Question

(2)XYZ is an exporting company based in New York. It expects to receive substantial payments denominated in UK pounds and euros. Based on today’s spot rate the dollar value of funds to be received in pounds is $600,000 and the dollar value of the funds to be received in euros is $400,000.The company wants to determine the maximum expected one-month loss due to a potential decline in the value of these two currencies ( based on 95% confidence level). Using the data for the past 20 months the firm found the standard deviation of monthly percentage changes to be 7% for the pound and 8% for the euro. It also estimates a correlation coefficient of 0.50 between both currencies.

If the monthly percentage changes for each currency are normally distributed and assuming the expected percentage change of ZERO for each currency during the next month (and this also implies an expected change of zero for the portfolio) find

(a)the maximum 1-month loss of the currency portfolio (hint: first find the portfolio standard deviation)  

(b)the maximum 1-month loss of the pound

(c)the maximum 1-month loss of the euro.

Answer 1

(a) Calculation of maximum 1-month loss for current portfolio

SD of portfolio = √Weight of pound * Variance of pound + Weight of Euro * Variance of Euro + 2 * Weight pound * Weight euro* Correlation * S.D.of pound * S.D.of Euro

= √0.36*49 + 0.16*64 + 2*0.6*0.4*0.5*7*8

= 6.4281%

Maximum 1- month loss = Portfolio value * Z (value of 95% confidence) * Standard Deviation of Portfolio

= 1,000,000 * 1.96 * 6.4281%

= $125,991

(b) Calculation of maximum 1-month loss of the pound

Maximum 1-month loss of pound = Pound investment * Z (value of 95% confidence) * S.D. of Pound

= $600,000 * 1.96 * 7%

= $82,320

(c) Calculation of maximum 1-month loss of the euro

Maximum 1-month loss of euro = Euro investment * Z (value of 95% confidence) * S.D. of Euro

= $400,000 * 1.96 * 8%

= $62,720