A U.S. investor purchased a U.K. bond one year ago. The exchange rate at the time was 1.5 to 1 (dollars to pounds) and the beginning-of-period ratio of the price levels of the consumption baskets was 2 to 1 (dollars to pounds). Beginning of the year interest rates were 7% in the U.S. and 12% in the U.K. Inflation during the year was expected to be 5% in the U.S. and 10% in the U.K. Today the exchange rate is 1.6. What is the ex-post domestic currency return on the U.K. bond to the U.S. investor?
Correct answer: 18.67%. The dollar was expected to appreciate (lower inflation), but depreciated by 6.67 percent (= 1.6/1.5 = 1.0667 or 6.67%) instead. Hence, the return to U.S. investor is the foreign interest rate plus currency appreciation, or 18.67 percent (= 12% foreign rate + 6.67% appreciation). Ex-post domestic currency return is the return, in term of domestic currency, for holding the foreign investment denominated in foreign currency. Inflation plays no role here. The inflation information is only useful when you calculate the real exchange rate.
Forward premium is obtained by interest rate parity. Since the UK intreset rate is more, the forward premium will be negative and is simply the interest rate differenctial, i.e. 7 - 12 = -5%
So the ex-post return = 7 + 11.67 = 18.67%
This is more lengthy (but you should atleast be aware of it). I prefer the (forerign return + foreign currency appreciation), as Krisztina mentioned.
OMG! 2011 Level II Mock Exam: Morning Session/ Result of Q21 seems to support your version of 19.46%. Not to mention logic! Schweser is a different story, isn’t it?
I knew there was something wrong here, because my numbers were always off!.
The good news is that I figured out the mistake in their calculations. You see the 6.67% appreciation of the pound, in their formula, affected only the initial exchange rate (the $1.5/pound), but in reality the appreciation of the pound impacts the final amount, the 1.12 pound after interest. So, you should do it like this:
remember in all this the delta-r+delta-s+delta-r*delta-s -> they ignore the 3rd component -> delta_r*delta_s saying if the numbers are small - they can ignore it.
I agree that in the exam the difference may not be important because the answer choices will be quite apart from each other, but it’s good to know the actual logic behind these things, and not rely completely on formulas.
I disagree with the book and agree with Dreary’s logic. The logic is right, however, the formula given in the CFA only works if there is a small difference in interest rate. If there is a large difference like in this example, the formula doesn’t work. Some econ textbook use the same formula for this to find nominal interest rate, but if there is a big difference in rates you have to use the multiple method. I always use the multiple method because it’s always right, but you might be safer to use the CFA formula in its exams.