1. International Finance FINA 5331 Lecture 7: Forward contracts Interest rate parity Read: Chapter 5 (125-129) Chapter 6 (125-129) Aaron Smallwood Ph.D.

2. Review: Terminology Long vs short: –A trader is long in a currency when they are owed that currency in the future. A trader is short in a currency when they owe that currency in the future. Hedging –The act of reversing a natural short or long position, such that no net position is taken. Speculation –The act of intentionally creating a short or long position in an attempt to profit on currency movements. This exposes the trader to risk. Arbitrage –The act of simultaneously buying and selling an asset, such that no net position remains.

3. Forward contracts Forward contracts: Allow traders to buy/sell foreign currency for delivery in the future, for a price that is known TODAY. We considered both outright forward contracts and non-deliverable forward contracts (NDFs). Example: Suppose the 3 month forward contract for Swiss Franc: $1.1280. 3 months from today, we could buy or sell SF at this price.

4. Forward contracts Let’s review aspects of deliverable forward contracts: 1. A forward contract is a derivative asset, based off of a spot contract. The forward market is known as an “over the counter” (OTC) market, as compared to futures markets, where trade typically occurs on a centralized exchange. 2. The terms of a forward contract are negotiated between a bank/dealer and their client. At least in theory, except where capital controls may be present, a forward contract can be written for any currency. 3. Based on 2, a forward contract can be written for delivery at any point in the future. 4. Again, based on 2, a forward contract can be written in any “lot size.”

5. Forward rates When the forward rate exceeds the spot rate, the foreign currency (currency in the denominator) is trading at a “forward premium.” –Example: S($/SF)= $1.1271…F($/SF) 3m =$1.1280, SF is selling at premium. …When the forward rate is less than the spot, the foreign currency is said to be selling at a “forward discount.” –Example: S($/£)=$1.6725… …F($/£) 3m =1.6714, the pound is selling at a discount.

6. Forward rates Like spot rates, banks will buy forward foreign currency at one price (the bid price) and sell it forward at another price (the ask price). When the spot quotation is provided, the dealer will simply quote basis points for the associated forward rates. –For the basis points, the trader will understand that if the first quote exceeds the second, the basis points are subtracted from the spot quotations. –If the first number in the quote is less than the second, the basis points are added. A basis point is defined as 0.0001.

7. Example Suppose we call our dealer and ask for forward quotes relative to the spot rate for Canadian $. Our dealer supplies the following information: Spot: $1.0480-86 –1 month forward “12-10” –3 month forward “14-8” –6 month forward “16-2” –One month forward rates: $1.0468-$1.0476 –Three month forward rates: $1.0466 - $1.0478 –Six month forward rates: $1.0464 - $1.0484.

8. Forward premia/discount In some sense, the premium or discount provides information related to how the value of a currency changes over time. We can express these values in percentage terms. We will typically apply annualization. The calculation: Where “days” is the number of days until the contract matures.

9. Example Suppose the three month forward rate on yen today is $0.009779. The current spot rate $0.009774. Suppose a contract written for yen matures 92 days from now. The yen is trading at a premium: The yen is selling at 0.200% premium.

10. Premia/Discount Cont. If F>S, in some sense, this might signal that we expect foreign currency to appreciate in value. If F<S, this might indicate that we expect the foreign currency to depreciate in value.

11. Interest Rates and Exchange Rates One of the most important relationships in international finance is the relationship between interest rates and exchange rate. The setup: Suppose a trader has the ability to borrow or lend in both the domestic market and a foreign market. –Denote the domestic annualized interest rate as i t and denote the foreign annualized interest rate as i t *. –Denote the spot and forward domestic currency price of the foreign as S t and F t. Suppose the forward contract matures in M days.

12. Interest Rate Adjustment The forward contract matures in M days. Interest rates are quoted in annualized terms. We need to adjust interest rates to allow a comparison:

13. Borrowing in the domestic currency; lending in the foreign If I borrow one unit of the domestic currency, in M days, I will repay: To lend in the foreign currency, I must convert domestic currency into foreign currency. For each unit of domestic currency I have, I receive, 1/S t units of the foreign currency.

14. Lending Now I lend the proceeds in the foreign country…I have 1/S t units of the foreign currency…I will receive: Problem…these proceeds are in foreign currency units…I want the proceeds in domestic currency. I could have acquired a forward contract, to sell (forward) foreign currency proceeds in M periods. The result:

15. The result: Suppose Then, to profit, I could borrow in the domestic currency, convert the proceeds into foreign currency, lend in the foreign market, and convert proceeds back into domestic currency using a forward contract. What if, I can still profit…Start by borrowing in the foreign currency.

16. Implications The no arbitrage condition implies: The equation, known as the no arbitrage condition, has important implications. To illustrate suppose the equation didn’t hold. Example, suppose: i t : 6.00% (annualized interest rate in the US for an asset maturing in one month). i t *: 5.25% (annualized interest rate in Germany for a similar asset maturing in 1 month). S t : $1.36537 (dollar price of the euro on the spot market). F t : $1.30 (assume asset matures in 30 days time).

17. An arbitrage opportunity exists: First, interest rates are adjusted: We have: As thus: PROFIT TIME!

18. How do we profit Start by borrowing in the foreign country. Let’s do it big! Let’s borrow €10,000,000. –We will have to repay: –€10,000,000*1.004375= €10,043,750 Note, as a result of our actions, demand for loanable funds in Germany increases. Foreign interest rates increase. Convert euros and lend in the US. –€10,000,000*$1.36537 = $13,653,700. –Lend at.5% yielding: –13,653,700*(1.005) = $13,721,968.50. Note, two things happen here. On the spot market, supply of euros increases, driving down S t. Supply of loanable funds increases in the US, driving down i t.

19. Last step… Finally, you use the pre-existing forward contract to sell the dollar proceeds for euros. The result: $13,721,968.50/1.30 = 10,555,360.38. Profit: €10,555,360.38 - €10,043,750 = €511,610.38. Note, in the final step, you sell forward dollars. You are buying forward euros. This likely causes, F t to rise.

20. No arbitrage opportunities? NOT ONCE YOU HAVE LEFT THE MARKET! Recall, our arbitrage opportunity existed because: However, as a result of your actions: –1. Foreign interest rates rise. –2. The spot rate falls. –3. Domestic interest rates fall. –4. The forward rate rises.

21. No arbitrage Thus, we can expect smart traders will eliminate profitable arbitrage opportunities quickly when they exist. Thus, as a rule: Implications: Suppose domestic interest rates fall as a result of, say, monetary policy. To ensure equilibrium: –1. Foreign interest rates could also fall… –2. and/or The forward rate could fall. –3. and/or…The spot rate COULD rise. An increase in the spot rate implies a DOMESTIC CURRENCY DEPRECIATION.

22. Covered Interest Rate Parity The no arbitrage condition is frequently re- arranged in a more convenient way:

23. Deviations from CIRP? Transactions Costs: Suppose we thought we could profit from borrowing in the US and lending in Japan. –The interest rate available to an arbitrageur for borrowing, i b,may exceed the rate she can lend at, i l. –There may be bid-ask spreads to overcome, F b /S a < F/S –Thus (F b /S a )(1 + i ¥ l )  (1 + i $ b )  0 Capital Controls –Governments sometimes restrict import and export of money through taxes or outright bans. Taxation differences on capital gains.

24. FRUH and UIP F t = E(S t+1 ) if investors are risk neutral. Since investors are assumed to be rational, E(S t+1 ) = S t+1 + ε t+1 where ε t+1 is a random (unforecastable) forecast error. Then F t = S t+1 + ε t+1 and the forward rate is an unbiased predictor of the future spot rate. From CIP = (1 + i * t ) (i t – i * t ) StSt F t – S t

25. FRUH and UIP Then it must be the case that This is the Uncovered Interest Parity condition. It will only hold if investors are risk neutral or equivalently they do not care about the currency denomination of the assets they hold = (1 + i * t ) (i t – i * t ) StSt E(S t+1 ) – S t E(s t+1 ) – s t =i t -i t *

26. FRUH and UIP If uncovered interest parity (UIP) holds then FRUH is true and investors are risk neutral. Risk neutrality implies that investors have no currency preference in which their investments are denominated. Assets with identical risk characteristics but denominated in different currencies will be viewed as perfect substitutes.

27. Purchasing Power Parity Purchasing Power Parity and Exchange Rate Determination PPP Deviations and the Real Exchange Rate

28. Purchasing Power Parity in a Perfect Capital Market Purchasing power parity (PPP) is built on the notion of arbitrage across goods markets and the Law of One Price. The Law of One Price is the principle that in a PCM setting, the same goods will sell for the same price in two markets, taking into account the exchange rate.

29. Purchasing Power Parity Let P US and P CHINA represent the weighted average price level for goods in the U.S. and Chinese market baskets respectively. Absolute PPP predicts that these two price measures will be equal after adjusting for the exchange rate: P US = S $/RMB  P CHINA Absolute PPP requires that the consumption baskets are identical across the two countries.

30. Purchasing Power Parity and Exchange Rate Determination The exchange rate between two currencies should equal the ratio of the countries’ price levels: S($/RMB) = P CHINA P$P$ S(RMB/$) = P$P$ P RMB $1,370.70 RMB8,413.36 == ¥6.138 For example, an ounce of gold on March 12 cost $1370.70 in the U.S. and RMB8,413.36 in China. Then the price of one dollar in terms of RMB should be:

31. Relative Purchasing Power Parity Note, that %Δp = π, the rate of inflation Relative PPP states that the rate of change in the exchange rate is equal to the differences in the rates of inflation: %Δs = (1 +  ¥ ) (  $ –  ¥ ) ≈  $ –  ¥ If U.S. inflation is 5% and Chinese inflation is 8%, the yuan should ordinarily depreciate by 2.78% or approximately 3%.

32. Ex-Ante PPP Ex-Ante PPP says that relative PPP will hold in an expected value sense, i.e. Where E is the expectations operator signifying that E(·) is an expected value.

33. PPP Deviations and the Real Exchange Rate The real exchange rate is If absolute PPP holds then Absolute PPP implies that price indices in all countries are computed with the same weights and the same basket of goods. Since this is never true, relative PPP is the more appropriate form. Under relative PPP, RER t will be constant but differ from unity.

34. Purchasing Power Parity and Overvalued or Undervalued Currencies Example Base period nominal exchange rate = $1.50/£ Prices of U.S. goods had risen by 8% Prices of U.K. goods had risen by 4% PPP spot rate = $1.50/£  1.08/1.04 = $1.5577/£ A nominal exchange rate of $1.5577/£ would reestablish PPP in comparison to the base period. Nominal exchange rates greater than $1.5577/£ represent £ “overvaluation” ($ undervaluation), while rates less than $1.5577/£ represent $ “overvaluation” (£ undervaluation).

35. Purchasing Power Parity and Overvalued or Undervalued Currencies Nominal exchange rates greater than the PPP implied exchange rate represent foreign currency overvaluation, while nominal exchange rates less than the PPP implied exchange rate represent domestic overvaluation (or foreign undervaluation).