Question

I am reviewing the International Economics textbook (10th edition), Chapter 14, Question 6. The question asks:

Part A: A 10,000 GBP deposit in a London bank in a year has an interest rate in pounds of 10%. The USD/GBP exchange rate moves from $1.50 per pound to $1.38 per pound. What is the dollar rate of return on this asset? This part I understood and I calculated as:

Year 0 = 10,000 GBP * 1.50 exchange rate = 15,000 USD

Year 1 = (10,000 GBP * 1.10) * 1.38 exchange rate = 15,180 USD

Therefore, the dollar rate of return = (15,180-15,000)/15,000 = 1.2%

Then in Part B, the question asks what the real rate of return would be if the above was also accompanied by a simultaneous 10% increase in all dollar prices? This part, the solution advises as follows: The rate of appreciation of the dollar = (1.38-1.50)/1.38 = -0.08. Combine this with the 10% interest on pounds = 10% - 8% = 2% is the rate of return. We then need to incorporate the 10% price increase, so 2% - 10% = -8% as the adjusted rate of return.

What I don't understand is the difference of the -8% versus what I had before as 1.2%. How do we relate the 1.2% dollar rate of return to this -8%?

Answer 1

You should not look at the rate of return of 1.2% because it is the dollar rate of return prior to the price change and is implictly derived without inflation. Now with an 8% appreciation of dollar against the 10% inflation in the dollar prices, the realized rate of return is only 2% and the same is negative because the inflation exceeds the rate of interest. With GBP depreciating by 8% and nominal interest rate being 10%, the realized rate of return on GBP deposits is 2% but is positive because nominal rate of interest is greater than rate of depreciation.  

So if you are looking at the changed perspective now, you are receiving a realized rate of interest at 2% on GBP deposits (and this was the case in part A also, but it was not asked so it was not discussed there) but considering the inflation in dollars at 10% (which is the case in part B and has to be looked now), the realized rate in dollar becomes 2% - 10% = -8%.