doctoral school of finance and banking bucharest uncovered interest parity and deviations from...
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Doctoral School of Finance and BankingDoctoral School of Finance and BankingBucharestBucharest
Uncovered interest parity and deviations from
uncovered interest parity
MSc student: Alexandru-Chidesciuc Nicolaie
Presentation contentsPresentation contents
Introducing UIP
Deviations from UIP
Methodology, data and empirical results
Why UIP?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 usedNotation 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)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).
The difference (ft – st) is called forward premium/discount
tttt sfii
t
t
t
t
S
F
i
i
1
1
)( tt sf
Uncovered interest parity Uncovered interest parity (UIP)(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:
t
te
tt S
Sii
111
tt
ett ssii
1
Uncovered interest parity Uncovered interest parity (UIP)(UIP)
The version that appears in leading econometric models:
- the disturbance term, which might represent time-varying risk premia or other effects
ttte
tt ssii
1
t
Forward premium puzzleForward premium puzzle
If both CIP and UIP hold, a common test of UIP considers the following regression:
In practice, for a wide range of currencies, is found significantly less than zeroThis is called the forward premium puzzle
(forward premium anomaly) – interest differential predicts the wrong direction in which exchange rate moves
11 ttttte sfss
Deviations from UIPDeviations from UIP
foreign exchange risk premiasystematic forecast errorstransaction costs intervention in the foreign exchange
marketcapital does not flow freely across borders
There are many reasons why Uncovered Interest Parity will not hold exactly, and can be even expected to fail:
Methodology, data and empirical Methodology, data and empirical
resultsresults 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 hypothesisWhy do deviations occur? Joint tests of three parity conditions
Estimation of UIPEstimation of UIP I specified the regression according to Flood and Rose
(1994) and Meredith and Chinn (1998)
The above equation incorporates rational expectations
I changed the interest rate series from annual percent to monthly percent. In this purpose we used two methods
ttttkt iiss
tte
t ss 11
12
at
t
ii 1112 a
tt ii
Estimation of UIPEstimation 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 testsUnit-root tests
Unit-root test for exchange rate change (in log)
Unit-root test for nominal interest rate differential
ADF Test -5.53916 1% Critical Value* -3.5267 5% Critical Value -2.9035 10% Critical Value -2.5889
*MacKinnon critical values for rejection of hypothesis of a unit root.
ADF Test Statistic
-3.617141 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.
Regression specification and resultRegression specification and resultI tested the following regression:
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)
ttttt ddiiss 9997 211
UIP estimationUIP estimation
Variable Coefficient Std. Error t-Statistic
Prob.
C 0.071911 0.009911 7.2558 0.0000
DIFD -1.679299 0.334462 -5.0209 0.0000
D97 0.236367 0.018631 12.687 0.0000D99 0.068999 0.013421 5.1411 0.0000
R-squared 0.724832 0.037837
Adjusted R-squared
0.712324 0.052703
S.E. of regression
0.028268 -4.238751
Sum squared resid
0.052738 -4.110265
Log likelihood 152.3563 57.95119Durbin-Watson stat
2.000283 0.000000
Mean dependent var
S.D. dependent var
Sample(adjusted): 1995:02 2000:11
Dependent Variable: L_EXCHRATE_DIF
Method: Least Squares
Date: 07/04/01 Time: 20:04
Included observations: 70 after adjusting endpoints
Akaike info criterion
Schwarz criterion
F-statistic Prob(F-statistic)
View correlogram
UIP estimationUIP estimationThere is another way to test UIP (very simple) If sample mean of (ex post deviations from UIP) is
statistically different from zero
Is a stationary process?
t
t0
5
10
15
20
25
30
-0.3 -0.2 -0.1 0.0 0.1
Series: DEVIATION01Sample 1995:02 2000:12Observations 71
Mean -0.008510Median -0.000495Maximum 0.098154Minimum -0.283265Std. Dev. 0.052682Skewness -3.437390Kurtosis 18.26626
Jarque-Bera 829.2841Probability 0.000000
ADF Test Statistic -4.23621 1% Critical Value* -3.5281
5% Critical Value -2.9042
10% Critical Value -2.5892
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.
*MacKinnon critical values for rejection of hypothesis of a unit root.
Why do deviations occur?Why do deviations occur? UIP equation can be written in terms of the real interest
rate differential and real exchange rate growth
ex post deviation from UIP is
Where: is real interest differential logarithm of the real
exchange rate
ett
ett
te
tr
rss
11
11ln1
ttt qrd
ttt rrrd
tttt ppsq
The real exchange rateThe real exchange rate
If real exchange rate is random walk, then all movements in real exchange rate are unexpected
I estimated
to see the effect of current information dataset on
ttit Zq 0
qtZ
Estimation of real exchange rateEstimation 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
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
L_EXCHRATE_DIF 0.98621 0.007002 140.8413 0.0000
R-squared 0.9972 0.001389
Adjusted R-squared 0.997075 0.046291
S.E. of regression 0.002504 -9.087498
Sum squared resid 0.00042 -8.960023
Log likelihood 326.6062 7954.866
Durbin-Watson stat 2.208492 0.000000
Included observations: 71 after adjusting endpoints
Dependent Variable: L_EXCHRATE_REALD
Method: Least Squares
Date: 06/29/01 Time: 00:44
Sample(adjusted): 1995:02 2000:12
F-statistic
Prob(F-statistic)
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Sources of variances in UIP deviationsSources 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))
anticipatedunanticipated
0.00359 0.00099 0.000006 0.0021 0.277 0.00164 0.5868 0.00177 0.12
Variance Var(.) as part of var
var rdvar var var rdvar var var ,cov rd ,cov rd
titt Zq 0
tit Z 0
Joint tests of three parity conditionsJoint 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
ttttt rpsii
1
tttttt spp
ttttt rprr
Joint tests of three parity conditionsJoint 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:
includes interest rate differential and inflation differential
ttttt uZsii 101
ttttt uZspp 20
tttt uZrr 30
tZ
Joint tests of three parity conditions – Joint tests of three parity conditions – resultsresults
Here the coefficients are:
Null Hypothesis:Chi-square 30.41684 Probability 0.0000
Wald Test:
System: SYS01
C(2)=0
Null Hypothesis:Chi-square 114.413 Probability 0.0000
Wald Test:
System: SYS02
C(4)=0
Null Hypothesis:Chi-square 265.1743 Probability 0.0000
Wald Test:
System: SYS01
C(6)=0
)2(c )4(c )6(c
Joint tests of three parity conditions – Joint tests of three parity conditions – results 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.
ConclusionsConclusions
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
ConclusionsConclusions
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 PointsKey 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) Nominal exchange rate (ROL against USD)
from 1995:01 to 2001:12from 1995:01 to 2001:12
0
5000
10000
15000
20000
25000
30000
RO
L/U
SD
EXCHRATE
Nominal exchange rate change (in logarithms)Nominal exchange rate change (in logarithms)
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
ian-9
5iul
-95
ian-9
6iul
-96
ian-9
7iul
-97
ian-9
8iul
-98
ian-9
9iul
-99
ian-0
0iul
-00
L_EXCHRATE_DIF
Average passive interest rate used by banks Average passive interest rate used by banks
with their clientswith their clients
0
20
40
60
80
100
120% p.a.
DPM
Interest rate in USA (Bank prime loan rate) –Interest rate in USA (Bank prime loan rate) –
averages of daily figuresaverages of daily figures
7.5
8
8.5
9
9.5
10% p.a.
MPRIME
Change in exchange rate (in logarithm) and the Change in exchange rate (in logarithm) and the
interest differentialinterest differential
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
DIFD L_EXCHRATE_DIF
Change in exchange rate (in logarithm) with Change in exchange rate (in logarithm) with
respect to interest differentialrespect to interest differential
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
difd
L_
ex
ch
rate
_d
if
System estimation (UIP and RIP)System estimation (UIP and RIP) Date:
07/05/01
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(5) 0.029584 0.002825 10.47084 0.0000
C(6) -0.550574 0.03381 -16.28417 0.0000
1.44E-07
R-squared 0.631657 -0.00851
Adjusted R-squared
0.615164 0.052682
S.E. of regression
0.032681 0.07156
Durbin-Watson stat
1.589725
R-squared 0.791153 -0.006997
Adjusted R-squared
0.78817 0.031592
S.E. of regression
0.01454 0.014799
Durbin-Watson stat
0.60682
System: SYS01
Estimation Method: Least Squares
Sample: 1995:01 2000:12
Determinant residual covarianceEquation: DEVIATION01=C(1)+C(2)*DIF_INFL+C(2)*DIFD+ C(7)*D97+C(8)*D99Observations: 71
---------------------------------------------------------------------------------------------------------------------------------
Mean dependent var
S.D. dependent var
Sum squared resid
Equation: DIF_REAL=C(5)+C(6)*DIF_INFL+C(6)*DIFD
Sum squared resid
Observations: 72
---------------------------------------------------------------------------------------------------------------------------------
Mean dependent var
S.D. dependent var
System estimation (UIP and PPP)System estimation (UIP and PPP)
Date: 07/05/01
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
1.23E-07
R-squared 0.631657 -0.00851
Adjusted R-squared
0.615164 0.052682
S.E. of regression
0.032681 0.07156
Durbin-Watson stat
1.589725
R-squared 0.671394 -0.001389
Adjusted R-squared
0.656681 0.046291
S.E. of regression
0.027124 0.049291
Durbin-Watson stat
1.909253
Mean dependent var
Equation: L_CPICUM_DIF - L_CPICUMUSA_DIF - L_EXCHRATE_DIF=C(3)+C(4)*DIF_INFL
Mean dependent var
Equation: DEVIATION01=C(1)+C(2)*DIF_INFL+C(2)*DIFD+ C(7)*D97+C(8)*D99
System: SYS02
Estimation Method: Least Squares
Sample: 1995:01 2000:12
S.D. dependent var
Sum squared resid
Determinant residual covariance
Observations: 71
---------------------------------------------------------------------------------------------------------------------------------
S.D. dependent var
Sum squared resid
+C(4)*DIFD+ C(9)*D97+C(10)*D99
Observations: 71
---------------------------------------------------------------------------------------------------------------------------------
System estimation (PPP and RIP)System estimation (PPP and RIP)
Date: 07/05/01
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
1.37E-07
R-squared 0.671394 -0.001389
Adjusted R-squared
0.656681 0.046291
S.E. of regression
0.027124 0.049291
Durbin-Watson stat
1.909253
R-squared 0.791153 -0.006997
Adjusted R-squared
0.78817 0.031592
S.E. of regression
0.01454 0.014799
Durbin-Watson stat
0.60682
System: SYS03
Estimation Method: Least Squares
Sample: 1995:01 2000:12
Sum squared resid
---------------------------------------------------------------------------------------------------------------------------------
Observations: 72
S.D. dependent var
Observations: 71
Determinant residual covarianceEquation: L_CPICUM_DIF - L_CPICUMUSA_DIF - L_EXCHRATE_DIF=C(3)+C(4)*DIF_INFL +C(4)*DIFD+ C(9)*D97+C(10)*D99
Mean dependent var
Equation: DIF_REAL=C(5)+C(6)*DIF_INFL+C(6)*DIFD
Mean dependent var
S.D. dependent var
---------------------------------------------------------------------------------------------------------------------------------
Sum squared resid
Correlogram for UIP regressionCorrelogram for UIP regressionDate: 07/07/01 Time: 17:11Sample: 1995:02 2000:11Included observations: 70
AutocorrelationPartial Correlation AC PAC Q-Stat Prob
. | . | . | . | 1 -0.008 -0.008 0.0045 0.947 . | . | . | . | 2 0.003 0.003 0.0053 0.997 . | . | . | . | 3 0.047 0.047 0.1685 0.983 . | . | . | . | 4 0.006 0.007 0.1714 0.997 .*| . | .*| . | 5 -0.058 -0.058 0.4320 0.994 . | . | . | . | 6 0.065 0.062 0.7628 0.993 .*| . | .*| . | 7 -0.093 -0.093 14.534 0.984 . | . | . | . | 8 -0.034 -0.030 15.477 0.992 .*| . | .*| . | 9 -0.098 -0.105 23.469 0.985 .*| . | .*| . | 10 -0.126 -0.126 36.822 0.961 . |*. | . |*. | 11 0.090 0.103 43.673 0.958 . | . | . | . | 12 0.011 0.007 43.779 0.976 .*| . | .*| . | 13 -0.145 -0.130 62.246 0.938 . |*. | . |*. | 14 0.165 0.154 86.872 0.851 . | . | . | . | 15 0.017 0.007 87.143 0.892 **| . | **| . | 16 -0.200 -0.204 12.443 0.713 . | . | . | . | 17 0.009 -0.034 12.451 0.772 .*| . | .*| . | 18 -0.078 -0.108 13.039 0.789 .*| . | .*| . | 19 -0.178 -0.180 16.186 0.645 .*| . | .*| . | 20 -0.066 -0.107 16.620 0.677 .*| . | .*| . | 21 -0.073 -0.066 17.166 0.701 . | . | . | . | 22 0.032 0.040 17.276 0.748 . | . | . | . | 23 0.045 0.016 17.497 0.784 .*| . | .*| . | 24 -0.149 -0.135 19.916 0.702 . | . | . | . | 25 0.058 -0.018 20.289 0.732 . |*. | . | . | 26 0.094 -0.020 21.296 0.727 . | . | . | . | 27 0.027 0.045 21.383 0.768 . |*. | . | . | 28 0.105 0.011 22.705 0.748 . |*. | .*| . | 29 0.068 -0.070 23.274 0.764 . | . | . |*. | 30 0.015 0.102 23.302 0.803 . | . | . | . | 31 0.009 -0.016 23.313 0.838 . | . | .*| . | 32 -0.054 -0.139 23.704 0.855
Deviations from UIP, PPP and RIPDeviations from UIP, PPP and RIP
-0.3
-0.2
-0.1
0.0
0.1
0.2
95 96 97 98 99 00
DEVIATION01
0.00
0.05
0.10
0.15
0.20
0.25
0.30
95 96 97 98 99 00
L_CPICUM_DIF
-0.20
-0.15
-0.10
-0.05
0.00
0.05
95 96 97 98 99 00
DIF_REAL