Exhibit 10-2
Volusia, Inc. is a U.S.-based exporting firm that expects to receive payments denominated in both euros and Canadian dollars in one month. Based on today's spot rates, the dollar value of the funds to be received is estimated at $500,000 for the euros and $300,000 for the Canadian dollars. Based on data for the last fifty months, Volusia estimates the standard deviation of monthly percentage changes to be 8 percent for the euro and 3 percent for the Canadian dollar. The correlation coefficient between the euro and the Canadian dollar is 0.30.
-Refer to Exhibit 10-2. What is the portfolio standard deviation?
A) 3.00%.
B) 5.44%.
C) 17.98%.
D) none of the above

Question

Quizplus · Accepted Answer

The portfolio standard deviation can be calculated using the following formula:

portfolio standard deviation = sqrt(w1^2 * sd1^2 + w2^2 * sd2^2 + 2 * w1 * w2 * sd1 * sd2 * rho)

where w1 and w2 are the weights of the two currencies (in this case, euros and Canadian dollars), sd1 and sd2 are the standard deviations of the monthly percentage changes for the two currencies, and rho is the correlation coefficient between the two currencies.

First, we need to calculate the weights of the two currencies:

euro weight = $500,000 / ($500,000 + $300,000) = 0.625
Canadian dollar weight = $300,000 / ($500,000 + $300,000) = 0.375

Next, we plug in the numbers:

portfolio standard deviation = sqrt(0.625^2 * 0.08^2 + 0.375^2 * 0.03^2 + 2 * 0.625 * 0.375 * 0.08 * 0.03 * 0.30)
= 0.0544 or 5.44%

Therefore, the answer is B.

Exhibit 10-2 Volusia, Inc. Is a U.S.-Based Exporting Firm That Expects to Expects