Review Questions for Interest Rate Parity Theorem for International Financial
Investment
In the Equilibrium of International Investment, Uncovered Interest (Rate) Parity says i= if + (E eE)/E
In the Equilibrium of International Investment, Covered Interest (Rate) Parity says i= if + (F- E)/E
If the two markets are perfect substitutes, then F = Ee
Case 1: On the other hand, Forward Premium/Discount may reflect the market’s expected change in
Spot Rates between Now and the future.
Rates:
For Canadians
E = How many # of CAN for USD 1 now.
Ee = How many # of CAN for USD 1 in the future.
F = How many # of CAN for USD 1 in the future. It is set now and its delivery is to be done in the future.

The future could be i = 1 months…….3 months, 6 months, …..18 months, …… ect.
Equilibrium, i= if + (F- E)/E.
We can also give the alternative form in line with the course PPP: (1+i) = (1+if) F/E, or (1+i) / (1+if) =
F/E
And here Forward Premium is defined as (F-E)/E= F/E – 1. If the value is of negative sign, it is called
Forward Discount.
Note that here interest rates are annual ones, and thus if the forward contract lasts for less than 12
months, the forward premium or discount has to be annualized by hypothetically lengthening the period to
one year. And then, it is quoted in percentage, and thus you have to multiplier it by 100.
F/E-1 x 12/i x 100 = ? (%).
Case 1: One Year interest rates and Forward of One year.
currency spot and forward rate
spot
Canadian Dollar (C$) / British Pound (£) 1.75 C$/£
interest rate
country
interest rate
Canada
Great Britain
4.0%
11.0%
1)FOREX Rate Quotations
Explain which quotation this is: an American or European quotation of FOREX for the
Canadians?
Carefully compare this expression with what the American (style) quotation would be
for the Canadian FOREX rate.
2) Covered Interest Rate Parity, and the ‘Equilibrium’ (Hypothetical) Forward Rate (what it
should be at equilibrium).
We are Canadian investors; our FOREX rate is how much CAN we need for one unit of FOREX
or British Pound:
(1+4%) = 1/E (1+11%) F*
(1+0.04) = (1+0.11) F*/ 1.75
F*= (1.04/1.11* 1.75
= 1.6396.
Note that this Forward Rate from the Covered Interest Parity Theorem is what the Forward Rate
should be in the long-run(F*). The actual Forward Rate(F) can deviate from this long-run Forward
Rate in the short-run for a number of reasons.
When forward rate is lower than spot rate, we say, “Forward Discount for FOREX (rate)”, or “GBP
carries Forward Discount”.
How many percentages? It is the way of quotation of Forward Premium/Discount in the industry?
3)(Hypothetical) Forward Premium / Discount at equilibrium
fd,f* = (F* - E) / E
= (1.6396 - 1.75) / 1.75
= -0.063
=-6.3 (percentage).
This could be the annualized Forward Discount if the international FOREX market were at the longrun equilibirum.
4) Actual Forward Rate in the Market and the (Actual) Forward Premium
The actual Forward Rate(F) and the actual Forward Premium/Discount may deviate the equilibrium
Forward Rate (F* from the CIP) or the equilibrium Forward Premium :
Suppose that this is published in the WSJ.
currency spot and forward rate
spot
1-year forward
Canadian Dollar (C$) / British Pound (£) 1.75 C$/£ 1.60 C$/£
interest rate
country
interest rate
Canada
4.0%
Great Britain
11.0%
Here the Actual Forward Rate is 1.60.
The Actual Forward Premium/Discount is
fd,f = (F - E) / E
= (1.60 - 1.75) / 1.75
= -0.085714286
= -8.5714%
5) How to make profits through FOREX market Arbitrage
If the actual Forward rate is not equal to the equilibrium Forward rate, you can make profits through
Arbitrage or International Capital Movement.
Here the Pound Forward should be in fact discounted only 6.3%, but is, in fact discounted, 8.5 %.
Thus
(1+4%) = (1+11%) -6.3% at eq.
In Actuality, i > if+ F-E/E or (1+4%) > (1+11%)- 8.5%.
Investing in Canada is better than investing in Great Britain, and thus you should move capital from
UK to Canada. In order for the investment to become an ‘Arbitrage’, there should be no risk
uncovered.
The following is the strategy for the profitable and riskless transaction, or ‘Arbitrage’:
Assume £1,000 to simplify the numbers:
time
today
1-year
Spot: Borrow (short) £1,000 at 11%
Your UK Repayment in one
year(future liability) will become:
+£1,000
-£1,000*(1+11%)
=-£1,110
Your Canadian Investment Return
Spot: Use that borrwed £1,000, and cover it into CAN at
will be(future assets):
1.75 C$/£ = 1,750 C$; ant then bring C$ to Canada and C$1,750
C$1,750*(1+4%)
deposit it at a Canadian bank
= C$1,820
You will have CAN and need Pound in a year:
In the FOREX Future market, you (should now agree to)
sell CAN and to buy Pound:
Forward: Now agree to deliver CAN$1,820 (of the future)
for £ at the actual current forward rate F = 1.60 C$/£ in
a year
We will deliver CAN 1820, and get
£1,137.5 in return in one year
(1820/1.60=1,137).
Your Net Profits in one year will be
£1,137.5-£1,110
= £27.5
Additional Examples —
2.Calculating the equilibrium Forward Exchange Rate
If the spot price for USD/EUR = 0.7395, then this means that 1 USD = .7395
EUR. The interest rate in Europe is currently 3.75%, and the current interest rate
in the United States is 5.25%. In 1 year, 1 dollar earning United States interest
will be worth $1.0525 and 0.7395 Euro earning the European interest rate of
3.75% will be worth0.7672 Euro. Thus, the forward spot rate 1 year from now is
equal to 0.7672/1.0525, or, using the above equation
(note, however, that rounding
errors between the 2 different methods of calculating the forward rate results in slight differences) :
─
Forward
Exchang
F
Rate
S(1+rq)
=
1
=
(1+rb)n
0.7395 *1.037
5
0.7395(1+0.0375)
n
=
(1+0.0525)1
=
0.729
0
1.0525
Thus, the forward exchange rate, which is often expressed simply as the Long-run
forward rate, is 1 USD = 0.7290 (rounded) Euro.
3. Actual Forward Premiums and Discounts on quotes; How to relate F to Ee
Review Questions
The above is the Forward FOREX quotation at January 25, 3:32 pm.
As a Canadian, you would like to know what the market expectations are like for a change in
Canadian FOREX rate in the future.
What does the Market expect the value of USD against CAD for the next 1 month, 3 months, 6
months, and 12 months? Use the 1 month Forward rate, 3 month-, 6 month- and 12 monthForward rates respectively for your calculations.
Case 1: Suppose that there is no expected change in S:
The forward premium is equal to differences in domestic and foreign interest
rate. You do not have to use the linear formula and may use:
(1+i ) = (1/S )(i+if) / 1/F
which is essentially the same thing as
i = if + (F-S)/S.
You may use either one of these two.