Question

You are an investment manager in Denmark. You see different interest rates around the world and your foreign exchange trading team (as always staffed by Stern alums) has provided you with the current spot rate and an expected future spot rate between the Danish and Mexican currencies. Hint/Warning: Be sure to check if you’ve adjusted interest rates for period and if you are really looking at “e” in the info.
*Current spot exchange rate is 3.60 Pesos per Danish Krone.
*Expected future spot rate in 30 days is 3.47 Pesos per Danish Krone
*The 1 year interest rate on the Danish Krone-denominated bank deposit is 6.0%
*The 1 year interest rate on the Mexican Peso-denominated bank deposit is 4.5%
In which country will you earn the higher rate of return?
Roughly speaking (we allow for rounding errors): If you invested 1 million Krone (converted to Pesos) into a Mexican bank and then returned it using this expected future spot rate and assuming it turned out to be accurate, how much more money would our firm make or lose in Mexico than our home country of Denmark (be sure to note if this was a gain or loss)?

Answer 1

It looks like Denmark has a higher interest rate , but this does not mean that the rate of return is also higher in Denmark. It depends upon how different currencies move with respect to each other. and hence rate of returns comparison cannot be done that way.

If 1 million Krone is invested in Denmark , one would earn 6%/12 = 0.5% for 30 days deposit (assuming 360 day year and annual percentage rate of 6%)

So, Final amount after one month = 1 million *1.005 = 1.005 million Krone

If 1 million Krone is converted to Pesos today, one gets 3.6 million Pesos, which if invested in Pesos would result in an amount of 3.6 million* (1+0.045/12) = 3.6135 million Pesos after one month . Now, if the forecast is correct, one can convert the Pesos amount to Krones after one month at 3.47 pesos/krone  to get 3.6135/3.47 million Krones or 1.041354 million Krones

So, if the forecast is correct , one can make 1.041354-1.005 =0.036354 million Krones or 36,354 Krones more by investing in Pesos. Thus, the rate of return in Pesos is more given the current exchange rates and provided the forecast of expected spot rate after 30 days is correct.