Foreign Exchange

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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

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Huge growth in daily turnover
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Global Foreign Exchange Market Turnover(average
daily turnover)
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Currency Turnover
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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

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Yen-dollar Spot rate
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Dollar Price of a Euro, Spot
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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)

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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

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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

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Covered Interest Arbitrage
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Interest Parity Line
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Adding Transactions Costs
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Dont Try This
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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

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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

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Covered Interest Parity
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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

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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

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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

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Market Efficiency
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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

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Euro Six Months Forward
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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,

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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

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Empirical Test of UIPC
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Yen Spot and Forward
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Actual change in spot rate and forward discount
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U.S. and U.K. 3-month Libor Rates and Exchange
RateAugust 2001 until July 2005
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U.S. and Euro 3-month Libor Rates and Exchange
RateAugust 2001 until July 2005
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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

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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

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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

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Estimated Beta at different horizons
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Short Horizon Tests
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Longer Horizons
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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????

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DXY Index
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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

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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

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Example
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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.

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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.

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US Dollar/Yen Exchange Rate
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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

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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.

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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

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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

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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.

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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

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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

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Hong Kong Peso Problem
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Argentina Peso Problem
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Thailand / U.S. Foreign Exchange Rate
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Realized Profits on Yen Carry Trade
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Realized Profits on Yen Carry Trade
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Yen Positions of non-commercial traders at the
Merc
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UIPC Regressions, in Sterling
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Volatility Puzzle
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Implied Yen Volatility (3 month)
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Implied Yen Volatility (3 mo)
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New Zealand 3 month T Bill
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Yen/NZD Spot Rate and the Interest Differential
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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?

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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

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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

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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

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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

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Historical View on Exchange Rate Regimes
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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?

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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.

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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

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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.

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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

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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

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Foreign Exchange Reserves and MB, Sept 1994(pct
of GDP)
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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

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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

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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.

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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

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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

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Effect on Monetary Policy
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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

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Carrying Costs (pct of GDP)
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Foreign Reserves net of currency
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Valuation Changes on Foreign Reserves
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China Balance of Payments Transactions
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Capital Account Components
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Annual Changes in NFA, NDA, and Reserves
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Time of Collapse
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Reserve Flow
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Sustainable exchange rate
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Unsustainable Exchange Rate
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Mexicos External Balances
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Ruble Exchange Rate
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Monetary Base and Gross Reserves
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Russian Foreign Exchange Reserves (billions of
)MB 6.7 billion in Sept 1998
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Market for Foreign Exchange
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Varieties of Exchange Rate Regimes