Transcript Chapter 1

Chapter 4 Outline
A. Arbitrage and the Law of One Price
B. Key Terms
C. Theoretical Economic Relationships
D. Currency Forecasting
E. In real life, all calculations are handled by computer models.
Therefore the emphasis is on the Directional Analysis!
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4.A Arbitrage and the Law of One Price

Arbitrage – the simultaneous purchase and sale of the same assets
or commodities on different markets to profit from price
discrepancies

Law of One Price – in competitive markets, exchange-adjusted
prices of identical tradable goods and financial assets must be
within transaction costs of equality worldwide.

Absent market imperfections, arbitrage ensures that exchangeadjusted prices of identical traded goods follow the Law of One
Price.
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4.B Key Terms

Spot rate e0 – current exchange rate of currency

Forward rate f1 – exchange rate of currency on a specified future
date

Forward discount – the discount applied to a currency if the
forward rate is below the spot rate

Forward premium – the premium applied to a currency if the
forward rate is above the spot rate. Must be able to do!!!!!
Forward premium/discount =
f1 – e0
e0
x
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Forward
contract
number of days
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4.C Theoretical Economic Relationships (1)

In the absence of market imperfections, risk-adjusted expected returns on
financial assets in different markets should be equal.

Five key theoretical economic relationships result from arbitrage.
i.
Purchasing power parity (PPP) – for prices in two countries to be equal, the
exchange rate between the two countries must change by the difference between the
domestic and foreign rates of inflation.
ii.
Fisher effect (FE) – If expected real interest rates differ between the home and
foreign countries, capital will flow to the country with the higher real rate until the real
rates in both countries are equal and equilibrium is reached.
iii. International Fisher effect (IFE) – combines the conditions underlying PPP and FE;
if real interest rates differ between the home and foreign countries, capital will flow to
the country with the higher real rate until the exchange-adjusted returns are equal in
both countries and equilibrium is reached.
iv. Interest rate parity (IRP) – in an efficient market with no transaction costs, the
interest rate differential between two countries should approximate the forward
differential.
v.
Forward rates as unbiased predictors of future spot rates (UFR) – Equilibrium is
achieved when the forward differential equals the expected change in the spot rate.
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4.C Theoretical Economic Relationships (2)

Note: The equations presented in the discussions of the theoretical
economic relationships are “approximations” of formal equations.
For example, in the discussion of purchasing power parity, we
present the equilibrium state as achieved when
e1 – e0
e0
= ih – if
This equation is a commonly used and accepted approximation of
the following formal equation, which is presented and discussed in
the textbook.
et
e0
=
(1 + if)t
(1 + ih)t
The approximation equations are used to graphically illustrate each
theoretical economic relationship.
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4.C.i

Theoretical Economic Relationships:
Purchasing Power Parity (PPP) (4*)
Nominal exchange rate versus real exchange rate, continued
–
If changes in et are offset by changes in inflation between two
countries, et’ remains unchanged.
–
Thus, a change in et’ is equivalent to a deviation from PPP.
–
E.g., compute and compare changes in the real and nominal values of
the yen relative to the dollar (i.e., et and et’ = $/¥) from 1982 to 2006
1. et in 1982 (e0 = base year) = $1/¥249.05, et in 2006 (e25) = $1/¥116.34
2. CPIJapan in 1982 = 80.75, CPIJapan in 2006 = 97.72; if = 21%
3. CPIUS in 1982 = 56.06, CPIUS in 2006 = 117.07; ih = 109%
e25’ = $1/¥116.34
(1 + 21%)
(1 + 109%)
= $.004981
4. e0’ = $1/¥249.05 = $.004015.
5. Change in et’ = ($.004981 - $.004015) / $.004015 = 24%, meaning the yen
appreciated 24% against the dollar in real terms – that is, the real dollar prices of
Japanese exports rose by 24%.
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4.C.i

Theoretical Economic Relationships:
Purchasing Power Parity (PPP) (5*)
Nominal exchange rate versus real exchange rate, continued
–
E.g., compute and compare the changes in the real and nominal
values of the yen relative to the dollar from 1982 to 2006, continued
6. Change in et = (($1/¥116.34) – ($1/¥249.05)) / ($1/¥249.05) = 114%,
meaning the nominal dollar prices of Japanese exports rose by 114% over
the period.
7. Difference between et and et’ = 114% - 24% = 90%.
8. Conclusion: Inflation differentials justify only a 90% rise in et . Thus, the
increase in et’ causes a deviation from PPP by 24%.
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4.C.ii
Theoretical Economic Relationships:
Fisher Effect (FE) (1)

The nominal interest rate compensates lenders for the erosion of future
purchasing power of dollars loaned.

Because virtually all financial contracts are stated in nominal terms, the
real interest rate a must be adjusted to reflect expected inflation.

FE states that the nominal interest rate r = a required rate of return a and
an inflation premium equal to expected inflation i:
r = a + i + ai

Real returns are equalized across countries through arbitrage; i.e.,
over time, ah = af.

If expected ah ≠ af, capital would flow to the country with the higher real
rate until ah = af and equilibrium is reached.

In equilibrium with no government interference,
rh - rf = ih - if
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4.C.iii Theoretical Economic Relationships:
International Fisher Effect (IFE) (1)

IFE combines the conditions underlying PPP and FE.

Thus, in equilibrium,
rh – rf =
ē1 – e0
e0

If rh ≠ rf, capital will flow from the country with the lower expected
return to the country with the higher expected return, causing e0 to
adjust by the interest rate differential such that rh = rf and a new
equilibrium is established.

Interest rate differentials are thus unbiased (while not necessarily
accurate) predictors of ē1.
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4.C.iv Theoretical Economic Relationships:
Interest Rate Parity (IRP) (2*)

Covered interest arbitrage (CIA) – profiting from interest rate
differentials in rh and rf (when IRP does not hold). E.g.:
– rUK = 12%, rUS = 7%
– e0 = $/£ = $1.95, f1 = $1.88
– rUK – rUS = 5%
– (f1 – e0)/e0 = ($1.88 - $1.95)/$1.95 = -3.6% = forward discount
– rUK – rUS ≠ (f1 – e0)/e0
– Funds will flow from U.S. to U.K. to exploit profit opportunity (CIA)
– As pounds are bought spot and sold forward, e0 will increase and f1 will
decrease, increasing the forward discount
– As funds flow from U.S. to U.K., rUS will increase and rUK will decrease.
– CIA will continue until IRP is achieved.
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4.C.v
Theoretical Economic Relationships:
Forward Rate and Future Spot Rate (1)

Absent government intervention, e0 and f1 are heavily influenced by
current expectations of future events.

The two rates move in tandem, linked by interest differentials.

E.g., the pound is expected to depreciate.
– Holders of pounds sell pounds forward.
– Sterling-area dollar earners reduce sales of dollars in the forward
market.
– f1 will decrease.
– Banks will sell e0 to offset f1 positions.
– Earners of pounds will accelerate their collection and conversion of
pounds.

Thus, pressure from the forward market is transmitted to the spot
market, and vice versa.
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4.C.v
Theoretical Economic Relationships:
Forward Rate and Future Spot Rate (2)

Equilibrium is achieved when the forward differential equals the
expected change in e0 (ē1).

Thus, in equilibrium,
f1 – e0
e0
ē1 – e0
=
e0

In equilibrium, incentives to buy or sell currency forward do not exist.

ft should reflect ēt on the date of settlement of the forward contract.

Thus, the unbiased forward rate (UFR) condition is
ft =
ēt
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4.D Currency Forecasting (1)

Requirements for successful currency forecasting
– Exclusive use of a superior forecasting model
– Consistent access to information
– Exploiting small, temporary deviations from equilibrium
– Predicting the nature of government intervention in the foreign exchange
market

Market-based forecasts can be obtained by extracting the
predictions embodied in interest and forward rates.
– f1 is an unbiased estimate of ē1 (forecasting usefulness limited to one
year given the general absence of longer-term forward contracts)
– Interest rate differentials can be used as predictors beyond one year.
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4.D Currency Forecasting (2)

Model-based forecasts are based on technical and/or fundamental
analysis
– Fundamental analysis involves examining macroeconomic variables and
policies likely to influence a currency’s prospects.
– Technical analysis focuses exclusively on past price and volume
movements to identify price patterns.
– Model-based forecasts are inconsistent with the efficient market
hypothesis – because markets are forward looking, exchange rates will
fluctuate randomly as market participants assess and react to news.

Exchange controls and restrictions on imports and capital flows often
mask the true pressures on a currency to devalue.
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