EXCHANGE RATES Preliminaries Nominal exchange rate is the by alicejenny

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                                  EXCHANGE RATES

I. Preliminaries.

•   Nominal exchange rate is the relative price between two currencies.

•   We define the nominal spot exchange rate of the Canadian dollar in terms of a
    foreign currency as the number of units of the foreign currency needed to buy one
    Canadian dollar or, simply: the price of one $CAN in the other country’s currency
    (e.g. $US 0.8211)

•   In this definition:

                nominal means: in terms of money. The opposite is real – in terms of
                goods and services;

                spot means: for immediate delivery. The opposite is forward – for future
                delivery.

    •   The Foreign Exchange Market is an electronic market, linking banks around the
        world, on which assets denominated in different currencies are exchanged.

    •   This market is huge: the volume of foreign currency trading is estimated to be 2
        trillion (2 000 billion) US dollars a day.

    •   For comparison, the total value of international trade is about 10 trillion US
        dollars a year.

    •   So the yearly volume of international trade is equal to just one week of foreign
        exchange transactions.

    •   Clearly, most transactions on the foreign exchange market are unrelated to the
        trade in goods and services.


II. Flexible and Fixed Exchange rates.

    •   The responsibility for the exchange rate policy usually rests with the central
        bank (e.g. Bank of Canada).

    •   The most important decision is whether the exchange rate system should be
        flexible or fixed.

    •   An exchange rate arrangement for a country is called a flexible exchange rate
        system when the country allows its exchange rate to be determined in the
        international exchange markets. (e.g US dollar and the Euro.)
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•   Definitions:

           appreciation: an increase in the value of the currency, in the case of
           flexible exchange rate;

           depreciation: a decrease in the value of the currency, in the case of
           flexible exchange rate.

•   Under a pure flexible exchange rate system the central bank does not undertake
    transactions on the foreign exchange market; such complete absence from the
    foreign exchange market is rare.

•   Most countries follow a system called a dirty float (or a managed exchange rate).

•   This is an arrangement in which the central bank controls the exchange rate but, at
    least in principle, it is flexible (e.g. Israel).

•   Under flexible exchange rates, the value of the exchange rate changes daily and
    may vary quite a bit over time.

•   This instability of flexible exchange rates is a main reason some countries
    choose fixed exchange rates.

•   An exchange rate arrangement is called a fixed exchange rate system when the
    country:

    sets the value of the exchange rate at a certain level;

     and its central bank intervenes on the foreign exchange markets by buying or
    selling its currency so as to maintain the fixed value of the exchange rate.
    (e.g Chinese yuan)

•   Definitions:

    revaluation: an increase in the value of the currency, in the case of fixed
    exchange rate;

    devaluation: a decrease in the value of the currency, in the case of fixed exchange
    rate;

    Foreign currency reserves: stocks of assets, denominated in foreign currencies
    (usually – bonds issued by foreign governments) held by the central bank.
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III. Maintaining fixed exchange rate.

   •   How does the central bank control the exchange rate? By buying and selling the
       country’s currency on the foreign exchange market.

1. Preventing appreciation.

   •   Consider the recent pressure for the Chinese yuan to appreciate.

   •   A pressure to appreciate means that, at the fixed exchange rate the demand for
       yuan exceeds the supply.

   •   If demand for yuan exceeds supply, the price of the yuan tends to increase (i.e.
       the number of US dollars needed to get one yuan increases).

   •   In order to prevent the appreciation the Chinese central bank must increase the
       supply of yuan on the foreign exchange market.

   •   To do this the central bank sells yuan (or yuan-denominated assets, usually
       government bonds) on the foreign exchange market and buys foreign currency
       (or foreign-currency denominated assets).

   •   In the end, the Chinese central bank’s net holdings of yuan-denominated assets
       fall, and foreign currency reserves increase.

   •   In principle, the Chinese central bank can prevent appreciation of the yuan
       indefinitely, since it issues (prints) the domestic currency.



2. Preventing depreciation.

   •   Consider now the pressure for the currency to depreciate – which was the case
       with the Mexican peso in 1994.

   •   In 1994 negative internal political developments in Mexico scared investors and
       led to increase in the supply of Mexican pesos on the foreign exchange market
       and reduction in demand for the Mexican pesos.

   •   At the current fixed exchange rate there was excess supply of Mexican pesos on
       the foreign exchange market.

   •   Another reason for the excess supply of pesos was that it became overvalued –
       because the inflation rate in Mexico was significantly higher than in the US
       Mexican goods were more expensive than US goods (after taking the exchange
       rate into account).
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•   The overvaluation of the peso reduced Mexican exports and increased imports
    contributing to the excess supply of Mexican pesos on the foreign exchange
    market.

•   The third reason for excess supply of pesos is that investors sensed that the
    current situation is not sustainable and the currency may be devalued.

•   They therefore sold pesos in the expectation of buying them back at a lower price
    after devaluation.

•   To avoid depreciation the Mexican central bank (Banco de Mexico) had to
    intervene on the foreign exchange market by increasing the demand for pesos by
    buying pesos and selling its foreign exchange reserves.

•   After a large loss of reserves, on December 20 1994, the government gave up and
    devalued the peso by 15% .

•   Post mortem: the Mexican government did too little too late. The pressure on the
    peso resumed and on December 22 the Banco de Mexico switched to a flexible
    exchange rate.
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                           Exchange Rates in the Long Run
I. Overview.

   •   Predicting exchange rates is very difficult.

   •   One theory which economists make use of is the Purchasing Power Parity
       (PPP) theory, which describes the determination of exchange rates in the long
       run.

   •   Before we start, you should be aware that:

               the theory only deals with long run (many years); it cannot explain day-
               to-day changes in the exchange rates;

               there are two theories: Absolute PPP and Relative PPP; while most
               people think of Absolute PPP, the Relative version is better.


   •   Basic idea: goods should cost the same amount in different countries.

   •   Does it hold? The evidence is conflicting:

               No: Japanese cameras are cheaper in New York than in Tokyo; similar
               goods are more expensive in Switzerland than in Italy; they are more
               expensive in Europe than in the US, more expensive in the US than in
               Canada etc.

               Yes: Price differences for cars in the EU have been declining since the
               introduction of the Euro.
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II. The Law of One Price.

1. Conditions under which the Law of One Price holds:

   •     If:
         (a) the good is tradable,
         (b) the cost of transportation are low,
         (c) there are no obstacles to trade (tariffs, quotas, regulation),
         (d) markets are equally competitive.

   •     then the cost of the good should be the same in both countries.

                                                      e ⋅ pi = pi *
                                                                                          (1)

   •     Here:

   e denotes the nominal exchange rate of the Canadian dollar in terms of the US dollar,

       pi denotes the price of good i in Canada in Canadian dollars,

   e ⋅ pi
            is the price of the same good in Canada in US dollars,

    pi *
         denotes the price of the same good in the US in US dollars.




2. Why?
                                                                    e⋅ p > p *
   •     If the good is cheaper in the US than in Canada, i.e. if    i   i  and the
         conditions for the law of one price hold, the good will be imported from the US
         to Canada.


   •
                                                                             p * ↑ ), and
         The increased demand will increase the price of the good in the US ( i
                                                                           p ↓
         the increased supply will reduce the price of the good in Canada ( i ).

   •     In addition the nominal exchange rate may change (higher supply of the Canadian
         dollars will lead to the depreciation of the Canadian dollar, i.e. a reduction in e,
         but of course this effect is small in case of a single good).
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   •     So: pi * increases, pi falls and, perhaps, e falls a little. As a result the difference
         between the price in Canada and the US becomes smaller.

   •     The process of taking advantage of price differences between countries is called
         arbitrage.


III. Real Exchange Rate.

   •     The real exchange rate is the relative price of goods in the two countries.


   •     Using symbols, the formula for the real exchange rate is:
                                                    eP
                                              ε=
                                                    P*                                         (2)

where:
   ε   is the real exchange rate,
   P is the price level in Canada in Canadian dollars,
    eP is the price level in Canada in US dollars,
    P* is the price level in the US in US dollars.


   Real exchange rate and net exports.

   •     You can see from equation (2) that the higher is the real exchange rate, the more
         expensive are goods in Canada compared to the US.

   •     An increase in the real exchange rate will reduce Canadian exports, raise
         Canadian imports and so reduce net exports.
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IV. Absolute Purchasing Power Parity (PPP).

1. Absolute PPP.

   •   The Absolute PPP is simply the Law of One Price applied to the aggregate of
       all consumption goods.

   •   Let P denote, as before, the price level in Canada in Canadian dollars, P* denote
       the price level in the US in US dollars.

   •   Then PPP says:

                                         eP=P*                                          (3)



   •   Dividing both sides by the price level in Canada we obtain a formula for (spot
       nominal) exchange rate:

                                               P*
                                          e=
                                                P                                       (4)

   •   Equation (4) says that, if absolute purchasing power parity holds, the spot nominal
       exchange rate is simply equal to the ratio of price levels in the two countries.

   •   When absolute purchasing power parity holds, the real exchange rate is equal to
       1. 0: the price level in both countries is the same.


2. Law of One Price and Absolute PPP.

   •   If the Law of One Price holds for every good, Absolute PPP holds as well; the
       reverse is not true.

   •   Absolute PPP may hold if prices of individual goods differ across countries.

   •   What Absolute PPP says is that the average level of prices in two countries is the
       same; some goods may be more expensive in one country, other goods more
       expensive in the second.
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3. Why Absolute PPP often does not hold?

(a) Most goods are not tradable.

   •   Examples of important nontradables: housing, transportation services, wholesale
       trade services, advertising, retail services.

   •   The last is very important! When you buy something, the price of the product is
       only a portion of what you pay. So it is not surprising that retail prices differ
       across countries.

   •   For example Japanese cameras are more expensive in Tokyo than in New York.
       Why? The wholesale price is probably a bit lower in Tokyo, but the cost of
       wholesale and retail services, rent etc. are much higher there. So the gross
       wholesale and retail markups are higher and the retail price is higher.

(b) Costs of transportation are high for many goods.

   •   In recent years the costs of transportation fell and price differences between
       countries became lower.

(c) If there are obstacles to trade, PPP does not hold.

   •   If the trade restriction is a tariff, the price will obviously differ by an amount
       similar to a tariff.

   •   If the trade restriction is a quota or a technical specification, arbitrage is not
       possible.

   •   Example: Cars are more expensive in Britain than elsewhere in the EU.


(d) Competitiveness differences.

   •   If there are differences in the competitiveness of the market, retailers will have
       different markups and prices will differ.

   •   This can be seen even within one country. For example cameras are cheaper in
       New York than in Kansas City. This is because the market in New York is more
       competitive.
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4. Evidence on Absolute PPP.

Italy.

   •     Before the introduction of the Euro the price level in Italy was (about) 1000 times
         higher than in Germany. The exchange rate was (about) 1000 lira/DM.

Turkey.

   •     Until last year the exchange rate of the Canadian dollar was about 1 million
         Turkish lira. Price level was about 1000000 times higher in Turkey.

Argentina:
   • Read case study in Lecture Notes.
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V. Relative Purchasing Power Parity.

   •   Since:
       (a) many goods are not tradable,
       (b) transportation costs are sometimes significant,
       (c) there are obstacles to trade (tariffs, quotas, regulation),
       (d) markets competitiveness differs across countries
       Then: the Absolute PPP often does not hold.

   •   Idea for Relative PPP: if the differences remain constant over time, the ratio of
       price levels should stay constant.

   •   So, for example, if prices in Switzerland are 30% higher, they should stay 30%
       higher.

   •   This means that changes in the exchange rate will reflect differences in inflation
       rates.

   Numerical example.


   •   The price level in Canada is P=100, the price level in the US is P*=90. In other
       words, a basket of goods that costs 100 Canadian dollars in Canada costs 90 US
       dollars in the US.

   •   The nominal exchange rate is e=0.81. This means that the real exchange rate is
                                          100 * 0.81
                                     ε=              = 0.9
                                             90

   •   This means goods are, on the average, 10% cheaper in Canada than in the US.

   •   Inflation in Canada is 1%, inflation in the US is 3%.

   •   This means that, in a year, the price level in Canada will be
       P2006 = 100 ⋅ (1 + 0.01) = 101.00
                                                *
                                               P2006 = 90 ⋅ (1 + 0.03) = 92.70
       and the price level in the US will be

   •   If the relative purchasing power parity holds, the nominal exchange rate in 2006
               e
       will be. 2006
                     = 0.826

   •   How did we get this? Under relative purchasing power parity, goods will remain
       10% cheaper in Canada than in the US in 2006.

   •   The basket of goods costs $US92.70 in the US.
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   •   To be 10% cheaper in Canada, the basket of goods must cost $US92.70 ⋅ 0.9
       =$US83.42 in Canada.

   •   It costs $101.00 Canadian in Canada.

   •   This means the exchange rate must be e=83.43/101.00=0.826.


A formula:
                                 e2006 − e2005
                                               = πUS − π C
                                     e2005

   •   The term on the left hand side is the percentage change in the exchange rate.

   •   The term on the right hand side is the difference in the inflation rates over the
       period.

   •   Relative PPP says that the change in the exchange rate equals the difference in
       the inflation rates between the two countries.



Purchasing Power Parity and the real exchange rate.

   •   If the Relative PPP holds, the real exchange rate is constant (=0.9 in the
       example).

   •   If the Absolute PPP holds, the real exchange rate is constant and equal to 1.0.
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                 AN ASSET APPROACH TO EXCHANGE RATES.

   •   We have assumed before (see page 4 of chapter 8 notes) that Canada is a small
       open economy which means that the Canadian interest rates are equal to the
       world interest rate.

   •   But in fact interest rates can, and do, differ between countries.

   •   For example, on July 26, 2005, the interest rate on a 2-year Canadian bond was
       2.95% per year while the interest rate on a 2-year US bond was 3.93% per year.

   •   We will now discuss the relationship between interest rates in Canada, in the rest
       of the world (we will treat the US as the rest of the world) and expected changes
       in the exchange rate of the Canadian dollar.

I. Preliminaries.

   •   The asset approach to exchange rates explains the behaviour of exchange rates
       in the short run.

   •   The determination of exchange rates is attributed to differences in asset returns
       across countries.

   •   These differences cause investors to move their funds from one currency to
       another.




II. Interest rate parity condition.

   •   The idea is very simple. Corrected for risk, investors will reallocate their assets
       across countries until the expected rate of return is the same.

   •   On July 26, 2005 a Canadian investor has 1 million Canadian dollars, which he
       will need in 2 years.

   •   He considers buying Canadian or US government bonds.

   •   A 2-year Canadian bond yields 2.95% per year. If he buys the Canadian bond he
       will have, in two years:


                     $1000000 ⋅ (1 + 2.95%) 2 = $1059870
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•   Alternatively, he can

    (a) sell the Canadian dollars and buy US dollars at the current spot rate.
    (b) buy 2-year US bond
    (c) in 2 years cash the bond.
    (d) in two years sell the US dollars and buy Canadian dollars at the spot
        exchange rate in effect on July 26, 2007.

•   The current spot rate is 0.8207 and the interest rate on 2-year US bond is 3.93%.
    We compute:

(a) He will have $US 820 700 today;
(b) He buys US bond for $US820 700
(c) in two years he will have
    $US 820 700 ⋅ (1 + 3.93%) 2 = $US 886 474.58
(d) he does not know the spot exchange rate two years into the future so he has to
                             E
    form expectations. Let e+2 denote the exchange rate he expects in two years. If
    he converts his $US 886 474.58 into Canadian dollars he expects to receive
                 E
    886474.58/ e+2 Canadian dollars.


•   To compute the interest rate parity condition we need to equate the expected
    return on investing in Canada and in the U.S. We get:

                            1059870 = 886 474.58 / e+2
                                                    E



•   This is one equation with one unknown, the expected spot exchange rate in two
            E
          e
    years, +2 . We get:

                                      886 474.58
                              e+2 =
                               E
                                                 = 0.8364
                                       1059870

•   This means the market expects the Canadian dollar to appreciate by:
    (0.8364-0.8207)/0.8207=1.9% over the two years.
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•   Using symbols, the formula for interest rate parity is:

                                               e ⋅ (1 + r*)2
                                 (1 + r )2 =        E
                                                   e+2                              (5)

•   here r is the Canadian interest rate and r* is the world interest rate.

•   The expression on the left of the equal sign is the amount received from investing
    one Canadian dollar in Canadian bonds for two years.

•   e is the number of US dollars obtained for one Canadian dollar, and so
    e ⋅ (1 + r*) 2 is the amount of US dollars received in two years by exchanging one
    Canadian dollar for US dollars today and investing the proceeds in a two-year US
    bond.

•   This amount is then converted into Canadian dollars using the expected spot
    exchange rate.

•   The example was a bit unusual because the saving was for two years, hence the
    exponent.

•   For one year investments the formula would be:

                                          e ⋅ (1 + r*)
                                 1+ r =          E
                                                e+1                                 (6)

•   This is equivalent to:
                                 e+1 (1 + r*)
                                  E
                                    =
                                  e   (1 + r )                                      (7)

•   The formula can be simplified by using, on the right hand side, the
    approximation: V/W ≈ V-W+1.
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   •   This approximation can be used when V and W are close to 1. Since the interest
       rates are small, we can use the formula on the right hand side of equation (7). We
       get:

                                    e+1 − e
                                     E
                                            ≈ r * −r
                                       e                                                  (8)

   •   This formula is the interest rate parity condition.

   •   It simply says that the expected percentage appreciation of the domestic currency
       (Canadian dollar) is approximately equal to the difference between the foreign
       and domestic interest rates.

   •   The intuition is straightforward. If investors expect the Canadian dollar to
       appreciate relative to the US dollar by 1%, they accept 1% lower rate of return on
       Canadian bonds.

   •   What they lose in lower return they make up in the Canadian dollar becoming
       more valuable.

   •   How does it fit with our previous assumption? If people do not expect the
       exchange rate to change (for example, under fixed exchange rates) then the
       Canadian interest rate must be equal to the world interest rate.



III. Changes in the interest rates and exchange rates.

   •   Assume Bank of Canada reduces Canadian interest rates.

   •   This means that, in equation (8), the right hand side increases.

   •   In order for the interest rate parity condition to hold, the left hand side of
       equation (8) must increase as well.

   •   Investors must be compensated for the lower return in Canada by expected
       appreciation of the Canadian dollar.

   •   Expected appreciation of the Canadian dollar will happen if the expected
       exchange rate increases or if the current exchange rate falls.


   •   The first possibility is not likely (Why should investors expect future exchange
       rate to change when the interest rate falls now?)
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•   So, to achieve the interest parity condition, the current exchange rate will fall.

•   Assume now world interest rates increase (for example the FED increases the
    US interest rate).

•   As in the previous case this means that, in equation (8), the right hand side
    increases. The rest of the reasoning is the same as before.

•   Conclusion: a decrease in Canadian interest rates, or an increase in the world
    interest rate, lead to a depreciation of the Canadian dollar.

								
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