Question

Consider a FI with a bond portfolio comprised of sovereign country debt that has both interest rate and exchange rate risk exposure. The duration of assets is 3.4 years and the duration of liabilities is 5.2 years. The portfolio has assets of US$18 billion (including 2.5 billion euro) and liabilities of US$16 billion (including 4.15 billion euro) with no other currencies bought or sold forward.

What is the foreign exchange rate risk of the bond portfolio?

a. Long 2.5 billion euro – exposed to euro/US dollar exchange rate declines.

b. Short 1.65 billion euro – exposed to euro/US dollar exchange rate declines.

c. Short 1.65 billion euro – exposed to euro/US dollar exchange rate increases.

d. Short 2.5 billion euro – exposed to euro/US dollar exchange rate increases.

e. Short 4.15 billion euro – exposed to euro/US dollar exchange rate increases.

the right answer is C but I have no idea how to do it

Answer 1

Basically let us fist understand that the question is focusing only on the exchange rate risk which is affected by the currency exchange rates.

Now we have assets of 2.5 billion euros and liabilities of 4.15 billion euros. so net we have 4.15-2.5 = 1.65 billion euros in liability, which implies that we have to pay 1.65 billion euros. Now let's first eliminate those options which we can using this piece of information:

a. Long 2.5 billion euro – exposed to euro/US dollar exchange rate declines: this is eliminated because it is dealing with 2.5 euros whereas we only need to deal with 1.65 euros so we dont even need to consider the long/short position in this case.

d. Short 2.5 billion euro – exposed to euro/US dollar exchange rate increases: this is eliminated because it is dealing with 2.5 euros whereas we only need to deal with 1.65 euros so we dont even need to consider the long/short position in this case.

e. Short 4.15 billion euro – exposed to euro/US dollar exchange rate increase: this is eliminated because it is dealing with 4.15 euros whereas we only need to deal with 1.65 euros so we dont even need to consider the long/short position in this case.

Now we need to analyse options b and c which are as follows:

b. Short 1.65 billion euro – exposed to euro/US dollar exchange rate declines.

c. Short 1.65 billion euro – exposed to euro/US dollar exchange rate increases.

As both take short position we are sure of this much at least, also, if we think logically, as we have a liability of 1.65 euros, when time comes, we will have to payback, that means we will sell euros or take a short position in it and buy USD. If we need to buy USD, we have risk if the price of it in terms of euros increases, i.e. euro depreciates and USD appreciates.

As per convention of exchange rates, Euro/USD implies the number of euros required to purchase 1 unit of USD and when we say the exchange rate has appreciated, it always means that the currency in the denominator, also known as the base currency has appreciated, which in this case is the USD and the currency in the numerator, also known as the price currency has depreciated which in this case is Euro.

Going by the above analysis, option C is correct because it says the FI is exposed to euro/US dollar exchange rate increases i.e. in return of 1.65 billion euro, he will get fewer USD and if the exchange rate decreases or depreciates, as in option b, then same 1.65 billion euros will fetch more USD in exchange. Therefore the correct option is option C