Topic 3 Solutions: International Parity Conditions

1. Discuss the implications of interest rate parity for exchange rate determination.
   Assuming that the forward rate unbiasedness condition holds, IRP can be written as follows:
    t t  E S I
   i
   S i * |
   1
   1
   1
   
   
   
   
   In this case, the exchange rate is determined by the two interest rates, and the expected future
   spot rate, conditional on information, I, available at time t. Expectations can be self-fulfilling.
   Since the information set will be continuously updated as news hits the market, the exchange
   rate will exhibit highly dynamic, random behaviour.
2. Explain purchasing power parity, both the absolute and relative version. What
   causes deviations from purchasing power parity?
   The absolute version of PPP relates the exchange rate to the absolute price levels in two
   countries, while relative PPP relates the change in the exchange rate to the change in price
   levels in the two countries.
   PPP can be violated if there are barriers to trade, transaction costs or if people in different
   countries have different tastes.
3. Discuss the implications of the deviations from purchasing power parity for
   countries’ competitive positions in the world market.
   If the exchange rate changes satisfy PPP, competitive positions of countries will remain
   unaffected following exchange rate changes. Otherwise, exchange rate changes will affect the
   relative competitiveness of countries. If a currency appreciates (depreciates) by more than
   what is warranted by PPP, it will hurt (strengthen) the country’s competitive position.
4. Suppose that the treasurer of IBM has an extra cash reserve of $100 million to
   invest for six months. The six-month interest rate is 8 percent per annum in the
   United States and 7 percent per annum in Germany. Currently, the spot exchange
   rate is €1.01 per dollar and the six-month forward exchange rate is €0.99 per dollar.
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   The treasurer of IBM does not wish to bear any exchange risk. Where should he or
   she invest to maximize the return?
   i$ = 4%, iDM = 3.5%, S = €1.01/$ and F = €0.99/$
   $1,000,000 invested in the US for 6 months will be worth $100,000,000 (1.04) =
   $104,000,000
   If it is invested in €, it will be worth: $100,000,000 * 1.01 * (1.035) * (1/0.99) =
   $105,590,909
   Therefore, it is better to invest in Germany.
   Note: The six-month interest rate of 8% per annum means 8% of annualized interest rate
   calculated based on the appropriate interest rate (six-month). The word “six-month” is
   describing the type of interest rate that we use to work out the annualized interest rate of 8%.
   Therefore, to get interest rate for 6 months (period), you can use 8% / 2 = 4%.
5. Currently, the spot exchange rate is $1.50/£ and the three-month forward exchange
   rate is $1.52/£. The three-month interest rate is 8.0 percent per annum in the U.S.
   and 5.8 percent per annum in the U.K. Assume that you can borrow as much as
   $1.5 million or £1 million.
   (a) Determine whether interest rate parity is currently holding.
   i$ = 2%, i£ = 1.45%, S = $1.5/£ and F = $1.52/£
   (1+ i$) = 1.02 (wealth from investing in the US)
   (F/S)* (1+ i£) = 1.028 (wealth from investing in the UK)
   IRP does not hold.
   In this question, the pound is overvalued in the forward market.
   Note: Subtracting 1 from both sides of
   1 *
   1
   i
   i
   S
   F
   
   
    gives us
   1 *
   *
   i
   i i
   S
   F S
   
   
   
   
   (b) If IRP is not holding, how would you carry out covered interest arbitrage?
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   Show all the steps and determine the arbitrage profit.
   (1) Borrow $1.5m – will have to repay $1.53m
   (2) Buy £1m using $1.5m at the prevailing spot rate
   (3) Invest £1m at the pound interest rate of 1.45% and the maturity value will be £1,014,500
   (4) Sell £1,014,500 forward for $1,542,040
   Arbitrage profit is $12,040
   (c) Explain how IRP will be restored as a result of covered arbitrage activities.
   Following the arbitrage transactions described above:
   The $ interest rate will rise;
   The £ interest rate will fall;
   The spot exchange rate will rise;
   The forward rate will fall;
   The adjustments will continue until IRP holds.
6. The annual inflation of Netherlands is given to be 4.22% and that of the US is 3.8%.
   According to purchasing power parity (PPP) will the US dollar appreciate or
   depreciate? And by how much?
   US has lower inflation than the Netherlands, therefore we expect the USD will appreciate.
   Since we are interested in the USD, we will have USD in the denominator in the equation
   below (i.e. USD = currency B, NGL = currency A in the formula)
   B
   A B
   
    
   
      
   S 1
   S S
   A/B
   t
   A/B
   t
   A/B
   t 1
   = (0.0422-0.038)/1.038 = 0.004046
   Therefore the USD will appreciate by 0.405%
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7. When PPP fails, does it imply the presence of profit making opportunities?
   Deviations from PPP that are measured using available data reflect many factors including
   transport costs, taxes and customs duties, products sold with financing included with aftersales
   service contracts, quality differences, price indices with different mixtures of traded and
   non-traded goods etc. Measured deviations from PPP are not necessarily indicative of profit
   opportunities through arbitrage.
8. In July, the one-year interest rate is 12% on British pounds and 9% on US dollars
   (a) If the current exchange rate is $1.63: 1 GBP. What is the expected future exchange
   rate in one year?
   IFE states that  
   1 *
   1 *
   i
   i i
   S
   E S S
   t
   t t
   
   
   
    
     t1 E S = (0.09 – 0.12)/1.12 * 1.63 + 1.63
   = $1.5863
   (b) Suppose a change in expectations regarding future US inflation causes the expected
   future spot rate to decline to $1.52: GBP 1. What should happen to the U.S. interest
   rate?
   The US interest rate is unknown. Let us assume that the UK interest rate stayed at 12%
   (due to no change in expectations of British inflation), then according to IFE
   (1.52 – 1.63)/1.63 = (iUS – 0.12)/1.12
   iUS = 4.44%
9. Derive the relative PPP formula using Absolute PPP.
   Recall, that Relative PPP links the change in the exchange to the difference in the
   inflation rates.
   At time t, Absolute PPP is Pt = St Pt*
   At t+1, Absolute PPP is Pt+1 = St+1 Pt+1*
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   
   
      
   t
   t
   t
   t
   t
   t
   P
   P
   S
   S
   P
   P 1 1 1 where, 1 1  inf
   t
   tP
   P
    1  1 inf
   t
   tP
   P
   Substituting, we get
   1 inf  1 1 inf  
   t
   tS
   S
   Subtracting 1 from both sides, we get
   1 1
   1 inf
   1 inf   1 
   
    
   
   t
   tS
   S
   t
   t t
   S
   S  S
   
   
    
   
   
   1
   1 inf
   inf inf
10. Assume the interest rate is 16% on Pounds and 7% on Deutsche marks. At the same
    time, inflation is running at an annual rate of 3% in Germany and 9% in England.
    (a) If the Deutsche mark is selling at a one-year forward premium of 10% against the
    pound, is there an arbitrage opportunity? Explain.
    IRP states that
    1 *
    *
    i
    i i
    S
    F S
    
    
    
    
    The % forward premium [(F-S)/S] has been given. The DEM is buying 10% more Pounds in
    a year’s time than today.
    1.07
    0.10 0.07 
     i
    i = 17.7%
    The £ interest rate should be 17.7% instead of 16%. To take advantage of this arbitrage
    opportunity, we borrow at 16% and convert into DEM and invest it at 7%. Then sell forward,
    locking the £ return of 17.7%.
    (b) What is the real interest rate in Germany? In England?
    1 inom.  1 ireal 1 inf 
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    Germany : 1 3.88%
    1.03
    1.07  
    UK: 1 6.42%
    1.09
    1.16  
11. If the USD/Yen spot rate is Yen 218/USD and the interest rates in Tokyo and NY
    are 6% and 12% respectively. What is the expected USD/Yen exchange rate one
    year hence?
     
    1 *
    1 *
    i
    i i
    S
    E S S
    t
    t t
    
    
    
     
      t t t E S S  S
    
       1.06
    0.12 0.06
    1
      0.004587
    1.06
    0.004587 0.12 0.06 1 
    
      t E S
    ESt1   USD 0.004847 /Yen Yen206.32/USD
12. Discuss the impact of transaction costs on the interest rate parity condition.
    When transaction costs are present, the Interest Rate Parity condition need no longer hold
    exactly. Deviations as large as, but not larger than, transaction costs may exist, forming a
    neutral band around the parity line.
13. In France in 1994, short-term interest rates and bond yields remained higher than
    in Germany, despite a better outlook for inflation in France. Does this situation
    indicate a violation of the Fisher effect? Explain.
    No. The Fisher effect is based on Expected Future inflation. Investors are saying that they
    believe that Germany would likely to have a lower rate of inflation in the future, despite its
    current higher rate of inflation. Hence, investors have accorded a lower interest rates to
    Germany than France. (Some background information: Both countries had high
    unemployment rates in ’94 and there were calls to ease up on monetary policy to boost
    economic growth even if it meant high inflation rates. The market’s expectation was based on
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    the view that the French central bank is more likely to succumb to the temptation of allowing
    inflation, to increase economic growth, than the Bundesbank.)
14. The Economist constructs the Big Mac index (compares the relative prices of the
    Big Mac) on a quarterly basis. This index is used to determine if the Law of One
    Price holds across countries in which McDonalds operates. Comment on the
    usefulness of the index. Describe the characteristics of an index that will overcome
    the shortcomings of the Big Mac index.
    The fact that the index is so sensitive to the (potentially very short-term) pricing strategies of
    one firm on one product should be of concern! A better RPPP index would be based on:
    (i) a basket of goods
    (ii) goods which are tradable (see p155 of the textbook for further discussion on this
    point)
    (iii) goods that have low transportation costs (i.e. are not perishable)
    Moreover, even an ideal RPPP-index is only expected to hold in the long run. Thus, we
    cannot expect to be able to understand short-term changes in currency valuations based on
    any RPPP-index, let alone based on the Big Mac Index.
15. Tomoko Matsubara, is a currency arbitrager for Sumitomo in Tokyo. The spot rate
    this morning is Yen 120.50/$ and the early indications are that the 90-day interest
    rates in the US will rise from their current level of 4.1250% per annum. The US
    Federal Reserve is worried about rising inflation and has been considering raising
    interest rates by 25 basis points (0.25%). The 90-day forward exchange rate quoted
    to Matsubara-san by local banks such as Daichi-Kangyo are all Yen 119.60/$. The
    current 90-day Yen interest rate is 0.5% (half of one percent) per annum.
    Matsubara-san has Yen 300 million at her disposal. Can Matsubara-san make a
    profit through covered interest arbitrage? If so, what is her profit in Yen in 90
    days?
    In this case, IRP doesn’t hold.
    (a) Borrow ¥ 300 million
    (b) Convert ¥ into dollars at the current spot rate of ¥120.50/$ and receive $2,489,626
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    (c) Invest for 90 days in US$ securities yielding 4.1250% per annum (1.03125% for 90
    days). Will yield $2,489,626 * 1.0103125 = $2,515,300
    (d) Sell $2,515,300 forward 90 days at ¥119.60. Total proceeds ¥300,829,880
    (e) Repay ¥300m loan plus the 0.5% (0.1250% for 90 days) – ¥300,375,000
    (f) Covered interest arbitrage profits = ¥ 454,880 (300,829,880 – 300,375,000)
16. General Motors exports cars to Korea. Suppose that the Korean Won/US$
    exchange rate changes from Won 172/$ to Won 215/$ over one year. Over the same
    period the inflation rate in the US is 4% and the inflation rate in Korea is 30%. Is
    GM less competitive at the end of the year assuming that currencies of key
    competitors remain unchanged against the Won? Show your workings and briefly
    explain.
    If the Actual exchange rate is different from the Predicted exchange rate, the competitiveness
    will be affected. Therefore, need to see if the real exchange rate (E) is 1 or not.
    PPP
    t
    t
    S
    S
    E
    1
    1
    
      (Formula is given: 0 marks)
    To calculate SPPP need to use the PPP formula (also given)
     
      215/ $
    1 0.04
    172 / $ 1 0.30 1 S PPP Won Won
    t 
    
    
      
    1
    215
    E  215 
    Since E = 1, competitiveness is unaffected.
    (b) FALSE. The real exchange rate would be one and NOT the nominal exchange rate.
17. Past exam question
    Assume that today the following rates of exchange of the Swedish Krona against the
    U.S. dollar are being quoted:
    Spot Krona 1.65/$
    3-month forward Krona 1.67/$
    In addition, the 3-month CD rate in the U.S. is 4% per annum.
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    As a result of an export transaction, your company has a receivable outstanding in
    Krona from a company in Sweden, which is due today. The Krona amount of the
    receivable was sold forward three months ago to your bank at a rate of Krona 1.68/$
    when the spot rate was Krona 1.65/$. The delivery on the forward contract is also due
    today.
    Suppose that your Swedish customer is on the phone right now asking for an extension
    of the credit period for another three months and is offering to pay 14% interest on the
    outstanding balance in Krona. When your firm borrows in U.S. dollars from the bank,
    it pays the CD rate plus 2%.
    (a) If your Swedish customer is considered to be of about the same credit-worthiness
    as yourself, what annual rate of interest would he approximately have to pay
    today for a three-month credit in Krona?
    (b) Given the circumstances, would you agree to provide the extension of the credit at
    the terms offered? Why? Why not?
    (a) If your Swedish customer is considered to be of about the same credit-worthiness as
    yourself, what annual rate of interest would he approximately have to pay today for a threemonth
    credit in Krona?
    0.1092
    3
    1 12
    1.65
    1.67(1 .06(3/12))
    3
    1 12
    ( / $)
    ( / $)(1 (3/12))
    (1 (3/12))
    (1 (3/12))
    ( / $)
    ( / $)
    $
    $
      
    
    
     
    
      
    
    
    
    
    
    
    
    
    
    
    
    S Kr
    i F Kr i
    i
    i
    S Kr
    F Kr
    Kr
    Kr
    Thus, the Swedish customer would pay 10.92% < 14.0%.
    (b) Given the circumstances, would you agree to provide the extension of the credit at the
    terms offered? Why? Why not?
    Yes. The extension is a positive NPV project and should be accepted unless I am
    totally cash constrained (cannot borrow). True, I have to acquire Krona at the spot rate
    (Krona1.65/$) and sell at the (old) forward rate to the bank at (Krona 1.68/$) which
    results in a loss of 1.8% [(1/1.68)‐(1/1.65)]/[1/1.65] of the Krona receivable. However,
    that is a “sunk cost.” Ask yourself if your answer to b) would be different if instead the
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    Krona had depreciated to Krona 1.70/$. If you think it should be, you are deciding on
    future NPV projects based on past “sunk” decisions! Not a good idea!

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