# INTERNATIONAL PARITY RELATIONSHIPS AND FORECASTING FOREIGN EXCHANGE RATES 2

$25.00

- Suppose that the treasurer of IBM has an extra cash reserve of $100,000,000 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. The treasurer of IBM does not wish to bear any exchange risk. Where should he/she invest to maximize the return?

- While you were visiting London, you purchased a Jaguar for £35,000, payable in three months. You have enough cash at your bank in New York City, which pays 0.35% interest per month, compounding monthly, to pay for the car. Currently, the spot exchange rate is $1.45/£ and the three-month forward exchange rate is $1.40/£. In London, the money market interest rate is 2.0% for a three-month investment. There are two alternative ways of paying for your Jaguar.

(a) Keep the funds at your bank in the U.S. and buy £35,000 forward.

(b) Buy a certain pound amount spot today and invest the amount in the U.K. for three months so that the maturity value becomes equal to £35,000.

Evaluate each payment method. Which method would you prefer? Why?

- 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% per annum in the U.S. and 5.8% per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000.
- Determine whether the interest rate parity is currently holding.

- If the IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit.
- Explain how the IRP will be restored as a result of covered arbitrage activities.

- Suppose that the current spot exchange rate is €0.80/$ and the three-month forward exchange rate is €0.7813/$. The three-month interest rate is 5.6 percent per annum in the United States and 5.40 percent per annum in France. Assume that you can borrow up to $1,000,000 or €800,000.

- Show how to realize a certain profit via covered interest arbitrage, assuming that you want to realize profit in terms of U.S. dollars. Also determine the size of your arbitrage profit.
- Assume that you want to realize profit in terms of euros. Show the covered arbitrage process and determine the arbitrage profit in euros.

- In the issue of October 23, 1999, the Economist reports that the interest rate per annum is 5.93% in the United States and 70.0% in Turkey. Why do you think the interest rate is so high in Turkey? Based on the reported interest rates, how would you predict the change of the exchange rate between the U.S. dollar and the Turkish lira?

- As of November 1, 1999, the exchange rate between the Brazilian real and U.S. dollar is R$1.95/$. The consensus forecast for the U.S. and Brazil inflation rates for the next 1-year period is 2.6% and 20.0%, respectively. How would you forecast the exchange rate to be at around November 1, 2000?

- (CFA question) Omni Advisors, an international pension fund manager, uses the concepts of purchasing power parity (PPP) and the International Fisher Effect (IFE) to forecast spot exchange rates. Omni gathers the financial information as follows:

Base price level | 100 |

Current U.S. price level | 105 |

Current South African price level | 111 |

Base rand spot exchange rate | $0.175 |

Current rand spot exchange rate | $0.158 |

Expected annual U.S. inflation | 7% |

Expected annual South African inflation | 5% |

Expected U.S. one-year interest rate | 10% |

Expected South African one-year interest rate | 8% |

Calculate the following exchange rates (ZAR and USD refer to the South African and U.S. dollar, respectively).

- The current ZAR spot rate in USD that would have been forecast by PPP. b. Using the IFE, the expected ZAR spot rate in USD one year from now.
- Using PPP, the expected ZAR spot rate in USD four years from now.

- Suppose that the current spot exchange rate is €1.50/₤ and the one-year forward exchange rate is €1.60/₤. The one-year interest rate is 5.4% in euros and 5.2% in pounds. You can borrow at most €1,000,000 or the equivalent pound amount, i.e., ₤666,667, at the current spot exchange rate.

- Show how you can realize a guaranteed profit from covered interest arbitrage. Assume that you are a euro-based investor. Also determine the size of the arbitrage profit.
- b. Discuss how the interest rate parity may be restored as a result of the above transactions

- Suppose you are a pound-based investor. Show the covered arbitrage process and determine the pound profit amount.

- Due to the integrated nature of their capital markets, investors in both the U.S. and U.K. require the same real interest rate, 2.5%, on their lending. There is a consensus in capital markets that the annual inflation rate is likely to be 3.5% in the U.S. and 1.5% in the U.K. for the next three years. The spot exchange rate is currently $1.50/£.

- Compute the nominal interest rate per annum in both the U.S. and U.K., assuming that the Fisher effect holds.
- b. What is your expected future spot dollar-pound exchange rate in three years from now?

- Can you infer the forward dollar-pound exchange rate for one-year maturity?

- After studying Iris Hamson’s credit analysis, George Davies is considering whether he can increase the holding period return on Yucatan Resort’s excess cash holdings (which are held in pesos) by investing those cash holdings in the Mexican bond market. Although Davies would be investing in a peso- denominated bond, the investment goal is to achieve the highest holding period return, measured in U.S. dollars, on the investment. Davies finds the higher yield on the Mexican one-year bond, which is considered to be free of credit risk, to be attractive but he is concerned that depreciation of the peso will reduce the holding period return, measured in U.S. dollars. Hamson has prepared selected economic and financial data, given in Exhibit 3-1, to help Davies make the decision.

**Selected Economic and Financial Data for U.S. and Mexico **Expected U.S. Inflation Rate 2.0% per year Expected Mexican Inflation Rate 6.0% per year U.S. One-year Treasury Bond Yield 2.5%

Mexican One-year Bond Yield 6.5%

__ Nominal Exchange Rates __

Spot 9.5000 Pesos = U.S. $ 1.00

One-year Forward 9.8707 Pesos = U.S. $ 1.00

Hamson recommends buying the Mexican one-year bond and hedging the foreign currency exposure using the one-year forward exchange rate. She concludes: “This transaction will result in a U.S. dollar holding period return that is equal to the holding period return of the U.S. one-year bond.”

- Calculate the U.S. dollar holding period return that would result from the transaction recommended by Hamson. Show your calculations. State whether Hamson’s conclusion about the U.S. dollar holding period return resulting from the transaction is correct or incorrect

After conducting his own analysis of the U.S. and Mexican economies, Davies expects that both the U.S. inflation rate and the real exchange rate will remain constant over the coming year. Because of favorable political developments in Mexico, however, he expects that the Mexican inflation rate (in annual terms) will fall from 6.0 percent to 3.0 percent before the end of the year. As a result, Davies decides to invest Yucatan Resorts’ cash holdings in the Mexican one-year bond but not to hedge the currency exposure.

- b. Calculate the expected exchange rate (pesos per dollar) one year from Show your calculations.

Note: Your calculations should assume that Davies is correct in his expectations about the real exchange rate and the Mexican and U.S. inflation rates.

- Calculate the expected U.S. dollar holding period return on the Mexican one-year bond. Show your calculations. Note: Your calculations should assume that Davies is correct in his expectations about the real exchange rate and the Mexican and U.S. inflation rates.

- Jason Smith is a foreign exchange trader with Citibank. He notices the following quotes.

Spot exchange rate SFr1.6627/$ Six-month forward exchange rate SFr1.6558/$ Six-month $ interest rate 3.5% per year

Six-month SFr interest rate 3.0% per year

- Ignoring transaction costs, is the interest rate parity holding?

- b. Is there an arbitrage possibility? If yes, what steps would be needed to make an arbitrage profit?

Assuming that Jason Smith is authorized to work with $1,000,000 for this purpose, how much would the arbitrage profit be in dollars?

**12.** Mini Case: Turkish Lira and the Purchasing Power Parity

Veritas Emerging Market Fund specializes in investing in emerging stock markets of the world. Mr. Henry Mobaus, an experienced hand in international investment and your boss, is currently interested in Turkish stock markets. He thinks that Turkey will eventually be invited to negotiate its membership in the European Union. If this happens, it will boost the stock prices in Turkey. But, at the same time, he is quite concerned with the volatile exchange rates of the Turkish currency. He would like to understand what drives the Turkish exchange rates. Since the inflation rate is much higher in Turkey than in the U.S., he thinks that the purchasing power parity may be holding at least to some extent. As a research assistant for him, you were assigned to check this out. In other words, you have to study and prepare a report on the following question: Does the purchasing power parity hold for the Turkish lira-U.S. dollar exchange rate? Among other things, Mr. Mobaus would like you to do the following:

- Plot the past exchange rate changes against the differential inflation rates between Turkey and the U.S. for the last four years.

- b. Regress the rate of exchange rate changes on the inflation rate differential to estimate the intercept and the slope coefficient, and interpret the regression

Data source: You may download the consumer price index data for the U.S. and Turkey from the following website: http://www.oecd.org/pages/0,3417,e__n_33816563_33816769_1_1_1_1_1,00.html__, “hot file” (Excel format) . You may download the exchange rate data from the website: http://pacific.commerce.ubc.ca/xr/data.html.