1. For an odd function, as x limits to positive infinity, f(x) limits to positive infinity and as x limits to negative infinity, f(x) limits to negative infinity. Therefore, every odd function must cross the x-axis at least once. (Hint: Consider an odd function with the opposite end behavior.) 2. Reword the conditions to indicate that the end behavior is opposite but don’t specify that positive infinity for x implies positive infinity for f(x)… (Hint: Consider an odd function that is not a polynomial.) 3. Specify that the odd function is a polynomial. (Hint: Consider an odd polynomial that doesn’t have the stated end behavior) Note: Continuity is essential. Polynomials are continuous. Solution Great question, and the answer is basically yes, but it\'s a little complicated for type 1. Here are some examples for each type: Type 1: Degree of N > Degree of D N(x) = 5x^3 + 2x + 5, D(x) = -9x + 3 In this case, when x goes to positive or negative infinity, N(x) behaves like 5x^3, and D(x) behaves like -9x. Thus, the ratio will behave like 5x^3 / -9x = -(5/9) * x^2. In both cases, N(x) / D(x) will be negative infinity, since that\'s a frowny parabola. N(x) = 5x^2 + 2x + 5, D(x) = -9x + 3 In thise case, we have N(x) / D(x) behaving like 5x^2 / -9x = -5/9 * x. In this case, it\'s a like that goes like this: \\. So as x approaches inifnity, f(x) approaches -inf, and as x approaches -inf, f(x) approaches +inf. Type 2: N(x) and D(x) of the same degree N(x) = 4x^2 + 3x - 9 D(x) = 2x^2 + 9 In this case, at the extremes, N(x) / D(x) behaves like 4x^2 / 2x^2 = 4/2 = 2. Type 3: N(x) has a smaller degree N(x) = 3x - 4 D(x) = 5x^6 In this case, at the extremes, N(x) / D(x) behaves like 3x / 5x^6 = (3/5) * 1/x^5. In both directions, it approaches 0. Note that in type one, where N(x) has a greater degree, there are four patterns possible: If the degree of N(x) is of the same parity (ie both odd or both even) as D(x), their ratio will behave like x^2, x^4, x^6, etc. Or it will behave like -x^2, -x^4, -x^6, etc. In other words, either both limits are positive, or both are negative. If the degree of N(x) and D(x) are of different parity (ie one odd and the other even), then the ratio will look like x, x^3, x^5, or the respective negatives. In other words, it either goes down-to-up like x^3, or up-to-down like -x^3..

1. 1. For each of the following countries, find and report the major stock market index values for
January 2014 and January 2015 (in this exact order, please do not change): Switzerland (^SSMI),
Mexico (^MXX), India (^BSESN), Japan (^N225), France (^FCHI). You can find these data at:
http://finance.yahoo.com by entering the symbols above in parentheses for each country in the
“Search Finance” box at the top of the page. Click on “Historical Prices” on the left side. Select
“Monthly” frequency on the right side, click on “Get Prices,” and get the “Adjusted Closing”
price (local currency) on the right side of the screen for January 2014 and January 2015. For the
same countries, go to the St. Louis Fed at http://research.stlouisfed.org/fred2/categories/95 and
find and report monthly ex-rates for January 2014 and January 2015. Once you select and click
on a currency, click on “View Data” (upper left corner of screen) to view the monthly exchange
rates. Quote ex-rates with both currencies to 4 decimal places. Note:France uses the euro.
a. For each country, report the stock index values and ex-rates for January 2014 and January
2015.
b. Calculate the annual percentage return (%) for each stock market from January 2014 - January
2015, measured in local currency (use the standard percentage change formula: [(P2 – P1) / P1] x
100), or the %CHG function on your HP calculator.
c. For each currency, calculate the annual percentage change (%) from January 2014 to January
2015 using the ex-rate exactly as quoted (do not reverse the quote), and for each currency
separately, clearly explain in a full sentence or two whether (and why) each of the foreign
currencies appreciated or depreciated versus the dollar (use the standard percentage change
formula or the %CHG function on your calculator).
d. Calculate the effective, annual US dollar return (%) for a U.S. investor who had invested
money in the stock markets of each of the 5 countries during the last year (January 2014 –
January 2015), using the formula:
Effective Dollar Return (%)= % Foreign Stock Market Return +/- % CHG
(Appreciation/Depreciation) in the Foreign Currency
e. Explain your answers from part d for each country, in five separate, short essays of a few
sentences per country that explains the effective dollar return for an American investor in each
country. Specifically mention both the return on the foreign stock market and the percentage
change in the foreign currency over the last year, which together determine the one-year
Effective Dollar Return to a U.S. investor.
Now do a five-year analysis using the same countries by getting the stock market and ex-rate
data for the months January 2010 and January 2015.

2. f. Using a time value of money calculation, calculate and report the average, annual compounded
rate of change in each of the five stock markets, using the formula FV = PV (1 + i)t. Using the
financial calculator you would enter the January 2010 value as PV, the January 2015 value as FV
(with one of the values being positive and one being negative), enter N = 5, PMT = 0 and solve
for I/YR.
g. Using a time value of money calculation, calculate and report the average, annual
compounded rate of change in each of the five currencies over the five-year period.
h. Calculate the effective, average annual US dollar return (%) for a US investor who invested
money in the stock markets of each of the five countries during the five year period from January
2010 to January 2015.
i. Explain your answers from part h for each country, in five separate, short essays of a few
sentences per country that explains the effective dollar return for an American investor in each
country. Specifically mention both the average annual compounded return on the foreign stock
market and the average annual percentage compounded rate of change in the foreign currency
over the last five years, which together determine the average annual Effective Dollar Return to a
US investor.
Solution
(a)Stock Index Values
Exchange Rates
(b) Annual percentage return for Stock Markets
(c)Changes in exchange rates
c-1) Swiss Franc
Annual % change from Jan. 2014 to Jan. 2015 = [(0.9443 - 0.9038) / 0.9038 ] *100 = 4.48%
Swiss Franc depreciated by 4.48% against US Dollar from Jan. 2014 to Jan. 2015.
In 2014, Eurozone did badly in terms of economic growth and as a result the eurozone currency
i.e. Euro depreciated against US Dollar. In 2014 US economy achieved a growth rate of 2.4%
and as a result US dollar strengthened against major currencies of the world. Since Swiss Franc
was pegged to Euro (happebed in 2011), Swiss Franc depreciated against US Dollar as a result of
depreciation of Euro against US Dollar.
c-2) Mexican New Peso
Annual % change from Jan. 2014 to Jan. 2015 = [(14.6972 - 13.2220) / 13.2220 ] *100 = 11.16%
Mexican New Peso depreciated by 4.48% against US Dollar from Jan. 2014 to Jan. 2015.
In 2014 US economy grew by an impresive 2.4% which was highest since the great recession of
2008. This led to strengthening of US Dollar against major currencies of the world because

3. investors bought more US Dollars in 2014 compared to other currencies. This was the reason that
Mexican Peso depreciated against US Dollar in 2014.
c-3)Indian Rupee
Annual % change from Jan. 2014 to Jan. 2015 = [(62.1300 - 62.1057) / 62.1057 ] *100 = 0.039
%
Indian Rupee depreciated by 0.039% against US Dollar from Jan. 2014 to Jan. 2015.
The downward movement in Indian rupee was because of : strengthening of US Dollar, widening
trade deficit of India, slower growth in Indian economy compared to previous years and increase
in import bill which lead to a higher demand for US Dollars to settle the international
transactions.
c-4) Japanese Yen
Annual % change from Jan. 2014 to Jan. 2015 = [(118.2500 - 103.7614) / 103.7614 ] *100 =
13.96 %
Japanese Yen depreciated by 13.96% against US Dollar from Jan. 2014 to Jan. 2015.
Japanese Yen depreciated because of : a strengthening US Dollar, negative growth in economy
of Japan and a widening trade deficit because of increase in import bills.
c-5) France -euro
Annual % change from Jan. 2014 to Jan. 2015 = [(0.8609 - 0.7343) / 0.7343 ] *100 = 17.24 %
Euro (currency of France and other eurozone countries) depreciated by 17.24% against US
Dollar from Jan. 2014 to Jan. 2015.
Reasons for depreciation of euro: Weakning of economies of Eurozone (Crisis in Greece and
other countries like Spain, Portugal, Ireland and Italy) and high growth in US economy led to the
depreciation of Euro against US Dollar in 2014.
d)CountryJanuary 2014January
2015Switzerland8,191.308,385.30Mexico40,879.7540,950.58India20,513.8529,182.95Japan14,9
14.5317,674.39France4,165.724,604.25