Handout
Get-rich-quick scheme∗
Jorge F. Chavez
November 20, 2014
You read in the newspaper that the nominal interest rate is 12 percent per year in
Canada and 8 percent per year in the US. Suppose that the real interest rates are equalised
in the two countries and that PPP holds.
(a) Using the Fisher equation, what can you infer about expected inflation in both countries?
Answer. The Fisher equation states that the nominal interest rate is a function of
both the real interest rate and the expected inflation rate. In it’s approximate version
i = r + π e .1 Then we can use the fact that the real interest rate are equalized in the
the countries (e.g. Canada is a small-open economy relative to the US):
e
rCAN = iCAN − πCAN
= iU S − πUe S = rU S
Then:
e
πCAN
− πUe S = iCAN − iU S = 0.04
That is, even though we do not know the exact inflation rate expected in the two
countries, we do know from the information given that agents in Canada expect 4
additional percentage points of inflation that agents located in the U.S.
(b) What can you infer about the expected change in the exchange rate between the
Canadian dollar and the US dollar?
Answer. Here we can use the fact that PPP holds, or that the law of one price holds,
which implies that ePCAN = PU∗ S . Then rewriting this expression in terms of growth
rates of its components:
%∆e + %∆PCAN = %∆PU S ∗
and finally:
%∆e = πCAN − πU S
∗
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Problem 3.4 in Coursework 2014/2015
In its exact version (1 + i) = (1 + r)(1 + π e ).
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Therefore, given that we know the difference in expected inflation rates in the two
countries, we can infer that the expected change in the exchange rate between the
Canadian dollar and the US dollar will be 4%.
(c) A friend proposes a get-rich-quick scheme: borrow from a US bank at 8 percent, deposit
the money in a Canadian bank at 12 percent and make a 4 percent profit. What’s
wrong with this scheme?
Answer. The key piece of information to answer this part is the conclusion we got from
the previous question, that is that the expected depreciation of the Canadian dollar is
4%. If we do not take this into account, that is if we assume that the exchange rate
between the two countries is invariant, then the scheme makes perfect sense. However,
if use the information we got about the expected depreciation, then we will see that it
is not such a good idea.
To fix ideas it is better to assume an exchange rate for today (period t) and an amount
borrowed from a US bank at time t to be repaid at time t + 1 (tomorrow). Any
quantities will serve our purpose, but to simplify the analysis I’ll assume that the loan
taken is of US$ 1.00 and the exchange rate is one Canadian dollar per 1 US dollar.
Then:
At time t:
• Borrow US$1.00 from a US bank.
• Convert it into Canadian dollars. At the assumed exchange rate it will be CAN$
1.00.
• Cross the border and deposit CAN$ 1.00 in a Canadian bank.
At time t + 1:
• Withdraw your deposit of CAN$1.00 plus CAN$0.12 of interests gained (at 12%
interest rate).
• Convert them into US dollars, using the current exchange rate of 0.96 Canadian
dollars per 1 US dollar. The total amount of money you have now is the equivalent
of US$ 1.0752.
• Cross the border and repay your debt: the amount borrowed (US$ 1.00) plus
interests of US$ 0.08.
Clearly US$ 1.0752< US$ 1.08 which means that the scheme is not a good idea.
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