Doctoral School of Finance and Banking
Bucharest
Uncovered interest parity
and deviations from
uncovered interest parity
MSc student: Alexandru-Chidesciuc Nicolaie
Presentation contents
 Introducing
 Deviations
UIP
from UIP
 Methodology,
results
data and empirical
Why UIP?

UIP is the cornerstone of international finance (it
appears as a key behavioral relationship in almost
all of the prominent current-day models of
exchange rate determination)

Since UIP reflects the market’s expectations of
exchange rate changes, it represents the
benchmark from which any analysis which depends
on future exchange rate values must begin.

Because of this, if there are reasons to believe UIP
will not hold precisely, an investor must be able to
identify the source of deviation and respond
accordingly.
Notation used





St – nominal spot exchange rate at time t expressed as
the price, in “home-country” monetary units, of foreign
exchange (ROL against USD);
Ste – expected nominal spot exchange rate at time t;
Ft – forward rate at time t;
it, respective rt – nominal interest rate at time t,
respective real interest rate at time t in home country;
it* , respective rt* – nominal interest rate at time t,
respective real interest rate at time t in foreign country.
Covered interest parity (CIP)

The difference in interest rates between two countries
is equal to the expected appreciation as measured by
the forward exchange rate. In principal, this condition
always holds because of arbitrage (no risk involved).
1  it Ft


St
1  it


it  it  f t  st
( ft t– stt) is called forward
The difference (f
premium/discount
Uncovered interest parity
(UIP)
The difference in interest rates between
two countries is equal to the expected
rate of appreciation/depreciation in the
spot market (if market participants are
risk neutral).
Thus, UIP ex ante is:

1  it  1  it


S e t 1
St

it  it  s e t 1  st
Uncovered interest parity
(UIP)

The version that appears in leading econometric
models:

it  it  s e t 1  st   t

 t - the disturbance term, which might
represent time-varying risk premia or other
effects
Forward premium puzzle
If both CIP and UIP hold, a common test of
UIP considers the following regression:
s e t 1  st      f t  st    t 1
 In practice, for a wide range of currencies,
 is found significantly less than zero
 This is called the forward premium puzzle
(forward premium anomaly) – interest
differential predicts the wrong direction in
which exchange rate moves
Deviations from UIP
There are many reasons why Uncovered Interest
Parity will not hold exactly, and can be even
expected to fail:
foreign exchange risk premia
 systematic forecast errors
 transaction costs
 intervention in the foreign exchange
market
 capital does not flow freely across borders

Methodology, data and empirical
results

Empirical analysis has been made using
monthly data from 1995/01 to 2000/12 for:
– the average nominal exchange rate,
– average passive interest rate used by banks for LEI
operations (dpm),
– loan interest rate in USA (Bank prime loan rate)(mprime)

Test of UIP hypothesis
 Why do deviations occur?
 Joint tests of three parity conditions
Estimation of UIP

I specified the regression according to Flood and Rose
(1994) and Meredith and Chinn (1998)



st k  st     it  it   t

The above equation incorporates rational expectations
st 1  st 1   t
e

I changed the interest rate series from annual percent to
monthly percent. In this purpose we used two methods
a
i
it  t
12
it  12 1  it  1
a
Estimation of UIP

Is there any connection between exchange rate
change and interest rate differential?
– Change in exchange rate (in logarithm) with respect to
interest differential
– Change in exchange rate (in logarithm) and the interest
differential

Properties of the regression variables; for this
purpose we will perform unit-root tests:
augmented Dickey-Fuller and Phillips-Perron
Unit-root tests

Unit-root test for exchange rate change (in log)
ADF Test
1% Critical Value*
5% Critical Value
10% Critical Value
*MacKinnon critical values for rejection of hypothesis of a unit

-5.53916
-3.5267
-2.9035
-2.5889
root.
Unit-root test for nominal interest rate differential
ADF Test
Statistic
-3.617141
1% Critical
-3.5253
Value*
5% Critical
-2.9029
Value
10% Critical
-2.5886
Value of hypothesis of a unit root.
*MacKinnon critical values for rejection
Regression specification and result

I tested the following regression:



st 1  st     it  it   1  d 97   2  d 99   t

Dummy variable were included because of
the shocks in early 1997 (d97) and end of
1998 and early 1999 (d99)
 The result: UIP doesn’t hold in case of
Romania (it’s a standard result in international
finance)
UIP estimation
Dependent Variable: L_EXCHRATE_DIF
View correlogram
Method: Least Squares
Date: 07/04/01 Time: 20:04
Sample(adjusted): 1995:02 2000:11
Included observations: 70 after adjusting endpoints
Variable
Coefficient
Std. Error
C
DIFD
D97
D99
R-squared
0.071911
-1.679299
0.236367
0.068999
0.724832
tStatistic
7.2558
-5.0209
12.687
5.1411
Prob.
Adjusted Rsquared
S.E. of
regression
0.712324
0.009911
0.334462
0.018631
0.013421
Mean dependent var
S.D. dependent var
0.0000
0.0000
0.0000
0.0000
0.037837
0.028268
Akaike info criterion
-4.238751
Sum squared
resid
Log likelihood
DurbinWatson stat
0.052738
Schwarz criterion
-4.110265
152.3563
2.000283
F-statistic
Prob(F-statistic)
57.95119
0.000000
0.052703
UIP estimation
There is another way to test UIP (very simple)

If sample mean of  t (ex post deviations from UIP) is
statistically different from zero
30
Series: DEVIATION01
Sample 1995:02 2000:12
Obs erv ations 71
25
Mean
Median
Max imum
Minimum
Std. Dev .
Skewnes s
Kurtosis
20
15
10
5
J arque-Bera
Probability
-0.008510
-0.000495
0.098154
-0.283265
0.052682
-3.437390
18.26626
829.2841
0.000000
0
-0.3

-0.2
-0.1
Is  t a stationary process?
ADF Test Statistic
0.0
-4.23621
0.1
1%
Critical Value*
-3.5281
5%
Critical Value
-2.9042
10% Critical Value
-2.5892
*MacKinnon critical values for rejection of hypothesis of a unit root.
PP Test Statistic
-4.604387
1%
Critical Value*
-3.5253
5%
Critical Value
-2.9029
10% Critical Value
-2.5886
*MacKinnon critical values for rejection of hypothesis of a unit root.
Why do deviations occur?

UIP equation can be written in terms of the real interest
rate differential and real exchange rate growth
st 1

e

 
 

 1  rt   1   t e
 st  ln 

e
1

r

1


t
t

ex post deviation from UIP is
t  rd t  qt

rd t  rt  rt

qt  st  pt  pt

Where:

is real interest differential
logarithm of the real exchange rate
The real exchange rate

If real exchange rate is random walk, then
all movements in real exchange rate are
unexpected
 I estimated
qt   0   i  Z t   t
 to see the effect of current information
dataset Z t on q
Estimation of real exchange rate


real exchange rate change is not a random walk
test reveals that UIP deviations are predictable, but doesn’t
show how important is the predictable component
Dependent Variable: L_EXCHRATE_REALD
Method: Least Squares
Date: 06/29/01
Time: 00:44
Sample(adjusted): 1995:02 2000:12
Included observations: 71 after adjusting endpoints
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-0.002365
0.000923
-2.562331
0.0127
DIFD
-0.005104
0.034512
-0.147897
0.8829
DIF_INFL
-0.880121
0.010539
-83.51211
0.0000
0.98621
0.007002
140.8413
0.0000
0.9972
Mean dependent var
0.001389
L_EXCHRATE_DIF
R-squared
Adjusted R-squared
0.997075
S.D. dependent var
0.046291
S.E. of regression
0.002504
Akaike info criterion
-9.087498
Schwarz criterion
-8.960023
Sum squared resid
0.00042
Log likelihood
326.6062
F-statistic
7954.866
Durbin-Watson stat
2.208492
Prob(F-statistic)
0.000000
Sources of variances in UIP deviations
I decomposed ex post deviations from UIP
further into anticipated and unanticipated
components of real exchange rate growth
(Tanner (1998))
q    Z
 anticipated
 t  qt   0   i  Z t
 unanticipated

t
Variance
var   var rd  var  
var q 
0.00359 0.00099 0.000006 0.0021
0
i
t
Var(.) as part of var  
var rd  var   var q 
0.277
0.00164 0.5868
covrd ,   cov  rd , q
0.00177 0.12

Joint tests of three parity conditions

The test consists of parameter restrictions
 risk premia only affect nominal and real interest
rate differential, but not inflation differential
 systematic forecast errors of exchange rate only
affect nominal interest differential and inflation
differential, but not real interest differential

it  it  st 1  rpt   t

pt  pt  st  q t  t   t

rt  rt  rpt q t  t
Joint tests of three parity conditions

The system that connects deviations from parity
conditions to the current information set (I included
here interest rate differential and inflation
differential) is as follows:

it  it  st 1   0    Z t  u1t

pt  pt  st  0    Z t  u2 t

rt  rt   0    Z t  u3t
 Zt
includes interest rate differential and inflation
differential
Joint tests of three parity conditions –
results

Here the coefficients are:
c(4)  
c(2)  
c(6)  
Wald Test:
System: SYS01
Null
Hypothesis:
Chi-square
C(2)=0
30.41684
Probability
0.0000
Probability
0.0000
Probability
0.0000
Wald Test:
System: SYS02
Null
Hypothesis:
Chi-square
C(4)=0
114.413
Wald Test:
System: SYS01
Null
Hypothesis:
Chi-square
C(6)=0
265.1743
Joint tests of three parity conditions –
results
There are no common factors to generate deviations
from two parity conditions. I found evidence of
systematic departures from all three parity
conditions and this is consistent with the
coexistence of both foreign exchange risk premia
and systematic forecast errors in the foreign
exchange markets.
Conclusions

In line with results of other studies UIP
doesn’t hold for Romania either
– capital markets aren’t fully integrated with the
internationals ones
– there are bounds imposed to natural and legal
persons regarding their investments in other
countries
– capital account isn’t fully liberalized
Conclusions
The main components of deviations from UIP:

the variance of the real exchange rate (anticipated
and unanticipated)
 the risk premium bears an important influence too
Joint tests of three parity conditions had shown:

both factors are present on the foreign exchange
market (risk premium and forecast errors )
Key Points

Uncovered Interest Parity is the benchmark
from which to view future exchange rate
behavior;
 it requires having a clear understanding when
deviations from UIP can/do occur, so that we
can adjust our analysis accordingly;
 Ex-post deviations from Uncovered Interest
Parity can be identified as being generated by
systematic forecast errors and by risk premia
Nominal exchange rate (ROL against USD)
from 1995:01 to 2001:12
30000
20000
15000
10000
5000
0
ia
n95
iu
l-9
5
ia
n96
iu
l-9
6
ia
n97
iu
l-9
7
ia
n98
iu
l-9
8
ia
n99
iu
l-9
9
ia
n00
iu
l-0
0
ROL/USD
25000
EXCHRATE
Nominal exchange rate change (in logarithms)
0.35
0.3
0.25
0.2
0.15
0.1
0.05
ia
n95
-0.05
iu
l-9
5
ia
n96
iu
l-9
6
ia
n97
iu
l-9
7
ia
n98
iu
l-9
8
ia
n99
iu
l-9
9
ia
n00
iu
l-0
0
0
L_EXCHRATE_DIF
Average passive interest rate used by banks
with their clients
% p.a.
120
100
80
60
40
20
0
0
l-0
iu
00
nia
9
l-9
iu
99
nia
8
l-9
iu
98
nia
7
l-9
iu
97
nia
6
l-9
iu
96
nia
5
l-9
iu
95
nia
DPM
Interest rate in USA (Bank prime loan rate) –
averages of daily figures
% p.a.
10
9.5
9
8.5
8
7.5
0
l-0
iu
00
nia
9
l-9
iu
99
nia
8
l-9
iu
98
nia
7
l-9
iu
97
nia
6
l-9
iu
96
nia
5
l-9
iu
95
nia
MPRIME
Change in exchange rate (in logarithm) and the
interest differential
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
ian iul
i
i
i
i
i
i
i
i
i
i
-9 an-9 ul-9 an-9 ul-9 an-9 ul-9 an-9 ul-9 an-0 ul-0
-9
5
6
7
8
9
0
5
6
7
8
9
0
DIFD
L_EXCHRATE_DIF
Change in exchange rate (in logarithm) with
respect to interest differential
0.35
L_exchrate_dif
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
0
0.01
0.02
0.03
0.04
0.05
difd
0.06
0.07
0.08
0.09
System estimation (UIP and RIP)
System: SYS01
Estimation Method: Least Squares
Date:
07/05/01
Sample: 1995:01 2000:12
Coefficient
Std. Error
t-Statistic
Prob.
-0.038697
0.00845
-4.579408
0.0000
C(2)
0.707907
0.128357
5.515147
0.0000
C(7)
-0.314968
0.032576
-9.668771
0.0000
C(8)
-0.053372
0.015227
-3.505002
0.0006
C(5)
0.029584
0.002825
10.47084
0.0000
C(6)
-0.550574
0.03381
-16.28417
0.0000
C(1)
Determinant residual
1.44E-07
covariance
Equation: DEVIATION01=C(1)+C(2)*DIF_INFL+C(2)*DIFD+
C(7)*D97+C(8)*D99
Observations: 71
-------------------------------------------------------------------------------------------------------------------------------R-squared
0.631657
Mean dependent var
-0.00851
Adjusted Rsquared
S.E. of
0.615164
S.D. dependent var
0.052682
0.032681
Sum squared resid
0.07156
regression
Durbin1.589725
W
atson
stat
Equation: DIF_REAL=C(5)+C(6)*DIF_INFL+C(6)*DIFD
Observations: 72
-------------------------------------------------------------------------------------------------------------------------------R-squared
0.791153
Mean dependent var
-0.006997
Adjusted Rsquared
S.E. of
0.78817
S.D. dependent var
0.031592
0.01454
Sum squared resid
0.014799
regression
DurbinW atson stat
0.60682
System estimation (UIP and PPP)
System: SYS02
Estimation Method: Least Squares
Date:
07/05/01
Sample: 1995:01 2000:12
Coefficient
Std. Error
t-Statistic
Prob.
C(1)
-0.038697
0.00845
-4.579408
0.0000
C(2)
0.707907
0.128357
5.515147
0.0000
C(7)
-0.314968
0.032576
-9.668771
0.0000
C(8)
-0.053372
0.015227
-3.505002
0.0006
C(3)
-0.061555
0.007013
-8.776876
0.0000
C(4)
1.139478
0.106529
10.6964
0.0000
C(9)
-0.269374
0.027036
-9.963462
0.0000
C(10)
-0.064116
0.012638
-5.073396
0.0000
Determinant residual
1.23E-07
covariance
Equation: DEVIATION01=C(1)+C(2)*DIF_INFL+C(2)*DIFD+
C(7)*D97+C(8)*D99
Observations: 71
-------------------------------------------------------------------------------------------------------------------------------R-squared
0.631657
Mean dependent var
-0.00851
Adjusted Rsquared
S.E. of
0.615164
S.D. dependent var
0.052682
0.032681
Sum squared resid
regression
Durbin1.589725
W
atson stat
Equation:
L_CPICUM_DIF - L_CPICUMUSA_DIF L_EXCHRATE_DIF=C(3)+C(4)*DIF_INFL
+C(4)*DIFD+ C(9)*D97+C(10)*D99
0.07156
Observations: 71
-------------------------------------------------------------------------------------------------------------------------------R-squared
0.671394
Mean dependent var
-0.001389
Adjusted Rsquared
S.E. of
0.656681
S.D. dependent var
0.046291
0.027124
Sum squared resid
0.049291
regression
DurbinW atson stat
1.909253
System estimation (PPP and RIP)
System: SYS03
Estimation Method: Least Squares
Date:
07/05/01
Sample:
1995:01 2000:12
Coefficient
Std. Error
t-Statistic
Prob.
C(3)
-0.061555
0.007013
-8.776876
0.0000
C(4)
1.139478
0.106529
10.6964
0.0000
C(9)
-0.269374
0.027036
-9.963462
0.0000
C(10)
-0.064116
0.012638
-5.073396
0.0000
C(5)
0.029584
0.002825
10.47084
0.0000
C(6)
-0.550574
0.03381
-16.28417
0.0000
Determinant residual
1.37E-07
covariance
Equation: L_CPICUM_DIF - L_CPICUMUSA_DIF L_EXCHRATE_DIF=C(3)+C(4)*DIF_INFL
+C(4)*DIFD+ C(9)*D97+C(10)*D99
Observations: 71
-------------------------------------------------------------------------------------------------------------------------------R-squared
0.671394
Mean dependent var
-0.001389
Adjusted Rsquared
S.E. of
0.656681
S.D. dependent var
0.046291
0.027124
Sum squared resid
0.049291
regression
Durbin1.909253
W
atson
stat
Equation: DIF_REAL=C(5)+C(6)*DIF_INFL+C(6)*DIFD
Observations: 72
-------------------------------------------------------------------------------------------------------------------------------R-squared
0.791153
Mean dependent var
-0.006997
Adjusted Rsquared
S.E. of
regression
DurbinW atson stat
0.78817
S.D. dependent var
0.031592
0.01454
Sum squared resid
0.014799
0.60682
Correlogram for UIP regression
Date: 07/07/01 Time: 17:11
Sample: 1995:02 2000:11
Included observations: 70
Autocorrelation
Partial Correlation
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AC
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
-0.008
0.003
0.047
0.006
-0.058
0.065
-0.093
-0.034
-0.098
-0.126
0.090
0.011
-0.145
0.165
0.017
-0.200
0.009
-0.078
-0.178
-0.066
-0.073
0.032
0.045
-0.149
0.058
0.094
0.027
0.105
0.068
0.015
0.009
-0.054
PAC
-0.008
0.003
0.047
0.007
-0.058
0.062
-0.093
-0.030
-0.105
-0.126
0.103
0.007
-0.130
0.154
0.007
-0.204
-0.034
-0.108
-0.180
-0.107
-0.066
0.040
0.016
-0.135
-0.018
-0.020
0.045
0.011
-0.070
0.102
-0.016
-0.139
Q-Stat
Prob
0.0045
0.0053
0.1685
0.1714
0.4320
0.7628
14.534
15.477
23.469
36.822
43.673
43.779
62.246
86.872
87.143
12.443
12.451
13.039
16.186
16.620
17.166
17.276
17.497
19.916
20.289
21.296
21.383
22.705
23.274
23.302
23.313
23.704
0.947
0.997
0.983
0.997
0.994
0.993
0.984
0.992
0.985
0.961
0.958
0.976
0.938
0.851
0.892
0.713
0.772
0.789
0.645
0.677
0.701
0.748
0.784
0.702
0.732
0.727
0.768
0.748
0.764
0.803
0.838
0.855
Deviations from UIP, PPP and RIP
0.2
0.30
0.25
0.1
0.20
0.0
0.15
-0.1
0.10
-0.2
0.05
-0.3
0.00
95
96
97
98
99
00
95
96
D E V IA TION 01
98
99
L_C P IC U M_D IF
0.05
0.00
-0.05
-0.10
-0.15
-0.20
95
97
96
97
98
99
D IF_R E A L
00
00