Chapter 6
Arbitrage: the act of simultaneously buying and selling the same or equivalent assets or
commodities for the purpose of making certain guaranteed profits.
IRP: F = S ( (1+i$/ 1+ieu)
Law of one price:
IRP can be derived from a arbitrage portfolio which involves no net investment as well as no
risk and then requiring that such a portfolio should nog generate any net cash flow in
equilibrium.
1. Borrow in US
2. Lend in the UK
3. Sell the pound receivable forward
4. Net cash flow
Arbitrage opportunity last only for a short while. As soon as deviations from IRP are detected
traders will carry out transactions and IRP will be restored quite quickly.
S = ((1+ip) /( 1 +i$ )) * F
This equation shows that the forward exchange rate, the spot exchange rate depends on
relative interest rates. An increase in the US interest rate will lead to a higher foreign
exchange value of the dollar. Higher interest rate will attract capital to the Us increasing the
demand for dollars -> lower the foreign exchange value of the dollar.
Under certain conditions the forward exchange rate can be viewed as thee xpected futures
pot exchange rate conditional on all relevant information being available now
F= E (St+1 | It)
Where S t+1 is the future sport rate when the forward contract matures and It denotes the
set of information currently available. When we combine the 2 you get the equation:
When forward exchange rat eF is replaced by the expected future spot exchange rate we
obtain:
Uncovered interest parity: the interest rate differential between a pair of countries is
(approximately) equal to the expected rate of change in the exchange rate.
Currency trade: buying a high-yielding currency and funding it with a low-yielding currency
without any hedging.
IRP may not hold because of transaction costs and capital controls. Transaction costs do
exists, interest rates at which we borrow tend to be higher than interest rates against we
lend. Likewise, there exist bidd-ask spreads in the foreign exchange market. The arbitrager
has to buy foreign exchanges at the higher ask price and sell them at the lower bid price.
Because of spreads, arbitrage profits from each dollar borrowed may become no positive:
(F / S) (1 +I ) – (1 + I ) < 0
IF the arbitrage profit turns negative because of transaction costs, the current deviation
from IRP does not represent a profitable arbitrage opportunity. The IRP in 6.5 can be viewed
as included within a band around it, and only IRP outside the band such as point c represent
,profitable arbitrage opportunities. The wide of this band depend on the size of transaction
costs.
Another reason for deviations from IRP is capital controls imposed by the government.
Governments sometimes restrict capital flows inbound or outbound by jawboning, taxes or
bans.
Otani and Tiwari, investigated the effect of capital controls on IRP deviations, they computed
deviations from interest rate parity (DIRP) as follows:
DIRP = ((1 + iyen) S / (1 _i$) F) -1
Iyen= interest rate on three month gensaki bonds
I$= interest rate on three month euro-dollar deposits
S= yen/dollar spot exchange rate in Tokyo
F= yen/ dollar three-month forward exchange rate in Tokyo
Purchasing Power Parity: exchange rate between currencies of two countries should be
equal to the ratio of the countries’ price levels.
S = P$’/Ppound
S is the dollar price for 1 pound. PPP implies that if the standard commodity basket costs
$225 in US and 150pound in UK the exchange rate would be 225/150=1.5
PPP is the manifestation of the law of one price applied to the standard consumption basket.
Relative PPP = PPP relationship is presented in the rate of change form.
E=
E is the rate of change in the exchange rate. = pi –pi
If PPP does not hold, changes in nominal exchange rates cause changes in the real exchange
rates, affecting the international competitive positions of countries. This in turn would affect
countries’ Trade balances.
The real exchange rate q which measures deviations from PPP can be defined as
Q= 1+pi/ 1+e (1 + pi)
Q= 1 competitiveness of the domestic country unaltered
Q < 1 competitiveness of the domestic country improves
Q > 1 competitiveness of the domestic country deteriorates.
Regulations make it very difficult to carry out cross border arbitrage, resulting in a wide price
disparity for these products. Also for non tradable products like hair products, the price
difference can be big. The price disparity for a hamburger is substantially less.
As long as non tradable exists. PPP will not hold in absolute version. If PPP holds for
tradables and the relative prices between tradables and nontradables are maintained then
ppp can hold in its relative version. However this is not very likely.
PPP can still be useful, PPP can be used as a benchmark in deciding if a country’s currency is
undervalued or overvalued against others. Thereby, one can often make more meaningful
international comparisons of economic data using PPP determined rather than market
determined exchange rates.
Fisher effect: an increase (decrease) in the expected inflation rate in a country will cause a
proportionate increase (decrease) in the interest rate in the country.
I = p + E(pi)
P denotes equilibrium real interest rate.
, The fisher effect implies that the expected inflation rate is the difference between the
nominal and real interest rates in each country. When we substitute that into the relative
PPP we obtain the international Fisher Effect:
E=I–I
The nominal interest rate differential reflects the expected change in exchange rate.
Forward expectations parity: when the fisher effect is combined with IRP:
(F-S)/S
FEP states that any forward premium or discount is equal to the expected change in the
exchange rate when investors are risk-neutral, forward parity will hold as long as the foreign
exchange market is informationally efficient. Otherwise it need not hold even if the market is
efficient.
Exchange forecast can be done using 3 techniques
1. Efficient market approach
2. Fundamental approach
3. Technical approach
Financial market hypothesis: the current asset price fully reflect all the available and
relevant information.
If foreign exchange markets are efficient, than the exchange rate has already reflected all
relevant information, such as money supplies, inflation rates, trade balances and output
growth. The exchange rate will then change only when the market receives new information.
News is unpredictable -> exchange rate will change randomly over time. Incremental
changes in exchange rate will be independent of the past history of the exchange rate. If the
exchange rate follows a random walk, the future exchange rate is expected to be the same
as the current exchange rate.
Random walk hypothesis: suggests that today’s exchange rate is the best predictor of
tomorrow’s exchange rate.
The future exchange rate based on available information if the foreign exchange markets are
efficient: F = E( s t+1 | It)
Predicting the exchange rates using efficient market approach has 2 advantages:
1. The efficient market approach is based on market-determined prices it is costless to
generate forecasts. Both the current spot and forward exchange rate are pubic
information. As such everyone has access to it.
2. Given the efficiency of foreign exchange markets, it is difficult to outperform the
market-based forecasts unless the forecaster has access to private information that is
not yet reflected in the current exchange rate.
Fundamental approach: uses various models, suggests the exchange rate is determined by
three independent variables: 1 relative money supplies, 2 relative velocity of monies 3
relative national outputs. One can thus formulate the monetary approach:
S=
3 steps:
1. Estimation of the structural model like the equation to determine the numerical
values for the parameters such as alpha and beta
Arbitrage: the act of simultaneously buying and selling the same or equivalent assets or
commodities for the purpose of making certain guaranteed profits.
IRP: F = S ( (1+i$/ 1+ieu)
Law of one price:
IRP can be derived from a arbitrage portfolio which involves no net investment as well as no
risk and then requiring that such a portfolio should nog generate any net cash flow in
equilibrium.
1. Borrow in US
2. Lend in the UK
3. Sell the pound receivable forward
4. Net cash flow
Arbitrage opportunity last only for a short while. As soon as deviations from IRP are detected
traders will carry out transactions and IRP will be restored quite quickly.
S = ((1+ip) /( 1 +i$ )) * F
This equation shows that the forward exchange rate, the spot exchange rate depends on
relative interest rates. An increase in the US interest rate will lead to a higher foreign
exchange value of the dollar. Higher interest rate will attract capital to the Us increasing the
demand for dollars -> lower the foreign exchange value of the dollar.
Under certain conditions the forward exchange rate can be viewed as thee xpected futures
pot exchange rate conditional on all relevant information being available now
F= E (St+1 | It)
Where S t+1 is the future sport rate when the forward contract matures and It denotes the
set of information currently available. When we combine the 2 you get the equation:
When forward exchange rat eF is replaced by the expected future spot exchange rate we
obtain:
Uncovered interest parity: the interest rate differential between a pair of countries is
(approximately) equal to the expected rate of change in the exchange rate.
Currency trade: buying a high-yielding currency and funding it with a low-yielding currency
without any hedging.
IRP may not hold because of transaction costs and capital controls. Transaction costs do
exists, interest rates at which we borrow tend to be higher than interest rates against we
lend. Likewise, there exist bidd-ask spreads in the foreign exchange market. The arbitrager
has to buy foreign exchanges at the higher ask price and sell them at the lower bid price.
Because of spreads, arbitrage profits from each dollar borrowed may become no positive:
(F / S) (1 +I ) – (1 + I ) < 0
IF the arbitrage profit turns negative because of transaction costs, the current deviation
from IRP does not represent a profitable arbitrage opportunity. The IRP in 6.5 can be viewed
as included within a band around it, and only IRP outside the band such as point c represent
,profitable arbitrage opportunities. The wide of this band depend on the size of transaction
costs.
Another reason for deviations from IRP is capital controls imposed by the government.
Governments sometimes restrict capital flows inbound or outbound by jawboning, taxes or
bans.
Otani and Tiwari, investigated the effect of capital controls on IRP deviations, they computed
deviations from interest rate parity (DIRP) as follows:
DIRP = ((1 + iyen) S / (1 _i$) F) -1
Iyen= interest rate on three month gensaki bonds
I$= interest rate on three month euro-dollar deposits
S= yen/dollar spot exchange rate in Tokyo
F= yen/ dollar three-month forward exchange rate in Tokyo
Purchasing Power Parity: exchange rate between currencies of two countries should be
equal to the ratio of the countries’ price levels.
S = P$’/Ppound
S is the dollar price for 1 pound. PPP implies that if the standard commodity basket costs
$225 in US and 150pound in UK the exchange rate would be 225/150=1.5
PPP is the manifestation of the law of one price applied to the standard consumption basket.
Relative PPP = PPP relationship is presented in the rate of change form.
E=
E is the rate of change in the exchange rate. = pi –pi
If PPP does not hold, changes in nominal exchange rates cause changes in the real exchange
rates, affecting the international competitive positions of countries. This in turn would affect
countries’ Trade balances.
The real exchange rate q which measures deviations from PPP can be defined as
Q= 1+pi/ 1+e (1 + pi)
Q= 1 competitiveness of the domestic country unaltered
Q < 1 competitiveness of the domestic country improves
Q > 1 competitiveness of the domestic country deteriorates.
Regulations make it very difficult to carry out cross border arbitrage, resulting in a wide price
disparity for these products. Also for non tradable products like hair products, the price
difference can be big. The price disparity for a hamburger is substantially less.
As long as non tradable exists. PPP will not hold in absolute version. If PPP holds for
tradables and the relative prices between tradables and nontradables are maintained then
ppp can hold in its relative version. However this is not very likely.
PPP can still be useful, PPP can be used as a benchmark in deciding if a country’s currency is
undervalued or overvalued against others. Thereby, one can often make more meaningful
international comparisons of economic data using PPP determined rather than market
determined exchange rates.
Fisher effect: an increase (decrease) in the expected inflation rate in a country will cause a
proportionate increase (decrease) in the interest rate in the country.
I = p + E(pi)
P denotes equilibrium real interest rate.
, The fisher effect implies that the expected inflation rate is the difference between the
nominal and real interest rates in each country. When we substitute that into the relative
PPP we obtain the international Fisher Effect:
E=I–I
The nominal interest rate differential reflects the expected change in exchange rate.
Forward expectations parity: when the fisher effect is combined with IRP:
(F-S)/S
FEP states that any forward premium or discount is equal to the expected change in the
exchange rate when investors are risk-neutral, forward parity will hold as long as the foreign
exchange market is informationally efficient. Otherwise it need not hold even if the market is
efficient.
Exchange forecast can be done using 3 techniques
1. Efficient market approach
2. Fundamental approach
3. Technical approach
Financial market hypothesis: the current asset price fully reflect all the available and
relevant information.
If foreign exchange markets are efficient, than the exchange rate has already reflected all
relevant information, such as money supplies, inflation rates, trade balances and output
growth. The exchange rate will then change only when the market receives new information.
News is unpredictable -> exchange rate will change randomly over time. Incremental
changes in exchange rate will be independent of the past history of the exchange rate. If the
exchange rate follows a random walk, the future exchange rate is expected to be the same
as the current exchange rate.
Random walk hypothesis: suggests that today’s exchange rate is the best predictor of
tomorrow’s exchange rate.
The future exchange rate based on available information if the foreign exchange markets are
efficient: F = E( s t+1 | It)
Predicting the exchange rates using efficient market approach has 2 advantages:
1. The efficient market approach is based on market-determined prices it is costless to
generate forecasts. Both the current spot and forward exchange rate are pubic
information. As such everyone has access to it.
2. Given the efficiency of foreign exchange markets, it is difficult to outperform the
market-based forecasts unless the forecaster has access to private information that is
not yet reflected in the current exchange rate.
Fundamental approach: uses various models, suggests the exchange rate is determined by
three independent variables: 1 relative money supplies, 2 relative velocity of monies 3
relative national outputs. One can thus formulate the monetary approach:
S=
3 steps:
1. Estimation of the structural model like the equation to determine the numerical
values for the parameters such as alpha and beta
