2011 EXAMINATION QUESTION & ANSWERS (2)

1. 2011 EXAMINATION QUESTION & ANSWERS (2)

2. 2011 EXAMINATION (2) Question 2 (a) In what ways do the roles played by arbitrageurs, hedgers and speculators in the foreign exchange market differ from one another and yet have similar outcomes?

3. ANSWERS (a) Arbitrageurs seek to earn risk-free profits by taking advantage of differences in exchange rates and/or interest rates among countries. Hedgers, mostly multinational firms, engage in forward contracts to protect the home currency value of various foreign currency-denominated assets and liabilities on their balance sheets. Speculators expose themselves to risks associated with exchange rate changes, buying and selling in the spot and forward markets. However, the outcomes are similar in the sense that their activities tend to move the exchange rates towards equilibrium

4. 2011 EXAMINATION (2) Question 2 (b) Suppose that the euro (EUR) is offered at USD 1.3714 and GBP is sold at EUR 1.1737 in London, while the pound sterling (GBP) is bid at USD 1.6115 in New York. Do you see an arbitrage incentive here? If an arbitrageur were to convert USD 1 million into euro in Frankfurt, sell the euro for sterling in London and then re-sell sterling for the dollar in New York, what would be the profit in this example? How will this arbitrage affect the exchange rates in the three markets?

5. ANSWERS (b) Step 1: USD 1 million is converted into EUR 729,181.86 in Frankfurt Step 2: EUR 729,181.86 is converted into GBP 621,296.67 in London Step 3: GBP 629,296.67 is converted into USD 1,001,728.42 in New York PROFIT: USD 1,728.42

6. ANSWERS (b) • EUR strengthens against USD in Frankfurt • GBP strengthens against EUR in London • USD strengthens against GBP in New York • No arbitrage incentive if : EUR 1 = USD 1.3724 GBP 1 = EUR 1.1749 GBP 1 = USD 1.6126

7. Lecture 5INTERNATIONAL FINANCE (FN6053/5053) Parity Conditions in International Finance

8. PARITY CONDITIONS IN INTERNATIONAL FINANCE • If markets are not impeded, there is a set of equilibrium relationships that should apply to product prices, interest rates and spot and forward exchange rates. • There are 5 theoretical economic relationships : • Purchasing power parity (PPP) • Fisher effect (FE) • International Fisher effect (IFE) • Interest rate parity (IRP) • Unbiased forward rate (UFR) • These relationships are known as parity conditions.

9. PARITY CONDITIONS INTER. FINANCE (cont’d) Nominal Interest Rate FE IRP Inflation Rate Forward Exchange Rate IFF PPP Spot Exchange Rate UFR

10. PARITY CONDITIONS INTER. FINANCE (cont’d)  • In competitive markets, with numerous buyers & sellers, rational participants, low-cost information,exchange-adjustedprices of identical tradable goodsand financial assets must be within transactions costs of equality worldwide – i.e. equal prices after adjusting for exchange rates. • Otherwise, there is opportunity for arbitrage. • Similarly, risk-adjusted expected returns on financial assets in different markets should be equal. • The common denominator of these parity conditions is the adjustment of the various rates and prices to inflation i.e. inflation effects • PPP : relationship between inflation and nominal exchange rates • An important concept underlying these parity conditions is the law of one price. • FE : relationship between inflation and interest rates • IFE : relationship between interest rates and exchange rates

11. PARITY CONDITIONS INTER. FINANCE (cont’d) • According to modern monetary theory, inflation is the logical outcome of an expansion of money SS in excess of the growth in real output. • A further link in the chain relation of money SS growth, interest rates and exchange rates, is the notion that money is neutral. That is money should have no impact on real variables. • E.g. a 10%  in money SS, relative to DD for money should lead to a price increase of 10%. • So, though  in quantity of money should lead to  in prices and exchange rate (in nominal, not real, terms), the terms of trade (Px/Pm) shouldn’t . i.e. domestic goods for foreign goods: both numerator and denominator affected evenly). • This is the idea behind PPP, IFE and FE.

12. PARITY CONDITIONS INTER. FINANCE (cont’d) • If international arbitrage enforces the law of oneprice, then the “exchange-rate” between home currency and domestic goodsmust equal the exchange rate between home currency and foreign goods. • In other words, a unit of HC should have the same purchasing powerworldwide. If it gains (loses) purchasing power at home, it will gain (lose) purchasing power abroad too. • This is the idea behind PPP. first stated by Gustav Cassel in 1918. • Since, then PPP is widely used as one indicator of equilibrium exchange rate by Central Banks. • At a corporate financial management level, PPP is often used for a whole range of purposes from forecasting exchange rates, deciding which currency to borrow in or lend in to plant locations.

13. PARITY CONDITIONS INTER. FINANCE (cont’d) Ignores transportation costs, tariffs, quotas etc (product differentiation thus less relevant). Absolute Version PPP 2 versions RelativeVersion More relevant

14. PARITY CONDITIONS INTER. FINANCE (cont’d) • The relative version of PPP states that the exchange rate between the HC and any FC will adjust to reflect  in the price levels of the 2 countries. • E.g. if inflation in Japan = 2% Inflation in US = 6% • Then according to PPP, Yen should appreciate against US$ by approximately 4%. • Mathematically if ih = home inflation if = foreign inflation e0 current exchange rate : et exchange rate at time in future. then: …………………..(1)

15. PARITY CONDITIONS INTER. FINANCE (cont’d) • e.g. if US inflation (h) = 5%, German inflation (f) = 3% e0 is = $ 0.75 per DM then, the exchange rate 3 years from now is: • The one-period version of equation (1) above is commonly stated as: ……………………… (2)

16. PARITY CONDITIONS INTER. FINANCE (cont’d) • By subtracting 1 from both sides of the above equation, and if if is relatively small then we get: • This means that the  in exchange rate during a period should equal the inflation differential for that same period. • In effect, PPP says that currencies of countries with higher inflation should devalue/depreciate against currencies of countries with relatively lower inflation. ……………………(3) 

17. PARITY CONDITIONS INTER. FINANCE (cont’d) • Graphically, PPP can be shown as : %  in HC value of F.C. PPP Parity line Home has 3% higher inflation so FC value by 3% i.e. HC depreciates % Inflation differential of home country to foreign country.

18. PPP: THE PARITY LINE IMPLICATIONS • Every point on the parity line represents a certain real exchange rate (RER) • In other words, RER remains unchanged as one moves up or down the parity line: depreciation offset by inflation • Above the parity line (i.e. to the left) HC is undervalued, as HC depreciation is excessive relative to inflation differential • Below the parity line (i.e. to the right) HC is overvalued, as depreciation is insufficient to wash off the inflation effect • Along the parity line, no change in competitiveness • Above the parity line, gain in competitiveness • Below the parity line, loss of competitiveness

19. PARITY CONDITIONS INTER. FINANCE (cont’d) • Should the %  in exchange rate not equal the % inflation difference then there’s possible arbitrage opportunity in a world where PPP holds. • PPP  Exchange rate s should cancel out  in the foreign price level relative to domestic prices.  • *These offsetting movements should have no effect on the relative competitive positions of domestic or foreign firms.  • **Thus, changes in the nominal exchange rate may be of little or no significance in determining the true effects of currency  on a firm and a nation.

20. PARITY CONDITIONS INTER. FINANCE (cont’d) •  in competitiveness will depend on the real exchange rate. • E.g. if you had higher inflation of 5%, and as a result your currency  by 5%, you shouldn’t be anymore competitive as a result of the devaluation  why should you? The real exchange rate hasn’t . • If PPP holds perfectly, then real exchange rates do not , (holding other things constant). • The real exchange rate is the nominal exchange rate adjusted for inflation.

21. PARITY CONDITIONS INTER. FINANCE (cont’d) • The real exchange rate e1 at time t is : • If PPP holds perfectly: Equals e0 or current real exchange rate same as before since PPP ensures that all inflation differential is washed off. • *When PPP doesn’t hold or there’s deviation from PPP then real exchange rate  s  Thus, the competitive position changes. • **E.g. if your inflation is 5% higher but your currency only depreciates 3%, then ceterus paribus  your currency is overvalued, and you lose competitiveness.

22. PARITY CONDITIONS INTER. FINANCE (cont’d) • Empirical Evidence of PPP • The strictest from of PPP  that there’s one price for all goods everywhere obviously fails empirical tests. • However, there is very clear evidence of a relationship between relative inflation rates and s in nominal exchange rates. • The general conclusion from empirical studies is that PPP holds up well in thelong run but not as well over shorter time periods. • Adjustment to PPP occurs but usually with a lag. • One difficulty in empirical studies of PPP is that the price indices CPI, WPI etc. are often constructed and measured differently in different countries. • Still, there are dangers in attributing too much importance to a deviation from PPP, because PPP is not a complete theory of exchange rate determination  there are other things – like (IRP, GNP growth expectations, uncertainties etc).

23. A GENERALIZED VERSION OF PPP • A major problem of PPP is that it suggests that PPP should hold for all types of goods. • A generalized version of PPP differentiates between traded & non-traded goals. Goods • While traded goods are susceptible to international competition, non-traded goods like haircuts (services), houses (products) are not. • *Thus, PPP is more likely to hold for tradeables than non-tradeables. Traded  Tradeables Non Traded

24. A GENERALIZED VERSION OF PPP • Since PPP only holds for tradeables, the proportion of tradeables to non-tradeables can affect PPP as a determinant of exch. rates. • For example, if there is increased productivity in the non-tradeables sector, then the relative price of tradeable is lower, implying a PPP appreciation in exchange rate. • Suppose labour (non tradeable) becomes more productive, the amount of tradeable goods (say cars) increases  since SS  while DD is the same, price of cars , so less inflation HC appreciates.

25. TESTING PPP: MEASUREMENT PROBLEMS • In using indices like WPI etc., it is mostly tradeables that get captured , non–tradeables often are not. • Weights differ even within CPI between products and between countries • Quality differences among similar prods. across countries. • Base period of index differ between countries

26. EMPIRICAL EVIDENCE ON PPP • Frenkel (1981) shows that PPP tends to perform better for countries that are geographically close to one another and where trade linkages are high. E.g. countries within EC. (transport costs low, less impediment, similar products – thus the strong PPP). • *Still, prolonged deviations from PPP does happen. • Exchange rates have been more volatile than PPP dictates. • PPP tends to hold better in the long run than short run. • High inflation countries like Brazil, Argentina, Israel etc. – saw rapidly declining currencies  implying PPP is amajor determinant of exchange rates. • Overall, PPP tends to hold better for tradeables than non-tradeables.

27. THE FISHER EFFECT • According to Irwin Fisher, market interest rates fully adj. to  in inflation  since, lenders would want to be compensated for loss of purchasing power. • i.e. the nominal interest rate is made up of the real interest rate and the inflation rate: or • **The generalized version of the Fisher effect asserts that real returns are equalized across countries thru arbitrage  i.e. real r1h = real r1f . • **Currencies with higher rates of inflation should bear higher interest rates than currencies of lower inflation rates. …………………….. (1)

28. THE FISHER EFFECT • If real returns were higher in one currency than another, capital would flow from the lower to higher currency. In the absence of govt. intervention, the arbitrage will continue until expected real returns are equalized. • Thus, in equilibrium, it should follow that the nominal interest rate differential will approximately equal the inflation rate differential or • if rf and rh are relatively small, then this exact relationship can be approximate by • Nom rh – nom rf = infl.h – infl.f ……………………..(3)  • dif. in nom int = dif. in infl. rates ……………………….(2)

29. THE FISHER EFFECT • Generalized Version: Currencies with high rates of inflation should bear higher interest rates than currencies with lower rates of inflation • Example: Given 4% inflation in US and 7% inflation in UK, Fisher effect says nominal interest rates should be 3% higher in UK than in US • If nominal interest rate differential is less than 3% in UK, funds would flow from UK to US • If nominal interest rate differential is more than 3%, funds would flow from US to UK

30. THE FISHER EFFECT % Interest differential in favour of Home Country Parity Line using Equation (3) above Since, HC has 2% higher inflation than FC, it has 2%  interest % Inflation differential, home relative to foreign country.

31. FISHER EFFECT IMPLICATIONS • Every point on the parity line represents equality between inflation differential and interest rate differential: no reason for to funds to move from one country to the other, as interest differential is offset by inflation differential • Above the parity line (i.e. to the left), interest rate differential exceeds inflation differential: funds would flow into the home country • Below that parity line (i.e. to the right), interest differential is less than inflation differential: funds would move out of the home country

32. THE FISHER EFFECT • Empirical studies of FE appear to show evidence consistent with the hypothesis that most of the variation in nominal interest rates across countries can be attributed to differences in inflationary trends. • In today’s world of integrated financial markets, it is unlikely that significant real interest differentials could last for long  especially due to “HOT MONEY”. • In an integrated capital market (integrated with other international markets) the domestic real interest rate depends on both what is happening within and outside the country. • It also means that, as a result, real interest rates in other countries like US and Japan could also , if there is an  in worldwide DD for funds. • Capital market integration has homogenized markets around the world, eroding much - if not all- of the real interest rate differentials between comparable domestic and off-shore securities.

33. THE FISHER EFFECT • So what could account for the real interest rate differentials that still exist for some currencies: a) Can’t be totally attributed to currency risk, since this type of risk is unsystematic and can therefore be diversified away. • So, more likely b) Differences in tax policies, (difference in taxation rates on savings etc) and / or imposition of regulatory barriers to capital flows  and consciously presenting varying risks to would-be investors e.g. CB may stop domestic banks paying interest on hot money  meant for currency speculation c) Political risks  e.g. currency controls, expropriations etc. • Given reason (b) and (c) one could explain why real interest rates in developing countries can exceed those in developed countries and still not be arbitrageable. **Finally, when comparing / analyzing currencies for int. dif. be careful to use “appropriate” comparison since there are many quotedinterest rates.

34. THE INTERNATIONAL FISHER EFFECT (IFE) • IFE is really the result you get when you combine the results of PPP and FE. • Recall that • So IFE is essentially t

35. THE INTERNATIONAL FISHER EFFECT (IFE) • Again, if rf is relatively small, then equation (4) can be rewritten as; • Graphically, the IFE can be shown as; Expected in HC value of FC 4 Interest* dif. in favor of HC -4 4 -4 • Since, HC has 4%  inflation, that means, it would have 4% higher nominal interest rate (FE), thus, according to IFE, the HC depreciates 4% against FC (since FC  in HC value by 4%) • IFE also implies that interest dif. bet. 2 currencies is also an unbiased predictor of future exchange rates. • *Thus IFE combines all we know from PPP, FE and UFR too.

36. IFE& CAPITAL MOVEMENTS • Every point on the parity line represents equilibrium where interest rate differential is just offset by currency depreciation: no arbitrage incentive to shift funds • Above the parity line (i.e. to the left), expectedcurrency depreciation (forward discount) exceeds interest rate differential: there is arbitrage incentive for funds to move from home to foreign country • Below the parity line (i.e. to the right), expected currency depreciation (forward premium) is less than interest rate differential: there is arbitrage incentive for funds to move from foreign to home country

37. THE INTERNATIONAL FISHER EFFECT (IFE) • The implication of IFE is that the expected return from investing at home (1+rn), should equal the expected return from investing abroad • Example: • Invest at home => (1+rn) • Invest abroad • Suppose: US infl. =4%,nom. r = 8% UK infl. =8%, nom. r =12% • Invest at home in US = 8% return • Invest in UK (1+rƒ) ∆ in each rate 12% interest earned -4% exch. loss Total Ret = 8 In effect, IFE states that currencies with low interest rates should appreciate relative to currencies with high interest rates.

38. INTERNATIONAL FISHER EFFECT (IFE) • Equilibrium position: interest differential in favour of home country (say 4%) is just offset by anticipated depreciation of the home currency (i.e. 4%) • If home currency is expected to depreciate by only 3%, then funds will flow from foreign to home country • Conversely, if home currency is expected to depreciate by >4%, then funds will flow from home to foreign country

39. EMPIRICAL EVIDENCE • There is clear evidence that currencies with high interest rates tend to depreciate and those with low interest rates tend to appreciate. • Empirical studies have also found evidence that interest differentials do anticipate currency s; especially a long-run tendency for these interest differentials to offset exchange rate s. • Thus, at any point in time, currencies bearing higher interest rates can reasonably be expected to depreciate relative to currency with lower interest rates.

40. INTEREST RATE PARITY (IRP) • The movement of funds across countries is an “arbitrating” (equalizing) factor in exchange rates. • According to IRP, the currency of country with a lower interest rate should be at aforwardpremium in terms of a currency with higher interest rate. • So, IRP really connects the forward rate to spot rate.

41. INTEREST RATE PARITY (IRP) • In efficient markets  the % forward premium or discount should equal the % interest differential. IRP  Where f, is the forward rate, e0 is spot. • IRP ensures that the return on a “hedged” or “covered”foreign investment will equal the return from a domestic investment of similar risk. • In effect, IRP states that high interest rates from a currency are offset by forward discount and that low interest rates are offset by forward premiums.

42. INTEREST RATE PARITY (IRP) • Start with USD 1 million in New York • Convert USD 1 million to euros at EUR 0.740 per USD (or USD 1.351 per EUR) into EUR 740,000 • Invest EUR 740,000 in Frankfurt at 1.5% for 90 days, yielding EUR 751,000 in 90 days • At the same time sell EUR 751,000 forward at a rate of EUR 0.73637/USD (USD 1.358 per EUR) for delivery in 90 days (EUR at premium) • Receive USD 1,020,000 after 90 days [gain = USD 20,000] • Alternatively: Invest USD 1 million New York, for 90 days at 2% and receive USD 1,020,000 in 90 days • PARITY EXISTS, SO NO ARBITRAGE OPPORTUNITY!

43. IMPLICATIONS OF IRP • Currencies with low relative nominal interest rates would have forward premium. • Currencies with high relative nominal interest rates would face forward discounts. • Forward premium or discount = nominal interest differential at equilibrium when parity is established

44. COVERED INTEREST ARBITRAGE: EXAMPLE • Suppose £ interest in London  12% $ interest in New York  7% £/$ spot rate = $1.75 per £ And 1 year forward £/$= $1.68 per £ • These mean the forward discount on £ in $ terms is 4% • So, investing in £ would give net return of 8%  12% - 4% = 8%  higher than domestic return of 7% 1.75 - 1.68 x 100 = 4.166% 1.75

45. COVERED INTEREST ARBITRAGE

46. COVERED INTEREST ARBITRAGE • As more and more of this type of arbitrage takes place,  as£ are bought spot and sold forward, the spot-forward differential will widen until it meets/equals the interest differential. • As funds move from US to UK, nominal interest rate will rise in US and fall in UK, narrowing the US-UK interest rate differential until it meets/equals the sterling-dollar spot-forward differential. • IRP holds when there is no more arbitrage incentive or opportunity for covered – interest arbitrage.

47. THE CARRY TRADE • Borrowing a currency bearing low interest rate and investing in a currency bearing high interest rate. • Example: borrowing yen in Japan at rates close to zero and selling the yen to invest in high-yielding assets such as US treasury or European bonds (in trillion dollars a year). • Danger is that small, steady returns (say, 1% int. rate on yen loan and 5% int. earned in dollar investments: spread of 4%) may be more than offset by sudden, large dollar depreciation against yen: “picking up nickels in front of a steamroller”!

48. THE CARRY TRADE & THE INTERNATIONAL FISHER EFFECT • According to the IFE, carry trades should not yield a predictable profit, because the interest rate differential between two currencies should equal the rate at which investors expect the low-interest rate currency to appreciate against the high-interest currency. • But, the opposite may happen with low-interest yen depreciating (large capital outflows) and high-interest dollar appreciating (large capital inflows), providing more incentives for carry trades (interest rate spread plus exchange rate gains)

49. RELATIONSHIP BETWEEN FORWARD RATE AND FUTURE SPOT RATE • Given econ. fundamentals (e.g. interest rates etc.), ifa currency is expected to devalue, then it is only logical that the forward rate would be falling faster than the spot. • So, here the forward currency rate will be at a discountto the current spot rate. • The forward rate will be lower by the % of expected devaluation. • Why is the forward rate at adiscountto current spot rate? Because the future spot rate is expected to be lower. i.e.  which means that the current forward rate is an unbiased estimator of the future spot rate .

50. RELATIONSHIP BETWEEN FORWARD RATE AND FUTURE SPOT RATE • Suppose 90-dayforward rate for DM is DM1 = $0.40. This means the expected spot rate 90 days from now would be 1 DM = $0.40 • The above equation can be converted into % as follows: minus one on both sides Which really means the forward differential equals the expected change in the exchange rate. • It should be noted that market efficiency requires that people process information and form reasonable expectations, it does not require that f1 = e1 • Only that f1 is an unbiased estimator of e1