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.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 SD = [(w1 * SD1)^2 + (w2 * SD2)^2 + 2 * w1 * w2 * SD1 * SD2 * p]^(1/2)
where 
w1 and w2 are the weights of Euro and Canadian dollar in the portfolio, respectively; 
SD1 and SD2 are the standard deviations of the monthly percentage changes for Euro and Canadian dollar, respectively; 
p is the correlation coefficient between Euro and Canadian dollar.

Let's assume that Volusia will split the portfolio equally between euros and Canadian dollars, so w1 = w2 = 0.5

Using the given data, we can calculate the portfolio standard deviation as follows:

Portfolio SD = [(0.5 * 8%)^2 + (0.5 * 3%)^2 + 2 * 0.5 * 0.5 * 8% * 3% * 0.3]^(1/2) = 5.44%

Therefore, the best choice is B, with a portfolio standard deviation of 5.44%.