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