Volusia, ltd. is a UK-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. Assuming an expected percentage change of 0 percent for each currency during the next month, what is the maximum one-month loss of the currency portfolio? Use a 95 percent confidence level and assume the monthly percentage changes for each currency are normally distributed.

Question

Quizplus · Accepted Answer

The maximum one-month loss of the currency portfolio is -9.00%. This is calculated using the formula:Maximum loss = -Z * sqrt(Var(R_e) + Var(R_c) + 2 * Cov(R_e, R_c))where:Z is the z-score for the desired confidence level (95% in this case)Var(R_e) is the variance of the monthly percentage change for the euroVar(R_c) is the variance of the monthly percentage change for the Canadian dollarCov(R_e, R_c) is the covariance between the monthly percentage changes for the euro and the Canadian dollarPlugging in the given values, we get:Maximum loss = -1.645 * sqrt(0.08^2 + 0.03^2 + 2 * 0.30 * 0.08 * 0.03) = -9.00%

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