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. 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

Answer 1

Solution:-

this questions can be solved through the following two steps:

Step 1. calculation of portfolio risk

Where,

= Proportion of the portfolio invested in asset 1

   =  Proportion of the portfolio invested in asset 2

= Asset 1 standard deviation of returns

=  Asset 2 standard deviation of returns

= Correlation coefficient between the returns of Asset 1 and Asset 2

Here,

= $500000 / $800000 = .625

   = $300000 / $800000 = .375

= .08

=  .03

= .30

by substituting the value in the equation we get,

= 5.44%

Step 2. Maximum loss of the currency portfolio

The maximum one month loss of the current portfolio is determined by the lower boundary of the probability distribution, which is 1.65 standard deviations away from the expected percentage change in the currency portfolio. Assuming an expected percentage change of 0% for each currency during the next month,the maximum loss of the currency portfolio will be :-

=

Where,

(expected percentage change ) = 0%

by substituting the value in the equation we get,

  Maximum loss of the currency portfolio = 0% - (1.65 * 5.44%)

= -9.00%