International Parity
Conditions
- CIP (Part III)
Illustration of CIP
• Imagine that there are only two countries left on
earth: the US and Japan
• You are in the US
• You have 1 USD and you want to invest it
• You can invest either in Japan, or in the US
• The yearly interest rate in the US is 5%
• The yearly interest rate in Japan is 1%
• The (spot) exchange rate is 120JPY/USD
Analyze the Alternatives
• If you invest in US you will have to go the
bank, put your money into an account
• After one year your dollar will have
accumulated interest, so you get
• 1 USD*1.05=1.05 USD
• If you want to invest in Japan
– First you have to buy Japanese Yen
What is the price of JPY in term of USD?
Invest in Japan
• We said 120 JPY/USD
• So you go to the bank and buy Yen. How
many do you get?
– 1USD*120 JPY/USD= 120 JPY
• Now you are ready to invest in a Japanese
account for one year at 1%
• After one year you will get:
• 120JPY*(1.01)=121.2 JPY
Which is Better?
• Invest in US and get 1.05 USD?
• Invest in Japan and get 121.2
JPY?
The questions we want to answer
• How many JPY per USD should you
commit today to pay after one year?
• Would you pay more or less than
121.2 JPY per 1.05 USD = 115.35JPY/USD?
Framework
• Recall what is the no-arbitrage condition
• Recall the two investment opportunities:
Invest 1USD in US at 5%
TODAY
Buy 120JPY
with your
dollar
Get 1.05USD
How much
can you sell
your JPY
today?
Wait 1 year
Invest 120JPY in Japan at 1%
Get 121.2JPY
Answer
• The central idea is that both opportunities entail
no risk, hence they must yield the same return!
(Otherwise?)
• The no-arbitrage exchange rate that we have
determined 115.35JPY/USD is what we have
called 1-year forward exchange rate
• This is the fair price of 1 USD expressed in JPY
one year form today that everybody must accept
today to avoid memorable losses
The relation between forward rate
and future spot rate
• Forward rate should reflect the expected future spot
rate on the date of settlement of the forward contract.
• In other world, the forward rate should be an
unbiased predictor of the future spot rate.
• If this condition is violated there is an arbitrage
opportunity, or there may exist other market
imperfections
More formally
• Denote Ft a one-period forward rate observed
at time t. Then:
Ft  ES t 1 
• E[St+1] is the expected future exchange rate.
The actual, realized St+1 may or may be not
equal to E[St+1].
Forward premium
• The forward-spot rate differential, (Ft - St), is
called a forward premium.
• The forward premium should be equal to the
expected change in the exchange rate.
Ft  S t ES t 1   S t

St
St
Covered interest rate parity
• The CIP condition is:
Ft
1  i   1  iB 
St
A
• CIP is the relation between the return on a hedged
investment in a foreign currency in terms of the
domestic currency.
• It does guarantee that the return on foreign
investment will be equal the domestic interest rate on
investment of identical risk.
Example continued from UIP
• First investor purchases a 1-year U.S bond with 5%
interest rate.
• Second investor exchanges $ for DM, buys a 1-year
German bond with 3% interest rate, and takes a short
position in DM forward contract.
• The initial spot $/DM rate is 0.58.
• The forward one-year $/DM rate is 0.5913.
• The spot $/DM rate a year later is 0.59.
• Which investor is better off?
Example: the solution
• The U.S. dollar denominated return to the
first investor is 5%.
• The U.S. dollar denominated return to the
second investor is also 5%, since:
0.5913
A
1  i  
1  0.03 
0.5800
 1.050
How did it happen?
• The forward one-year $/DM rate of 0.5913
was determined based on the covered
interest rate parity condition.
• So, if Ft is an unbiased predictor of St+1,
investors should be indifferent between
investing in domestic versus foreign
securities.
Empirical evidence
• To test whether the forward rate is an unbiased
predictor of the future spot rate the framework of the
following regression model is used:
 Ft  S t 
S t 1  S t
 a  b
  ut 1
St
 St 
• If Ft = E[St+1], then we should find that a=0 and b=1.
• Estimation generally leads to b<1 or even b<0.
Implications of the test results
• Existence of simple profitable trading strategies
based on publicly available information.
• Violation of the semi-strong form of market
efficiency hypothesis.
• Existence of a foreign exchange risk premium with
no violation of market efficiency. High volatility of
forex vs. interest rates
Foreign exchange risk premium
• The origin of the risk premium (classical view):
– An investor invests in domestic and foreign bonds.
– The nominal riskiness of domestic and foreign assets is
different.
– This difference presents a source of risk.
– An investor demands a premium as a compensation for
bearing this risk in the portfolio.
• Foreign risk premium is time-varying.
Recent findings: from Bansal and
Dahlquist (1999)
• The negative relation between the expected currency
depreciation and interest rate differential (forward
premium) is observed only
– in developed economies.
– when the U.S. interest rate exceeds interest rates of other
industrialized countries.
• Cross-country differences in risk premia are related
to country-specific factors, such as per capita GNP,
inflation rates, inflation volatility.
3. Conclusion with the 4
Relations
Conclusions
• The law of one price (LOP) is the
fundamental no-arbitrage condition.
• All parity conditions follow from the LOP.
• All parity conditions do not account for
possible market imperfections.