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 50 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 percent
B) 5.44 percent
C) 17.98 percent
D) None of these are correct.

Question

Quizplus · Accepted Answer

To calculate the portfolio standard deviation, we need to use the following formula:

σp = √[(w1^2 × σ1^2) + (w2^2 × σ2^2) + (2 × w1 × w2 × σ1 × σ2 × ρ)]

where:
σ1 = standard deviation of euro
σ2 = standard deviation of Canadian dollar
w1 = weight of euro in the portfolio (in dollar terms)
w2 = weight of Canadian dollar in the portfolio (in dollar terms)
ρ = correlation coefficient between the euro and Canadian dollar

Here, we can assume that the weights are equal (i.e., 0.5 for each currency).

So, plugging in the given values, we get:

σp = √[(0.5^2 × 0.08^2) + (0.5^2 × 0.03^2) + (2 × 0.5 × 0.5 × 0.08 × 0.03 × 0.30)]
   = 0.0544 or 5.44%

Therefore, the portfolio standard deviation is 5.44%. The answer is B.

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