Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University LECTURE 23: FORWARD MARKET BIAS & THE CARRY TRADE Motivations: Efficient markets hypothesis Does rational expectations hold? Does the forward rate reveal all public information? Does Uncovered Interest Parity hold? Or is there a risk premium? = The carry trade: Does “borrow at low i & lend at high i*” make money? Outline of lecture 1.Specification of the test of unbiasedness. 2.Answer: F is biased. Carry trade makes money, on average. 3.How should we interpret the bias? ● Risk & introduction to the portfolio balance model.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Financial Times Jan. 30, 2009 Sample page of spot and forward exchange rates, local per $ (but $/₤ and $/€). Spot rate | Forward rates

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University TESTS OF UNBIASEDNESS IN THE FORWARD EXCHANGE MARKET OVERVIEW OF CONCEPTS H 0 : S t+1 = F t +  t+1 & E t (  t+1  Info t ) = 0 Specification of unbiasedness equation H0:H0: Does unbiasedness H 0 => accurate forecasts? No. <= (  t+1  0). Or, more succinctly, E t ( S t+1 ) = F t.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University TESTS OF UNBIASEDNESS IN THE FORWARD EXCHANGE MARKET OVERVIEW OF CONCEPTS (continued) Def.: Random Walk  (∆s t+1 = ε t+1 ). Does unbiasedness => RW? No. <= (fd t  0). Def.: Rational Expectations  S e t = E t (S t+1 ) Def.: Efficient Markets Hypothesis  F reveals all info Does RE => EMH ? Not necessarily. <= There could be transactions costs, capital controls, missing markets...

Most popular test: Unbiasedness of the fx market: No time-varying risk premium: where E t ε t+1 =0 conditional on info at time t. + Rational expectations: => H 0 : But usual finding: β<<1, e.g., ≈ 0. We proceed in logs. (See appendix on Siegal Paradox.) }

No. <= Could be rp  0. UIP version of unbiasedness. Finding: rejection of H 0. One can make money, on average, betting against the forward discount or, equivalently, doing the carry trade. How to interpret? (i) exchange risk premium (ii) expectations biased in-sample Does EMH => E t  s t+1 = fd t ?

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Pooling slope estimates across all emerging countries, the sign > 0 => much less bias than the estimates for rich countries. Even so, β unbiasedness still rejected. Source: J.Frankel & Jumana Poonawala, “ Are Forward Exchange Rates Biased Indicators of Spot Exchange Rates in Emerging Market Economies? ” JIMF (See appendix 2 for results on individual countries.)

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Applications of the forward discount bias (or interest differential bias) strategy The Convergence Play in the E uropean M onetary S ystem ( ): G o short in DM; long in £, Swedish kronor, Italian lira, Finnish markka & Portuguese escudo. The Carry Trade –( ) Go short in $, long in Mexican pesos, etc. –( ) Go short in ¥; long in $ assets, in Asia or US –( ) Go short $, ¥, SFr; long in Australia, Brazil, Iceland, India, Indonesia, Mexico, New Zealand, Russia, S. Africa, & Turkey. New convergence play (2007): –Go short in €; long in Hungary, Baltics, other EMU candidates. New carry trade ( ): Go short in $.

Carry trade: A strategy of going short in the (low-interest rate) ¥ and long in the (high interest rate) A$ made a little money every month : the 5% interest differential was not offset by any depreciation of the A$ during these years. Copyright 2007 Jeffrey Frankel, unless otherwise noted } interest differential = 500 basis points ”How to trade the carry trade,” Futures Magazine, Sept. 2011www.futuresmag.com

Suddenly in 2008, the strategy of going short in ¥ and long in A$ lost a lot of money, as risk concerns rose sharply, the carry trade “unwound,” and the A$ plunged against the ¥. ”How to trade the carry trade,” Futures Magazine, Sept. 2011www.futuresmag.com Unwinding of the carry trade

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Unanswered question: Is the systematic component of -- the fd bias -- due to: « a risk premium rp? or « a failure of Rational Expectations? Three possible approaches: 1) Find a measure of ∆s e. (See Appendix 3 on survey data.) 2) Model rp theoretically. See if prediction errors depend systematically on variables rp should depend on. ―> Subject of Lecture 24: Optimal portfolio diversification. 3) Cast a wider net, with respect to countries or horizons.

Each investor at time t allocates shares of his or her portfolio to a menu of assets, as a function of expected return, risk, & perhaps other factors (tax treatment, liquidity...): Sum across investors i to get the aggregate demand for assets, which must equal supply in the market. We will invert the function to determine what E t r t +1 must be, for supplies x t to be willingly held. x i, t = β i (E t r t+1, risk ). Introduction to the portfolio-balance model:

Now invert: rp t = B -1 x t - B -1 A. Special case : | B -1 | = 0, perfect substitutability ( |B|=∞ ), no risk premium (rp t = 0), and so no effect from sterilized forex intervention. We see that asset supplies are a determinant of the risk premium. x t = A + B rp t.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Appendix 1: Technical econometrics regarding error term: Overlapping observations => MA error process Heteroscedasticity “Peso problem:” small probability of big devaluation => error term not ~ iid normal. The Siegal paradox

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Appendix, cont.: The Siegal Paradox -- an annoying technicality– an instance of “Jensen’s inequality.” One would think that if the forward rate is unbiased when one currency is defined to be the domestic currency, it would also be unbiased when the other is. Unfortunately this is not the case, unless spot & forward rates are defined in logs. (A justification for using logs -- a Siegal paradox resolution – is available as an Addendum to this lecture.)

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Results reported in Engel survey are typical: On average, not only does S fail to move in the direction indicated by the forward discount, but it tends, if anything, to move opposite. Appendix 2: Tests of unbiasedness in the forward discount for individual countries

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University For each industrialized country, the slope β is negative. Source: Frankel & Poonawalla, JIMF, 2010

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University For emerging markets, some have negative slopes, but some have positive slopes. Source: Frankel & Poonawalla, JIMF, 2010

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Source: J.Frankel & Jumana Poonawala, “ Are Forward Exchange Rates Biased Indicators of Spot Exchange Rates in Emerging Market Economies? ” The estimates for the emerging countries show less bias than the estimates for rich countries.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Survey data to measure expectations: Test for risk premium:, no time-varying risk premium. Finding: Failure to reject H 0. (Allows for a constant risk premium α 2.) Appendix 3

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Coefficient on fd (β 2 ) is insignificantly different from 1. => time-variation in fd is variation in ∆se, not in rp.