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Foreign Exchange

- Purchase and sale of national currencies
- Huge market
- 4 trillion per day (April 2007), much growth

recently - Compared with US Treasury market 300 billion
- NYSE lt 10 billion
- Comprised of
- 1.005 trillion
- 2.076 trillion in derivatives, ie
- 362 billion in outright forwards
- 1.714 trillion in forex swaps
- Concentrated in few centers and few currencies

Huge growth in daily turnover

Global Foreign Exchange Market Turnover(average

daily turnover)

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Currency Turnover

Most Traded Currencies

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Exchange Rates

- Spot versus forward exchange rates
- Nominal exchange rate
- A forward contract refers to a transaction for

delivery of foreign exchange at some specified

date in the future. - Used to hedge currency risk
- Forward premium

Yen-dollar Spot rate

Dollar Price of a Euro, Spot

Forward versus futures

- Forwards sold by commercial banks, otc
- Futures sold in organized exchanges
- Originated in 1972 in the Merc
- Clearinghouse, currencies need not be delivered
- Contracts settled in cash
- Forward markets larger but futures markets more

liquid - Options
- Right to buy or sell at set price (strike price)

Covered Interest Parity

- Covered transactions eliminate currency risk
- Let i and i be the domestic and foreign interest

rate - Let et and Ft be the spot and forward rate at t
- Suppose we want to invest in foreign currency
- We face currency risk when we repatriate earning
- But we can hedge the risk by purchasing euros

forward today at Ft - One dollar invested in euros yields euros
- 3 months from now I have

euros - So 3 months hence I have

dollars

Covered Interest Parity

- Arbitrage requires that
- Which is called CIPC
- This implies
- or
- If not equal there are arbitrage profits to be

made - Thus, a positive interest differential implies a

forward premium - Interest must compensate for capital loss

Covered Interest Arbitrage

Interest Parity Line

Adding Transactions Costs

Dont Try This

CIPC

- Take logs of both sides of CIPC
- or, for small i
- Most studies show that CIPC holds
- Notice that there is no currency risk
- Forward price signals markets expectation

Riskless Arbitrage Covered Interest Parity

- Arbitrage profit?
- Considers the German deutschmark (GER) relative

to the British pound (UK), 1970-1994. - Determine whether foreign exchange traders could

earn a profit through establishing forward and

spot contracts - The profit from this type of arrangement is

Covered Interest Parity

Uncovered Interest Parity

- Suppose we do not hedge our investment
- Again we invest one dollar
- Let be the expected future spot rate
- In 3 months we earn
- Arbitrage requires
- UIPC, thus

CIPC and UIPC compared

- The two conditions differ only in one term
- versus
- CIPC involves no currency risk
- UIPC bears currency risk
- Holds only if agents are risk neutral
- Risk averse agents may require a risk premium
- Notice that if then UIPC holds
- This would be cool gt markets reveal expectations
- We can test for this

Efficient Markets

- Example of Efficient Markets Hypothesis
- Investors use available information efficiently
- Does not mean they are ex post correct, only that

prices reflect all available current information

in an efficient manner - Unbiased errors
- If I am efficient my error pattern looks like

that of Tiger Woods - Of course, the variance of my pattern is greater,

but we are both on target on average

Market Efficiency

Testing for UIPC

- We have data on F but not on
- Rational expectations implies that forecast

errors are unbiased - Then should be an unbiased predictor of
- That is, guesses are on average correct
- UIPC implies that
- Thus, if REH and UIPC holds, then should be

an unbiased predictor of - gt market is efficient!!!
- What does unbiased mean?
- If I have a lot of observations, then the average

value of Ft should differ from et1 only by a

random error - Hiawathas Last Arrow

Euro Six Months Forward

Testing UIPC

- So if I estimate
- where is any variable you can think of, and

is a random error - I should find
- That is, all the information valuable for

predicting is incorporated in the market

price,

Testing UIPC

- Typically one actually regresses changes, so
- With null hypotheses
- Notice this is a joint test
- REH and UIPC
- So rejection could mean either
- Expectations are not rational
- UIPC does not hold (perhaps agents are not risk

neutral) - Visual inspection does not vindicate UIPC

Empirical Test of UIPC

Yen Spot and Forward

Actual change in spot rate and forward discount

U.S. and U.K. 3-month Libor Rates and Exchange

RateAugust 2001 until July 2005

U.S. and Euro 3-month Libor Rates and Exchange

RateAugust 2001 until July 2005

Tests of UICP

- Most tests find forward premium puzzle
- Not only is in the data, it is often

negative - If UIPC held, the pound should, on average,

appreciate when it is at a forward premium, i.e.,

f gt 0 - The negative point estimates of ß imply that the

pound actually tends to depreciate when it is at

a forward premium. - UK interest rates exceed US by 2.41 on average,

but sterling appreciates by 22.25

Forward Premium Puzzle

- If UICP fails there are two possibilities
- Markets are not efficient
- risk premium is missing
- We are testing a joint hypothesis
- If marginal agents are risk averse ignoring this

could explain the forward puzzle - If income is volatile perhaps risk premium varies
- Or it could be Central Bank Behavior

Central Banks

- Central Banks move exchange rates in short run
- They could set policy based on observations of F
- E.g., intervene when risk premium rises
- Seems that when CBs intervene heavily the

forward discount increases - Forward discount is larger in floating rate

regimes - Forward discount larger at shorter horizons
- Interesting because CBs can only move e over

short periods - Less risk at longer horizons

Estimated Beta at different horizons

Short Horizon Tests

Longer Horizons

Risk Premium

- But time varying risk premia hard to observe
- To explain risk premium must be more

volatile than - Why would this be the case (assertion, see notes

for explanation)? - We dont seem to be able to find such a risk

premium - Why is forward discount larger for industrialized

economies? - Unlike major currencies, which generally show a

coefficient significantly less than zero,

suggesting that the forward rate actually points

in the wrong direction, the coefficient for

emerging market currencies is on average slightly

above zero, and even when negative is rarely

significantly less than zero. - Hard to reconcile with risk premium explanation
- Emerging markets appear riskier but have a

smaller risk premium????

DXY Index

Can we make money?

- If UIPC fails, can we make money?
- One can pursue carry trade borrow low invest

high - Let y be the amount of money borrowed, then
- With payoff
- So if my profit would be

Carry Trade

- Suppose we did this via dollar-yen
- September 1993 till August 2003
- Bet once a month for ten years, we have 120

observations - We would earn money, average profits positive

.0041 - Profits are volatile
- Sharpe ratio 0.12 lt than for SP 500
- Carry trade is a bet against arbitrage, on lower

volatility - Sometimes carry trade leads to big losses,

unexpected currency movements - Like selling puts out of the money
- Why dont investors arbitragers bet against it?
- Incentive problem for fund managers
- Rational inattention

Example

Example

- Example Japanese yen and Australian dollar
- 2001 steady increase in profits from carry

trades. - Despite several months of positive carry profits,

the yen did not sufficiently appreciate against

the Australian dollar to offset these profits. - Leverage and margin
- Example You have 2,000 and borrow an additional

48,000 in yen from a bank in Japan. - You have borrowed 25 times your own 2,000

capital, a leverage ratio of 25. You conduct

carry trade, investing 50,000 in the Australian

dollar. - If you lose 4 on the trade, youve lost your

initial capital investment. This initial capital

put up by the investor of 4 of the total

investment is known as a margin.

Summary

- Obviously if large institutions do this losses

could be huge. Duh! - Even if expected returns from arbitrage are equal

to zero, actual profits are often not equal to

zero. - Returns (profits/losses) are persistent.
- Returns are volatile/risky.

US Dollar/Yen Exchange Rate

Price Pressure

- Bid-ask spreads reduce size of profits
- Large amounts of speculation needed to earn money
- Speculator who be one pound on an

equally-weighted portfolio of carry-trade

strategies (across the USA, Canada, Belgium,

France, Germany, Japan, Netherlands, Switzerland

and the euro) from 1976 to 2005 would earn an

monthly payoff of 0.0025 pounds. - To earn an average annual payoff of 1 million

pounds would require a bet of 33.33 million

pounds per month. - Is there an effect of such large trades?
- Would they survive such speculation?
- Prices rise with order flow
- Could eat profits
- You could break up trades, but this chews up

profits as well - The marginal expected payoff can be zero, even

when the average payoff is positive - Speculators make profits but no money is left on

the table

Risk versus Reward

- Idea Examine traders strategies and other

finance theories to study tradeoff between risk

and return. - Data Positive 1 interest differential is

associated with only a 0.23 appreciation in the

currency, implying a 0.77 profit. - Problem despite the existence of profits
- Profits do not rise/fall linearly, line is a poor

fit for the data. At higher differentials,

variance in return higher. - Variance around the line is high in general,

creating uncertainty for investors.

Test of Efficient Markets

- Not the high variance of observations around the

line of best fit - Observations do not cluster around the line of

best fit - For the same interest differential there are

vastly different actual rates of depreciation

observed

Limits of Arbitrage

- Returns positive for currencies
- Very high volatility of returns
- Sharpe ratios lt 1
- Equal to 0.5 0.6 for market portfolio of

currencies - Differs little from stock market
- Puzzle like the equity premium puzzle

Predictability and Nonlinearity

- Linear model may be the problem
- Nonlinear models reveal that low interest

differentials are associated with very low

profits. - At high differentials, investors engage in carry

trades, bidding up the currency, sometimes

causing reversals (and losses). - At the extreme ends, arbitrage appears to work,

so what is happening for moderate interest

differentials? - Investors are willing to take on some risk, if

the return is large enough.

Peso Problems

- Could be due to peso problem
- Samples used in tests are not long enough to have

big losses - Suppose you studied the dollar-baht rate for

UIPC, 1990-1997 - You miss a big depreciation in July 1997 but

investors may have considered it a possibility - Suppose e 20c, and investors are 95 sure it

will stay - With prob .05 they believe it will fall to 10c.

Then, - So each period for which there is no change the

forecast error is positive - Casual observer might assume irrationality

Example

- Suppose peso is pegged to dollar
- Let
- Then UIPC implies
- Market predicts depreciation each period the peg

holds UIPC is violated - But does not mean market is inefficient
- Agents are calculating the small risk of a big

depreciation - When the market corrects, losses are large
- Argentina, Hong Kong

Hong Kong Peso Problem

Argentina Peso Problem

Thailand / U.S. Foreign Exchange Rate

Realized Profits on Yen Carry Trade

Realized Profits on Yen Carry Trade

Yen Positions of non-commercial traders at the

Merc

UIPC Regressions, in Sterling

Volatility Puzzle

Implied Yen Volatility (3 month)

Implied Yen Volatility (3 mo)

New Zealand 3 month T Bill

Yen/NZD Spot Rate and the Interest Differential

Real Interest Parity

- We have been looking at nominal returns, what

about real returns? - Fisher effect tells us that
- So
- If PPP holds, then so
- But PPP is too restrictive an assumption
- What happens in general?

Real Interest Parity

- We need to consider expected changes in Q
- So,
- If inflation and exchange rates change at the

same rate there is no change in Q - UICP implies
- so

RIPC

- So, using the Fisher equation we obtain
- This implies that real interest differentials are

equal to expected changes in Q - Suppose people expect
- Implies real value of the dollar will decline
- Investors will demand a premium to hold US assets
- Does this mean there are profits that are not

arbitraged? - No
- Differences in real returns are not on the same

asset - They are returns on different bundles of goods

RIPC Interpreted

- Real interest differentials reflect nominal rates

deflated by over different consumption

baskets - If agents were identical gt PPP, so differences

equalized - Because people in different countries consume

different baskets of goods, there is no way for

them to arbitrage away any difference. - Implies that we cannot look at real interest

differentials to study whether capital markets

are integrated - Capital markets can be perfect, but if large US

CA deficits lead to expectations of

then real returns on US assets would have to

exceed those in the rest of the world

Exchange Rate Regimes

- Two polar cases and many in the middle
- Fixed exchange rates
- CB buys or sells reserves to maintain a set price

of foreign exchange - Flexible exchange rates
- CB does not intervene in market for foreign

exchange - To understand, suppose demand and supply of

foreign exchange given by

Historical View on Exchange Rate Regimes

Fixed versus Flexible

- Shouldnt e be determined by market forces?
- Mundell versus Friedman
- Foreign exchange is not like a normal market
- Exchange rate is like a dictionary
- Exchange of national currencies, fiat monies
- A high price of foreign exchange does not lead to

more supply - No fundamentals driving the market
- Government policy must control supply of money
- Then why should they be flexible?

Friedman on Flexible Rates

- If internal prices were as flexible as exchange

rates, it would make little economic difference

whether adjustments were brought about by changes

in exchange rates or by equivalent changes in

internal prices. - The argument for flexible exchange rates is,

strange to say, very nearly identical with the

argument for daylight savings time. Isnt it

absurd to change the clock in summer when exactly

the same result could be achieved by having each

individual change his habits? All that is

required is that everyone decide to come to his

office an hour earlier, have lunch an hour

earlier, etc. But obviously it is much simpler to

change the clock that guides all than to have

each individual separately change his pattern of

reaction to the clock, even though all want to do

so. The situation is exactly the same in the

exchange market. It is far simpler to allow one

price to change, namely, the price of foreign

exchange, than to rely upon changes in the

multitude of prices that together constitute the

internal price structure.

Foreign Exchange

- If CB does not intervene, then market price of

foreign exchange is - Suppose demand for foreign exchange increases
- Then if CB does nothing, e must rise
- To keep e fixed CB must sell foreign exchange
- So international reserves fall
- Thus,
- where is the fixed exchange rate
- Notice that exchange rate can also be affected by

policy - By affecting demand or supply

Fixed Rates and Reserve Accumulation

- If the exchange rate is fixed, then reserves

adjust as demand and supply shifts - The peg is sustainable if these shocks offset
- Peg is unsustainable if shocks are biased
- But there is asymmetry
- Easier to accumulate foreign exchange
- You cannot print it if you are running out!
- When does a fixed rate collapse?
- When reserves run out? No.

Time to Collapse

- Suppose that the peg is unsustainable
- When reserves run out the rate must collapse to
- Implies that e will jump at that date, t
- Implies capital gain at date t 1
- So people will sell at t -1, implies capital

gain, so e collapses at t 1 - Implies e collapses at t 2,
- So e must collapse at earliest date at which

there is no capital gain - So e collapses before all reserves are depleted
- Why not sell before tc ?
- Because then they incur capital loss

Collapse

- Exchange rate collapses before reserves run out
- Nobody wants to be the last person to exit
- If agents are forward looking they anticipate

capital losses - So currency cannot collapse and then jump to

shadow rate - In practice we see that currency collapses before

reserves run out - Key is when CB is no longer willing to pay the

cost of maintaining the exchange rate - CB could always repurchase the MB
- Problem is the cost of doing so
- No longer lender of last resort, interest rates

may skyrocket - External versus internal balance

Foreign Exchange Reserves and MB, Sept 1994(pct

of GDP)

Fixing the Exchange Rate

- Under fixed rates IR is changing to offset any

excess demand for foreign exchange - When there is ED gt 0 the CB sells reserves, so
- If ED lt 0, the opposite takes place
- What is the effect of this operation?
- Suppose no sterilization
- That is no attempt to offset the operation of

pegging the exchange rate on the domestic money

supply

No Sterilization

- Start with the CBs balance sheet
- The assets of the CB, IR DS MB
- The money supply just depends on the MB, so
- Thus when reserves fall the money supply

contracts, and vice versa - Fixing the exchange rate means giving up control

over the supply of money

Example

- Central bank balance sheet condition
- Example
- Suppose the government purchases 500 million in

domestic bonds and 500 million in foreign assets

(reserves). - Money supply is therefore equal to 1000 million

pesos.

Central Bank Actions

- Suppose the Fed purchases foreign exchange
- 4 cases
- purchase from home-country banks
- in this case alongside the increase in IR is an

increase in bank reserves. - purchase from home-country non-bank residents
- in this case, residents would receive payment in

the form of currency in circulation. - purchase from home-country non-bank residents
- in this case, residents would receive payment in

the form of currency in circulation. - purchase from foreign banks or central banks via

changes in the foreign banks deposit at the Fed.

- In this case, once the bank uses this deposit to

purchase some interest-bearing security from a

domestic bank, bank reserves will rise. - In all cases, the reserve transaction results in

a simultaneous change in MB

Sterilization

- Sterilization occurs when the CB moves to

insulate the domestic economy from foreign

reserve transactions - Typically an open market operation if inflows of

foreign exchange are swelling the money supply

then the CB sells bonds to soak it up, e.g., - Notice that to persist in sterilization requires

large stocks of both foreign reserves and

domestic securities. - obviously difficult for debtor, what about for

surplus case? - Need to keep selling DS, but how much will the

public buy? - Depends on how financially developed the economy
- Interest cost of sterilization can be large

Effect on Monetary Policy

Impossible Trinity

- We see that a country cannot simultaneously have
- Independent monetary policy
- Fixed exchange rate
- Capital mobility
- With fixed e you interest rates cannot diverge

from i - Conflict between internal and external balance
- Chinas advantage
- China does not have open capital account
- So it can sterilize current account surpluses
- Lack of capital mobility depresses local interest

rates, reduces costs of sterilization - Effect of large sterilization in some countries

could be future inflation

Carrying Costs (pct of GDP)

Foreign Reserves net of currency

Valuation Changes on Foreign Reserves

China Balance of Payments Transactions

Capital Account Components

Annual Changes in NFA, NDA, and Reserves

Time of Collapse

Reserve Flow

Sustainable exchange rate

Unsustainable Exchange Rate

Mexicos External Balances

Ruble Exchange Rate

Monetary Base and Gross Reserves

Russian Foreign Exchange Reserves (billions of

)MB 6.7 billion in Sept 1998

Market for Foreign Exchange

Varieties of Exchange Rate Regimes