assumptions, as mentioned above, are rarely satisfied in the real world. Therefore, the real exchange rates exhibit a large deviation from the purchasing power parity.
f. In order to calculate the real exchange rates, consider an example of two countries A and B, and we are interested in calculating the exchange rates from country A’s resident’s perspective.
i. The direct exchange rate for the resident of country A (i.e. Sd/f) will be A/B.
ii. If this person wants to purchase goods from country B, he will suffer a loss of purchasing power in terms of country B’s goods and services if:
# either the exchange rates (i.e. A/B) go up, or
# if there is an inflation in country B, such that its consumer price index goes up (i.e. CPIB rises).
iii. But if there is also inflation in country A, such that there is an increase in both income (I) and consumer price index (CPIA), then this resident will gain purchasing power in terms of country B’s goods and services.
iv. Therefore, the foreign price level in terms of domestic currency (from the resident of country A’s perspective) can be:
SA/B × CPIB
v. And if the consumer price index in country A equals its price level then the real exchange rate will be:
Real Exchange RateA/B = SA/B × CPIB / CPIA
Where,
SA/B is the nominal or spot exchange rate, and
CPIB / CPIA is the relative price level.
g. Taking another example, suppose Adam is a US resident and wants to buy goods and services from China.
i. The nominal or the spot exchange rate is SUSD/CNY
ii. The Real exchange rate is SUSD/CNY × CPICNY / CPIUSD
iii. Now suppose that the nominal exchange rate goes up by 10%. There is also an increase in the CPI in China by 5% and the CPI in the US goes up 2%.
iv. Due to the above changes, the change in the real exchange rate would be:
[1 + %∆S(USD/CNY) × {(1 + %∆CPICNY) / (1 + %∆CPIUSD)}] – 1
That is:
1.10 × (1.05 / 1.02) = 0.1323 or 13.23%
v. This means that the real foreign exchange rate is 13.23% higher and it needs 13.23% more dollars to buy goods and services in China.