You read in a newspaper that the nominal interest rate is 12 percent per year in Canada and 8 percent per year in the United States. Suppose that the real interest rates are equalized in the two countries and that purchasing-power parity holds.
a) Using the Fisher equation, what can you infer about expected inflation in Canada and in the United States?
b) What can you infer about expected change in the exchange rate between the Canadian dollar and the U.S. dollar?
c) A friend proposes a get-rich-quick scheme: borrow from a US bank at 8%, deposit the money in a Canadian bank at 12%, and make a 4% profit. What is wrong with this scheme?
a) To find the expected inflation in Canada and the United States, we can use the Fisher equation, which states that the nominal interest rate is equal to the sum of the real interest rate and the expected inflation rate.
For Canada:
Nominal interest rate = 12%
Real interest rate = ?
Expected inflation = ?
Using the Fisher equation:
Nominal interest rate = Real interest rate + Expected inflation
12% = Real interest rate + Expected inflation
For the United States:
Nominal interest rate = 8%
Real interest rate = ?
Expected inflation = ?
Using the Fisher equation:
Nominal interest rate = Real interest rate + Expected inflation
8% = Real interest rate + Expected inflation
Since the real interest rates are assumed to be equalized in the two countries, we can assume that the real interest rates in Canada and the United States are the same.
Therefore, we can rewrite the equations as:
12% = Real interest rate + Expected inflation
8% = Real interest rate + Expected inflation
By subtracting the common real interest rate from both equations, we find that:
12% - Real interest rate = Expected inflation in Canada
8% - Real interest rate = Expected inflation in the United States
b) According to the purchasing-power parity (PPP) theory, the exchange rate should adjust to equalize the purchasing power of different currencies. In this case, since the real interest rates are equalized, we can infer that the expected change in the exchange rate between the Canadian dollar and the U.S. dollar would be equal to the difference in the expected inflation rates between the two countries.
Expected change in exchange rate = Expected inflation in Canada - Expected inflation in the United States
c) The friend's proposed scheme of borrowing from a US bank at 8%, depositing the money in a Canadian bank at 12%, and making a 4% profit may seem attractive on the surface. However, there are a few key points to consider:
1. Exchange rate risk: The friend would be subject to the risk of exchange rate fluctuations between the Canadian dollar and the U.S. dollar. If the Canadian dollar were to depreciate against the U.S. dollar, the profit from the interest rate differential may be eroded or even turn into a loss.
2. Transaction costs: Converting currencies and transferring funds between banks can involve transaction costs, such as exchange rate spreads and bank fees, which would reduce the overall profit.
3. Liquidity issues: Depending on the terms of the borrowing and deposit agreements, the friend may not have immediate access to the funds without incurring penalties or fees. This could limit liquidity and flexibility in managing the investment.
4. Assumptions and uncertainties: The friend's scheme assumes that the real interest rates and expected inflation rates will remain constant throughout the borrowing and deposit periods. However, economic conditions and inflation expectations can change, leading to unforeseen consequences.
In summary, while the friend's scheme may seem profitable in theory, it carries various risks, transaction costs, and uncertainties that could potentially outweigh the expected profit.