The forward currency market and international financial arbitrage
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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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The Forward Currency Market and International Financial Arbitrage

Why Exchange Rates Change? 2 theories

  • Purchasing Power Parity Theory (PPP)

    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 $.

  • Exchange rates change (in the long-run) because the purchasing power of one currency increases (or decreases) relative to another currency. The Economist compares the price of a McDonald’s Big Mac hamburger in the US and in various countries in an annual survey. In 2003, the average price in the US was $2.71 while in Japan the burger cost the equivalent of $2.19 (Yen 262 in local currency and actual exchange rate, 120Yen/$ so that 262/120= $2.19). According to PPP, the Yen will over time, result in changes in the exchange rate between 2 currencies. In this case, the Yen is expected to appreciate against the $. The reason is that the implied PPP of the dollar is (120-96.7)/120 = -19 (undervalued). That is, the Yen is undervalued by 19% relative to the dollar.


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Why Exchange Rates Change? continued Arbitrage

  • Theory of Interest Rate Parity– the foreign exchange market is in equilibrium when the expected rates of return on deposits of any two currencies measured in the same currency are equal. If rates differ, there would be excess demands or supplies. Thus, changes in exchange rates can be inferred by differences in interest rates. Investors would move funds across political boundaries until rates are equalized.


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Foreign Exchange Transactions ArbitrageSpot Transactions

  • Daily exchange rates that are quoted in the WSJ and other sources are spot rates --- market rates that hold for transactions that take place on the “spot”

  • Foreign exchange transactions based on these rates are “spot transactions.” For example, getting pounds sterling from the bank by converting dollars, the teller used the spot rate and the transaction is a spot transaction.


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Sources of Risk Arbitrage

  • Transaction exposure: the risk that the domestic cost or proceeds of a transaction may change.

  • Translation exposure: (also known as accounting exposure) the risk that the translation of value of foreign-currency-denominated assets is affected by exchange rate changes.

  • Economic exposure: (also known as operating) the risk that exchange rate changes may affect the present value of future income streams.

    Hedging and Speculating

  • Hedging is the act of offsetting an exposure to risk.

  • Covered Exposure refers to a foreign exchange risk that has been completely eliminated with a hedging instrument.


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Long and Short Positions Arbitrage

  • Traders are longin a foreign currency if the value of their foreign-currency-denominated assets exceeds the value of their foreign-currency-denominated liabilities (FCDA>FCDL)

  • Traders are short in a foreign currency if the value of their foreign-currency-denominated assets is less than the value of their foreign-currency-denominated liabilities.


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Hedging Arbitrage

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).


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Foreign Exchange Transactions ArbitrageForward Transactions or Forwards, 1

  • Forwards are useful for making trades, not today, but sometime in the future. These are “forward transactions” and use the forward rate.

  • The forward rate is greater or less than the spot rate, depending on whether the currency is expected to appreciate or depreciate.

  • If the currency is expected to appreciate in the future, the forward rate is priced higher than the spot rate and the rate contains a premium (+)

    (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.


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Forward Transactions, 2 Arbitrage

  • The forward rate is determined by the forces of supply and demand in the forward market.

  • A forward contract is an agreement between a buyer and seller to trade a particular currency on some future date for a fixed price, regardless of the currency’s spot rate on the future date. Typical maturity is 1,3,6, 9 and 12 months into the future. Forward contracts are usually negotiated between 2 parties – say a company and a bank – and customized for the maturity date and transaction amount (see Table 1 Handout).

  • Because of foreign exchange risk (changing exchange rates), it is possible to create what are called “perfect hedges” with forwards – when individuals or companies eliminate their risk exposure for the transaction amount and time frame needed (see the Handout for The Forward Contract Problem)


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Foreign Exchange Risk Arbitrage

  • Foreign exchange risk is the risk that the value of a future receipt or obligation will change due to a change in foreign exchange rates.

  • Because these international transactions span time, foreign exchange risk can arise.


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Forward Premium Arbitrage

  • The forward premium or discount is the difference between the forward exchange rate and the spot rate, expressed as a percentage of the spot rate.

  • The standard forward premium is the forward premium or discount annualized. The formula for the standard forward premium is:

N = 3 months here


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Example Arbitrage

  • For example, suppose the spot rate is 1.4926 (Euro/$) and the 3-month forward rate is 1.4887.

  • The forward premium on the Euro is:

    [(1.4887-1.4926)/1.4926]•(12/3)•100 =

    -1.05%


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Premium versus Discount Arbitrage

  • Note that in this example, the exchange rate is expressed as Euro/$, i.e., the Euro price of the dollar.

  • Because the forward price of the dollar is less than the spot price of the dollar, we say that the dollar is selling at a discount.

  • Likewise, we say that the Euro is selling at a premium.


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Covered Interest Arbitrage Arbitrage

  • Suppose the U.S. interest rate is 4.5% while the U.K. rate on a similar instrument is 2.25% (both for an annual debt instrument with similar risk characteristics). Hence, a saver would gain an additional 2.25% on the U.S. instrument.

  • suppose at the same time, the current spot rate is 1.6000 ($/£) and the one-year forward rate is 1.6200. The saver would gain 1.25% on the pound. [(1.62 – 1.60)/1.60 • 100].

  • The currency gain on the pound falls short of the interest differential in favor of the U.S. financial instrument. Hence, the saver should shift fund to the United States. This outcome is illustrated by point B in the following diagram.


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The Forward Rate as a Predictor Arbitrage

  • Because the forward rate is determined by the supply of and demand for the future delivery of a currency, it may convey information about the future spot rate.

  • Many empirical studies indicate that there is some co-movement between the forward and spot rate.

  • The co-movement is less than one-to-one; thus the forward rate has limited ability in forecasting the future spot exchange rate.


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The International Flow of Funds Arbitrage

  • If there were no restrictions on capital flows, we would see savers move funds from one nation to another in search of the greatest exchange-rate adjusted returns.

  • This flow of funds could potentially affect interest rates and exchange rates.

  • Individuals who save supply loanable funds.

  • Those who borrow demand loanable funds.

  • In a competitive market, the interest rate is determined by the supply and demand of loanable funds.


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The Market for Loanable Funds Arbitrage

  • In a competitive market, the supply and demand for loanable funds determines the equilibrium interest rate.

  • If the interest rate were R2, the quantity of loanable funds demanded would exceed the quantity of loanable funds supplied. Hence the interest rate would rise.

  • The equilibrium rate is R1. At R1, the quantity supplied equals the quantity demanded.


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Covered Interest Parity (CIP) or Covered Interest Arbitrage (CIA), 1

  • CIP or CIA theory postulates that spot and forward rates quoted at the same instant in time tend, in general, to diverge exactly in line with short-term interest differential on identical assets (in terms of political risk, default risk and other characteristics) across countries. Consider a domestic investor deciding whether to invest at home or abroad.

  • CIA is the force directing the flow of short-term capital funds between financial center. That is, short-term capital tends to flow from a low-return center to a high-return one, thus equalizing domestic return and covered foreign return.

  • Covered interest parity is a condition that relates interest differentials to the forward premium or discount.

  • It begins with the no-arbitrage condition when exchange risk is covered with a forward exchange contract:


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Covered Interest Parity (CIP) or Covered Interest Arbitrage (CIA), 2

(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.


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Covered Interest Parity (CIP) or Covered Interest Arbitrage (CIA),3

  • CIP is helpful in understanding short-term market movements.

  • As an equilibrium condition, it aids in our understanding of potential adjustments in various financial markets.

  • These adjustments occur if there is a flow of savings from one nation to another.

    Recall: Individuals who save supply loanable funds. Those who borrow demand loanable funds.

  • The covered-interest parity grid illustrates all of the interest differential and forward premium or discount combinations that satisfy CIP

  • These combinations lie on or near the 45 degree line.

  • The narrow band around the 45 degree line illustrates transaction and opportunity costs.


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Conditions for CIP or CIA to hold across countries (CIA),3

Assumptions required for CIA to be valid:

  • Domestic and foreign financial assets (KO items) are identical;

  • Capital and exchange markets across countries are efficient;

  • The supply curve for arbitrage funds is infinitely interest elastic, that is, a horizontal supply curve;

  • Transaction costs are sufficiently low to be negligible.

    In the real world, most of these assumptions are violated and thus affecting the empirical validity of the theory.


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Covered Interest Parity (CIP) or Covered Interest Arbitrage (CIA), 4

  • The CIP condition can be represented in a diagram drawn in ρ – (R –R*) or (F-S)/S – (R-R*) space by the CIP line.

  • Any point off CIP line is a violation of equilibrium condition (4.5 and hence 4.1) which triggers arbitrage.

  • A point such as B (right of the CIP line) imply profitable arbitrage for domestic resident investors, and hence capital outflows (out of the domestic currency). At point C, condition 4.1 is violated because (R – R*) < ρ or more precisely because the domestic return is lower than the covered foreign return given by (1+ R) < F/S (1 + R*) or F”< F. Under this scenario, domestic residents borrow funds at R, convert the borrowed funds at S, invest at R* and convert proceeds back at F. In the process, they will make profit, π = F/S (1+R*) – (1+R) >0. The process will eliminate arbitrage profit and restore equilibrium as in the following four steps (Point C leads to a reverse to what is described here)


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The Covered-Interest-Parity Grid (CIA), 4

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

Currency)

Fo


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Covered Interest Parity (CIP) or Covered Interest Arbitrage (CIA), 5

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]


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The Spot Market for the Pound (CIA), 5

  • As individuals move funds from pound-denominated instruments to dollar-denominated instruments, there is an increase in the demand for the dollar.

  • The increase in the demand for the dollar is equivalent to an increase in the supply of the pound.

  • The pound depreciates in the spot market (from S1 →to S2 )

UK investor:

1st: Increase in the supply of pounds(= increase in thedemand for dollars )

 ↓ S : ($/₤ ₤ depreciation; $ appreciation )


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The Forward Market for the Pound (CIA), 5

  • Initially the forward market for the pound is in equilibrium at the forward rate or 1.620.

  • An increase in the demand for the pound forward shifts the demand curve to the right.

  • This results in an appreciation of the pound.

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


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The U.K. Loanable Funds Market (CIA), 5

  • The flow of funds out of the United Kingdom is illustrated by the decrease in the supply of loanable funds.

  • Because of the decrease in the supply of loanable funds, the U.K. interest rate rises to R2.

3rd:UK Money Mkt: The supply of pounds will fall (=decrease in the demand for dollars),

their prices (P*) falls but R* rises


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The U.S. Loanable Funds Market (CIA), 5

  • The flow of funds into the United states increases the supply of loanable funds.

  • The increase in supply lowers the U.S. interest rate to R2.

4th:US Money Mkt: The supply of dollars increases (= increase in demand for pounds),

hence prices (P) will rise and R falls.


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The Spot Market (CIA), 5

  • Savers reallocate funds to pound-denominated financial instruments.

  • This results in an increase in the demand for the pound (as the demand for the pound is a derived demand).

  • The demand curve shifts to the right and the pound appreciates relative to the dollar.


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Uncovered Interest Parity (CIA), 5

  • If foreign exchange risk is not hedged when purchasing a foreign financial instrument, the transaction is said to be uncovered.

  • Uncovered interest parity (UIP), is a condition relating interest differentials to an expected change in the spot exchange rate of the domestic currency.

    (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


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Uncovered Interest Parity (CIA), 5

  • If a saving decision is uncovered, traders base their decision on their expectation of the future spot exchange rate.

  • The expected future spot exchange rate is expressed as Se+1. UIP is represented as:

    R – R* = (Se+1 – S)/S --- approximate version

  • In words, the right-hand-side of the UIP condition is the expected change in the spot rate over the relevant time period. But if

    R – R* ≠ (Se+1 – S)/S, the risk neutral agents move their uncovered funds across financial markets till they equalize.


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Deviations from UIP (CIA), 5

  • If a nation’s currency value is highly variable, individuals may be less confident about their expectations, making the purchase of a financial instrument a much riskier proposition. This risk is called currency risk.

  • In addition, there may also be country risk associated with the purchase of the financial instrument. Country risk is the possibility of loss due to political uncertainty in the nation.


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Risk Premium (CIA), 5

  • Because one instrument may be a riskier proposition than another financial instrument, borrowers may have to offer a higher rate of return on the debt instruments they issue.

  • Risk premium (ρR) is an increase in the return offered on a higher-risk financial instrument to compensate individuals for the additional risk they undertake.


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Risk Premium and UIP (CIA), 5

Using ρ to denote risk premium, the UIP condition can be rewritten as:

  • If the domestic instrument is the higher-risk instrument, then the positive interest differential should equal the expected rate of depreciation of the domestic currency plus an additional amount to compensate individuals for the additional risk they assume with the purchase of the domestic instrument.


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Foreign Exchange Market Efficiency (CIA), 5

  • We can link the CIP condition and the UIP condition through the interest rate differential as:

    (F-S)/S = R-R* = (Se+1–S)/S.

  • Through simplification, this can be restated as:

    F = Se+1.

  • The uncovered and covered interest parity conditions imply that the expected spot rate should equal the forward exchange rate at the time of the settlement of the forward contract.


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Market Efficiency (CIA), 5

  • Forward exchange market efficiency is a situation in which the equilibrium spot and forward rates adjust quickly to reflect all available information.

  • Hence, the forward premium or discount should equal the expected rate of currency depreciation and the risk premium.

  • This implies that, on average, the forward exchange rate should predict on average the expected future spot exchange rate.

  • Most studies conclude that risk premium is important but are divided on whether foreign exchange markets are efficient.


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Foreign Exchange Transactions; - A (CIA), 5Hedging Instrument - Futures,1

  • Future contracts - contracts that specify a standard volume of a currency to be exchanged on a settlement date sometime in the future. Are similar to forward contracts except that forward contracts are customized between buyers and sellers who are genuinely interested in conducting currency transactions whereas future contracts are standardized for trading on markets like the Chicago Mercantile Exchange (see Table 2. Handout for April 15, 2003)

  • A typical future contract specifies basic elements; type of currency; amount of currency; future rate, and settlement date. These elements are standardized to facilitate fast trading on the floor and they specify a standard volume of the currency being traded.

  • Example: Each Swiss contract contains 125,000 CHF (“CHF 125,000). Because futures can be bought in these increments and are not tailored to specific amounts, they are useful as a vehicle for currency speculation and a hedging tool since it is difficult to structure a “perfect hedge” with futures.


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Futures, 2 (CIA), 5

  • The notations “$ per CHF” etc mean the rates are listed under “open,” “high,” “low,” and “settle” columns are direct exchange quotes. The month in the left-most column represents the expiration of the contract (futures have standardized settlement dates, 3rd Wednesday of March; June, September, and December).

  • Price movements during the day (“Open,” “SETTLE,” “HIGH,” and “LOW” columns) and over the lifetime of the contract. Shows the number of open contracts with a expiration date on column headed “OPEN INT” (open interest). This number is important to traders because it indicates how popular that contracts is in the market: the higher is the demand, the greater is OPEN INT. “Est vol.” (estimated volume) shows the average number of contracts bought and sold in one day; “vol<day>” – the actual number of contracts bought and sold in one day. The “open int” value following “vol<day>” shows the number of contracts open for that currency in the entire exchange, and the negative or positive value at the end of the line – shows the net change in open interest. It indicates whether interest in futures for that currency is increasing or decreasing.


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Futures, 3 (CIA), 5

  • Compare Tables 1 and 2. (a) rates for currency futures are similar to those of currency forwards. Like forwards, futures allow traders to lock in prices at which they can purchase currencies sometime in the future. (b) Although futures don’t allow “perfect hedges” there are some companies that use them for “imperfect hedges” because of their smaller sized contracts. The typical size for a forward contract is over $1million whereas for a future contract it is about $100,000. ( c) Forward contracts end in the actual exchange of currencies but future contracts are “closed-out” – or sold – before settlement since most traders have no interest in taking delivery. The gain or loss to the holder of a futures contract is the difference between buy and sell prices of the contract.

  • The change in the price of a contract (with a given future rate and settlement date) depends on two things: (a) movement of the spot over time, and (b) changing expectations about the spot rate’s value on the settlement date. For example, if the spot rate of a British pound rose (appreciated) cover a one-month period, a British pound futures contract would rise in value by approximately the same amount. The subsequent sale of the contract would be profitable. If the spot depreciated, the reverse would occur and the sale of the contract would be unprofitable. These price movements account for gains and losses of the traders on the currency futures market.


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How to Read a Futures Contract (CIA), 5 (Table 2 Handout)

  • The listing for the June Swiss Franc (CHF) contract can be read as follows.

    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).


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International Financial Markets (CIA), 5

  • International capital markets are markets for cross-border exchange of financial instruments that have maturities of one year or more.

  • International money markets are markets for cross-border exchange of financial instruments with maturities of less than one-year.

  • Bonds are long-term promissory notes.

  • Equities are ownership shares that might or might not pay the holder a dividend, whose values rise and fall with savers’ perceived value of the issuing enterprise.


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Eurocurrencies (CIA), 5

  • Eurocurrencies are bank deposits denominated in a currency other than that of the nation in which the bank deposit is located.

  • The Eurocurrency market is a market for the borrowing and lending of Eurocurrency deposits.

  • The Eurocurrency market and the forward exchange market are highly integrated. Because of this, Eurocurrency interest differentials and the forward premium or discount tend to be in equilibrium.


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