Norway 2001-2006
Use geometric instead of arithmetic averages. Use exact instead of the approximate method
Please answer the following five questions: Q1. During the assigned time period: US dollar appreciated / depreciated (choose one) in real terms against the currency of foreign country Q2. During the assigned period, what was the average uncovered rate of return from the US viewpoint for the foreign country? Q3. During the assigned period, what was the average uncovered rule of relurn from the foreign country's viewpoint? Work Sheet: Statistical Report Country CANADA Four-year time period 1998 1999 2000 2001 Geom Avg Inflation Rate: US 1.5 2.2 3.4 2.8 Inflation Rate: Foreign Country 1.0 1.7 2.7 2.5 Interest Rate: US 5.5 5.3 6.5 3.7 Interest Rate: Foreign Country 5.0 5.2 5.8 2.1 % Change in CD SR (Indirect quote) 7.10 0.10 0.00 4.3 % Change in CD SR (Direct quote) = [1/(1+% change in TQ] - 1 PPP Implications: Q4. Based on your answers to questions 2 and 3. given perfect hindsight about interest rates and exchange rate changes during the assigned time period you should have: Invested/borrowed (choose one) in the US and invested / horrowed (choose one) in foreign country Q5. Assume that you could both borrow and invest at the average interest rates prevailing in foreign country and in the US during the assigned time period. Also assume that you have ulice of credit for one million dollars in the US or an equivalent amount in foreign country. Given perfect hindsigtil about interest rates and exchange rate changes, please calculate your total profit in dollars using uncovered interest arbitrage during the assigned time period if you followed the strategy chosen in 04. Annual Uncovered Rate (for US) Annual Uncovered Rate (for Canada) Suggest investment strategy based on IFE: Geometric and Arithmetic Means of Rates and Percentages If the rates for years 1, 2, 3, ... N are R1, R2, R3, .... Rp, then you can calculate the arithmetic and geometric mean or averages of these rates over the N years, as follows: Arithmetic Mean = (R+R, + R2 + .. +RNIN Geometric Mean = ((1+R, )* (1+R2)* (1+ R) * **(1+Rm)]N-1 Note, that in the geometric mean formula, the percentages are written in decimals. For example, we use 0.10 instead of 10% and -0.02 instead of -2%. Also in the end we take the Nth root of the product, where N is the number of years in the averaging period. It is important to know that the geometric mean is a more accurate measure than the arithmetic mean. Always try to use the geometric mean method when calculating averages of rate of returns or percentages. Let us assume the following rates of return for the five year period (2000-2004): 2000 2001 2002 2003 2005 7 % Rates of return 4.75 % -8% 0.5% 23% Our estimate of the average rate of return over the 2000-04 period based on: Arithmetic Mean = (0.0475 -0.08 +0.005 +0.23 +0.07)/5 = 0.0545 = 5.45% Geometric Mean = [(1+0.0475)*(1 - 0.08)*(1 + 0.005)*(1 +0.23)*(1 +0.07)]1/5 - 1 = (1.02746672)5 - 1 = 0.04973 = 4.973% 4.973 % is a more accurate measure of the average return over the 2000-04 period than 5.45% 2004 2005 2007 2003 2.8 1998 0.9 0.8 2006 3.5 2.7 Consumer Price Index Percent change from year ago 1995 1996 Australia 4.6 2.6 Austria 1.6 1.8 Canada 2.1 1.6 Chile 8.2 7.4 China 17.1 8.3 2.3 1997 0.2 1.2 1.6 6.1 1999 1.5 0.5 1.7 3.3 2000 4.5 2.0 2.7 2001 4.4 2.3 2.5 2002 3.0 1.7 2.3 1.0 5.1 3.6 2.5 2 0.5 -0.8 1.2 Denmark Euro Area Finland France Germany Greece Indonesia 11.5 - Ireland 11.9 4.7 5.7 4.0 0.7 Israel - 5.2 -0.4 - 1.3 Italy - 17 Japan 0.7 -0.3 Korea Malaysia Mexico ic Netherlands 1.4 - New Zealand 1.9 1.2 2.6 1.8 1.3 2.3 9.7 -0.3 2.0 -0.1 2.3 6.7 0.0 2.3 2.6 3.1 5.1 2.6 3.0 6.8 1.0 Norway 3.9 2.7 1.3 3.0 -0.4 2.2 1.8 2.5 1.5 3.0 1.5 1.7 3.4 2.3 0.5 0.7 Philippines Singapore 1.4 South Africa Spain 3.5 1.4 3.8 2.4 8.0 1.7 8.7 4.6 2.5 1.8 5.8 89.1 2.7 2.8 600 1.5 2.3 1.2 9.0 1.4 7.4 3.6 0.5 0.8 5.8 80.4 2.5 2.9 99.8 Sweden Switzerland Thailand 0.7 0.5 5.6 85.7 1.8 2.3 50.0 2.2 0.5 0.8 0.3 64.9 1.3 2.2 23.6 -0.3 0.0 8.1 84. 6 1.6 1.5 35.8 Turkey United Kingdom United States Venezuela 2.8 2.4 1.0 1.7 54.4 1.2 2.8 12.5 1.6 1.6 54.9 0.8 3.4 16.2 2.2 0.6 0.6 45.0 1.3 1.6 22.4 1.9 0.6 1.8 21.6 1.4 2.3 31.1 0.8 2.8 8.6 1.3 2.7 21.7 1.2 4.6 8.2 2.1 3.4 16.0 1.1 4.6 9.6 2.3 3.2 13.6 0.7 2.2 8.8 2.3 2.9 18.7 2002 4.9 1.4 2003 -16.7 2004 -11.5 2005 -3.4 2006 1.2 2007 - 10.1 Exchange Rates Percent appreciation (+) or depreciation (-) of the U.S. dollar against the local currency 1995 1996 1997 1998 1999 2000 2001 Australia -1.3 -5.3 5.3 18.1 -2.4 11.0 12.5 Canada 0.5 -0.7 1.6 7.1 0.1 -0.0 Chile -5.6 3.9 1.7 9.8 10.5 6. 1 17.7 China -0.4 -0.2 -0.2 -0.3 Denmark 13.9 4.3 - 10.8 -7.1 -6.9 -5.3 8.5 0.4 -11.8 o 0.0 -0.0 -5.3 - 16.6 -8.4 Euro Area 1.6 3.1 -5.3 -8.4 13.9 24.2 Indonesia 21.8 -9.3 Israel 6.0 -1.5 3.1 0.1 Japan 15.6 8.1 11.3 18.5 -6.7 1.8 -10.6 Korea 4.2 Malaysia 0.3 0.0 Mexico 90.2 18.4 3.4 11.7 4.6 -3.4 0.3 New Zealand -9.5 -4.6 -9.5 -20.2 -12.4 - 11.7 Norway 4.2 3.8 9.6 12.4 5.4 -11.4 i -4.8 -8.7 Philippines 3.4 -1.7 - 10.1 244.2 10.2 8.9 8.0 472 -15.3 39.3 3.2 15.4 4.6 23.4 1.4 6.6 3.3 38.8 4.4 12.5 1.4 20.0 10.6 4.1 3.9 -0.1 3.7 33.0 -8.3 71.7 60.6 -1.2 2.4 4.8 -1.6 12.0 10.6 Singapore -0.5 i -3.0 -1.5 -4.6 -5.2 12.7 14.2 0.0 -1.2 8.7 2.1 15.4 3.9 24.2 12.7 -0.1 10.7 96.0 5.3 6.0 6.5 South Africa 7.2 4.9 0.0 -1.1 15.9 12.9 13.1 1.8 13.6 11.0 12.5 6.2 49.3 6.7 4.9 12.3 -14.7 -1.4 6.4 4.2 Sweden -9.1 1.7 -1.3 -8.4 Switzerland -7.6 0.3 -11.2 1.2 -0.1 21.9 -6.0 -7.8 -3.3 23.0 4.2 -1.5 60.4 -4.3 0.6 -5.9 2.1 -7.5 -13.5 -0.9 54.8 2.9 -5.6 19.0 Thailand 18.5 -6.0 4.6 1.7 77.6 1.1 4.5 136.1 -3.1 13.9 17.3 22.5 86. 6 -4.7 7.7 17.1 -28.2 -16.9 - 13.6 -3.4 -0.4 -8.1 -12.3 38.4 -5.0 -5.7 -15.0 -8.8 -7.9 - 10.8 0.7 Turkey United Kingdom United States Venezuela -1.8 -1.5 -5.6 -8.2 17.7 -1.9 10.5 2.7 0.0 Percent appreciation (+) or depreciation (-) of the U.S. dollar against a group of currencies International Economic Trends Reference Tables 2003 2004 5.5 Short-Term Interest Rates Annual percent 1995 1996 1997 Australia 7.7 7.2 5.4 Canada 5.9 3.1 4. 6 Chile 13.7 13.5 12.0 China 10.4 9.0 8.6 Denmark 6.1 3.9 3.7 Euro Area 6.8 5.1 Indonesia 20.0 1998 5.0 5.0 14.9 4.6 4.1 1999 5.0 5.2 8.6 3.2 3.3 2000 6.2 5.8 9.2 3.2 4.9 2001 4.9 2.1 6.2 3.2 2002 4.7 2.9 3.8 2.7 4.9 2.7 2.7 2.7 2.6 1.9 3.3 2005 5.6 3.5 3.9 3.3 2006 6.0 4.3 5.1 3.3 2007 6.7 4.8 5.6 3.3 Israel 14.4 13.4 Japan* 1.2 0.6 Korea 0.6 13.3 6.4 12.4 6.4 32.9 39.1 11.3 0.7 15.0 6.9 27.1 7.3 5.8 Malaysia Mexico 48.2 22.3 New Zealand 7.7 Norway Philippines 11.8 12.3 15.0 3.7 12.9 4.4 15.3 Singapore 2.6 13.5 2.9 15.0 South Africa 16.5 4.2 12.9 3.1 2.6 10.1 4.0 2.0 9.7 4.0 1.0 11.2 4. 1 0.7 10.7 .0 7.5 2.1 6.9 1.7 7.3 2.3 Sweden 3 Switzerland 1.1 Thailand Turkey United Kingdom United States Venezuela 2.9 10.3 72.3 6.7 5.9 49.0 2.0 12.1 76.2 6.0 5.4 45.0 1.6 21.7 70.3 6.8 5.6 45.0 2.6 74.6 7.3 5.5 60.0 1.2 73.5 5.4 5.3 38.0 1.7 38. 9 6.1 6.5 38.0 2.1 92.4 5.0 3.7 37.0 1.6 59.5 4.0 1.7 40.0 1.0 38.5 3.7 1.2 28.5 1.8 23.8 4.6 1.6 28.5 4.7 3.5 28.5 4.8 5.2 28.5 6.0 5.3 28.5 *The actual value for 2003 is 0.037; the actual value for 2004 is 0.029; the actual value for 2005 is 0.029. Please answer the following five questions: Q1. During the assigned time period: US dollar appreciated / depreciated (choose one) in real terms against the currency of foreign country Q2. During the assigned period, what was the average uncovered rate of return from the US viewpoint for the foreign country? Q3. During the assigned period, what was the average uncovered rule of relurn from the foreign country's viewpoint? Work Sheet: Statistical Report Country CANADA Four-year time period 1998 1999 2000 2001 Geom Avg Inflation Rate: US 1.5 2.2 3.4 2.8 Inflation Rate: Foreign Country 1.0 1.7 2.7 2.5 Interest Rate: US 5.5 5.3 6.5 3.7 Interest Rate: Foreign Country 5.0 5.2 5.8 2.1 % Change in CD SR (Indirect quote) 7.10 0.10 0.00 4.3 % Change in CD SR (Direct quote) = [1/(1+% change in TQ] - 1 PPP Implications: Q4. Based on your answers to questions 2 and 3. given perfect hindsight about interest rates and exchange rate changes during the assigned time period you should have: Invested/borrowed (choose one) in the US and invested / horrowed (choose one) in foreign country Q5. Assume that you could both borrow and invest at the average interest rates prevailing in foreign country and in the US during the assigned time period. Also assume that you have ulice of credit for one million dollars in the US or an equivalent amount in foreign country. Given perfect hindsigtil about interest rates and exchange rate changes, please calculate your total profit in dollars using uncovered interest arbitrage during the assigned time period if you followed the strategy chosen in 04. Annual Uncovered Rate (for US) Annual Uncovered Rate (for Canada) Suggest investment strategy based on IFE: Geometric and Arithmetic Means of Rates and Percentages If the rates for years 1, 2, 3, ... N are R1, R2, R3, .... Rp, then you can calculate the arithmetic and geometric mean or averages of these rates over the N years, as follows: Arithmetic Mean = (R+R, + R2 + .. +RNIN Geometric Mean = ((1+R, )* (1+R2)* (1+ R) * **(1+Rm)]N-1 Note, that in the geometric mean formula, the percentages are written in decimals. For example, we use 0.10 instead of 10% and -0.02 instead of -2%. Also in the end we take the Nth root of the product, where N is the number of years in the averaging period. It is important to know that the geometric mean is a more accurate measure than the arithmetic mean. Always try to use the geometric mean method when calculating averages of rate of returns or percentages. Let us assume the following rates of return for the five year period (2000-2004): 2000 2001 2002 2003 2005 7 % Rates of return 4.75 % -8% 0.5% 23% Our estimate of the average rate of return over the 2000-04 period based on: Arithmetic Mean = (0.0475 -0.08 +0.005 +0.23 +0.07)/5 = 0.0545 = 5.45% Geometric Mean = [(1+0.0475)*(1 - 0.08)*(1 + 0.005)*(1 +0.23)*(1 +0.07)]1/5 - 1 = (1.02746672)5 - 1 = 0.04973 = 4.973% 4.973 % is a more accurate measure of the average return over the 2000-04 period than 5.45% 2004 2005 2007 2003 2.8 1998 0.9 0.8 2006 3.5 2.7 Consumer Price Index Percent change from year ago 1995 1996 Australia 4.6 2.6 Austria 1.6 1.8 Canada 2.1 1.6 Chile 8.2 7.4 China 17.1 8.3 2.3 1997 0.2 1.2 1.6 6.1 1999 1.5 0.5 1.7 3.3 2000 4.5 2.0 2.7 2001 4.4 2.3 2.5 2002 3.0 1.7 2.3 1.0 5.1 3.6 2.5 2 0.5 -0.8 1.2 Denmark Euro Area Finland France Germany Greece Indonesia 11.5 - Ireland 11.9 4.7 5.7 4.0 0.7 Israel - 5.2 -0.4 - 1.3 Italy - 17 Japan 0.7 -0.3 Korea Malaysia Mexico ic Netherlands 1.4 - New Zealand 1.9 1.2 2.6 1.8 1.3 2.3 9.7 -0.3 2.0 -0.1 2.3 6.7 0.0 2.3 2.6 3.1 5.1 2.6 3.0 6.8 1.0 Norway 3.9 2.7 1.3 3.0 -0.4 2.2 1.8 2.5 1.5 3.0 1.5 1.7 3.4 2.3 0.5 0.7 Philippines Singapore 1.4 South Africa Spain 3.5 1.4 3.8 2.4 8.0 1.7 8.7 4.6 2.5 1.8 5.8 89.1 2.7 2.8 600 1.5 2.3 1.2 9.0 1.4 7.4 3.6 0.5 0.8 5.8 80.4 2.5 2.9 99.8 Sweden Switzerland Thailand 0.7 0.5 5.6 85.7 1.8 2.3 50.0 2.2 0.5 0.8 0.3 64.9 1.3 2.2 23.6 -0.3 0.0 8.1 84. 6 1.6 1.5 35.8 Turkey United Kingdom United States Venezuela 2.8 2.4 1.0 1.7 54.4 1.2 2.8 12.5 1.6 1.6 54.9 0.8 3.4 16.2 2.2 0.6 0.6 45.0 1.3 1.6 22.4 1.9 0.6 1.8 21.6 1.4 2.3 31.1 0.8 2.8 8.6 1.3 2.7 21.7 1.2 4.6 8.2 2.1 3.4 16.0 1.1 4.6 9.6 2.3 3.2 13.6 0.7 2.2 8.8 2.3 2.9 18.7 2002 4.9 1.4 2003 -16.7 2004 -11.5 2005 -3.4 2006 1.2 2007 - 10.1 Exchange Rates Percent appreciation (+) or depreciation (-) of the U.S. dollar against the local currency 1995 1996 1997 1998 1999 2000 2001 Australia -1.3 -5.3 5.3 18.1 -2.4 11.0 12.5 Canada 0.5 -0.7 1.6 7.1 0.1 -0.0 Chile -5.6 3.9 1.7 9.8 10.5 6. 1 17.7 China -0.4 -0.2 -0.2 -0.3 Denmark 13.9 4.3 - 10.8 -7.1 -6.9 -5.3 8.5 0.4 -11.8 o 0.0 -0.0 -5.3 - 16.6 -8.4 Euro Area 1.6 3.1 -5.3 -8.4 13.9 24.2 Indonesia 21.8 -9.3 Israel 6.0 -1.5 3.1 0.1 Japan 15.6 8.1 11.3 18.5 -6.7 1.8 -10.6 Korea 4.2 Malaysia 0.3 0.0 Mexico 90.2 18.4 3.4 11.7 4.6 -3.4 0.3 New Zealand -9.5 -4.6 -9.5 -20.2 -12.4 - 11.7 Norway 4.2 3.8 9.6 12.4 5.4 -11.4 i -4.8 -8.7 Philippines 3.4 -1.7 - 10.1 244.2 10.2 8.9 8.0 472 -15.3 39.3 3.2 15.4 4.6 23.4 1.4 6.6 3.3 38.8 4.4 12.5 1.4 20.0 10.6 4.1 3.9 -0.1 3.7 33.0 -8.3 71.7 60.6 -1.2 2.4 4.8 -1.6 12.0 10.6 Singapore -0.5 i -3.0 -1.5 -4.6 -5.2 12.7 14.2 0.0 -1.2 8.7 2.1 15.4 3.9 24.2 12.7 -0.1 10.7 96.0 5.3 6.0 6.5 South Africa 7.2 4.9 0.0 -1.1 15.9 12.9 13.1 1.8 13.6 11.0 12.5 6.2 49.3 6.7 4.9 12.3 -14.7 -1.4 6.4 4.2 Sweden -9.1 1.7 -1.3 -8.4 Switzerland -7.6 0.3 -11.2 1.2 -0.1 21.9 -6.0 -7.8 -3.3 23.0 4.2 -1.5 60.4 -4.3 0.6 -5.9 2.1 -7.5 -13.5 -0.9 54.8 2.9 -5.6 19.0 Thailand 18.5 -6.0 4.6 1.7 77.6 1.1 4.5 136.1 -3.1 13.9 17.3 22.5 86. 6 -4.7 7.7 17.1 -28.2 -16.9 - 13.6 -3.4 -0.4 -8.1 -12.3 38.4 -5.0 -5.7 -15.0 -8.8 -7.9 - 10.8 0.7 Turkey United Kingdom United States Venezuela -1.8 -1.5 -5.6 -8.2 17.7 -1.9 10.5 2.7 0.0 Percent appreciation (+) or depreciation (-) of the U.S. dollar against a group of currencies International Economic Trends Reference Tables 2003 2004 5.5 Short-Term Interest Rates Annual percent 1995 1996 1997 Australia 7.7 7.2 5.4 Canada 5.9 3.1 4. 6 Chile 13.7 13.5 12.0 China 10.4 9.0 8.6 Denmark 6.1 3.9 3.7 Euro Area 6.8 5.1 Indonesia 20.0 1998 5.0 5.0 14.9 4.6 4.1 1999 5.0 5.2 8.6 3.2 3.3 2000 6.2 5.8 9.2 3.2 4.9 2001 4.9 2.1 6.2 3.2 2002 4.7 2.9 3.8 2.7 4.9 2.7 2.7 2.7 2.6 1.9 3.3 2005 5.6 3.5 3.9 3.3 2006 6.0 4.3 5.1 3.3 2007 6.7 4.8 5.6 3.3 Israel 14.4 13.4 Japan* 1.2 0.6 Korea 0.6 13.3 6.4 12.4 6.4 32.9 39.1 11.3 0.7 15.0 6.9 27.1 7.3 5.8 Malaysia Mexico 48.2 22.3 New Zealand 7.7 Norway Philippines 11.8 12.3 15.0 3.7 12.9 4.4 15.3 Singapore 2.6 13.5 2.9 15.0 South Africa 16.5 4.2 12.9 3.1 2.6 10.1 4.0 2.0 9.7 4.0 1.0 11.2 4. 1 0.7 10.7 .0 7.5 2.1 6.9 1.7 7.3 2.3 Sweden 3 Switzerland 1.1 Thailand Turkey United Kingdom United States Venezuela 2.9 10.3 72.3 6.7 5.9 49.0 2.0 12.1 76.2 6.0 5.4 45.0 1.6 21.7 70.3 6.8 5.6 45.0 2.6 74.6 7.3 5.5 60.0 1.2 73.5 5.4 5.3 38.0 1.7 38. 9 6.1 6.5 38.0 2.1 92.4 5.0 3.7 37.0 1.6 59.5 4.0 1.7 40.0 1.0 38.5 3.7 1.2 28.5 1.8 23.8 4.6 1.6 28.5 4.7 3.5 28.5 4.8 5.2 28.5 6.0 5.3 28.5 *The actual value for 2003 is 0.037; the actual value for 2004 is 0.029; the actual value for 2005 is 0.029
