© 1999-2020, Douglas A.Ruby (06-02-2020)

Exchange Rates represent the linkage between one country and its partners in the global economy. They affect the relative price of goods being traded (exports and imports), the valuation of assets, and the yield on those assets. In the period of fixed exchange rates these prices, values, and yields were predictable over time. However, since 1973 we have been living in a world of flexible exchange rates where foreign exchange markets determine these rates based on trade flows, interest rate differentials, differing rates of inflation, and speculation about future events.

Exchange rates can be expressed as the foreign price of a domestic currency (i.e., the Euro price of a U.S. dollar) or its reciprocal -- the domestic price of foreign currency. We will express these values using the following notation:

the Euro price of a Dollar:€P$

or

the Dollar price of a Euro:$P/€

Currently this particular ratio of currencies is near parity ($1.30:1). Note that in the table below the rate between the U.S.
and Canada is near parity (1:1). The following represents the foreign-exchange value of a U.S. dollar
as of April 2013 and 2017 (*from here on out, exchange rates will be expressed as the Foreign
Price of a Dollar 'FP/$'*):

Country / Region |
Currency |
Rate (2013) |
Rate (2017) |

Britain | Pound '£' |
0.652 | 0.756 * |

Canada | Dollar'C$' |
1.018 | 1.278 * |

China | Yuan'RMB' |
6.20 | 6.63 * |

Europe | Euro '€' |
1.299 | 0.851 |

Indonesia | Rupiah'Rp' |
9,753.8 | 13,533.0 * |

Japan | Yen'¥' |
97.52 | 112.58 * |

Mexico | Peso | 12.322 | 18.993 * |

Russia | Ruble | 31.669 | 59.342 * |

Singapore | Dollar'S$' |
1.242 | 1.357 * |

South Korea | Won | 1,125.3 | 1,097.1 |

Switzerland | Franc | 0.934 | 0.991 |

** a stronger dollar (weaker foreign currency) between 2013 and 2017*

All of the above rates represent **Nominal Exchange Rates** in that they
are the actual posted trading rates on foreign exchange markets. These particular
rates can be used to find the domestic price of foreign goods. For example,
suppose that we are interested in the price of a litre of whiskey (Suntory) player manufactured
in Japan:

P_{Japan}= ¥ 8,060

if the exchange rate is:

¥124 = $1

then the domestic (U.S.) price of this same good is:

P_{U.S.}= $65 (8,060/124)

As exchange rates fluctuate, the domestic prices of foreign goods will often be affected:

New exchange rate: ¥140 = $1( a weaker Yen)Price of a litre in Japan: P_{Japan}= ¥ 8,060( unchanged)Price of that litre in the U.S.: P_{U.S.}= $57.60( less expensive)

The *weaker yen* (it now takes more yen to buy a U.S. dollar) or *stronger
dollar* (a dollar now buys more yen), has led to a reduction in the
price of Japanese exports and U.S. imports. We would expect that this
change will lead to an increase in the flow of goods from Japan to the
U.S. However, trade flows are affected not by **nominal exchange rates**,
but instead, **Real Exchange Rates**

In order to understand the determination of **real exchange rates**, we need
to examine the concept of Purchasing Power Parity
or **PPP**

Suppose that we compare the price of a common good in two different countries.
The *Economist* magazine often used a McDonald's Big Mac.^{™} for
this purpose. McDonald's operates in many countries around the world selling
products governed by strict specifications and standards. The presentation
and taste of a Big Mac.^{™} (based on this author's experience) is identical
in Beijing, Denver, Jakarta, Singapore, and Seoul. Using this homogeneous
worldwide product, we expect the following to be true:

Exchange rate: ¥124 = $1Price of a Big Mac. ^{™}in the U.S.:P_{U.S.}= $2.25Price of Big Mac. ^{™}in Japan:P_{Japan}= ¥ 279

If Purchasing Power Parity holds then the **nominal exchange rate** should be:

¥P(Big Mac.^{™}) / $P(Big Mac.^{™}) = ¥ 279 / $2.25 = ¥124 : $1

But what if we had the following:

Exchange rate: ¥124 = $1Price of a Big Mac. ^{™}in the U.S.:P_{U.S.}= $2.25Price of Big Mac. ^{™}in Japan:P_{Japan}= ¥300

In this case,

¥P(Big Mac.^{™}) / $P(Big Mac.^{™}) greater thannominal exchange rate.

We could therefore take $1,000 and buy 444 Big Macs.^{™}; export the Big Macs.^{™}
to Japan and sell them for ¥300 each. This would generate ¥ 133,200 in
revenue. We then *sell* yen on foreign exchange markets and *buy* dollars.
At the current exchange rate, this would allow us to buy $1074 (¥133,200/¥124)
and earn a profit of $74.

However, this process of arbitrage (on a larger scale) should affect
Big Mac.^{™} prices and the nominal exchange rate. The *buying*
of Big Macs.^{™} in the U.S. should push the domestic price upwards.
The *selling* of Big Macs.^{™} should drive prices down in Japan.
The *selling* of Yen on foreign exchange markets should weaken the
Yen and the *buying* of Dollars should strengthen the dollar. This
activity will continue until the ratio of Big Mac.^{™} prices is just
equal to the **nominal exchange rate**.

This information between **nominal exchange rates** and foreign/domestic prices
of a common good can be expressed as a single value -- the
Real Exchange Rate'ε_{r}':

ε_{r}= e.r._{nominal}[P_{domestic}/ P_{foreign}]

or

ε_{r}= (¥P/$)[$P(Big Mac.^{™}) / ¥P(Big Mac.^{™})]

This **real exchange rate 'ε**_{r}' is a unit-free measure where,
in the case of a single good, its value can be interpreted relative to 1.0 (PPP). In
our above example where '¥P/$ = 124:1, the ¥P(Big Mac.^{™}) = 300, and the
$P(Big Mac.^{™}) = 2.25 we would calculate the real rate to be:

ε_{r}= (124)[2.25 / 300] = 0.93

or 1 Big Mac.^{™} in the U.S. is equivalent to 0.93 Big Macs.^{™} in Japan
allowing for arbitrage opportunities. Either the Yen must *weaken*, the price
of Big Macs.^{™} in the U.S. must increase, or the price of Big Macs.^{™} in Japan
must fall. However, other economic events or conditions (capital flows, trade barriers,
price-making power) may prevent this from happening.

These real exchange rates do provide a foundation for the direction of trade flows such that:

Net Exports 'NX' = f_{(-)}(ε_{r})

The above rate of 0.93 would lead to the export of Big Macs.^{™} from the U.S.
and imported into Japan.

The calculation of real exchange rates are more-likely based on a basket of goods rather that a single homogeneous commodity. Thus, price indices in different countries are used such that:

ε_{r}= e.r._{nominal}[CPI_{domestic}/ CPI_{foreign}]

In constructing the real exchange rate this way we can then think about how differences in rates of inflation among nations either affect this real rate and thus trade flows or perhaps leads to changes in nominal exchange rates:

if %ΔP_{U.S.}> %ΔP_{Japan}then either: ε_{r}↑ or e.r._{nominal}↓

In using these indices, we can no longer interpret the real exchange rate relative to a unit value (1.0). Instead we are forced to look at the direction of change in the real rate to understand the effect on exports and imports.

- Exchange Rates
- Fixed Exchange Rates
- Flexible Exchange Rates
- Purchasing Power Parity
- Real Exchange Rates