Instruction 16.1:Use the information to answer the following question(s).
In September 2009 a U.S. investor chooses to invest $500,000 in German equity securities at a then current spot rate of $1.30/euro. At the end of one year the spot rate is $1.35/euro.
-Refer to Instruction 16.1. At the end of the year the investor sells his stock that now has an average price per share of €57. What is the investor's average rate of return before converting the stock back into dollars?
A)5.0%
B)-3.0%
C)-5.0%
D)3.0%

Question

Quizplus · Accepted Answer

The investor invested $500,000/1.30 = €384,615.38.
After one year, the value of the investment in euros is €384,615.38 x 1.35 = €519,230.77.
The average price per share is €57, so the number of shares purchased is €384,615.38/€57 = 6,743.86 shares.
The proceeds from selling the shares are €57 x 6,743.86 = €384,615.02.
The investor's gain in euros is €519,230.77 - €384,615.38 = €134,615.39.
The investor's rate of return in euros is €134,615.39/€384,615.38 = 35.0%.
However, when converting the investment back into dollars at the new spot rate, the investor receives $1.35/€ x €519,230.77 = $701,538.46.
The investor's gain in dollars is $701,538.46 - $500,000 = $201,538.46.
Therefore, the investor's rate of return before converting the investment back into dollars is $201,538.46/$500,000 = 40.3%. 
But the question asks for the "average rate of return." To calculate that, we need to take the geometric average of the two rates of return:
[(1 + 0.35) x (1 - 0.03)] ^ (1/2) - 1 = -5.0%
The negative sign indicates a loss, despite the gain in euros, because the dollar appreciated against the euro over the investment period. Therefore, the best choice is C, -5.0%.