Foreign Exchange вЂў Purchase and sale of national currencies вЂў Huge market вЂ“ $4 trillion per day (April 2007), much growth recently вЂў Compared with US Treasury market = $300 billion вЂў NYSE < $10 billion вЂ“ Comprised of вЂ“ $1.005 trillion вЂ“ $2.076 trillion in derivatives, ie В» $362 billion in outright forwards В» $1.714 trillion in forex swaps вЂў Concentrated in few centers and few currencies Huge growth in daily turnover Global Foreign Exchange Market Turnover (average daily turnover) Currency Turnover Most Traded Currencies Exchange Rates вЂў Spot versus forward exchange rates вЂў Nominal exchange rate вЂў A forward contract refers to a transaction for delivery of foreign exchange at some specified date in the future. вЂ“ Used to hedge currency risk вЂў Forward premium Yen-dollar Spot rate Dollar Price of a Euro, Spot Forward versus futures вЂў Forwards sold by commercial banks, otc вЂў Futures sold in organized exchanges вЂ“ Originated in 1972 in the Merc вЂ“ Clearinghouse, currencies need not be delivered вЂў Contracts settled in cash вЂў Forward markets larger but futures markets more liquid вЂ“ Options вЂў Right to buy or sell at set price (strike price) Covered Interest Parity вЂў Covered transactions eliminate currency risk вЂ“ Let i and i* be the domestic and foreign interest rate вЂ“ Let et and Ft be the spot and forward rate at t вЂў Suppose we want to invest in foreign currency вЂ“ We face currency risk when we repatriate earning вЂ“ But we can hedge the risk by purchasing euros forward today at Ft вЂ“ One dollar invested in euros yields euros вЂ“ 3 months from now I have euros вЂ“ So 3 months hence I have dollars Covered Interest Parity вЂў Arbitrage requires that вЂ“ Which is called CIPC вЂў This implies вЂў or Ft пЂ e t et пЂЅ i пЂ i* 1пЂ« i* вЂ“ If not equal there are arbitrage profits to be made вЂ“ Thus, a positive interest differential implies a forward premium вЂ“ Interest must compensate for capital loss Covered Interest Arbitrage Interest Parity Line 0 .0 4 D A Ft пЂ e t et 0 C B -0 .0 4 -0 .0 4 0 i пЂ i* 1пЂ« i* 0 .0 4 Adding Transactions Costs 0 .0 4 D P L A P U Ft пЂ e t et 0 C B -0 .0 4 -0 .0 4 0 i пЂ i* 1пЂ« i* 0 .0 4 DonвЂ™t Try This CIPC вЂў Take logs of both sides of CIPC вЂ“ or, for small i вЂў Most studies show that CIPC holds вЂ“ Notice that there is no currency risk вЂ“ Forward price signals markets expectation Riskless Arbitrage: Covered Interest Parity вЂў Arbitrage profit? вЂ“ Considers the German deutschmark (GER) relative to the British pound (UK), 1970-1994. вЂ“ Determine whether foreign exchange traders could earn a profit through establishing forward and spot contracts вЂ“ The profit from this type of arrangement is: Covered Interest Parity Uncovered Interest Parity вЂў Suppose we do not hedge our investment вЂў Again we invest one dollar вЂ“ Let be the expected future spot rate вЂ“ In 3 months we earn вЂ“ Arbitrage requires вЂ“ UIPC, thus CIPC and UIPC compared вЂў The two conditions differ only in one term вЂ“ versus вЂ“ CIPC involves no currency risk вЂ“ UIPC bears currency risk вЂў Holds only if agents are risk neutral вЂў Risk averse agents may require a risk premium вЂ“ Notice that if then UIPC holds вЂў This would be cool => markets reveal expectations вЂ“ We can test for this Efficient Markets вЂў Example of Efficient Markets Hypothesis вЂ“ Investors use available information efficiently вЂ“ Does not mean they are ex post correct, only that prices reflect all available current information in an efficient manner вЂў Unbiased errors вЂў If I am efficient my error pattern looks like that of Tiger Woods вЂ“ Of course, the variance of my pattern is greater, but we are both on target on average Market Efficiency Testing for UIPC вЂў We have data on F but not on вЂў Rational expectations implies that forecast errors are unbiased вЂ“ Then should be an unbiased predictor of et пЂ«1 вЂў That is, guesses are on average correct вЂў UIPC implies that eЛ† t пЂ«1 пЂЅ Ft вЂ“ Thus, if REH and UIPC holds, then F t should be an unbiased predictor of e t пЂ«1 вЂў => market is efficient!!! вЂ“ What does unbiased mean? вЂў If I have a lot of observations, then the average value of Ft should differ from et+1 only by a random error вЂ“ HiawathaвЂ™s Last Arrow Euro Six Months Forward Testing UIPC вЂў So if I estimate et пЂ«1 пЂЅ пЃЎ пЂ« пЃў Ft пЂ« пЃ§ X t пЂ« пЃҐ t вЂ“ where X t is any variable you can think of, and random error вЂў I should find вЂў That is, all the information valuable for predicting e is incorporated in the market price, F t пЂ«1 t пЃҐt is a Testing UIPC вЂў Typically one actually regresses changes, so вЂў With null hypotheses вЂ“ Notice this is a joint test вЂў REH and UIPC вЂў So rejection could mean either вЂ“ Expectations are not rational вЂ“ UIPC does not hold (perhaps agents are not risk neutral) вЂў Visual inspection does not vindicate UIPC Empirical Test of UIPC Yen Spot and Forward Actual change in spot rate and forward discount Tests of UICP вЂў Most tests find forward premium puzzle вЂ“ Not only is пЃў пЂј 1 in the data, it is often negative вЂў If UIPC held, the pound should, on average, appreciate when it is at a forward premium, i.e., f > 0 вЂў The negative point estimates of ОІ imply that the pound actually tends to depreciate when it is at a forward premium. вЂў UK interest rates exceed US by 2.41% on average, but sterling appreciates by 22.25% Forward Premium Puzzle вЂў If UICP fails there are two possibilities вЂ“ Markets are not efficient вЂ“ risk premium is missing вЂў We are testing a joint hypothesis вЂў If marginal agents are risk averse ignoring this could explain the forward puzzle вЂў If income is volatile perhaps risk premium varies вЂў Or it could be Central Bank Behavior Central Banks вЂў Central Banks move exchange rates in short run вЂ“ They could set policy based on observations of F вЂў E.g., intervene when risk premium rises вЂў Seems that when CBвЂ™s intervene heavily the forward discount increases вЂ“ Forward discount is larger in floating rate regimes вЂ“ Forward discount larger at shorter horizons вЂў Interesting because CBвЂ™s can only move e over short periods вЂў Less risk at longer horizons Estimated Beta at different horizons Short Horizon Tests Longer Horizons Risk Premium вЂў But time varying risk premia hard to observe вЂ“ To explainпЃў пЂј 1 2 risk premium must be more volatile than вЂў Why would this be the case (assertion, see notes for explanation)? вЂ“ We donвЂ™t seem to be able to find such a risk premium вЂў Why is forward discount larger for industrialized economies? вЂ“ 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. вЂ“ Hard to reconcile with risk premium explanation вЂў Emerging markets appear riskier but have a smaller risk premium???? DXY Index Can we make money? вЂў If UIPC fails, can we make money? вЂ“ One can pursue carry trade: borrow low invest high вЂ“ Let y be the amount of money borrowed, then вЂ“ With payoff вЂ“ So if my profit would be Carry Trade вЂў Suppose we did this via dollar-yen вЂ“ September 1993 till August 2003 вЂў вЂў вЂў вЂў 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 < than for S&P 500 п‚» .6 to 1 .1 вЂ“ Carry trade is a bet against arbitrage, on lower volatility вЂў Sometimes carry trade leads to big losses, unexpected currency movements вЂ“ Like selling puts out of the money вЂў Why donвЂ™t investors arbitragers bet against it? вЂ“ Incentive problem for fund managers вЂ“ Rational inattention Example Example вЂ“ Example: Japanese yen and Australian dollar вЂў 2001: steady increase in profits from carry trades. вЂў Despite several months of positive carry profits, the yen did not sufficiently appreciate against the Australian dollar to offset these profits. вЂ“ Leverage and margin вЂў Example: You have $2,000 and borrow an additional $48,000 in yen from a bank in Japan. вЂ“ 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. вЂ“ If you lose 4% on the trade, youвЂ™ve 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 вЂў Obviously if large institutions do this losses could be huge. Duh! вЂ“ Even if expected returns from arbitrage are equal to zero, actual profits are often not equal to zero. вЂ“ Returns (profits/losses) are persistent. вЂ“ Returns are volatile/risky. US Dollar/Yen Exchange Rate Price Pressure вЂў Bid-ask spreads reduce size of profits вЂў Large amounts of speculation needed to earn money вЂ“ Speculator who be one pound on an equally-weighted portfolio of carrytrade 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. вЂ“ To earn an average annual payoff of 1 million pounds would require a bet of 33.33 million pounds per month. вЂў Is there an effect of such large trades? вЂ“ Would they survive such speculation? вЂ“ Prices rise with order flow вЂў Could eat profits вЂ“ You could break up trades, but this chews up profits as well вЂ“ The marginal expected payoff can be zero, even when the average payoff is positive вЂў Speculators make profits but no money is left on the table Risk versus Reward вЂў Idea: Examine tradersвЂ™ strategies and other finance theories to study tradeoff between risk and return. вЂ“ Data: Positive 1% interest differential is associated with only a 0.23% appreciation in the currency, implying a 0.77% profit. вЂ“ Problem: despite the existence of profits: вЂў Profits do not rise/fall linearly, line is a poor fit for the data. At higher differentials, variance in return higher. вЂў Variance around the line is high in general, creating uncertainty for investors. Test of Efficient Markets вЂў Not the high variance of observations around the line of best fit вЂў Observations do not cluster around the line of best fit вЂ“ For the same interest differential there are vastly different actual rates of depreciation observed Limits of Arbitrage вЂў Returns positive for currencies вЂў Very high volatility of returns вЂў Sharpe ratios < 1 вЂ“ Equal to 0.5 вЂ“ 0.6 for market portfolio of currencies вЂ“ Differs little from stock market вЂў Puzzle like the equity premium puzzle Predictability and Nonlinearity вЂў Linear model may be the problem вЂў Nonlinear models reveal that low interest differentials are associated with very low profits. вЂ“ At high differentials, investors engage in carry trades, bidding up the currency, sometimes causing reversals (and losses). вЂ“ At the extreme ends, arbitrage appears to work, so what is happening for moderate interest differentials? вЂў Investors are willing to take on some risk, if the return is large enough. Peso Problems вЂў Could be due to peso problem вЂ“ Samples used in tests are not long enough to have big losses вЂў Suppose you studied the dollar-baht rate for UIPC, 1990-1997 вЂў You miss a big depreciation in July 1997 but investors may have considered it a possibility вЂ“ Suppose e = 20c, and investors are 95% sure it will stay вЂ“ With prob = .05 they believe it will fall to 10c. Then, вЂў So each period for which there is no change the forecast error is positive: вЂў Casual observer might assume irrationality Example вЂў Suppose peso is pegged to dollar вЂ“ Let i пЂЅ . 05 вЂ“ Then UIPC implies US вЂ“ Market predicts depreciation; each period the peg holds UIPC is violated вЂў вЂў вЂў вЂў 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 9 100 8 90 7 80 6 70 5 60 4 50 3 40 2 30 1 20 int diff yen per NZD Yen per NZD NZD Yen Interest differential Yen/NZD Spot Rate and the Interest Differential Real Interest Parity вЂў We have been looking at nominal returns, what about real returns? вЂ“ Fisher effect tells us that вЂ“ So вЂ“ If PPP holds, then so вЂ“ But PPP is too restrictive an assumption вЂў What happens in general? Real Interest Parity вЂў We need to consider expected changes in Q вЂ“ So, вЂ“ If inflation and exchange rates change at the same rate there is no change in Q вЂ“ UICP implies вЂ“ so RIPC вЂў So, using the Fisher equation we obtain: вЂ“ This implies that real interest differentials are equal to expected changes in Q вЂ“ Suppose people expect пЃ„ Q e пЂѕ 0 вЂ“ Implies real value of the dollar will decline вЂў Investors will demand a premium to hold US assets вЂў Does this mean there are profits that are not arbitraged? вЂ“ No вЂў Differences in real returns are not on the same asset вЂў They are returns on different bundles of goods RIPC Interpreted вЂў Real interest differentials reflect nominal rates deflated by over different consumption baskets пЃ° 's вЂ“ If agents were identical => PPP, so differences equalized вЂ“ Because people in different countries consume different baskets of goods, there is no way for them to arbitrage away any difference. вЂў Implies that we cannot look at real interest differentials to study whether capital markets are integrated вЂ“ Capital markets can be perfect, but if large US CA deficits lead to expectations of пЃ„ Q пЂѕ 0 then real returns on US assets would have to exceed those in the rest of the world e Exchange Rate Regimes вЂў Two polar cases and many in the middle вЂ“ Fixed exchange rates вЂў CB buys or sells reserves to maintain a set price of foreign exchange вЂ“ Flexible exchange rates вЂў CB does not intervene in market for foreign exchange вЂў To understand, suppose demand and supply of foreign exchange given by Historical View on Exchange Rate Regimes Fixed versus Flexible вЂў ShouldnвЂ™t e be determined by market forces? вЂ“ Mundell versus Friedman вЂ“ Foreign exchange is not like a normal market вЂў Exchange rate is like a dictionary вЂ“ Exchange of national currencies, fiat monies вЂў A high price of foreign exchange does not lead to more supply вЂў No fundamentals driving the market вЂў Government policy must control supply of money вЂ“ Then why should they be flexible? Friedman on Flexible Rates вЂў 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. вЂў The argument for flexible exchange rates is, strange to say, very nearly identical with the argument for daylight savings time. IsnвЂ™t 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 вЂў If CB does not intervene, then market price of foreign exchange is вЂў Suppose demand for foreign exchange increases вЂ“ Then if CB does nothing, e must rise вЂ“ To keep e fixed CB must sell foreign exchange вЂў So international reserves fall вЂ“ Thus, вЂў where is the fixed exchange rate вЂў Notice that exchange rate can also be affected by policy вЂ“ By affecting demand or supply Fixed Rates and Reserve Accumulation вЂў If the exchange rate is fixed, then reserves adjust as demand and supply shifts вЂ“ The peg is sustainable if these shocks offset вЂ“ Peg is unsustainable if shocks are biased вЂ“ But there is asymmetry вЂў Easier to accumulate foreign exchange вЂў You cannot print it if you are running out! вЂ“ When does a fixed rate collapse? вЂў When reserves run out? No. Time to Collapse вЂў Suppose that the peg is unsustainable вЂ“ When reserves run out the rate must collapse to e вЂў Implies that e will jump at that date, t вЂў Implies capital gain at date t вЂ“ 1 вЂў So people will sell at t -1, implies capital gain, so e collapses at t вЂ“ 1 вЂў Implies e collapses at t вЂ“ 2, вЂ¦ вЂў So e must collapse at earliest date at which there is no capital gain вЂ“ So e collapses before all reserves are depleted вЂў Why not sell before tc ? вЂў Because then they incur capital loss Collapse вЂў Exchange rate collapses before reserves run out вЂ“ Nobody wants to be the last person to exit вЂ“ If agents are forward looking they anticipate capital losses вЂў So currency cannot collapse and then jump to shadow rate вЂ“ In practice we see that currency collapses before reserves run out вЂ“ Key is when CB is no longer willing to pay the cost of maintaining the exchange rate вЂў CB could always repurchase the MB вЂ“ Problem is the cost of doing so В» No longer lender of last resort, interest rates may skyrocket вЂ“ External versus internal balance Foreign Exchange Reserves and MB, Sept 1994 (pct of GDP) Fixing the Exchange Rate вЂў Under fixed rates IR is changing to offset any excess demand for foreign exchange вЂ“ When there is ED > 0 the CB sells reserves, so вЂ“ If ED < 0, the opposite takes place вЂў What is the effect of this operation? вЂ“ Suppose no sterilization вЂў That is no attempt to offset the operation of pegging the exchange rate on the domestic money supply No Sterilization вЂў Start with the CBвЂ™s balance sheet вЂў The assets of the CB, IR + DS = MB вЂў The money supply just depends on the MB, so вЂ“ Thus when reserves fall the money supply contracts, and vice versa вЂ“ Fixing the exchange rate means giving up control over the supply of money Example вЂў Central bank balance sheet condition: вЂ“ Example: вЂў Suppose the government purchases 500 million in domestic bonds and 500 million in foreign assets (reserves). вЂў Money supply is therefore equal to 1000 million pesos. Central Bank Actions вЂў Suppose the Fed purchases foreign exchange вЂ“ 4 cases 1. purchase from home-country banks: вЂў 2. purchase from home-country non-bank residents: вЂў 3. 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 bankвЂ™s deposit at the Fed. вЂў вЂў in this case, residents would receive payment in the form of currency in circulation. purchase from home-country non-bank residents: вЂў 4. in this case alongside the increase in IR is an increase in bank reserves. In this case, once the bank uses this deposit to purchase some interestbearing security from a domestic bank, bank reserves will rise. In all cases, the reserve transaction results in a simultaneous change in MB Sterilization вЂў Sterilization occurs when the CB moves to insulate the domestic economy from foreign reserve transactions вЂ“ 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., вЂ“ Notice that to persist in sterilization requires large stocks of both foreign reserves and domestic securities. вЂ“ obviously difficult for debtor, what about for surplus case? вЂ“ Need to keep selling DS, but how much will the public buy? вЂў Depends on how financially developed the economy вЂў Interest cost of sterilization can be large Effect on Monetary Policy i пѓ¦ M пѓ¶ пѓ§ пѓ· пѓЁ P пѓё0 пѓ¦ M пѓ¶ пѓ§ пѓ· пѓЁ P пѓё 1 пЃ пЃ„ IR P i0 i1 L (Y , i) M /P Impossible Trinity вЂў We see that a country cannot simultaneously have: вЂ“ Independent monetary policy вЂ“ Fixed exchange rate вЂ“ Capital mobility вЂў With fixed e you interest rates cannot diverge from i* вЂў Conflict between internal and external balance вЂ“ ChinaвЂ™s вЂњadvantageвЂќ вЂў China does not have open capital account вЂ“ So it can sterilize current account surpluses вЂ“ Lack of capital mobility depresses local interest rates, reduces costs of sterilization вЂ“ 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 MexicoвЂ™s 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

1/--страниц