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International Finance Dr. Angela Ng FINA 342 HKUST Class Notes 6 INTERNATIONAL PARITY CONDITION II: COVERED AND UNCOVERED INTEREST RATE PARITY I. COVERED INTEREST RATE PARITY EXAMPLE Mr. David Sylvian, an arbitrageur for the Hong Kong & Shanghai Banking Corporation in Hong Kong, arrives at work on Tuesday morning to be faced with the following quotations on his Reuters’ screen: Spot rate: ¥125.00/$ One year forward rate: ¥130.00/$ Euroyen one year interest rate: 10% Eurodollar one year interest rate: 5% What should Mr. Sylvian do? Solution: 1 DERIVATION OF A GENERAL EXPRESSION FOR COVERED INTEREST RATE PARITY Notations: it = U.S. interest rate it* = “comparable” foreign interest rate St = spot exchange rate ($/FC) Ft+1 = forward exchange rate ($/FC) An investor has two options: 1. Invest in U.S. $ terminal wealth = 1+ it 2. Invest abroad $ terminal wealth = (1/St)(1+it*)Ft+1 To avoid arbitrage opportunities, we need equality of dollar returns so that one statement of interest rate parity, with exchanges rates expressed in “American terms”, is Ft 1 (1 i* ) (1 i t ) t St Dividing both sides of the above expression by (1+it*) gives Ft 1 1 i t St 1 i* t Now subtracting 1 from both sides gives Ft 1 St i t i* t St 1 it* 2 Alternatively, the covered interest rate parity can be written as: Ft 1 i t S0 1 i* where i and i* are the geometric mean US and foreign interest rates over the t periods. Forward premiums and discounts are entirely determined by interest rate differentials. Suppose StFC/$ is the spot rate in European terms and Ft+1FC/$ is the forward rate in European terms. How would the interest rate parity formula look like? Exercise: Spot (FF/$) = 7.4825 90-day Forward = 7.5650 90-day Eurodollar interest rate = 8.2% p.a. 90-day Eurofranc interest rate = 12.7% p.a. Does the covered interest rate parity hold? 3 If Ftd/f/S0d/f > [(1+id)/(1+if)]t, then Ftd/f must fall, S0d/f must rise, id must rise, and/or if must fall. Sell FC at Ftd/f. Buy FC at S0d/f. Borrow at id. Lend at if. If Ftd/f/S0d/f < [(1+id)/(1+if)]t, then Ftd/f must rise, S0d/f must fall, id must fall, and/or if must rise. Buy FC at Ftd/f. Sell FC at S0d/f. Lend at id. Borrow at if. Example: i$ = 7% i£ = 3% S0$/£ = $1.20/£ Ft$/£ = $1.25/£ How could one make a riskless arbitrage profit? Covered interest arbitrage is the profit-seeking activity that forces interest rate parity to hold. Interest rate parity line (see Exhibits 6.1 & 6.2) 4 RELAXING THE BASIC ASSUMPTIONS Transaction costs If you are holding a dollar asset, foreign investment requires four transaction costs: 1. Brokerage fees on sale of dollar security t 2. Buy spot exchange (1/2 bid-ask spread) tS 3. Buy foreign security – brokerage fee t* 4. Sell forward (1/2 bid-ask spread) tF How do you construct the neutral band within which covered interest arbitrage transactions will not occur, when transaction costs are present? Illustration: Exhibit 6.3 Taxes Consider the case where income is taxed at a rate of y and capital gains at k. On an after-tax basis, the parity condition is modified as Ft 1 St it it* (1 k ) (1 y ) St 1 it* or Ft 1 St it it* 1 y St 1 it* 1 k Illustration: Exhibit 6.4 Uncertainty 5 IRP WITH BID-ASK SPREAD Notations: Spot rate ($/¥) St b – St a Forward rate ($/¥) Ft,Tb – Ft,Ta Interest on $ iTb – iTa Interest on ¥ iTb* – iTa* To see whether there is a riskless profit, there are two approaches. (1) Borrow $ Borrow $ at the rate of iTa. Get $ 1/(1+ iTa) Convert this $ amount into ¥ Have ¥ 1/[(1+ iTa)Sta] Invest this ¥ amount Obtain ¥ (1+ iTb*)/[(1+ iTa)Sta] Sell all of the ¥ amount in the forward market End up with $ [(1+ iTb*) Ft,Tb]/[(1+ iTa)Sta] So, if this final amount is great than 1, then there is a profit opportunity. To eliminate arbitrage, we require 1 ia F S b t,T a t T * 1 iT b 6 (2) Borrow ¥ Borrow ¥ at the rate of iTa*. Get ¥ 1/(1+ iTa*) Convert this amount into $ Have $ Stb/(1+ iTa*) Invest this $ amount in the US Obtain $ Stb(1+ iTb)/(1+ iTa*) Sell this amount of $ forward End up with ¥ Stb(1+ iTb)/ Ft,Ta(1+ iTa*) To eliminate arbitrage, we require 1 iT b F S a t,T b t * 1 ia T IMPORTANCE OF IRP One-way arbitrage: One-way arbitrage is simply picking the lowest-priced alternative when buying or the highest-priced alternative when selling. Example: Consider an investor who holds US$ cash and wants to make a DM payment in 3 months. The investor is given the following quotations: Spot $/DM: 0.6793 – 0.6803 3-month Forward $/DM: 0.6800 – 0.6830 3-month Euro DM: 4.00 – 4.125% p.a. 3-month Euro $: 6.0625 – 6.1875% p.a. Can the investor make a one-way arbitrage profit? 7 The search for one-way arbitrage opportunities will limit the possibility of round-trip, covered interest arbitrage profits. Cost of hedging for firms: Consider a manager wishes to own the Japanese yen in 6 months from now. The following two hedging strategies are possible: 1. Bank forward contract 2. Money market hedge Firms with lower credit rating and firms with lower borrowing capacity prefer to hedge using a bank forward. Country risk: IRP provides a market determined measure of political risk differences between countries. To evaluate risky cash flows from foreign countries, one needs a risk-adjusted discount rate. IRP provides a market determined measure of this discount rate. 8 II. INTERNATIONAL FISHER EFFECT Fisher Relation: (1 i) (1 r)(1 p) Nominal returns are part real return and part inflation. Uncovered Interest Rate Parity or International Fisher Effect states that returns in different countries’ money markets should be equalized “in an expected sense.” DERIVATION OF A GENERAL EXPRESSION FOR INTERNATIONAL FISHER EFFECT Notations: it = U.S. interest rate it* = “comparable” foreign interest rate St = spot exchange rate, in American terms ($/FC) An investor has two options: 1. Invest in U.S. $ terminal wealth = 1+ it 2. Invest abroad and covert at future spot $ terminal wealth = St+1(1+ it*)/St International Fisher Effect (in American terms) states: S E[St 1 ] 1 i t E (1 i* ) t 1 (1 i* ) t t St St E[St 1 ] 1 i t E[St 1 ] St i t i* or t St 1 i* t St 1 it* 9 What would be the formulation for the International Fisher Effect in European terms? Foreign investment proposed in the IFE contains exchange rate risk. When the U.S. interest rates are higher than foreign interest rates, the dollar is expected to depreciate, and vice versa. International Fisher and PPP combined: real interest rate parity Based on PPP, the expected percentage change in the exchange rate is E[St 1 ] St E[Ptus1 ] Ptus E[Ptf1 ] Ptf us f p us1 p ft 1 t St Pt Pt where pt+1us and pt+1f are the expected inflation rates. Combining with the International Fisher Effect gives p us p f i i* Thus, the nominal interest differential is equal to the expected inflation differential. Alternatively, if we assume that real interest rates are equal across countries, then the Fisher relation implies 1 i 1 p us 1 i* 1 p f Measured over t periods, the relation becomes t 1 i 1 p t us 1 i* 1 p f 10 The IFE does not hold at any particular point in time, but does hold in the long run. THE FORWARD RATE UNBIASED CONDITION Recall that the International Fisher Effect is given by 1 it E[S t 1 ] St 1 i* t This is equivalent to Ft E[St ] Thus, the forward rate is an “unbiased predictor” of the future spot rate. If speculators think the spot rate will close above the forward rate, they can buy the forward contract and settle in the spot market at a positive expected profits. This type of speculative activity forces the forward price to rise and ensures that forward exchange rates are close to expected future spot rates. Consider a 90-day forward exchange contract to purchase the British pounds. Think of an investor as intentionally speculating, that is, as wanting to bear the risk. If you contract to buy pound forward at $1.50/£ and you do not hold any pounds, then you are taking on exchange risk. You will profit if the future spot exchange rate is greater than $1.50/£, because you could sell the pounds for more than it takes to buy them. Your profit at time t+90 from a contract entered at time t is St+90 - Ft,90. (See Exhibit 6.5) 11 If the forward rate is an unbiased predictor of the future spot exchange rate, the forecast error made by the forward rate has a mean of zero. This has two important practical implications: 1. When you make a sequence of purchases in the forward market over a long time period, profits average out to zero. 2. At any time t, we can describe the possible future spot rates in any 90 days by a probability distribution. This gives us the probability of profits and losses. 12 III. INTERNATIONAL PARITY CONDITIONS: WRAP- UP Summary PPP Absolute version: link exchange rate and price ratio Relative version: link inflation rates and exchange rate changes Interest Rate Parity Covered Interest Rate Parity: link forward premium and interest differential Uncovered Interest Rate Parity or International Fisher Effect: link expected exchange rate changes and interest rates What about links between interest rates and inflation? The PPP, CIRP and IFE relations are sometimes referred to as the International Parity Conditions. (See Exhibit 6.6) If they all hold simultaneously, they imply equal real interest rates across countries. 13 Exhibit 6.1 The Interest Rate Parity Line Equilibrium and Disequilibrium Points Note: Points A and B are on the interest rate parity line. Points off the parity line generate economic incentives for capital to flow out of investments in one currency and into another currency. The arrows indicate the marginal impact of arbitrage transactions on prices of F, S is, and iforeign. Exhibit 6.2 Covered Interest Rate Parity in European Terms i* i t t 45° line 1 it Region of Arbitrage Ft S t St Region of Arbitrage 14 Exhibit 6.3 The Interest Rate Parity Line Transaction Costs and the Neutral Band Note: Points A, A”, and B are inside the neutral band and considered equilibrium points with no arbitrage profit possibility. For points A’, B’ and B”, the profit opportunity is greater than the cost of executing arbitrage transactions. Exhibit 6.4 Interest Rate Parity Lines Pretax (PT) and After-Tax (AT) Lines 15 Exhibit 6.5 Speculative Long Position of a £ Forward Contract Profit per unit of £ 0.10 1.40 Future Spot Rate ($/£) 1.50 1.60 -0.10 16 Exhibit 6.6 International Parity Conditions Forecast Change in Spot Exchange Rate (E) (A) Forward Premium on Forecast Difference Foreign Currency (C) in Inflation Rates (D) (B) Difference of Nominal Interest Rates 17

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posted: | 7/8/2010 |

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