Exchange Rate
Theories/International
Parity Conditions
Mint Parity Theory
Mint parity theory explains the determination of
exchange rate between the two countries which are a
gold standard.
In a country which is on gold standard, the currency
is either made of gold or is convertible into gold at a
fixed rate. There are also no restrictions on the
export or import of gold.
Mint Parity Theory
The rate of exchange between the gold standard
countries is determined on a weight to weight basis
of the gold countries of their currencies. In other
words, the exchange rate is determined by the gold
equivalents of the currencies involved.
Mint Parity Theory
The mint par is an expression of the ratio of weights
of gold's used for the coinage of the currencies. For
examples before World War 1 England and
American were on gold standard. The mint par
between these two countries was pound, one of
England +4.866 dollars of America. One pound
worth fine gold= 4.866 dollars
Mint Parity Theory
The ratio of weights of metal 1 pound= $4.866 was
called the mint parity.
The mint par was a fixed rate. It remained so long as
the monetary laws of the country remain unchanged.
The current or the market rate of exchange, however,
fluctuated from time to time due to changes in the
balance of payments of the respective countries.
International Parity Conditions
■ The forex participants must have to answer some
questions like:- What are the determinants of exchange rates?
- Are changes in exchange rates predictable?
■ The economic theories that link exchange rates,
price levels, and interest rates together are called
international parity conditions.
■ Parity conditions form the core of the financial
theory that is unique to international finance.
Prices and Exchange Rates
■ If the identical product or service can be sold in
two different markets, and no restrictions exist
on the sale or transportation costs of moving
the product between markets, the products
price should be the same in both markets.
■ This is called the law of one price.
Prices and Exchange Rates
■ A primary principle of competitive markets is
that prices will equalize across markets if
frictions (transportation costs) do not exist.
■ Comparing prices then, would require only a
conversion from one currency to the other:
8
Rr^stRs^rRr '
Absolute PPP
■ If the law of one price were true for all goods and
services, the purchasing power parity (PPP)
exchange rate could be found from any individual
set of prices.
■ By comparing the prices of identical products
denominated in different currencies, we could
determine the “real” or PPP exchange rate that
should exist if markets were efficient.
■ This is the absolute version of the PPP theory.
Parity Condition
A
= S(A/B) *PB
Purchasing Power Parity (PPP)
-5
Percent change in the spot exchange 6
rate for foreign currency
-6
Percent difference in
expected rates of inflation
(foreign relative to
home country)
Relative PPP
■ If the assumptions of the absolute version of the
PPP theory are relaxed a bit more, we observe
what is termed relative purchasing power parity
(RPPP).
■ RPPP holds that PPP is not particularly helpful in
determining what the spot rate is today, but that
the relative change in prices between two
countries over a period of time determines the
change in the exchange rate over that period.
Prices and Exchange Rates
■ More specifically, with regard to
RPPP, if the spot exchange rate
between two countries starts in
equilibrium, any change in the
differential rate of inflation between
them tends to be offset over the long
run by an equal but opposite change
in the spot exchange rate.
If S*($/£) is the percentage change in the spot
exchange rate over a year and P*US and P*UK are the
percentage change in the price levels in US and
UK then
PUS(1+ P*US) = S($/£)(1+ S*($/£)) x PUK (1+ P*UK ) (1+
P*US) = (1+ S*($/£)) x (1+ P*UK ) S*($/£) = (P*US- P*UK
)/(1+P*UK )
In approximation
S*($/£) = (P*US- P*UK )
The absolute or expectations form of PPP implies
that exchange rate differential should be equal to
inflation rate differential to avoid any permanent
bias, if the markets are efficient.
Departure from PPP
■ PPP holds up well over the very long run but
poorly for shorter time periods
■ PPP holds better for countries with relatively high
rates of inflation and underdeveloped capital
markets
■ Restrictions on movement of goods
- Import Tariffs
- Quotas
■ Price Indexes and non-traded outputs
Statistical problems of evaluating PPP
S*($/£) = β0+ β1(P*US- P*UK )+µ
It is presumed that β0=0 and β1 =1, where µ is the
ex-ante regression error
# errors in measuring P*US- P*UK
# simultaneous determination of S*($/£) and
inflation differential.
Prices and Exchange Rates
■ Individual national currencies often need to be
evaluated against other currency values to
determine relative purchasing power.
■ The objective is to discover whether a nation’s
exchange
rate
is
“overvalued”
or
“undervalued” in terms of PPP.
■ This problem is often dealt with through the
calculation of exchange rate indices such as
the nominal effective exchange rate index.
Prices and Exchange Rates
The degree to which the prices of imported and exported goods
change as a result of exchange rate changes is termed passthrough.
■ Although PPP implies that all exchange rate changes are passed
through by equivalent changes in prices to trading partners,
empirical research in the 1980s questioned this long-held
assumption.
■ For example, a car manufacturer may or may not adjust pricing of
its cars sold in a foreign country if exchange rates alter the
manufacturer’s cost structure in comparison to the foreign
market.
Pass-through can also be partial as there are many mechanisms
by which companies can compartmentalize or absorb the impact
of exchange rate changes.
Price elasticity of demand is an important factor when determining
pass-through levels.
Interest Rate Parity
■ The currency of a country with lower interest
rates should be at a forward premium in
terms of the currency of the country with the
higher rate.
■ In an efficient market with no transaction
costs, the interest rate differential should be
approximately equal to forward differential.
■ When this is met , the forward rate is said to
be interest rate parity and equilibrium
Prevails in the money market.
Interest Rate Parity contd..
Interest rate parity ensures that return on a
hedged (covered) foreign investment will just
equal the domestic rate on investment of
identical risk, thereby eliminating the possibility
of money machine.
Fisher Effect
■ The Fisher Effect states that nominal interest
rates in each country are equal to the required
real rate of return plus compensation for
expected inflation.
■ This equation reduces to (in approximate
form):
i = r + TT
Where i = nominal interest rate, r = real
interest rate and TT = expected inflation.
■ Empirical tests (using ex-post) national
inflation rates have shown the Fisher effect
usually exists for short-maturity government
securities (treasury bills and notes).
Interest Rates & Exchange Rates
■ The relationship between the percentage change
in the spot exchange rate over time and the
differential between comparable interest rates in
different national capital markets is known as the
international Fisher effect
■ “Fisher-open”, as it is termed, states that the spot
exchange rate should change in an equal amount
but in the opposite direction to the difference in
interest rates between two countries.
Currency Yield Curves & The Forward Premium
Interest
yield
Eurodollar
yield curve
10.0 %
9.0 %
8.0 %
7.0 %
6.0 %
5.0 %
Euro Swiss franc
yield curve
4.0 %
3.0 %
2.0 %
1.0 %
30
60
90
120
Days Forward
150
180
Interest Rate Parity (IRP)
Start
i $ = 8.00 % per
annum (2.00 % per
90 days)
End
►
$1,000,000
►
x 1.02 --------
$1,020,000
$1,019,993*
t
S = SF 1.4800/$
F90 = SF 1.4655/$ ▲
Dollar money market
Swiss franc money market
SF 1,480,000
------ ►
x 1.01 ----------------- ►
SF 1,494,800
i SF = 4.00 % per annum
(1.00 % per 90 days)
•Note that the Swiss franc investment yields $1,019,993, $7 less on a $1 million investment.
Covered Interest Arbitrage
■ The spot and forward exchange rates are not,
however, constantly in the state of equilibrium
described by interest rate parity.
■ When the market is not in equilibrium, the
potential for “risk-less” or arbitrage profit exists.
■ The arbitrager will exploit the imbalance by
investing in whichever currency offers the higher
return on a covered basis.
■ This is known as covered interest arbitrage (CIA).
Covered Interest Arbitrage
(1+r$)=Fn($/£)/($/£) *(1+r£)
Covered Interest Arbitrage (CIA)
Eurodollar rate = 8.00 % per annum
Start
$1,000,000
►
x 1.04
-----
+
End
$1,040,000~LArbitrage
$1,044,638X Potential
Dollar money market
S =¥106.00/$
180 days
F180 = ¥ 103.50/$
Yen money market
¥ 106,000,000
> x 1.02 ------Euroyen rate = 4.00 % per annum
►
¥ 108,120,000
Uncovered Interest Arbitrage
■ A deviation from covered interest arbitrage is
uncovered interest arbitrage (UIA).
■ In this case, investors borrow in countries and
currencies exhibiting relatively low interest rates
and convert the proceed into currencies that offer
much higher interest rates.
■ The transaction is “uncovered” because the
investor does no sell the higher yielding currency
proceeds forward, choosing to remain uncovered
and accept the currency risk of exchanging the
higher yield currency into the lower yielding
currency at the end of the period.
Uncovered Interest Arbitrage
S*($/£) = r*US- r*UK
Interest Differential should be equal to
expected rate of change in spot rate
Uncovered Interest Arbitrage (UIA):
The Yen Carry Trade
Investors borrow yen at 0.40% per annum
Start
¥ 10,000,000 --------------- ►
x 1.004 --------------- ►
Japanese yen money market
360 days
S =¥120.00/$
End
¥ 10,040,000 Repay
¥10,500,000 Earn
¥ 460,000 Profit
t
S360 = ¥120.00/$
A
US dollar money market
$ 83,333,333
►
x 1.05 --------------- ►
Invest dollars at 5.00% per annum
$ 87,500,000
Interest Rates
and Exchange Rates
■ The following exhibit illustrates the conditions
necessary for equilibrium between interest rates
and exchange rates.
■ The disequilibrium situation, denoted by point U,
is located off the interest rate parity line.
■ However, the situation represented by point U is
unstable because all investors have an incentive
to execute the same covered interest arbitrage,
which is virtually risk-free.
Interest Rate Parity (IRP) and Equilibrium
Percentage premium on
foreign currency (¥)
Percent difference between foreign (¥)
-4
and domestic ($) interest rates
u
International Parity Conditions in Equilibrium
(Approximate Form)
Forward rate
as an unbiased
predictor ( E )
Purchasing
power
parity
(A)
Forecast change in
spot exchange rate
+4%
(yen strengthens)
/
Forward premium
on foreign currency
+4%
(yen strengthens)
\
Interest
rate
parity (
D)
Forecast difference
in rates of inflation
-4 %
International
Fisher Effect
(C)
B
Difference in nominal
interest rates
-4 %
(less in Japan)
(less in Japan)
/
Fisher
effect
(B)
Forward Rate as an Unbiased Predictor for
Future Spot Rate
Exchange rate
t1
t2
t3
t4
S1
t
1
t
2
t
3
t
4
►
Illustration 1
The following are the quotes available at the market:
Spot $ / € 0.8775 / 0.8777
3 months Forward 0.0015 / 0.0010
3 months interest rates are: $ 2.25/2.50% per annum; €
3.50/3.75% per annum
Verify whether there is any scope for covered interest
arbitrage. What should be the amount borrowed to
make an arbitrage profit of $ 1000, if there is scope for
arbitrage.
Illustration 2
A FII invested in Indian capital market on December
01, 2000. When the Mumbai stock exchange sensex was
quoting at 3800. The rupee-dollar spot exchange rate at
that time was Rs./$ 46.30 / 33. The FII sold the
investment on November 30, 2001. When Sensex was
quoting at 3250, to take back the amount in dollars.
The spot rate quoted on November 30, 2001 was Rs./$
48.02/05. Inflation rate in India was 6%, and in US was
2.5% during the same period. Compute nominal and
real rate of return to FII. Compute the real return to
an Indian investor who invested Rs.100,000 in the
capital market for the same period.
Illustration 2
A FII invested in Indian capital market on December
01, 2000, $1000. The rupee-dollar spot exchange rate at
that time was 46.30. The FII sold the investment on
November 30, 2001 forRs 58000. The spot rate quoted
on November 30, 2001 was Rs./$ 48.02. Inflation rate in
US was 2.5% during the same period. Compute
nominal and real rate of return to FII.