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 fiF t y 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?

Question

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 fiF t y 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?​

Quizplus · Accepted Answer

To calculate the portfolio standard deviation, we need to use the formula:
Portfolio SD = sqrt [(w1^2 x SD1^2) + (w2^2 x SD2^2) + 2(w1 x w2 x Corr x SD1 x SD2)]
Where w1 and w2 are the weights of euros and Canadian dollars in the portfolio, SD1 and SD2 are the standard deviations of the percentage changes in euros and Canadian dollars, and Corr is the correlation coefficient between the two currencies.

Given:
- w1 = 500,000 / (500,000 + 300,000) = 0.625 (the proportion of the portfolio in euros)
- w2 = 1 - w1 = 0.375 (the proportion of the portfolio in Canadian dollars)
- SD1 = 8%
- SD2 = 3%
- Corr = 0.30

Applying the formula, we get:
Portfolio SD = sqrt [(0.625^2 x 0.08^2) + (0.375^2 x 0.03^2) + 2(0.625 x 0.375 x 0.30 x 0.08 x 0.03)]
Portfolio SD = sqrt [0.0039 + 0.000421875 + 0.0003375]
Portfolio SD = sqrt(0.004659375)
Portfolio SD = 0.06823 or 6.823%

Thus, the portfolio standard deviation is 6.823%, which is closest to option B, 5.44%.

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