Question

​Treck Co. expects to pay £350,000 in one month for its imports from Northern Ireland. It also expects to receive £325,000 for its exports to Scotland in one month. Treck Co. estimates the standard deviation of monthly percentage changes of the pound to be 2% percent over the last 3 years. Assume that these percentage changes are normally distributed. Using the value-at-risk (VaR) method based on a 95 percent confidence level, what is the maximum one-month loss in dollars if the expected percentage change of the pound during next month is -2 percent? The current spot rate of the pound (before considering the maximum one-month loss) is $1.38.

Answer 1

Solution:

Given:

Expected Payment = £350,000

Expected Income = £325,000

Percentage change of the pound = 2 % over last 3 years.

% changes are normally distributed in VaR Method based on 95 % confidence level.

Expected Percentage change of the Pound during next month = - 2 %

Current Spot Rate of the Pound = $ 1.38

To Calculate:

The maximum one-month loss in dollars if the expected percentage change of the pound during next month is -2 percent.

Process: Calculations

Step: 1 Calculation of VAR (Value at Risk):

Formula:

VAR (Value at Risk) = E (Rp) – Z × σp

As given that 95 % confidence level should be used in VaR so, our formula can also be written as:

VAR (Value at Risk) at 95 % confidence level = E (Rp) – 1.65 × σp

Where:

E (Rp) = Expected Percentage Change in Portfolio

Z = It is the constant which gives the appropriate 1 tailed confidence level value, its value is 1.65 at 95 % confidence level

σp = Standard Deviation of Portfolio

Here:

E (Rp) = - 2 % or – 0.02

Z = 1.65 (At 95 % confidence level)

σp = 2 % or 0.02

On putting these values in the above formula, we get,

VAR = (- 0.02 - 1.65) × 0.02

VAR = (- 1.67) × 0.02

VAR = - 0.0334 or – 3.34 %

VAR = - 3.34 %

Step: 2 Calculation of Maximum one-month loss in dollars:

Formula:

Maximum one-month loss in dollars = VAR × (Expected Income – Expected Payment) × Current Spot Rate of the Pound

Here:

VAR = -3.34 %

Expected Income = £325,000

Expected Payment = £350,000

Current Spot Rate of the Pound = $ 1.38

On putting these values in the above formula, we get,

Maximum one-month loss in dollars = -3.34 % × (£325,000 – £350,000) × $ 1.38

= - 3.34 % × (- 25,000) × 1.38

= 835 × 1.38

= $ 1152.3

Maximum one-month loss in dollars = $ 1152.3

Ans: Maximum one-month loss in dollars when the expected percentage change of the pound during next month is -2 percent = $ 1152.3