The following pages contain annual data on interest rates, inflation rates, and percentage change in exchange rates (based on indirect quotes) for foreign countries, including the US, for the period 1995 - 2007.
Each one of you is assigned to a foreign country and a six-year time period
----->>>> Singapore 1995-2000
Please use the attached sheets to answer the questions listed based on calculations using the data for the assigned country and the US during the assigned time period.
Use geometric instead of arithmetic averages. Use exact instead of the approximate method.
There is only one correct answer to these questions.
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 rate of return from the foreign country's viewpoint? 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 / borrowed (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 a line of credit for one million dollars in the US or an equivalent amount in foreign country. Given perfect hindsight 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 Q4. 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 IQ)] -1 PPP Implications: 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, Rz, .... Rn, then you can calculate the arithmetic and geometric mean or averages of these rates over the N years, as follows: Arithmetic Mean = (R, + R2 + R2 + .. + Rx)/N Geometric Mean = [(1+R, )* (1+R, )* (1+ R3 ) * **(1+ Ry)]'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 4.75 % 2001 -8% 2002 0.5 % 2003 23% 2005 7% Rates of return 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) ]/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% Consumer Price Index Percent change from year ago 1995 1996 United States 2.8 2.9 Singapore - 1.7 1.4 1997 2.3 2.0 1998 1.5 -0.3 1999 2.2 0.0 2000 3.4 1.4 2001 2.8 1.0 2002 1.6 -0.4 2003 2.3 0.5 2004 2.7 1.6 2005 3.4 0.5 2006 3.2 1.0 2007 2.9 2.1 Exchange Rates Percent appreciation (+) or depreciation (-) of the U.S. dollar against the local currency 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 United States -5.6 4.5 7.7 4.8 -1.6 4.9 6.0 -1.5 -12.3 -8.2 -1.9 -1.5 -5.6 Singapore -7.2 -0.5 5.4 12.5 1.4 1.8 3.9 -0.1 -2.7 -3.0 -1.5 -4.6 -5.2 Short-Term Interest Rates Annual percent 1995 1996 1997 5.9 5.4 5.6 1998 5.5 5.0 United States 1999 5.3 2.0 2002 2001 2002 2003 2004 2005 2006 2007 2000 6.5 2.6 2001 3.7 2.0 2002 1.7 1.0 2003 1.2 0.7 2004 1. 6 1.0 2005 3.5 2.3 2006 5.2 3.5 2007 5.3 2.7 Singapore 2.6 2.9 4.4 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 rate of return from the foreign country's viewpoint? 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 / borrowed (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 a line of credit for one million dollars in the US or an equivalent amount in foreign country. Given perfect hindsight 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 Q4. 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 IQ)] -1 PPP Implications: 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, Rz, .... Rn, then you can calculate the arithmetic and geometric mean or averages of these rates over the N years, as follows: Arithmetic Mean = (R, + R2 + R2 + .. + Rx)/N Geometric Mean = [(1+R, )* (1+R, )* (1+ R3 ) * **(1+ Ry)]'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 4.75 % 2001 -8% 2002 0.5 % 2003 23% 2005 7% Rates of return 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) ]/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% Consumer Price Index Percent change from year ago 1995 1996 United States 2.8 2.9 Singapore - 1.7 1.4 1997 2.3 2.0 1998 1.5 -0.3 1999 2.2 0.0 2000 3.4 1.4 2001 2.8 1.0 2002 1.6 -0.4 2003 2.3 0.5 2004 2.7 1.6 2005 3.4 0.5 2006 3.2 1.0 2007 2.9 2.1 Exchange Rates Percent appreciation (+) or depreciation (-) of the U.S. dollar against the local currency 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 United States -5.6 4.5 7.7 4.8 -1.6 4.9 6.0 -1.5 -12.3 -8.2 -1.9 -1.5 -5.6 Singapore -7.2 -0.5 5.4 12.5 1.4 1.8 3.9 -0.1 -2.7 -3.0 -1.5 -4.6 -5.2 Short-Term Interest Rates Annual percent 1995 1996 1997 5.9 5.4 5.6 1998 5.5 5.0 United States 1999 5.3 2.0 2002 2001 2002 2003 2004 2005 2006 2007 2000 6.5 2.6 2001 3.7 2.0 2002 1.7 1.0 2003 1.2 0.7 2004 1. 6 1.0 2005 3.5 2.3 2006 5.2 3.5 2007 5.3 2.7 Singapore 2.6 2.9 4.4
