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Currency Risk in Brazil during the Real
Plan
Márcio Garcia
Gino Olivares
Dept. of Economics, PUC-Rio
Conference “One Year of Inflation Targeting”
Central Bank of Brazil
Rio de Janeiro - July 10-11, 2000
Motivation
Why is the currency risk relevant?
 Uncovered Interest Parity (UIP) / Covered
Interest Parity (CIP);
 Capital Flows;
 Domestic interest rate calibration (Central Bank);
 Inflation Targeting.
Covered Interest Parity Differential
(up to the devaluation)
25%
0.60
0.50
20%
0.40
0.30
10%
0.20
5%
Libor
Forward Premium
Covered Interest Parity Differential
Nov-98
Set-98
Jul-98
Mai-98
Mar-98
Jan-98
Nov-97
Set-97
Jul-97
Mai-97
Mar-97
Jan-97
Nov-96
Set-96
Jul-96
Mai-96
Mar-96
Jan-96
Nov-95
Set-95
Jul-95
Mai-95
Mar-95
0%
Jan-95
0.10
Covered Interest Parity Differential
0.00
Ln
15%
Covered Interest Parity Differential
(post devaluation)
25%
0.60
0.50
20%
0.30
10%
0.20
5%
Libor
Forward Premium
Covered Interest Parity Differential
Abr-00
Mar-00
Fev-00
Jan-00
Dez-99
Nov-99
Out-99
Set-99
Ago-99
Jul-99
Jun-99
Mai-99
Abr-99
Mar-99
Jan-99
0%
Fev-99
0.10
Covered Interest Parity Differential
0.00
Ln
0.40
15%
Objectives of this research:



To measure and analyze the Currency Risk in
Brazil during the Real Plan;
To identify some of the relations between the
currency risk and the fundamentals of the
Brazilian economy;
To obtain policy lessons about the
management of monetary and exchange rate
policy.
Main questions:


How can we measure the currency risk ?
What are the determinants of the currency
risk?
Outline
Introduction;
Futures price bias: theory and intuition;
Fama’s methodology: theory and results;
Currency Risk estimation using the Kalman
Filter;
Interest rate parity conditions;
Conclusions.
Definitions

Forward Premium
ft - s t



Forward Discount
ft - st+1
Currency Risk (Insurance Premium)
ft - Et(st+1)
Covered Interest Rate Parity
1 + it = (1 + it*)Ft/St
Fama’s methodology: Theory and results (1)


Fama (JME,1984): “Forward and Spot Exchange Rates”.
Attempt to rationalize the existence of a time-varying risk
premium using a simples framework.
The model is as follows:
f t  E t (s t 1 )  p t
Rational Expectations:
s t 1  E t (s t 1 )  v t 1
(1)
(2)
(1)  s t  f t  s t  E t (s t 1  s t )  p t
p t  v t 1  f t  s t 1  1  1 (f t  s t )  1,t 1
(3)
(4)
E t (s t 1  s t )  v t 1  s t 1  s t   2   2 (f t  s t )   2,t 1
(5)
Fama’s methodology: Theory and results (2)





Efficiency hypothesis:
H0: 2=0, 2=1
Fama used data of nine international currencies from the
period 1973:08 - 1982:12 and rejected H0 in all the cases.
He found that his estimates of 2 were not just different
from 1, but also negative.
This seemingly counter-intuitive result became known as
the Forward Premium Puzzle.
Based on his results, Fama formulated his two
“fundamental” conclusions.
Fama’s methodology: Theory and results (3)


First conclusion: The exchange rate risk premium
(currency risk) and the expected depreciation rate are
negatively correlated.
He obtained this conclusion form his negative estimates
of 2.
p lim( 
OLS
2
Var ( Et ( st 1  st ))  Cov( pt , Et ( st 1  st ))
)
0
Var ( f t  st )
Implying:
Cov(E t (s t 1  s t ), p t )  0
Metodologia de Fama: Teoria e resultados (4)


Second conclusion: The variance of the currency risk is
greater than the variance of the expected depreciation
rate.
He obtained this conclusion from the fact that his
estimates of 2 were all less than 1/2.
p lim( 
OLS
2
Var ( Et ( st 1  st ))  Cov( pt , Et ( st 1  st ))
1
)

Var ( pt )  Var ( Et ( st 1  st ))  2Cov( pt , Et ( st 1  st )) 2
Implying:
Var (p t )  Var (E t (s t 1  s t ))
Fama’s methodology: Theory and results (5)
Case
I
2 
Cov(d,p)
Cov(d,p)=0
or
Cov(d,p)<0
<0
Var(p) > |Cov(d,p)| > Var(d)
Cov(d,p) <0
III
>1
Var(d) > |Cov(d,p)| > Var(p)
Cov(d,p) <0
IV
=0.5
Var(d) = Var(p)
Indeterminate
Forward premium
puzzle
=1
Var(p) and Var(d)
Var(d) > Var(p) = 0
or
Var(p) = |Cov(d,p)|
II
Uncovered
interest rate parity
Covd, d  p 
Var d  p 
0.85
24/Dez/98
16/Nov/98
05/Out/98
25/Ago/98
16/Jul/98
04/Jun/98
24/Abr/98
12/Mar/98
29/Jan/98
17/Dez/97
07/Nov/97
30/Set/97
21/Ago/97
14/Jul/97
03/Jun/97
22/Abr/97
10/Mar/97
27/Jan/97
16/Dez/96
05/Nov/96
25/Set/96
16/Ago/96
09/Jul/96
29/Mai/96
18/Abr/96
07/Mar/96
25/Jan/96
14/Dez/95
03/Nov/95
22/Set/95
14/Ago/95
05/Jul/95
25/Mai/95
11/Abr/95
02/Mar/95
R$ / US$
Fama’ s methodology: Theory and results (6)
Spot Exchange Rate and Exchange Rate Futures
1.30
1.25
1.20
1.15
1.10
1.05
1.00
0.95
0.90
-1.0
ft - st+1
ft - st
st+1 - st
1998:12
1998:10
1998:08
1998:06
1998:04
1998:02
1997:12
1997:10
1997:08
1997:06
1997:04
1997:02
1996:12
1996:10
1996:08
1996:06
1996:04
1996:02
1995:12
1995:10
1995:08
1995:06
1995:04
Percentage per month
Fama’s methodology: Theory and results (7)
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
Fama’s methodology: Theory and results (8)

Ous results using Brazilian monthly data from the period
1995:04 - 1998.12 were not consistent with Fama’s first
“fundamental” conclusion.
Results from the OLS Estimation of Fama's regresssions using brazilian data
Period 1995:04 - 1998:12
Coefficients estimated and standard deviations
ft - st+1 =
st+1 - st =
Autocorr. and Partial Autocorr.
of wt
Lag
AC
ACP
a1 + b1 (ft - st ) + w1,t
a2 + b2 (ft - st ) + w2,t
a1
-0,3579
a2
0,3579
1
-0,09
-0,09
s(a1 )
0,1370
s(a2 )
0,1370
2
-0,19
-0, 20
b1
0,7050
b2
0,2950
3
-0,25
-0,30
s(b1 )
0,1789
s(b2 )
0,1789
4
0,06
-0,06
R42
0,5308
R52
0,1653
5
-0.02
-0,15
s(w1,t )
0,3295
s(w2,t )
0,3295
6
0,08
-0,02
Note: All the standard deviations are"White Heteroskedasticity-Consistent"
.
Fama’s methodology: Theory and results (9)



Froot e Thaler (1989) report that the majority of empirical
papers using the Fama methodology obtains negative
estimates of 2.
In the case of Brazil we obtained a positive estimate of
2, but the null-hypothesis H0: 2 = 1 was rejected.
Why do we obtain a different result?
 Bansal and Dahlquist (1999). “The Forward Premium
Puzzle: Different Tales from Developed and Emerging
Economies”.
Fama’s methodology: Theory and results (10)
B&D (1999): There is a negative relation
between the estimates 2 in the Fama
equation and per capita GDP.
Estimates of
2
1,0
0,0
-1,0
Per capita GDP
-2,0
0,4
0,6
0,8
(as a proportion
1,0 of US per capita
GDP)
Fama’s methodology: Theory and results (11)
B&D (1999): There is a positive relation
between the estimates of 2 in the Fama
equation and the inflation rate.
Estimates of
2
1,0
0,0
-1,0
Log of inflation
-2,0
-1,0
-0,5
0,0
0,5
1,0
1,5
(compared
with the US
inflation)
12/01/00
12/12/99
12/11/99
12/10/99
12/09/99
12/08/99
12/07/99
12/06/99
12/05/99
12/04/99
12/03/99
12/02/99
12/01/99
12/12/98
12/11/98
12/10/98
12/09/98
12/08/98
12/07/98
12/06/98
12/05/98
Fama’s methodology: Theory and results (12)
Figure 1: Beta 2 estimates using one-month swaps
Rolling regressions using a window with one-hundred observations
5
4
3
2
1
0
-1
Fama’s methodology: Theory and results (13)
Case
I
2 
Cov(d,p)
Cov(d,p)=0
or
Cov(d,p)<0
<0
Var(p) > |Cov(d,p)| > Var(d)
Cov(d,p) <0
III
>1
Var(d) > |Cov(d,p)| > Var(p)
Cov(d,p) <0
IV
=0.5
Var(d) = Var(p)
Indeterminate
Forward premium
puzzle
=1
Var(p) and Var(d)
Var(d) > Var(p) = 0
or
Var(p) = |Cov(d,p)|
II
Uncovered
interest rate parity
Covd, d  p 
Var d  p 
Currency Risk estimation (1)


How to measure the risk premium?
Two possibilities:
 Structural models of the risk premium
 Signal-extraction models
Structural models:
The ideia is modelling the determinants of the risk
premium. The main problem with this type of models is
that we need to identify the determinants of the risk
premium and their relationships (functional form) with it.
Currency Risk estimation (2)


Signal-extraction models:
They do not need the hypothesis the structural models
need. But, on the other side, they do not give us
information about the relationships between the risk
premium and other economic variables. In this sense, the
signal-extraction models and the structural models would
be complementary.
Examples of this type of models:
 Wolff (JF,1987). “Forward Foreign Exchange Rates,
Expected Spot Rates, and Premia: A SignalExtraction Approach”.
 Cheung (JIMF,1993).”Exchange Rate Risk Premium”.
Currency Risk estimation (3)

Wolff presents the following model:
f t  E t (s t 1 )  p t
v t 1  E t (s t 1 )  s t 1
f t  s t 1  p t  v t 1
p t    p t 1  z t
 0   Q 2
 zt 
  ~ i.i.d.N  , 

 vt 
 0   0
0 
2 
R 
Currency Risk estimation (4)




Estimation using Brazilian monthly data from the period
1995:04 - 1998:12.
We use a AR(1) specification for pt.
The results show a currency risk with a higher degree of
persistence.
The ADF test reject the null-hypothesis of existence of a
unit root in the estimated risk premium series.
-5%
1998:12
1998:10
1998:08
1998:06
1998:04
Forward discount
1998:02
1997:12
1997:10
1997:08
1997:06
30%
1997:04
1997:02
1996:12
1996:10
1996:08
1996:06
1996:04
1996:02
1995:12
1995:10
1995:08
1995:06
1995:04
Percentage per year
Currency Risk estimation (5)
Currency Risk estimated using the Kalman filter
35%
Currency Risk Premium
25%
20%
15%
10%
5%
0%
0%
1998:12
1998:10
1998:08
1998:06
Expected depreciation
1998:04
1998:02
1997:12
1997:10
1997:08
45%
1997:06
1997:04
1997:02
1996:12
1996:10
1996:08
1996:06
1996:04
1996:02
1995:12
1995:10
1995:08
1995:06
1995:04
Percentage per year
Interest rate parity conditions (1)
Forward Premium decomposition
50%
Currency risk
40%
35%
30%
25%
20%
15%
10%
5%
Interest rate parity conditions (3)
Estimated series statistics (1995:04 - 1998:12):
Currency Risk
Expected
depreciation
Actual
depreciation
Average
4,33%
8,27%
8,34%
Standard
deviation
4,96%
3,33%
4,78%
Interest rate parity conditions (4)
Hull (2000): The relationship between the futures price and
the spot price is:
F  Se
( r  r * )( T  t )
This formula must be adapted to take into account the
country risk.
Country risk = Convenience yield = Covered interest rate
parity differential.
F  Se
( r  r *  y )( T  t )
Interest rate parity conditions (5)
Thus:
Foreign interest rate +
Expected depreciation +
Currency risk +
Country risk
Domestic interest rate
0%
1998:12
1998:10
1998:08
Currency risk
1998:06
1998:04
1998:02
Expected depreciation
1997:12
1997:10
1997:08
1997:06
1997:04
US interest rate
1997:02
1996:12
1996:10
1996:08
1996:06
70%
1996:04
1996:02
1995:12
1995:10
1995:08
1995:06
1995:04
Percentage per year
Interest rate parity conditions (6)
Domestic interest rate decomposition
80%
Country risk
60%
50%
40%
30%
20%
10%
Interest rate parity conditions (8)
Correlations between the estimated series
Et(st+1 - st)
pt
Country
Risk
Et(st+1 - st)
pt
1,000
0,505
Country
Risk
0,066
1,000
0,499
1,000
Conclusions (1)


Our estimates for Brasil were not consistent the Fama’s
first “fundamental” conclusion, but they were consistent
with the results obtained for other emerging market
economies (Bansal and Dahlquist (1999)):
* The currency risk has a higher volatility than the
expected depreciation, but the correlation between them
is positive;
* After the change of regime in January 1999, the
expected depreciation turned to be more volatile than the
currency risk.
Using the methodology of Wolff (1987) it was possible to
obtain an estimated series of the currency risk.
Conclusions (2)




Using our estimated series of the risk premium it was
possible separate it from the expected depreciation.
The estimates were consistent with the results obtained
with the Fama’s methodology.
We use our estimated currency risk and expected
depreciation series to decompose the domestic interest
rate.
It was shown that the covered interest parity does not
hold in the brazilian case during the period analyzed. In
other words, it was shown that the covered interest parity
differential (country risk) is a significant component of the
domestic interest rate.
Conclusions (3)


The country risk shows a higher correlation with the
currency risk (0,50) than with the expected depreciation
(0,07). We interpret this fact as an evidence that both
risks had a common source during the period analyzed.
With no econometric evidence, we argue this common
source would be the higher degree of uncertainty about
the fundamentals of the brazilian economy (fiscal
desequilibrium, basically).
Conclusions (4)


If our hypothesis is correct, it would help to explain that
fact that, eighteen months after the change of the regime,
the real interest rates in the brazilian economy continue
being extremely higher for international standards.
On the other side, the continuation of a series of good
news about fiscal efforts, jointly with the perception that
the fiscal equilibrium as a long-lasting event, could
generate significant interest rate reductions, by reducing
both the currency risk and the country risk.