Lecture 23: Forward Market Bias & the Carry Trade

Transcription

1 Lecure 23: Forward Marke Bias & he Carry Trade Moivaions: Efficien markes hypohesis Does raional expecaions hold? Does he forward rae reveal all public informaion? Does Uncovered Ineres Pariy hold? Or is here a risk premium? The carry rade: Does borrow a low i & lend a high i* make money? Ouline of lecure 1. Specificaion of he es of unbiasedness. 2. Answer: F is biased. 3. How should we inerpre he bias? Risk premium: Inroducion o he porfolio balance model. API Macroeconomic Policy Analysis I, Professor Jeffrey Frankel, Kennedy School of Governmen, Harvard Universiy

2 Sample page of spo and forward exchange raes, local per $ (bu $/ and $/ ). Spo rae Forward raes Financial Times Jan. 30, 2009 API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Governmen, Harvard Universiy

3 Tess of Unbiasedness in he Forward Exchange Marke OVERVIEW OF CONCEPTS H 0 : E ( S +1 ) = F. Specificaion of unbiasedness equaion s H 0 : 1 fd 1 +1 predicion error E ( +1 ) = 0. Would unbiasedness H 0 => accurae forecass? No. <= ( +1 0). API Macroeconomic Policy Analysis I: Prof. J.Frankel, Harvard Universiy

4 We proceed in logs. (See appendix on Siegal Paradox.) E s Es s 1 1 f f s E s 1 fd Mos popular es: Unbiasedness of he fx marke: s 1 ( fd ) 1 H0 : 1 No ime-varying risk premium: + Raional expecaions: s s e e where E ε +1 =0 condiional on info a ime. => H 0 : fd E s s } 1 s 1 1, 1 fd 1 Bu usual finding: β<<1, e.g., 0.

5 Does EMH => E s +1 = fd? No necessarily. <= Could be rp 0. UIP version of unbiasedness s 1 ( i i*) 1. Finding: rejecion of H 0. One can make money, on average, being agains he forward discoun or, equivalenly, doing he carry rade. How o inerpre? (i) exchange risk premium, or (ii) expecaions biased in-sample

6 Tess of forward marke bias exended o emerging markes: A majoriy of currencies show a rejecion of unbiasedness and an inabiliy o rejec a coefficien of zero (same as advanced counries). Saisical significance levels probabiliy ha rejecion of β=0 (random walk) is jus chance. probabiliy ha rejecion of β=1 (unbiasedness) is jus chance. Brian Lucey & Grace Loring, 2013, Forward Exchange Rae Biasedness Across Developed and Developing Counry Currencies: Do Observed Paerns Persis Ou of Sample? Emerging Markes Review, vol.17, pp

7 Applicaions of he forward discoun bias (or ineres differenial bias) sraegy The Convergence Play in he European Moneary Sysem ( ): Go shor in DM; long in, Swedish kronor, Ialian lira, Finnish markka & Poruguese escudo. The Carry Trade ( ) Go shor in $, long in Mexican pesos, ec. ( ) Go shor in ; long in $ asses, in Asia or US ( ) Go shor $,, SFr; long in Ausralia, Brazil, Iceland, India, Indonesia, Mexico, New Zealand, Russia, S. Africa, & Turkey. New convergence play (2007): Go shor in ; long in Hungary, Balics, oher EMU candidaes. New carry rade ( ): Go shor in $. API Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Harvard Universiy

8 Carry rade: A sraegy of going shor in he (low-ineres rae) and long in he (high ineres rae) A$ made a lile money every monh : he 5% ineres differenial was no offse by any depreciaion of he A$ during hese years. }ineres differenial = 500 basis poins How o rade he carry rade, Fuures Magazine, Sep. 2011

9 Suddenly in 2008, he sraegy of going shor in and long in A$ los a lo of money, as risk concerns rose sharply, he carry rade unwound, and he A$ plunged agains he. Unwinding of he carry rade How o rade he carry rade, Fuures Magazine, Sep. 2011

10 Unanswered quesion: Is he sysemaic componen of -- he fd bias -- due o: «a risk premium rp? or «a failure of Raional Expecaions? Three possible approaches: 1) Find a measure of s e. (See Appendix 4 on survey daa.) 2) Model rp heoreically. See if predicion errors depend sysemaically on variables rp should depend on. > Subjec of Lecure 23: Opimal porfolio diversificaion. 3) Cas a wider ne, wih respec o counries or horizons. API Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Harvard Universiy

11 Inroducion o he porfolio-balance model: Each invesor a ime allocaes shares of his or her porfolio o a menu of asses, as a funcion of expeced reurn, risk, & perhaps oher facors (ax reamen, liquidiy...): x i, = β i (E r +1, risk ). Sum across invesors i o ge he aggregae demand for asses, which mus equal supply in he marke. We will inver he funcion o deermine wha E r +1 mus be, for supplies x o be willingly held.

12 x = A + B rp. Now inver: rp = B -1 x - B -1 A. We see ha asse supplies are a deerminan of he risk premium. Special case : B -1 = 0, perfec subsiuabiliy ( B = ), no risk premium (rp = 0), and so no effec from serilized forex inervenion.

13 How he supply of deb x deermines he risk premium rp in he porfolio balance model A large x forces up he expeced reurn ha porfolio holders mus be paid.

14 API Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Kennedy School of Governmen, Harvard Universiy

15 Appendix 1: TESTS OF UNBIASEDNESS IN THE FORWARD EXCHANGE MARKET, OVERVIEW OF CONCEPTS (coninued) Definiion: Random Walk ( s +1 = ε +1 ). Does unbiasedness => RW? No. <= (fd 0), so E s Def.: Raional Expecaions S e = E (S +1 ) Def.: Efficien Markes Hypohesis F reveals all info Does RE => EMH? No necessarily. <= There could be ransacions coss, capial conrols, missing markes...

16 Appendix 2: Technical economerics regarding error erm: Overlapping observaions => MA error process Peso problem: small probabiliy of big devaluaion => error erm no ~ iid normal. The Siegal paradox: Is H 0 F = E (S +1 )? or 1/F = E (1/S +1 )? API Macroeconomic Policy Analysis I ; Professor Jeffrey Frankel, Harvard Universiy

17 Appendix, con.: The Siegal Paradox -- an annoying echnicaliy an insance of Jensen s inequaliy. One would hink ha if he forward rae is unbiased when one currency is defined o be he domesic currency, i would also be unbiased when he oher is. Unforunaely his is no he case, unless spo & forward raes are defined in logs. (A jusificaion for using logs -- a Siegal paradox resoluion is available as an Addendum o his lecure.) API Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Harvard Universiy

18 Appendix 3: Tess of unbiasedness in he forward discoun for individual counries Resuls repored in Engel survey are ypical: On average, no only does S fail o move in he direcion indicaed by he forward discoun, bu i ends, if anyhing, o move opposie.

19 Pooling slope esimaes across all emerging counries, he sign > 0 => much less bias han he esimaes for rich counries. Even so, β<<1 => unbiasedness sill rejeced. (See below for resuls on individual counries.) Source: J.Frankel & Jumana Poonawala, 2010, Are Forward Exchange Raes Biased Indicaors of Spo Exchange Raes in Emerging Marke Economies? JIMF.

20 For each indusrialized counry, he slope β is negaive. Source: Frankel & Poonawalla, JIMF, 2010

21 For emerging markes, some currencies have negaive slopes, bu some have posiive slopes. Source: Frankel & Poonawalla, 2010

22 The esimaes for he emerging counries show less bias han he esimaes for rich counries. Source: J.Frankel & Jumana Poonawala, Are Forward Exchange Raes Biased Indicaors of Spo Exchange Raes in Emerging Marke Economies? API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Governmen, Harvard Universiy

23 Lucey & Loring, Forward Exchange Rae Biasedness Across Developed and Developing Counry Currencies: Do Observed Paerns Observed Paerns Persis Ou of Sample? Emerging Markes Review, 2013.

24 Appendix 4 Survey daa o measure expecaions: ˆ s e Tes for risk premium: s e u sˆ e ( 2 2 fd ) u H 0 : 2 1, no ime-varying risk premium. Finding: Failure o rejec H 0. (Allows for a consan risk premium α 2.) API Macroeconomic Policy Analysis I ; Professor Jeffrey Frankel, Harvard Universiy

25 Coefficien on fd (β 2 ) is insignificanly differen from 1. => ime-variaion in fd is variaion in s e, no in rp. API Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Kennedy School of Governmen, Harvard Universiy