International Economic Trends: 1988-2000
Federal Reserve Bank of St. Louis
Source: www.stls.frb.org/publications/index.html#data
Required Data for: Statistical Report
FINA 5500
Professor: Niranjan Tripathy
College of Business Administration, Rm 175
voice: 940.565.3045
fax: 940.565.4234
email: tripathy@unt.edu
Instructions for Statistical Report: FINA 5500
The following pages contain annual data on interest rates, inflation rates, and percentage change
in exchange rates (based on indirect quotes) for 32 countries, including the US, for the period:
1988 - 2000.
Each one of you is assigned to two foreign countries and a six-year time period (1988-1993
or 1995-2000). Please consult the attached list to determine your assigned countries and
time period.
Please use the attached sheet (next two pages) to answer the questions listed in it based on
calculations using the data for the assigned countries 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. You will be graded on whether or not
your answers are correct.
The necessary information and concepts are all from chapter 4. I will discuss the solutions
techniques to these problems only during class. I will not discuss them with anyone on an
individual basis outside the class.
Statistical Report: FINA 5500
Please complete the next two pages and return to me by the due date (listed in the syllabus):
Name:
UNT ID:
Foreign Country 2:
Foreign Country 2:
Assigned Time Period:
Economic Variables
Inflation Rate: US
Inflation Rate: Foreign Country 1
Inflation Rate: Foreign Country 2
Interest Rate: US
Interest Rate: Foreign Country 1
Interest Rate: Foreign Country 2
Percentage change in indirect quote: Foreign Country 1
Percentage change in direct quote: Foreign Country 1
Percentage change in indirect quote: Foreign Country 2
Percentage change in direct quote: Foreign Country 2
Average
Please answer the following five questions.
Q1. During the assigned time period:
(a) US dollar appreciated / depreciated (choose one) in real terms against the currency of Foreign Country 1.
(b) US dollar appreciated / depreciated (choose one) in real terms against the currency of Foreign Country 2.
Q2. During the assigned period, what was the average uncovered rate of return from the US viewpoint for:
(a) Foreign Country 1?
(b) Foreign Country 2?
Q3. During the assigned period, what was the average uncovered rate of return from the:
(a) Foreign Country 1's viewpoint?
(b) Foreign Country 2's viewpoint?
Q4. Based on your answers to questions 2 and 3, given perfect hindsight about interest rates and exchange
rates changes during the assigned time period you should have:
(a) Invest ed/ borrowed (choose one) in the US and invested / borrowed (choose one) in Foreign Country 1.
(b) Invested / borrowed (choose one) in the US and invested / borrowed (choose one) in Foreign Country 2.
Q5. Assume that you could both borrow and invest at the average interest rates prevailing in foreign
countries 1 and 2 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 and an equivalent amount in foreign countries 1 and 2. Given perfect
hindsight about interest rates and exchange rates changes in these two countries, please calculate your total
profit in dollars using uncovered interest arbitrage during the assigned time period:
(b) If you followed the strategy chosen in Q4(a):
(b) If you followed the strategy chosen in Q4(b):
Work Sheet: Statistical Report
Country
CANADA
Four-year time period
1998 1999 2000 2001 Geom Avg
Inflation Rate: US
1.6
2.2
3.4
3.3
Inflation Rate: Foreign Country
1.0
1.7
2.7
2.9
Interest Rate: US
5.5
5.3
6.5
4.8
Interest Rate: Foreign Country
5.0
4.9
5.7
8.3
% Change in CD SR (Indirect quote)
7.10 0.10
0.00
-2.30
% 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, R3, .... RN , then you can calculate the arithmetic and geometric mean or averages
of these rates over the N years, as follows:
Arithmetic Mean
=
(R1 + R2 + R3 + .. + RN ) / N
Geometric Mean
=
[(1+R1 )* (1+ R2 )* (1+ R3 ) * **(1+ RN ) ]1/ 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) :
Rates of return
2000
2001
2002
2003
2005
4.75 %
-8 %
0.5 %
23%
7%
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)1/ 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%