Question

Cerra Co. expects to receive 5 million euros and 5 million pounds as a result of selling goods to the Europe.

1. Based on the following information, estimates the standard deviation of monthly percentage changes in the exchange rate of the portfolio (euros and pounds) based on the data in the last 7 months.

Month	Euro	Pound
1	$1.13	$1.27
2	$1.12	$1.25
3	$1.11	$1.22
4	$1.10	$1.24
5	$1.11	$1.27
6	$1.13	$1.29
7	$1.11	$1.31

2. Assume that these percentage changes are normally distributed. Use the value-at-risk (VAR) method based on a 95% confidence level. What is the maximum one-month loss if the expected percentage change of the portfolio is 0.1%?

Answer 1

1. Standard Deviation is given by:

Month	Euro	Pound	% Euro change	% Pound change
1	1.13	1.27
2	1.12	1.25	-0.88%	-1.57%
3	1.11	1.22	-0.89%	-2.40%
4	1.1	1.24	-0.90%	1.64%
5	1.11	1.27	0.91%	2.42%
6	1.13	1.29	1.80%	1.57%
7	1.11	1.31	-1.77%	1.55%
		STDEV	1.35%	2.00%

2. Assume that the current spot rate of the euro (before considering the maximum one-month loss) is $1.11

PART - 1 : Payment in EURO

Given:

Expected amount to be received = 5 million euros

Standard deviation of monthly percentage change of euros, σ = 1.35%

Confidence level = 95%

Expected percentage change of the euro next month= 0.1%

Let the current spot rate of the euro (before considering the maximum one-day loss = $1.11

Now,

The maximum one-month percentage loss

= Expected change of euro - 1.65 × σ                  

(here 1.65 is constant for 95% confidence)

= 0.1% - 1.65 × 1.35%

= -2.13%     (Here negative sign depicts the loss)

Therefore,

maximum one-month loss in dollars

= maximum one-month percentage loss × Exchange rate × Amount to be received

= -2.13% × $1.11 × 5 million euros

= -$118,076 (Here negative sign depicts the loss)

PART - 2 : Payment in POUND

Given:

Expected amount to be received = 5 million pounds

Standard deviation of monthly percentage change of euros, σ = 2.00%

Confidence level = 95%

Expected percentage change of the pound next month= 0.1%

Let the current spot rate of the pound (before considering the maximum one-day loss) = $1.31

Now,

The maximum one-month percentage loss

= Expected change of pound - 1.65 × σ                  

(here 1.65 is constant for 95% confidence)

= 0.1% - 1.65 × 2.00%

= -3.20%     (Here negative sign depicts the loss)

Therefore,

maximum one-month loss in dollars

= maximum one-month percentage loss × Exchange rate × Amount to be received

= -3.20% × $1.31 × 5 million pounds

= -$177,362 (Here negative sign depicts the loss)

Total maximum one-month loss = $117,952 + $177,362 = $295,314