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The Forward Currency Market and International Financial Arbitrage. Why Exchange Rates Change? 2 theories Purchasing Power Parity Theory (PPP)
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Why Exchange Rates Change? 2 theories
Data (2003) : Big Mac: US =$2.71 Japan: Yen 262 (local currency), $2.19 (in dollars); Implied PPP of the $: 96.7; Actual Dollar Exchange Rates= Yen120/$; Under(-)/Over(+) valuation against the $.
Hedging and Speculating
There are a number of instruments that can be used to hedge foreign exchange risk.
Foreign Exchange Transactions
In general, there are five main groups of transactions: spot transactions; forward transactions; futures; swaps, and options (derivatives – contracts that derive their value from some underlying asset – in this case, the asset is currency). All these instruments are used to manage foreign exchange risk or take speculative positions on currency movements.
These notes do not cover swaps and derivates (Chapter 5).
(b) If the currency is expected to depreciate in the future, the forward rate is priced lower than the spot rate and the rate contains a discount (-).
Thus, a premium or discount simply denotes the expected direction of the forward rate in relation to the spot rate.
N = 3 months here
(4.1) (1+R) = (1+R*)(F/S)
This may be written as the following equilibrium condition
(4.2) F” = F where F” is the interest parity forward consistent with CIA equilibrium given by
(4.3) F” = S[1+R]/1+R*. From this two forms of CIP or CIA can be obtained from (4.1) by solving for the forward premium (discount), p = (F – S)/S; a precise form and a crude form.
(4.4) ρ = (R-R*)/(1+ R) --- precise form
The condition can be rewritten, and with a slight approximation, yields
(4.5) R - R* = (F-S)/S. -- crude form that assumes R*(F – S)/S is so small that it can be ignored.
Recall: Individuals who save supply loanable funds. Those who borrow demand loanable funds.
Assumptions required for CIA to be valid:
In the real world, most of these assumptions are violated and thus affecting the empirical validity of the theory.
F” = S[1+R]/1+R* -> CIP or CIA equilibrium
Domestic investor’s arbitrage
(capital outflows from domestic currency)
Foreign investor’s arbitrage
(Capital inflows into foreign
1ST: UK investor: Increase in the supply of pounds(= increase in thedemand for dollars ) ↓ S : ($/₤₤ depreciation; $ appreciation )
2nd: UK Investor: Thedemand for pounds rises (= increase in the supply of pounds) and henceF will increase, ₤ appreciation, $ depreciation
3rd: UK Money Mkt: The supply of pounds will fall (=decrease in the demand for dollars), their prices (P*) falls but R* rises
4th: US Money Mkt: The supply of dollars increases (= increase in demand for pounds), hence prices (P) will rise and Rfalls
Note: (a) The 1st and 2nd changes in the FX result in a fall in ↑(F/S) ↑F/↓S
(b) Changes in the 3rd and 4th involve money markets in both countries so that interest differentials widen, ↓ BECAUSE(↓ R – ↑R*)
All these mean that CIA equilibrium is re-established:
Position of a US investor at the Start: (1+ R) > F/S (1 + R*)
(1+ R) ↓ < ↑ F/S (1 + R* ↑) → (1+ R) = F/S (1 + R*)
[CIP disequilibrium at Point B] →[CIP equilibrium along 45-degree line]
1st: Increase in the supply of pounds(= increase in thedemand for dollars )
↓ S : ($/₤ ₤ depreciation; $ appreciation )
NOTE: stated as ($/₤): an ↑ is a ₤ appreciation
2nd: UK Investor: Thedemand for pounds rises (= increase in the supply of pounds)
and henceF will increase, ₤ appreciation, $ depreciation
3rd:UK Money Mkt: The supply of pounds will fall (=decrease in the demand for dollars),
their prices (P*) falls but R* rises
4th:US Money Mkt: The supply of dollars increases (= increase in demand for pounds),
hence prices (P) will rise and R falls.
(4.1): (1+R) = Se/S (1+R*). We can solve for both the exact version and an approximate version:
(4.2): (Se+1–S)/S. = (R-R*)/(1+R) ---- exact version
(4.3): (Se+1–S)/S = (R –R*) ------- approximate version
Can solve (4.1) for
(4.4): UIP: Se+1 = S[1+R]/[1+R*]. -- Uncovered Transaction
Compare with CIP: F’= S[1+R]/[1+R*].- Covered transaction
R – R* = (Se+1 – S)/S --- approximate version
R – R* ≠ (Se+1 – S)/S, the risk neutral agents move their uncovered funds across financial markets till they equalize.
Using ρ to denote risk premium, the UIP condition can be rewritten as:
(F-S)/S = R-R* = (Se+1–S)/S.
F = Se+1.
On Friday, April 11, 2003, a Swiss futures contract with an expiration on the 3rd Wednesday, June 2003 opened at 0.7182 USD/CHF and settled at 0.7213 USD/CHF. The rate hit a high of 0.7239 and a low of 0.7170 for the day, compared to a lifetime high and low of 0.7577 and 0.5940, respectively. There was a 0.0020 USD/CHF increase from Thursday’s settle price to Friday’s settle price.
In the market for CHF futures, there are approximately 2,570 contracts bought and sold per day, with 12,408 contracts bought and sold on Friday April 11, 2003. In the entire Chicago Mercantile Exchange, there are 37,292 CHF futures contracts open. Though there was activity in 12,408 contracts Friday, the net change in number of open contracts was only 1.721 (interest in CHF futures increased by 1,721 contracts).