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API119: Advanced Macroeconomics for the Open Economy II
Staff  Professors: Jeffrey Frankel (1st 5 lectures), Filipe Campante (from Feb. 9 on).
Teaching Fellow: Tilahun Emiru Course Assistants: Alfonso de la Torre, Richard Medina & Na Zhang.
Times Lectures: Tues. & Thurs., 10:1511:30 p.m., L230
Review sessions: Fri., 10:1511:30 & 11:451:00, Land Hall
Frankel Office hours: Mon.Tues., 3:004:00, Littauer 217
 Macroeconomic Policy Analysis Professor Jeffrey Frankel, Kennedy School, Harvard Universi00ty
Lectures 15: Risk, Diversification & Emerging Market Crises
L1: The carry trade Forward market bias
Risk premium & introduction to portfolio balance model
L2: Optimal portfolio diversification Foreign exchange risk
Equity market risk
Home bias
L3: Country risk Sovereign spreads
Debt dynamics
Professor Jeffrey Frankel
Lecture 1: The Carry Trade
Motivations for testing unbiasedness:
Efficient Markets Hypothesis (EMH) 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: The forward market is biased; the carry trade works.
3. How should we interpret the bias? Risk premium: Introduction to the portfolio balance model.
API120  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
Macroeconomic Policy Analysis: Prof. J.Frankel
Tests of unbiasedness in the forward exchange market
Overview of concepts
where Et (t+1) = 0 .
Specification of unbiasedness equation
Would unbiasedness H0 => accurate forecasts?
No.
Most popular test:
Unbiasedness of the fx market:
No timevarying risk premium:
where Et t+1 =0 conditional on info at time t.
+
Rational expectations:
But usual finding is
Not necessarily. Et st+1 = fd t ?
How to interpret? (i) exchange risk premium, or (ii) expectations biased insample.
Tests of forward market bias extended to emerging markets:
probability that rejection of =0 (random walk) is just chance. probability that rejection of =1 (unbiasedness) is just chance.
Brian Lucey & Grace Loring, 2013, Forward Exchange Rate Biasedness Across Developed and Developing Country Currencies: Do Observed Patterns Persist Out of Sample? Emerging Markets Review, vol.17, pp. 1428.
Statistical significance levels
A majority of currencies show a rejection of unbiasedness and an inability to reject a coefficient of zero (same as advanced countries).
Test of Test of
Macroeconomic Policy Analysis, Professor Jeffrey Frankel
Unanswered question: Is the systematic component of  the fd bias  due to: a risk premium rp? or a failure of Rational Expectations?
Two possible approaches:
1) Find a measure of se : survey data.
2) Model rp theoretically. See if prediction errors depend systematically on variables rp should depend on. > Subject of Lecture 2: Optimal portfolio diversification.
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 Et rt+1 must be, for asset supplies xt to be willingly held.
xi, t = i (Et rt+1 , risk ) .
Introduction to the portfoliobalance model:
Now invert: rp t = B1 x t  B
1 A .
Special case :  B1  = 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 rp in the portfolio balance model
A large x forces up the expected return that portfolio holders must be paid.

API120  Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Kennedy School of Government, Harvard University
http://beyond438.files.wordpress.com/2007/12/50zarand.jpghttp://images.google.com/imgres?imgurl=http://www.countryreports.org/economy/getCurrency.aspx?Currency%3DPK&imgrefurl=http://www.countryreports.org/economy/currency.aspx?countryid%3D186&usg=__A79Z86A6euGoIVoJEkTSw01aw3c=&h=209&w=375&sz=21&hl=en&start=2&um=1&tbnid=9Ob2v3alwUG0vM:&tbnh=68&tbnw=122&prev=/images?q%3Dpakistan%2Bcurrency%26hl%3Den%26rlz%3D1T4RNWE_enUS312US312%26sa%3DN%26um%3D1http://images.google.com/imgres?imgurl=http://farm4.static.flickr.com/3359/3290689416_13542cba25_m.jpg&imgrefurl=http://www.visitingeu.com/turkey/2009/09/turkishcurrency.html&usg=__oJUXlxmipoLU6oA4f22RU_zlYs=&h=180&w=240&sz=23&hl=en&start=1&um=1&tbnid=ma4FMkmoHhDKJM:&tbnh=83&tbnw=110&prev=/images?q%3Dturkey%2Bcurrency%2Bcode%26ndsp%3D21%26hl%3Den%26rlz%3D1T4RNWE_enUS312US312%26sa%3DN%26um%3D1
Appendix 1: Test of forward market unbiasedness Overview of concepts, continued
Definition: Random Walk (s t+1 = t+1 ).
Does unbiasedness => RW?
No. EMH ?
Not necessarily.
Appendix 2: Applications of the forward discount bias
(or interest differential bias) strategy
The Convergence Play in the European Monetary System (199092): Go short in DM; long in , Swedish kronor, Italian lira, Finnish markka & Portuguese escudo.
The Carry Trade (199194) Go short in $, long in Mexican pesos, etc.
(199598) Go short in ; long in $ assets, in Asia or US
(200207) 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 trades: 200913: Go short in $. 2016: Go short in .
Carry trade: A strategy of going short in the (lowinterestrate) and long in the (high interest rate) A$ made a little money every
month 200108: the 5% interest differential was not offset by 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
http://www.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, www.futuresmag.com, Sept. 2011
Unwinding of the carry trade
http://www.futuresmag.com/
API120  Macroeconomic Policy Analysis I ; Professor Jeffrey Frankel, Harvard University
Appendix 3: Technical econometrics regarding error term:
Overlapping observations => Moving Average error process
Peso problem: small probability of big devaluation => error term not ~ iid normal.
The Siegal paradox: What is the H0 : Ft = Et(St+1)? or 1/Ft = Et(1/St+1)?
Professor Jeffrey Frankel,
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 so, an instance of
Jensens inequality.
Appendix 3, continued: The Siegal Paradox  an annoying technicality in tests of unbiasedness
API119  Macroeconomic Policy Analysis II , Professor Jeffrey Frankel,
Or (the expression used in lecture): Et(st+1) = (fd)t.
Equivalently: Et(st+1)  st = ft  st .
Thus our null hypothesis, H0, is: Et(st+1) = ft .
Running the equation with spot & forward rates defined in logs avoids the Siegal paradox.
(Is that specification legitimate? It is, if St+1 is distributed lognormally.)