Measuring Exposure to Exchange Rate Risk

Recall the situation of Whaler Publishing Company from the previous chapter. Whaler

needed to develop confidence intervals of four exchange rates to derive confidence

intervals for U$.$S$.$ dollar cash flows to be received from four different countries. Each

confidence interval was isolated on a particular country.

Assume that Whaler would like to estimate the range of its aggregate dollar cash flows to be

generated from other countries. The company will develop a spreadsheet to facilitate this

exercise.

Whaler plans to simulate the conversion of the expected currency cash flows to dollars,

using each of the previous years as a possible scenario $($recall that exchange rate data are

provided in the original case in Chapter $9).$ Specifically, Whaler will determine the annual

percentage change in the spot rate of each currency for a given year. Then it will apply that

percentage to the respective existing spot rates to determine a possible spot rate in one

year for each currency. Recall that today$$s spot rates are assumed to be as follows:

Once the spot rate is forecast for one year ahead for each currency, the U$.$S$.$ dollar

revenues received from each country can be forecast. For example, from year

the Australian dollar declined by about$13\mathrm{.}6\%.$ If this percentage changed occurred this year, the spot rate of the Australian dollar will decline from today$$s rate of $$0\mathrm{.}7671$to about $$0\mathrm{.}6629.$ In this case, the A$$38$million to be received would convert to $$25,190,200.$ The same tasks must be done for the other three currencies as well to estimate the aggregate dollar cash flows under this scenario.

This process can be repeated, using each of the previous years as a possible future

scenario. There will be $15$ possibles scenarios, or $15$ forecasts of the aggregate US dollars cash flows. Each of these scenarios is expected to have an equal probability of occurring.

deviation of the possible aggregate cash flows for all

and

of U$.$S$.$ dollar cash flows to be received in one year.

a$.$ Perform these tasks for Whaler to determine these confidence intervals on the

aggregate level of U$.$S$.$ dollar cash flows to be received. Whaler uses the

methodology described here, rather than simply combining the results for individual

countries $($from the previous chapter$)$ because exchange rate movements may be

correlated.

b$.$ Review the annual percentage changes in the four exchange rates. Do they appear to

be positively correlated? Estimate the correlation coefficient between exchange rate

movements with either a calculator or a spreadsheet package. Based on this analysis,

you can fill out the following correlation coefficient matrix:

A$ C$ NZ$ $$

A$ $1\mathrm{.}00$

C$ $1\mathrm{.}00$

NZ$ $1\mathrm{.}00$

$1\mathrm{.}00$

Would the aggregate dollar cash flows to be received by Whaler in this case be more

risky than if the exchange rate movements were completely independent? Explain.

c$.$ One Whaler executive has suggested that a more efficient way of deriving the

confidence intervals would be to use the exchange rates instead of the percentage

changes as the scenarios, and to derive U$.$S$.$ dollar cash flow estimates directly from

them. Do you think this method would be as accurate as the method now used by

Whaler? Explain