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International Parity Relationships and Forecasting Foreign Exchange Rates

International Parity Relationships and Forecasting Foreign Exchange Rates. Chapter 5. Chapter Five Outline. Interest Rate Parity Purchasing Power Parity The Two Fisher Effects Forecasting Exchange Rates. Chapter Outline. Interest Rate Parity Covered Interest Arbitrage

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International Parity Relationships and Forecasting Foreign Exchange Rates

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  1. International Parity Relationships and Forecasting Foreign Exchange Rates Chapter 5

  2. Chapter Five Outline • Interest Rate Parity • Purchasing Power Parity • The Two Fisher Effects • Forecasting Exchange Rates

  3. Chapter Outline • Interest Rate Parity • Covered Interest Arbitrage • IRP and Exchange Rate Determination • Reasons for Deviations from IRP • Purchasing Power Parity • The Fisher Effects • Forecasting Exchange Rates

  4. Chapter Outline • Interest Rate Parity • Purchasing Power Parity • PPP Deviations • Evidence on Purchasing Power Parity • The Fisher Effects • Forecasting Exchange Rates

  5. Chapter Outline • Interest Rate Parity • Purchasing Power Parity • The Fisher Effects: International vs. Generalized • Forecasting Exchange Rates

  6. Chapter Outline • Interest Rate Parity • Purchasing Power Parity • The Fisher Effects • Forecasting Exchange Rates • Efficient Market Approach • Performance of the Forecasters

  7. 5.1 Interest Rate Parity • Interest Rate Parity Defined • Covered Interest Arbitrage • Interest Rate Parity & Exchange Rate Determination • Reasons for Deviations from Interest Rate Parity

  8. Interest Rate Parity Defined • IRP is an arbitrage condition. • If IRP did not hold, then it would be possible for an astute trader to make unlimited amounts of money exploiting the arbitrage opportunity. • Since we don’t typically observe persistent arbitrage conditions, we can safely assume that IRP holds.

  9. Interest Rate Parity Defined • Suppose you have $100,000 to invest for one year. • You can either • invest in Canada at i$. Future value = $100,000(1 + i$) or • trade your dollars for pounds at the spot rate, invest in UK at i£ and hedge your exchange rate risk by selling the future value of the British investment forward. The future value = $100,000(F/S)(1 + i£) • Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage condition would exist, therefore (F/S)(1 + i£) = (1 + i$)

  10. Interest Rate Parity Defined Part Deux Suppose you have $100,000 to finance for one year. You can either Finance in Canada at i$. Future value = $100,000(1 + i$) or Finance in pounds then buy dollars at the spot rate. Buy pounds forward to hedge. The future value in dollars of the British financing debt service payment equals $100,000(F/S)(1 + i£) Since both of these financing alternatives have the same risk, they must have the same future value, therefore (F/S)(1 + i£) = (1 + i$)

  11. Invest £100,000 at i£ S Interest Rate Parity $100,000 $100,000(1 + i$) • Trade $100,000 for £ at S $100,000(F/S)(1 + i£) • One year later, trade £ for $ at F

  12. 1 + i$ F = 1 + i£ S Interest Rate Parity Defined Formally, (F/S)(1 + i£) = (1 + i$) • or if you prefer,

  13. 1 + i£ F£/$ = 1 + i$ S£/$ 1 + i$ F$/£ = 1 + i£ S$/£ Interest Rate Parity Carefully Defined (formula assumes direct quotation) Depending upon how you quote the exchange rate ($ per £ or £ per $) we have: or

  14. IRP and Covered Interest Arbitrage • If IRP failed to hold, an arbitrage would exist. It’s easiest to see this in the form of an example. • Consider the following set of foreign and domestic interest rates and spot and forward exchange rates.

  15. IRP and Covered Interest Arbitrage • A trader with $1,000 to invest could invest in Canada, in one year his investment will be worth $1,071 = $1,000(1+ i$) = $1,000(1.071) • Alternatively, this trader could exchange $1,000 for £800 at the prevailing spot rate, (note that £800 = $1,000÷$1.25/£) invest £800 at i£ = 11.56% for one year to achieve £892.48. Translate £892.48 back into dollars at F360($/£) = $1.20/£, the £892.48 will be exactly $1,071.

  16. Interest Rate Parity $1,000 $1,071 • Trade $100,000 for £800 $1,071 • One year later, trade £892.48 for $ at F360($/£) = $1.20/£ • Invest £800 at 11.56% = i£

  17. Interest Rate Parity & Exchange Rate Determination • According to IRP only one 360-day forward rate, F360($/£), can exist. It must be the case that F360($/£) = $1.20/£ Why? If F360($/£)  $1.20/£, an astute trader could make money with one of the following strategies:

  18. Arbitrage Strategy I If F360($/£) > $1.20/£. F is too high. Invest foreign & finance domestic. • Borrow $1,000 at t = 0 at i$ = 7.1%. • Exchange $1,000 for £800 at the prevailing spot rate, (note that £800 = $1,000÷$1.25/£) invest £800 at 11.56% (i£) for one year to achieve £892.48 • Translate £892.48 back into dollars, if • F360($/£) > $1.20/£ , £892.48 will be more than enough to repay your dollar obligation of $1,071.

  19. Arbitrage Strategy II If F360($/£) < $1.20/£. F is too low. Invest domestic and finance foreign. • Borrow £800 at t = 0 at i£= 11.56% . • Exchange £800 for $1,000 at the prevailing spot rate, invest $1,000 at 7.1% for one year to achieve $1,071. • Translate $1,071 back into pounds, if • F360($/£) < $1.20/£ , $1,071 will be more than enough to repay your £ obligation of £892.48.

  20. IRP intuition: Description of market in equilibrium • A high interest rate currency exhibits a forward discount. • What if high interest rate and forward premium? • Attractive venue for investment!! • A low interest rate currency exhibits a forward premium. • What if low interest rate and forward discount? • Attractive venue for financing!! • High (low) interest rate offsets forward discount (premium)

  21. Reasons for Deviations from IRP • Transactions Costs • The interest rate available to an arbitrageur for borrowing, ib may exceed the rate he can lend at, il. • There may be bid-ask spreads to overcome, Fb/Sa < F/S Thus (Fb/Sa)(1 + i£l)  (1 + i£ b)  0 • Capital Controls • Governments sometimes restrict import and export of money through taxes or outright bans.

  22. 5.2 Purchasing Power Parity • Purchasing Power Parity and Exchange Rate Determination • PPP Deviations • Evidence on PPP

  23. P$ P$ $300 S($/£) = P£ = = $2/£ S($/£) = P£ £150 Purchasing Power Parity at a point in time • The exchange rate between two currencies should equal the ratio of the countries’ price levels: • For example, if an ounce of gold costs $300 in the U.S. and £150 in the U.K., then the price of one pound in terms of dollars should be:

  24. (1+$) (1 + £ ) 1+a = Purchasing Power Parity over an interval of time • Relative PPP states that 1 + % rate of change in the exchange rate, (1+a) = (S1 / S0), is equal to the ratio of (1 + inflation rates): • If Canadian inflation is 5% and U.K. inflation is 8%, the pound should depreciate by 2.78% or around 3%.

  25. Evidence on PPP • PPP probably doesn’t hold precisely in the real world for a variety of reasons. • Haircuts cost 10 times as much in the developed world as in the developing world. • Film, on the other hand, is a highly standardized commodity that is actively traded across borders. • Shipping costs, as well as tariffs and quotas can lead to deviations from PPP. • PPP-determined exchange rates still provide a valuable benchmark.

  26. Expected Inflation • The domestic Fisher effect implies that the real interest rate remains constant equaling the nominal interest rate with the effect of inflation removed (1 + $)= (1 + i$) / ( 1 + $ )

  27. (1 + ¥) 1 + i¥ 1 + i$ (1 + $) Generalized Fisher Effect • If the Fisher effect holds in Canada 1 + i$ = (1 + $ ) × (1 + $) and the Fisher effect holds in Japan, 1 + i¥ = (1 + ¥ ) × (1 + ¥) and if the real rates are the same in each country $ = ¥ then we get the Generalized Fisher Effect: =

  28. S1 (1 + i$) = S0 (1 + i¥) International Fisher Effect or IFE(aka Uncovered Interest Parity) • The International Fisher Effect is IRP without any forward hedging. For S (dollars per yen): • IFE: A low (high) interest rate currency will appreciate (depreciate). • IFE & GFE: A low (high) inflation currency will appreciate (depreciate). Hey, that’s PPP!

  29. IFE PPP 1 + i¥ IRP 1 + i$ No Name (1 + ¥) (1 + $) Exact Equilibrium Exchange Rate Relationships UFR GFE

  30. 5.4 Forecasting Exchange Rates • Unbiased Forward Rate Approach • Fundamental Approach: construct economic models • Technical Approach: looks for patterns in the graphs • Performance of the Forecasters

  31. Unbiased Forward Rate Approach • The forward rate reveals what financial markets expect the spot rate will be in the future. Ft = E[St+1] Unbiased Forward Rate Model • Predicting future spot exchange rates using the forward rate approach is cheap and is hard to beat.

  32. Performance of the Forecasters • Forecasting is difficult, especially with regard to the future. • As a whole, forecasters cannot do a better job of forecasting future exchange rates than the forward rate. • The founder of Forbes Magazine once said: “You can make more money selling financial advice than following it.”

  33. Summary • Interest rate parity: A high (low) interest rate currency exhibits a forward discount (premium). • Purchasing power parity: the exchange rate between two currencies equals the ratio of their price levels. • Relative PPP: A high (low) inflation currency will depreciate (appreciate). • G. Fisher effect: Interest rates and inflation rates go together. • I. Fisher effect: A high (low) interest rate currency will depreciate (appreciate). • Three approaches to exchange rate forecasting: • Unbiased forward rate (the best!), fundamental, technical.

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