3. ARBITRAGE AND THE LAW OF ONE PRICE
FIVE KEY THEORETICAL RELATIONSHIPS AMONG SPOT RATE, FORWARD RATES,
INFLATION RATES, AND INTEREST RATES
Expected percentage
change of spot exchange
rate of foreign currency
- 3%
Expected inflation rate
differential
+ 3%
Forward discount or
premium on foreign
currency
- 3%
Interest rate
differential
+ 3%
FE
IFE
UFR
PPP
IRP
7. ABSOLUTE PPP
• Extension of law of one price to a standard commodity basket:
purchasing power parity
• Absolute PPP states that the spot exchange rate is determined by the relative
prices of similar basket of goods
• Absolute PPP examines price levels
– Apply the law of one price to a standard commodity basket with price P£ and PUS
7
𝑆 =
𝑃$
𝑃£
14. RELATIVE PURCHASING POWER PARITY
The idea is that the relative change in prices between countries over a
period of times determines the change in exchange rates
– if the spot rate between 2 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 rate. Higher
inflation currency should depreciate
14
𝒆𝒕
𝒆𝟎
=
(𝟏 + 𝒊𝒉)𝒕
(𝟏 + 𝒊𝒇)𝒕
∆e =
𝒊𝒉 − 𝒊𝒇
𝟏 + 𝒊𝒇
= 𝒊𝒉 − 𝒊𝒇
15. RELATIVE PURCHASING POWER PARITY
Example: Price of a product is $100 in the US and ¥100 in Japan. For simplicity also
assume that exchange rate is $1.00/¥. Now suppose that due to inflation product’s price
increase to $110 in the US and to ¥105 in Japan (10% inflation in the US and 5% in
Japan). At the same time the new exchange rate is $1.02/¥. What are the implications of
these in terms of PPP?
Arbitrage is possible: Japanese product is relatively cheaper. A US based person now
needs $110 for the product if purchased in the US and only ¥105 x $1.02/¥ = $107.10 if
purchased in Japan. Therefore buy it in Japan spending $107.10 in dollars for purchase
and sell it in the US for $110. Your profit is $2.90. If exchange rate had changed to
$1.05/¥ (representing 5% inflation difference) then $ cost would be ¥105 x $1.05/¥ =
~$110.00
15
18. DOES PPP HOLD?
Empirical tests of both relative and absolute purchasing power parity show
that for the most part, PPP is not accurate in predicting future exchange rates
Reasons:
1. Price indexes not include non tradable goods
2. Goods baskets are not similar
3. Differential inflation rates might be inaccurate
4. Test periods are subject to government interventions
Two general conclusions can be drawn from the tests:
– PPP holds up well over the very long term but is poor for short term
estimates
– The theory holds better for countries with relatively high rates of
inflation and underdeveloped capital markets
18
19. THE FISHER EFFECT
• Fisher condition in U.S. and France: €
(1 + r$(Real)) = (1 + r$) / (1 + i$)
(1 + r€(Real)) = (1 + r€) / (1 + i€)
• If real rates are equal, then the Fisher condition implies:
• The difference in interest rates is equal to the expected difference in
inflation rates
19
f
h
f
h
i
i
r
r
1
1
1
1
20. INTERNATIONAL FISHER EFFECT – IFE
The International Fisher Effect, or Fisher-open, states that the
spot exchange rate should change in an amount equal to but in the
opposite direction of the difference in interest rates between
countries
20
t
f
t
h
t
r
r
=
e
e
)
1
(
)
1
(
0
21. CURRENCY FORECATING
• Currency forecasting can lead to consistent profits only if the forecaster meets at least
one of the following four criteria.
– Has exclusive use of a superior forecasting model
– Has consistent access to information before other investors
– Exploits small, temporary deviations from equilibrium
– can predict the nature of government intervention in the foreign exchange
• As a general rule, in a fixed rate system, the forecaster must focus on the
governmental decision-making structure because the decision to devalue or revalue at
a given time is clearly political.
• In case of floating system, currency forecasting have the choice of using either
market or model-based forecasts, neither of which guarantees success.
21
23. FORECASTING EXCHANGE RATES: EFFICIENT MARKETS APPROACH
Financial markets are efficient if prices reflect all available and relevant
information.
− The efficient market hypothesis (Prof. Eugene Fama)
If this is true, exchange rates will only change when new information arrives,
thus:
St = E[St+1]
− The random walk hypothesis suggest that today’s ER is the best predictor of
tomorrow’s ER
Ft = E[St+1| It]
− Predicting exchange rates using the efficient markets approach is affordable and
is hard to beat.
24. FORECASTING EXCHANGE RATES: FUNDAMENTALAPPROACH
• Involves econometrics to develop models that use a variety of
explanatory variables. This involves three steps:
– Step 1: Estimate the structural model.
– Step 2: Estimate future parameter values.
– Step 3: Use the model to develop forecasts.
• The downside is that fundamental models do not work any
better than the forward rate model or the random walk model.
25. FORECASTING EXCHANGE RATES:
FUNDAMENTAL APPROACH
• S: natural logarithm of spot ER
• m-m*: natural logarithm of domestic/foreign money supply
• - *: natural logarithm of domestic/foreign velocity of money
• y-y*: natural logarithm of domestic/foreign output
• : random error term, with zero mean
• , : model parameter
)
(
)
(
)
( *
3
*
2
*
1 y
y
m
m
s
28. FORECASTING EXCHANGE RATES:
TECHNICAL APPROACH
• Technical analysis looks for patterns in the past behavior
of exchange rates.
• Clearly it is based upon the premise that history repeats
itself.
29. MOVING AVERAGE CROSSOVER RULE: GOLDEN CROSS vs DEATH CROSS
29
LMA: Long-term Moving Average SMA: Short-term Moving Average
31. PERFORMANCE OF THE FORECASTERS
• Forecasting is difficult, especially with regard to the future.
• As a whole, forecasters cannot do a better job of
forecasting future exchange rates than the forecast implied
by the forward rate.
• The founder of Forbes Magazine once said, “You can
make more money selling financial advice than
following it.”
32. Chapter 4 32
)
(
)
(
F
MAE
S
MAE
R
MAE(S): mean absolute forecast error of a forecasting service
MAE(F): mean absolute forecast error of the forward exchange rate as a predictor
i i
i A
P
N
MAE
1
33. Chapter 4 33
)
(
)
(
S
MSE
B
MSE
R
MSE(B): mean squared forecast error of a bank
MSE(S): mean squared forecast error of the spot exchange rate
MSE(B)<MSE(S): A bank provide more accurate forecast than spot ER, R<1
34. INVESTOR PSYCHOLOGYAND BANDWAGON EFFECTS
How are exchange rates influenced by investor psychology?
The bandwagon effect occurs when expectations on the part
of traders turn into self-fulfilling prophecies, and traders join
the bandwagon and move exchange rates based on group
expectations
• Governmental intervention can prevent the bandwagon from starting,
but is not always effective