Question

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

Answer 1

From the details that are contained in the question, the portfolio standard deviation is 0.0544 or 5.44%

How to solve for the portfolio standard deviation

w1 = weight of euros 1 = 500000/800000

w2 = weight of canadian dollars = 300000/800000

Standard deviation 1 = 8%

Standard deviation 2 = 3%

Correlation coefficient = 0.30

(w1*σ1)² + (w2*σ2)² + (2* w1*σ1* w2*σ2 * 0.30)^0.5

$((0.625*0.08)^{2} +(0.375*0.03)^{2} +(2*0.625*0.08*0.375*0.03*0.3)^0^.^5\\\\= 0.0544$

Therefore the portfolio standard deviation is given as 0.0544 or 5.44%

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