IRP: Implication

CFA Level III Fixed Income
#1

Hi guys -

Wonder if anyone could explain this for me.

In the Schweser book, fixed income, IRP:

  • The currency of the country with higher nominal interest rate trades at a forward discount to the spot exchange rate.

  • The currency of the country with lower nominal interest rate trades at a forward premium to the spot exchange rate.

  • Selling forward the currency trading at a forward discount will earn a negative return vs. the spot exchange rate.

  • Selling forward the currency trading at a forward premium will earn a positive return vs. spot exchange rate.

Why is that? I couldnt explain this to myself with IRP formula. Can you please explain with an example? Thanks!

#2

Ill try to give it a go…

Lets say country A has an interest rate of 3% and country b has an interest rate of 10%

Here country B has the higher nominal interest rate so B is depreciating in value at a higher rate so its going to be worth less in the future, hence its trading at a forward discount than its worth now, because it will be worth less at the end of the future.

#3

Suppose that the USD/AUD spot rate is USD0.8000 per AUD1.0000, that the 1-year USD (nominal) risk-free rate is 5% and the 1-year AUD (nominal) risk-free rate is 2%. In that case, in one year (today’s) USD0.8000 will be worth USD0.8000 × 1.05 = USD0.8400, and (today’s) AUD1.0000 will be worth AUD1.0000 × 1.02 = AUD1.0200. To maintain interest rate parity, the 1-year forward exchange rate must equate those values: USD0.8400 per AUD1.0200, or USD0.8235 per AUD1.0000. The AUD is trading at a forward premium because if interest rate parity holds it will take more USD to buy one AUD one year from today than it takes today.

Conversely, the AUD/USD spot rate is AUD1.2500 per USD1.0000. In one year (today’s) AUD1.2500 will be worth AUD1.2500 × 1.02 = AUD1.2750, and (today’s) USD1.0000 will be worth USD1.0000 × 1.05 = USD1.0500. To maintain interest rate parity, the 1-year forward exchange rate must equate those values: AUD1.2750 per USD1.0500, or AUD1.2143 per USD1.0000. The USD is trading at a forward discount because if interest rate parity holds it will take fewer AUD to buy one USD one year from today than it takes today.

The last two statements are a bit weird. In the situation described if you sell USD forward you will get only AUD1.2143 per USD1.0000 whereas if you sell USD in the spot market you’ll get AUD1.2500 per USD1.0000. So far, so good. However, if you sell in the spot market you’ll have AUD to invest today and you’ll get only 2%, whereas if you sell in the forward market you’ll have USD to invest today at 5%. One year from now you’ll have the same number of AUD either way, so the statement is . . . well . . . weird. Similarly, if you sell AUD today you’ll get fewer USD than if you sell them in the forward market, but you’ll earn 5% instead of 2% and one year from today you’ll have the same amount of USD either way.