API-120 - Macroeconomic Policy Analysis I, Professor Jeffrey Frankel, Kennedy School of Government, Harvard University

LECTURE 22: 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. 3. How should we interpret the bias?

● Risk premium: Introduction to the portfolio balance model.

API-120 - 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

API-120 - Macroeconomic Policy Analysis I: Prof. J.Frankel, Harvard University

TESTS OF UNBIASEDNESS IN THE FORWARD EXCHANGE MARKET

OVERVIEW OF CONCEPTS

Et ( t+1 ) = 0 .

• Specification of unbiasedness equation

H0: 11 ttt fds

Would unbiasedness H0 => accurate forecasts?

No. <= ( t+1 0).

H0: Et ( St+1 ) = Ft .

t+1 ≡ prediction error

Most popular test:

Unbiasedness of the fx market:

No time-varying risk premium:

where Et εt+1 =0 conditional on info at time t.

ttt fsE 1

ttttt sfssE 1

ttt fdsE 1

1)(1 ttfdts

1:0 H

tte fds

,111 ttttte ssEs

+

Rational expectations:

=> H0: 11 ttt fds

But usual finding: β<<1, e.g., ≈ 0.

We proceed in logs.(See appendix on Siegal Paradox.)

}

Not necessarily. <= Could be rp 0.

• UIP version of unbiasedness .

Finding: rejection of H0 .

One can make money, on average, betting against the forward discount or, equivalently, doing the carry trade.

How to interpret?

(i) exchange risk premium, or(ii) expectations biased in-sample

11 *)( ttt iis

• Does EMH => Et st+1 = fd t ?

Tests of forward market bias extended to emerging markets:

† probability that rejection of β=0 (random walk) is just chance.‡ probability that rejection of β=1 (unbiasedness) is just chance.

Lucey, Brian M. and Loring, Grace, “Forward Exchange Rate Biasedness Across Developed and Developing Country Currencies: Do Observed Patterns Persist Out of Sample? “ Emerging Markets Review, vol. 17, 2013, pp. 14-28.

Statistical significance levels

† ‡

A majority of currencies show a rejection of unbiasednessand an inability to reject a coefficient of zero (same as advanced countries).

API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Harvard University

Applications of the forward discount bias (or interest differential bias) strategy

• The Convergence Play in the European Monetary System (1990-92): Go short in DM; long in £, Swedish kronor, Italian lira, Finnish markka & Portuguese escudo.

• The Carry Trade– (1991-94) Go short in $, long in Mexican pesos, etc.– (1995-98) Go short in ¥; long in $ assets, in Asia or US– (2002-07) 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 (2009-12): 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 2001-08: the 5% interest differential was not offsetby any depreciation of the A$ during these years.

}interest differential = 500 basis points

”How to trade the carry trade,” Futures Magazine, www.futuresmag.com, Sept. 2011

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, www.futuresmag.com, Sept. 2011

Unwinding ofthe carry trade

API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, 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) Cast a wider net. Look at EM currencies.

2) Find a measure of ∆se. (See Appendix 4 on survey data.)

3) Model rp theoretically. See if prediction errors depend systematically on variables rp should depend on.―> Subject of Lecture 23: Optimal portfolio diversification.

Each investor at time t allocates sharesof 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 Et rt+1 must be, for supplies xt to be willingly held.

xi, t = βi (Et rt+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 (rpt = 0), and so

• no effect from sterilized forex intervention.

We see that asset supplies are a determinant of the risk premium.

xt = A + B rpt .

How the supply of debt x determines the risk premium rpin the portfolio balance model

A large x forces up the expected return that portfolio holders must be paid.

Let x be the share assigned to foreign bonds.In lecture 23 “foreign” will be defined as denominated in foreign currency.In lecture 24 “foreign” will be defined as issued by the foreign government.

API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Kennedy School of Government, Harvard University

API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Harvard University

Appendix 1: TESTS OF UNBIASEDNESS IN THEFORWARD EXCHANGE MARKET, OVERVIEW OF CONCEPTS (continued)

Definition: Random Walk (∆s t+1 = ε t+1 ).

Does unbiasedness => RW?

No. <= (fdt 0), so Et ∆s t+1 0.

Def.: Rational Expectations Set = Et (St+1)

Def.: Efficient Markets Hypothesis F reveals all info

Does RE => EMH ?

Not necessarily. <= There could be transactions costs, capital controls, missing markets...

API-120 - Macroeconomic Policy Analysis I ; Professor Jeffrey Frankel, Harvard University

Appendix 2:Technical econometrics regarding error term:

• Overlapping observations => MA error process

• “Peso problem:” small probability of big devaluation

=> error term not ~ iid normal.

• The Siegal paradox: Is H0 Ft = Et(St+1)? or 1/Ft = Et(1/St+1)?

API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Harvard University

Appendix 2, 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 unbiasedwhen 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.)

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 3:Tests of unbiasedness in the forward discount for individual countries

Pooling slope estimates across

all emerging countries, the sign > 0 =>

much less bias than the

estimates for rich countries.

Even so, β<<1 => unbiasedness

still rejected.

Source: J.Frankel & Jumana Poonawala, “Are Forward Exchange Rates Biased Indicators of Spot Exchange Rates in Emerging Market Economies?” JIMF 2010 .

(See below for results on individual countries.)

For each industrialized country, the slope β is negative.

Source: Frankel & Poonawalla, JIMF, 2010

For emerging markets, some currencies have negative slopes, but some have positive slopes.

Source: Frankel & Poonawalla, JIMF, 2010

API-120 - 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?” 2010 .

The estimates for the emerging countries show less bias than the estimates for rich countries.

Lucey & Loring, “Forward Exchange Rate Biasedness Across Developed and Developing Country Currencies: Do Observed Patterns Observed Patterns Persist Out of Sample? “ Emerging Markets Review, 2013.

API-120 - Macroeconomic Policy Analysis I ; Professor Jeffrey Frankel, Harvard University

Survey data to measure expectations:

Test for risk premium:

, no time-varying risk premium.

Finding: Failure to reject H0 .

(Allows for a constant risk premium α2.)

tuss t

et

e ˆ

tu

tfds t

e )(ˆ 22

1: 20 H

Appendix 4

API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Kennedy School of Government, Harvard University

Coefficienton fd (β2) is

insignificantly different from 1.

=> time-variation in fd is variation in

∆se, not in rp.