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FinalExamNewMaterialExamples - 7. Measuring Forecast...

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7. Measuring Forecast Accuracy. You are hired as a consultant to assess a firm’s ability to forecast. The firm has developed a point forecast for two different currencies presented in the following table. The firm asks you to determine which currency was forecasted with greater accuracy. ANSWER: Yen Actual Pound Actual Period Forecast Yen Value Forecast Pound Value 1 $.0050 $.0051 $1.50 $1.51 2 .0048 .0052 1.53 1.50 3 .0053 .0052 1.55 1.58 4 .0055 .0056 1.49 1.52 Absolute Forecast Error as a Percentage of the Realized Value Period Yen Forecast Pound Forecast 1 1.96% .66% 2 7.69 2.00 3 1.92 1.89 4 1.79 1.97 Mean 3.34% 1.63% Because the mean absolute forecast error of the pound is lower than that of the yen, the pound was forecasted with greater accuracy. 1
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10. Forecasting with a Forward Rate. Assume that the four-year annualized interest rate in the United States is 9 percent and the four-year annualized interest rate in Singapore is 6 percent. Assume interest rate parity holds for a four-year horizon. Assume that the spot rate of the Singapore dollar is $.60. If the forward rate is used to forecast exchange rates, what will be the forecast for the Singapore dollar’s spot rate in four years? What percentage appreciation or depreciation does this forecast imply over the four-year period? Country Four - Year Compounded Return U.S. (1.09) 4 – 1 = 41% Singapore (1.06) 4 – 1 = 26% 11.9% = 1 - 1.26 1.41 = Premium ANSWER: Thus, the four-year forward rate should contain an 11.9% premium above today’s spot rate of $.60, which means the forward rate is $.60 × (1 + .119) = $.6714. The forecast for the Singapore dollar’s spot rate in four years is $.6714, which represents an appreciation of 11.9% over the four-year period. 2
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19. Probability Distribution of Forecasts. Assume that the following regression model was applied to historical quarterly data: e t = a 0 + a 1 INT t + a 2 INF t-1 + μ t where e t = percentage change in the exchange rate of the Japanese yen in period t INT t = average real interest rate differential (U.S. interest rate minus Japanese interest rate) over period t INF t-1 = inflation differential (U.S. inflation rate minus Japanese inflation rate) in the previous period a 0 , a 1 , a 2 = regression coefficients μ t = error term Assume that the regression coefficients were estimated as follows: a 0 = 0.0 a 1 = 0.9 a 2 = 0.8 Also assume that the inflation differential in the most recent period was 3 percent. The real interest rate differential in the upcoming period is forecasted as follows: Interest Rate Differential Probability 0% 30% 1 60 2 10 If Stillwater, Inc., uses this information to forecast the Japanese yen’s exchange rate, what will be the probability distribution of the yen’s percentage change over the upcoming period? ANSWER:
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FinalExamNewMaterialExamples - 7. Measuring Forecast...

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