The Foreign Exchange Market. Explain how the foreign exchange rate reflects the demand and supply of goods, services, and assets, and the other flows that make up the balance of payments. Explain geographic arbitrage, triangular arbitrage, and intertemporal arbitrage.
** -- next week
Currency Percent in: 1989 1992 1995 1998 2001
U.S. dollar 90% 82.0% 83.3% 87.3% 90.4% **
Deusche mark 27 39.6 36.1 30.1
Japanese yen 27 23.4 24.1 20.2 22.7
British pound 15 13.6 9.4 11.0 13.2
Swiss franc 10 8.4 7.3 7.1 6.1
French franc 2 3.8 7.9 5.1
Canadian dollar 1 3.3 3.4 3.6 4.5
Australian dollar 2 2.5 2.7 3.1 4.2
Euro - - - - 37.6
All others 26 23.4 25.8 32.5 21.3
Total 200% 200% 200% 200% 200%
Source: BIS (2001), Central Bank Survey of Foreign Exchange and Derivatives Market Activity, Basle: BIS
**Note the role of the $ as a “vehicle currency.”
1989 1992 1995 1998 2001
Spot Transactions 317 394 494 568 387
Forward Transactions 27 58 97 128 131
Foreign Exchange Swaps 190 190 324 546 734
Total Turnover1 590 820 1,190 1,490 1,210
1 Total is greater than sum of the three categories because of gaps in reporting.
Source: BIS (2001), Central Bank Survey of Foreign Exchange and Derivatives Market Activity, Basle: Bank for International Settlements
NEW YORK: The zloty (Z) is trading for 3.7826 (Z/$) in New York.
The cross-rate in London is:
=(Z/£)/(S/£) = Z/£ *£/S = (Z/S)= 6.5492/1.7936 =
3.6514 (Z/$) in London Versus 3.7826 (Z/$) in New York.
Hence, an arbitrage opportunity exists, i.e. profitableTriangular Arbitrage: Example
Buy $1.7936 with £1
Start with £1
Buy Z6.7845 with $s
Purchase £s in London using Zs
Purchase Zs in New York
END: Purchase £1.0359 in London using Z6.7845 purchased in New York
Profit = £1.0359 - £1.00 = £0.0359
Spatial Arbitrage refers to buying a currency in one market and selling it in another.
Note:e =$/MXP: a ↑e ≈ depreciation of the $ (appreciation of the MXP)
(a) Price of foreign currency in units of domestic currency, $/MXP =e OR
(b) price of domestic currency in terms of foreign currency, MXP/$ =1/e
Mexicans supply more pesos because they demand dollars
[n(n – 1)]/2 different foreign exchange markets.
$wt+1 = $100(1 + rUS ) =$100 +$100* rUS
given that rUS is the return on U.S. assets.
Decision to Invest at Home or Abroad
£wt+1 = ($100/et)(1 + rUK).
£wt+1 = £wt+1(ftt+1) = ($100/et)(1 + rUK )(ftt+1 ).
Now you can compare this dollar value of the British investment to the
dollar value of the U.S. investment:
US → $100(1 + rUS )versus($100/et)(1 + rUK)(ftt+1) ←[UK].
Suppose $100(1 + ↑rUS)< ↓[($100/ ↑et)(1 + ↓rUK)(↓ftt+1)]. With unrestricted
international asset trade, there will be international investment
arbitrage until the inequality becomes an equality, or when
$100(1 + rUS) = ($100/et)(1 + rUK)(ftt+1) ****
Adjustment: (a) UK investors stay home & US investors supply $s to the
US money market and demand £s . The effect is to increase e ($depreciation,
£ appreciation). (b) US investors need to sell £s forward next year and
demand $ (increase in £s; increase demand for $s) – cause ↓ftt+1). Both (a)
and (b) reduce the RHS until **** is established. Note that the interest rates
are affected too (↑rUS as less funds are available in the US money market,
while ↓rUK as more funds are available in the UK money market).
Idea: 4 markets are involved in the adjustment process; UK & US money markets (↑rUS & ↓rUK); Forward & Spot Markets (↓ftt+1 & ↑et)
The relationship $100(1 + rUS) = ($100/et)(1 + rUK)(ftt+1) can
be rearranged to yield the interest parity condition. Dividing
each side by $100 gives us: (1 + r) = (1/et)(1 + r*)(ftt+1).
Dividing each side by (1 + rUS) and multiplying each side by et
et = [(1 + rUK)/(1 + rUS)](ftt+1). Let [(1 + rUK)/(1 + rUS)] =μ
Thus, et = μ ftt+1. This states that the relationship of today’s
exchange rate (et) to the forward rate (ftt+1) is a factor μwhich is
a ratio of respective interest rates (or rates of return). This is
known as CIP or CIA because investors can hedge against
future changes in et by using the forward rate ftt+1. It is
“covered” because the use of the forward market eliminates
exchange risk. In the absence of forward market rates, hedging
is not possible. Our best estimate of the future value of the
spot rate uses the expected (Et ) rate, Et(et+1).
When there is no forward exchange market, investors must compare
returns across countries using their expectations of the spot rate one year
from now, denoted as Et(et+1). The choice is thus:
US → $100(1 + rUS )versus($100/et)(1 + rUK)(Et (et+1)) ←[UK].
Suppose $100(1 + ↑rUS)< ↓[($100/ ↑et)(1 + ↓rUK)(↓ftt+1)]. Intertemporal
arbitrage will still occur if the difference between the right-hand and left-
hand sides of the relationship is big enough to overcome exchange rate risk.
Arbitrage will occur until the inequality becomes an equality, or when
$100(1 + rUS) ≈ ($100/et)(1 + rUK)(Et (et+1)) ****
Simplifying as before yields:
et = [(1 + rUK)/(1 + rUS)] (Et (et+1)). This is known as the uncovered
Interest parity condition (UIP) or UNCIA or simply as the interest parity
condition. Let [(1 + rUK)/(1 + rUS)] =μ
Thus, et = μ Et (et+1).
This states that unlike before (when we had the forward rate), now the
future exchange rate in the face of our ignorance, depends on expectations
of every investor engaged in buying or selling financial assets and currencies! In a global economy, different cultures, different political
conditions etc and any other idiotic stuff impacts the exchange rate!
(rUS – rUK ) ≈ (Et (et+1) – et)/et = Et(Δe)/et [**)
where the Δ stands for “the change in.”
If Et(Δe)/et >0, there is expected appreciation of the foreign currency (depreciation of the home currency):
Et(Δe)/et =$1.80/£ -$1.60/£]/$1.60/£ *100 = +12.5%. The £ has appreciated by 12.5% against the $. Thus, it pays to invest Abroad.
2. If Et(Δe)/et<0, there is expected depreciation of the foreign currency
Et(Δe)/et=$1.60/£ -$1.80/£]/$1.80/£ *100 =-12.5%. The £ has depreciated by 12.5% against the $. It doesn’t pay to invest abroad.
Numerical Example [**]
Suppose that the interest rate in the United States is higher at 12%
per year (rUS) than the interest rate on British assets at 7% (rUK ).
Suppose also that economic conditions and policies in the two
countries lead investors to expect that the exchange rate will be
$2 dollars = £1, one year from now, so that Et (et+1 )= $2/£1=2.
Applying the simplified equation,
(rUS – rUK ) ≈ (Et (et+1) – et)/et = Et(Δe)/et
where Δe =(et+1- et)
implies that the dollar is expected to fall by 5 percent over the
percent implies that the current spot rate must be about
($2.00 x0.05) = 10 cents) so ($2.00- 0.10cents)= $1.90.
Intertemporal arbitrage links all future exchange rates according
to the interest parity condition.
For example, if the rates of return in the United States and
Britain are expected to be rUS and rUK , respectively, for the
next two periods, then in the case of perfect arbitrage, the
following two-period interest parity condition will hold:
$100(1 + r)2 = ($100/et)(1 + r*)2 Et (et+2)
The spot rate is thus a function of the expected exchange rate
two periods from now:
et = Et (et+2)[(1 + rUK)/(1 + rUS)]2.
In general, for n periods into the future:
et = Et (et+n)[(1 + rUK)/(1 + rUS)]n
Note: ↑e – depreciation of $
↓e – appreciation of the £
If people set their expectations rationally they will make
use of all relevant information to set their expectations,
which consists of:
Economists define items 1 and 2 as the information set.
The expected exchange rate at time t + n (n years in the
future), given the current information set Ωt is written as:
Et (et+n | Ωt ).
The information set Ωt of course keeps changing as time passes
as news arrives. The expected exchange rate for the period
t + n at time t will generally not be the same as the expected
exchange rate for period t + n at t +1 because Ωt ≠ Ωt+1.
That is, in general: Et [(et+n)* Ωt ] ≠ Et+1[(et+n)* Ωt+1].
The spot rate will deviate from its long-run time path whenever news
arrives. News is, by definition, unpredictable
Thus, the logical conclusion is that:
In general, when expectations are rationally set and the interest parity
condition holds (international investment is not restricted), future changes
in the exchange rates are unpredictable.
The exchange rate between just two currencies tells a firm little
about an economy’s competitive position in the global
Many government agencies and private financial firms compile
broader exchange rate measures that attempt to capture the
overall value of a country’s currency vis-a-vis many countries.
Effective exchange rates are weighted averages of sets of foreign exchange rates.
The U.S. Federal Reserve Bank compiles several effective
exchange rates, including the Broad Dollar Index, the Major
Currencies Dollar Index, and the Other Important Trading Partners Dollar Index.
Broad Major Other Trading
Canada 17.3 30.3 -
Euro Area 16.4 28.7 -
Japan 14.6 25.6 -
Mexico 8.6 - 19.9
China 6.6 - 15.3
U.K. 4.6 8.0 -
Taiwan 3.9 - 9.1
Korea 3.7 - 8.6
Singapore 3.1 - 7.2
Hong Kong 2.8 - 6.6
Malaysia 2.4 - 5.5
Brazil 1.9 - 4.4
Switzerland 1.8 - -
Other 12.3 4.2 23.4