BUS330: International Finance Workshop 06
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BUS330: International Finance
Workshop 06 (Chapter 10): Forecasting Exchange Rates
Solutions to Problems
1 Motives for forecasting Explain corporate motives for forecasting exchange rates.
ANSWER: Several decisions of MNCs require an assessment of the future. Future exchange rates will affect all critical characteristics of the firm such as costs and revenues. To be more specific, various operations of MNCs use exchange rate projections, including hedging, short-term financing and investing, capital budgeting decisions, long-term financing, and earnings assessment. Such operations will be more effective if exchange rates are forecasted accurately.
2 Technical forecasting Explain the technical technique for forecasting exchange rates. What are some limitations of using technical forecasting to predict exchange rates?
ANSWER: Technical forecasting involves the review of historical exchange rates to search for a repetitive pattern that may occur in the future. This pattern would be the basis for future exchange rate movements.
Even if a technical forecasting model turns out to be valuable, it will no longer be valuable once other market participants use it. This is because their actions in the market due to the model’s forecast will cause the currency values to move as suggested by the model immediately instead of in the future. Also, MNCs often prefer long-term forecasts. Technical forecasting is typically conducted for short time horizons.
3 Fundamental forecasting Explain the fundamental technique for forecasting exchange rates. What are some limitations of using a fundamental technique to forecast exchange rates?
ANSWER: Fundamental forecasting is based on underlying relationships that are believed to exist between one or more variables and a currency’s value. Given these relationships, a change in one or more of these variables (or a forecasted change in them) will lead to a forecast of the currency’s value.
Even if a fundamental relationship exists, it is difficult to accurately quantify that relationship in a form applicable to forecasting. Even if the relationship could be quantified, there is no guarantee that the historical relationship will persist in the future. It is difficult to determine the lagged impact of some variables. It is also difficult to incorporate some qualitative factors into the model.
4 Market-based forecasting Explain the market-based technique for forecasting exchange rates. What is the rationale for using market-based forecasts? If the euro appreciates substantially against the dollar during a specific period, would market-based forecasts have overestimated or underestimated the realised values over this period? Explain.
ANSWER: Market-based forecasts should reflect an expectation of the market on future rates. If the market’s expectation differed from existing rates, then the market participants should react by taking positions in various currencies until the current rates do reflect an expectation of the future. The market determines the spot exchange rate and forward exchange rate. These market-based rates can be used to forecast since if they were not good indicators of the future rates, speculators would take positions. This speculative movement would force the rates to gravitate toward the expectation of the future spot rate.
Market-based forecasts would have underestimated the realised values of the euro over this period because the actual values were above the spot rates and forward rates quoted earlier.
5 Mixed forecasting Explain the mixed technique for forecasting exchange rates.
ANSWER: Mixed forecasting involves a combination of two or more techniques. The specific combination can differ in terms of techniques included and the weight of importance assigned to each technique.
6 Detecting a forecast bias Explain how to assess performance in forecasting exchange rates. Explain how to detect a bias in forecasting exchange rates.
ANSWER: Performance can be evaluated by computing the absolute forecast error as a percentage of the realised value for all periods where a forecast was necessary. Then an average of this type of error can be computed. This average can be compared among all currencies or among all forecasting models.
A forecast bias exists from consistently underestimating or overestimating exchange rates. If the majority of points are above the 45-degree perfect forecast line, then the forecasts generally underestimate the realised values. If the majority of points are below the 45-degree perfect forecast line, then the forecasts generally overestimate the realised values.
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:
Period
1
2
3
4
Yen
Forecast
A$.0050
0.0048
0.0053
0.0055
Actual
Yen Value
A$.0051
0.0052
0.0052
0.0056
Ringgit
Forecast
A$0.3500
0.3800
0.4000
0.3400
Actual
ringgit Value
A$0.3600
0.3500
0.4300
0.3700
Absolute Forecast Error as a Percentage of the Realised Value
Period
1
2
3
4
Yen Forecast
1.96%
7.69
1.92
1.78
Pound Forecast
2.78%
8.57
6.98
8.11
10 Forecasting with a forward rate Assume that the four-year annualised interest rate in the
Australia is 9 per cent and the four-year annualised interest rate in Singapore is 6 per cent. Assume interest rate parity holds for a four-year horizon. Assume that the spot rate of the Singapore dollar is A$0.60. If the forward rate is used to forecast exchange rates, what will be the
forecast for the Singapore dollar’s spot rate in four years? What percentage appreciation or depreciation does this forecast imply over the four-year period?
ANSWER:
Country
Australia
Singapore
Four-Year Compounded Return
(1.09)4 – 1 = 41%
(1.06)4 – 1 = 26%
1.41
= − 1 = 11.9%
Thus, the four-year forward rate should contain an 11.9% premium above today’s spot rate of
he forecast for the
Singapore dollar’s spot rate in four years is A$.6714, which represents an appreciation of 11.9% over the four-year period.
13 Forecasting exchange rates of currencies that previously were fixed When some countries in Eastern Europe initially allowed their currencies to fluctuate against the US dollar, would the fundamental technique based on historical relationships have been useful for forecasting future exchange rates of these currencies? Explain.
ANSWER: Fundamental forecasting typically relies on historical relationships between economic factors and exchange rate movements. However, if exchange rates were not allowed to move in the past, historical relationships would not help predict future exchange rates of these currencies.
16 Forward rate forecast Assume that you obtain a quote for a one-year forward rate on the Chinese yuan. Assume that China’s one-year interest rate is 40 per cent, while the Australian one- year interest rate is 7 per cent. Over the next year, the yuan depreciates by 12 per cent. Do you think the forward rate overestimated the spot rate one year ahead in this case? Explain.
ANSWER: A quoted forward rate for the Chinese yuan would contain a large discount because of the high interest rate in China relative to Australia. Since the discount exceeds 12 per cent, the forward rate would have actually underestimated the future spot rate in this example.
18 Interpreting an unbiased forward rate Assume that the forward rate is an unbiased but not necessarily accurate forecast of the future exchange rate of the yen over the next few years. Based on this information, do you think Raven Co. should hedge its remittance of expected Japanese yen profits to the Australian parent by selling yen forward contracts? Why would this strategy be advantageous? Under what conditions would this strategy backfire?
ANSWER: If the forward rate is an unbiased forecast, the amount of Australian dollars received from remittances when hedging should be the same (on average, over time) as the amount of Australian dollars received from remittances when not hedging. Under these conditions, Raven may be able to more accurately predict the Australian dollar cash flows that will result from
remitted foreign cash flows, without reducing the expected amount of Australian dollar cash flows received. This strategy could backfire in those periods that the spot rate of yen at the time of remittances exceeds the previously agreed upon forward rate at which the yen would be converted to Australian dollars.
19 Probability distribution of forecasts Assume that the following regression model was applied to historical quarterly data:
et = a0 + a1 INTt + a2 INFt-1 + µt
where et = percentage change in the exchange rate of the Japanese yen in period t
INTt = average real interest rate differential (US interest rate minus Japanese interest rate) over period t
INFt-1 = inflation differential (US. inflation rate minus Japanese inflation rate) in the previous period
a0 , a1 , a2 = regression coefficients
µt = error term
Assume that the regression coefficients were estimated as follows:
a0 = 0.0
a1 = 0.9
a2 = 0.8
Also assume that the inflation differential in the most recent period was 3 per cent. The real interest rate differential in the upcoming period is forecasted as follows:
Interest Rate
Differential
0%
1
2
Probability
30%
60
10
If Stillwater, Pty Ltd 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:
Forecast of
Interest Rate
Differential
0%
1%
2%
Forecast of the Percentage Change in the Japanese Yen
.9(0%) + .8(3%) = 2.4% .9(1%) + .8(3%) = 3.3% .9(2%) + .8(3%) = 4.2%
Probability
30%
60%
10%
20. Testing for a forecast bias You must determine whether there is a forecast bias in the forward rate. You apply regression analysis to test the relationship between the actual spot rate and the forward rate forecast (F):
S = a0 + a1 (F)
The regression results are as follows:
Coefficient
a0 = .006
a1 = .800
Standard error
.011
.05
Based on these results, is there a bias in the forecast? Verify your conclusion. If there is a bias, explain whether it is an overestimate or an underestimate.
ANSWER: This question is appropriate for students with a background in regression analysis. If there is no bias, a0 is hypothesised to equal zero and a1 is hypothesised to equal one. The t- statistics are estimated below:
t-statistic for a0:
= = = 0.55
t-statistic for a1:
= = = −4.0
The results suggest that while a0 is not significantly different from its hypothesised value of zero, a1 is significantly below its hypothesised value of 1. This implies that the realised spot rate is significantly below the forecasted rate. Thus, the forecast contains an upward bias, because it is overestimating the future spot rate.
22 Interpreting forecast bias information The treasurer of Glencoe, Pty Ltd detected a forecast bias when using the 30-day forward rate of the New Zealand dollar to forecast future spot rates of the New Zealand dollar over various periods. He believes he can use this information to determine whether imports ordered every week should be hedged (payment is made 30 days after each order). Glencoe’s president says that, in the long run, the forward rate is unbiased and that the treasurer should not waste time trying to ’beat the forward rate’ but should just hedge all orders. Who is correct?
ANSWER: Even if the forward rate is unbiased over the long run, Glencoe could save money if it could effectively detect a forward bias (assuming that the bias would continue after being detected). Glencoe may decide to hedge only when the forward rate is expected to be less than the future spot rate. The Treasurer is correct if the bias continues beyond the point at which it is detected.
23 Forecasting South Asian currencies The value of each South Asian currency relative to the Australian dollar is dictated by supply and demand conditions between that currency and the Australian dollar. The values of South Asian currencies have generally declined substantially against the Australian dollar over time. Most of these countries have high inflation rates and high interest rates. The data on inflation rates, economic growth, and other economic indicators are subject to error, as limited resources are used to compile the data.
a. If the forward rate is used as a market-based forecast, will this rate result in a forecast of appreciation, depreciation, or no change in any particular South Asian currency? Explain.
ANSWER: The forward rate of each South Asian currency would have a large discount, because the Latin American interest rate would be much higher than the Australian interest rate. The discount serves as the forecast of the percentage change in the value of the South Asian currency over the length of time represented by the forward contract period.
b. If technical forecasting is used, will this result in a forecast of appreciation, depreciation, or no change in the value of a specific South Asian currency? Explain.
ANSWER: Technical forecasting would result in a forecast of depreciation, because the South Asian currencies have declined consistently in the past, and most technical methods would apply the past trends to the future.
c. Do you think that Australian companies can accurately forecast the future values of South Asian currencies? Explain.
ANSWER: Australian companies cannot forecast South Asian currency values accurately, because they are so volatile. Australian companies even have trouble forecasting the values of currencies of industrialised countries. The values change in response to economic conditions, which are volatile and difficult to anticipate. The values are also affected by political conditions, which are also difficult to predict.
30 Forecast errors from forward rates Assume that interest rate parity exists. One year ago, the spot rate of the New Zealand dollar was A$0.759 and the spot rate of the Japanese yen was A$0.0123. At that time, the one-year interest rate of the New Zealand dollar and Japanese yen was 3 per cent and the one-year Australian interest rate was 7 per cent. One year ago, you used the one-year forward rate of the New Zealand dollar to derive a forecast of the future spot rate of the New Zealand dollar and the yen one year ahead. Today, the spot rate of the New Zealand dollar is A$0.739, while the spot rate of the yen is A$0.0103. Which currency did you forecast more accurately?
ANSWER: FR premium of New Zealand dollar and yen = [(1.07)/(1.03)] -1 = .03883 Euro Forecast = (1 + ,03883) x A$0.759 = A$0.7885
Yen forecast = (1 + .03883) x A$0.0123 = A$0.0128
New Zealand dollar forecast error = (A$0.739-A$0.7885)/A$0.739 = 6.7%Yen forecast error = (A$0.0103 – A$0.0128)/A$0.0103 = 24.27
The New Zealand dollar was forecasted more accurately.
32 Forward versus spot rate forecast Assume that interest rate parity exists. The one-year risk- free interest rate in Australia is 3 per cent versus 16 per cent in Singapore. You believe in purchasing power parity, and you also believe that Singapore will experience a 2 per cent inflation rate and Australia will experience a 2 per cent inflation rate over the next year. If you wanted to forecast the Singapore dollar’s spot rate for one year ahead, do you think that the forecast error would be smaller when using today’s one-year forward rate of the Singapore dollar as the forecast or using today’s spot rate as the forecast? Briefly explain.
ANSWER: The spot rate should have a smaller forecast error because the spot rate would be a more appropriate forecast of the future when inflation rates are expected to be the same (if you believe in PPP). The forward discount on the Singapore dollar is large, which reflects a substantial depreciation of the Singapore dollar if you use the forward rate as a forecast.
2022-03-21
Forecasting Exchange Rates