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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
ICF
INTRODUCTION.................................................................................................................................................. 4
LITERATURE REVIEW........................................................................................................................................... 5
INTEREST RATE PARITY........................................................................................................................................ 6
Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
METHODOLOGY................................................................................................................................................ 10
DATA.......................................................................................................................................................................10Spot Exchange Rate Data:.................................................................................................................................10Forward Rate Data:...........................................................................................................................................10Interest Rate Data for India:..............................................................................................................................11Interest Rate Data for US:.................................................................................................................................11
ANALYSIS AND DISCUSSION.............................................................................................................................. 11
DEVIATIONS FROM INTEREST RATE PARITY (DIRP):..........................................................................................................11One Month Forwards:.......................................................................................................................................113 Month Forwards:............................................................................................................................................136 Month Forwards:............................................................................................................................................149 Month Forwards:............................................................................................................................................1512 Month Forwards...........................................................................................................................................16
ECONOMETRICS................................................................................................................................................ 17
UNIT TESTING FOR VALIDATING STATIONARY DATA............................................................................................................17REGRESSION ANALYSIS................................................................................................................................................18
ANALYSIS.......................................................................................................................................................... 18
ONE-MONTH FORWARD...............................................................................................................................................18THREE-MONTH FORWARD............................................................................................................................................20SIX MONTH FORWARD................................................................................................................................................21NINE MONTH FORWARD.............................................................................................................................................22TWELVE MONTH FORWARD.........................................................................................................................................24
ANALYSIS USING CAPITAL INFLOWS.................................................................................................................. 25
CONCLUSION.................................................................................................................................................... 27
Introduction
Financial openness exists when residents of one country are able to tradeassets with residents
of another country, i.e. when financial assets are traded goods. Aweak definition of complete
financial openness, which one might refer to as financialintegration, can be given as a situation
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
in which the law of one price holds forfinancial assets- i.e. domestic and foreign residents trade
identical assets at the sameprice. A strong definition would add to this the restriction that
identically definedassets e.g. a six-month Treasury bill, issued in different political jurisdictions
anddenominated in different currencies are perfect substitutes in all private portfolios.
The degree of financial integration has important macroeconomic implications interms of the
effectiveness of fiscal and monetary policy in influencing aggregatedemand as well as the scope
for promoting investment in an economy.The free and unrestricted flow of capital in and out of
countries and the everincreasingintegration of world capital markets can be attributed to the
process ofGlobalization. The benefits of such integration are liquidity enhancement on one
handand risk diversification on the other, both of which are instrumental in makingmarkets more
efficient and also facilitate smooth transfers of funds between lendersand borrowers. India
began a very gradual and selective opening of the domesticcapital markets to foreign residents,
including non-resident Indians (NRIs), in theeighties. The capital market opening picked up pace
during the nineties.
Real interest parity, uncoveredinterest parity and covered interest parity gives a indication of
financial integration of economy.Three definitions of financial integration are as follows:
(i) Real interest parity hypothesis states that international capital flows equalize real
interest rates across countries.
(ii) Uncovered interest parity states that capital flows equalize expected rates of return
on countries’ bonds regardless of exposure to exchange risk.
(iii) Covered interest parity states that capital flows equalize interest rates across
countries when contracted in the same currency.
Only definition (iii) that the covered interest differential is zero is an unalloyed criterion for
“capital mobility” in the sense of the degree of financial market integration across national
boundaries. Condition (ii) that the uncovered interest differential is zero requires that (iii) hold
and that there be zero exchange risk premium. Condition (i) that the real interest differential be
zero requires condition (ii) and in addition that expected real depreciation is zero.
Literature ReviewThe uncovered interest parity (UIP) theory states that differences betweeninterest rates across
countries can be explained by expected changes in currencies.Empirically, the UIP theory is
usually rejected assuming rational expectations, and explanations for this rejection include that
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
expectations are irrational. There appears to be overwhelming empirical evidence against UIRP,
at least at frequencies less than one year. Other research shows that UIRP holds in long term.
The results of these long horizon regressions are much more positive — the coefficients on
interest differentials are of the correct sign, and most are closer to the predicted value of unity
than to zero. Research done by Ravi Bansal and Magnus Dahlquistconclude that the often
found negative correlation between the expected currency depreciation and interest rate
differential is, contrary to popular belief, not a pervasive phenomenon. It is confined to
developed economies, and here only to states where the U.S. interest rate exceeds foreign
interest rates. Research done for emerging markets by Frank S. Skinner shows that there
isindeed violations in covered interest rate parity in the long-term capital markets andthe source
of these violations is credit risk rather than the size of the economy orliquidity of the foreign
exchange market. The covered interest parity (CIP) postulates that interest rates denominated
in different currencies are equal once you cover yourself against foreign exchange risk. Unlike
the UIP, there is empirical evidence supporting CIP hypothesis. Empirical studies by various
researchers shows that the CIP holds in most cases on the Eurocurrency market (where
remunerated assets have similar default and political risk characteristics) since the collapse of
the Bretton Woods regime in early 1970’s.
In the Indian context, Varma (1997) has undertaken an analysis of the covered interest parity.
He posits a structural break in the money market in India in September 1995, with CIP become
effective from that point on for the first time in the Indian money market. The structural break
itself is attributed to interplay between the money market and the foreign exchange market. The
period after 1995 is however witness to several deviations from the CIP. Varma has used rates
on Treasury bills, certificates of deposit and commercial paper and call money rate to analyze
the Indian money market.
One problem encountered in examining covered interest rate parity is a lack of highquality
observations on long-term interest rates the terms of which are comparableacross different
markets. A ready solution is the interest rate swap market. Thismarket has evolved into one of
the most important international fixed income markets. Benefits of using swap interest rates are
as follows:
a) swap terms and conditions arecomparable across different markets
b) swaps are liquid instruments so high quality information is available even for long
terms in emerging markets
c) swap rates areclosely related to the underlying national bond markets and reflect the
interest ratesavailable for borrowing and investment
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
In our analysis in this report we have not used swap rates as they are available only for
International swap dealers association members. Literature suggests that zero coupon bond
yields are close proxy for the interest rates.
Interest Rate ParityInterest rate parity is an economic concept, expressed as a basic algebraic identity that relates
interest rates and exchange rates. The identity is theoretical, and usually follows from
assumptions imposed in economic models. There is evidence to support as well as to refute the
concept. In this report, we will analyze the data available to find whether this concept can be
supported or refuted in case of India and US.
Interest rate parity is a non-arbitrage condition which says that the returns from borrowing in one
currency, exchanging that currency for another currency and investing in interest-bearing
instruments of the second currency, while simultaneously purchasing futures contracts to
convert the currency back at the end of the holding period, should be equal to the returns from
purchasing and holding similar interest-bearing instruments of the first currency. If the returns
are different, an arbitrage transaction could, in theory, produce a risk-free return. This can be
shown as
(1+ irs) = (Frs/$/Srs/$) (1+ i$ )
Where
irs= interest rates in India
i$= interest rates in US
Frs/$= Forward exchange rate
Srs/$= Spot exchange rate
Looked at differently, interest rate parity says that the spot price and the forward, or futures
price, of a currency incorporate any interest rate differentials between the two currencies
assuming there are no transaction costs or taxes.IRP is a manifestation of the Law of One
Price (LOP)applied to international money market instruments.
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
Being an arbitrage equilibrium condition involving the spot exchange rate, IRP has an
immediate implication for exchange rate determination. Reformulating the IRP relationship in
terms of spot exchange rate gives
S = [(1+i$)/(1+irs)] F
Above equation indicates that the forward exchange rate, the spot exchange rate depends upon
relative interest rates. All else equal, an increase in Indian interest rates will lead to higher
foreign exchange value of Indian rupee. This is so because a higher Indian interest rates will
attract capital to India, increasing the demand for Indian rupee. In contrast, a decrease in Indian
interest rates will lower the foreign exchange value of Indian rupee.
In addition to relative interest rates, the forward exchange rates is an important parameter in
spot exchange rate determination. Under certain conditions the forward exchange can be
viewed as the expected future spot exchange rate conditional on all relevant information being
available now
F = E(St+1| It)
Where St+1 is the future spot rate when the forward contract matures and It denotes the set of
information currently available. Hence the final relation will be as follows
S = [(1+i$)/(1+irs)] E (St+1 | It)
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
Two things are noteworthy here that expectations play a key role in exchange rate
determination. Specifically, the expected future rate is shown to be a major determinant of the
current exchange rate when people expect the exchange rate to go up in future, it goes up now.
People’s expectations thus become self fulfilling. Second, exchange rate expectations will be
driven by the news event. People form their expectations based on the set of information (It)
they possess. As they receive news continuously, they are going to update their expectations
continuously. As a result, the exchange rate will tend to exhibit a dynamic and volatile short term
behavior, responding to various news events. By definition, news events are unpredictable,
making forecasting future exchange rates an arduous task.
When the forward exchange rate F is replaced by the expected future spot exchange rate, we
can rewrite IRP as
(irs – i$)= E(e)= [E(St+1) – St]/St
Above equation states that interest rate differential between a pair of countries is approximately
equal to the expected rate of change in the exchange rate. This relationship is known as
uncovered interest rate parity.
Although IRP tends to hold quite well, it may not hold all the times precisely all the times for at
least two reasons: transaction costs and capital controls. In reality, transaction costs do exist.
The interest rate at which the arbitrager borrows, ia, tends to be higher than the rate at which he
lends, ib, reflecting the bid-ask spread. Likewise, there exists a bid-ask spread in the foreign
exchange market as well. Because of the transaction costs, the IRP line can be viewed as
included within a band around it. The width of band depends upon the size of transaction cost.
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
Another major reason for deviations from IRP is capital controls imposed by governments. For
various macroeconomic reasons, governments sometimes restrict capital flows, inbound and/or
outbound. Governments achieve this objective by means of jawboning, imposing taxes or even
outright bans on cross border capital movements. These control measures imposed by
governments can be effectively impair the arbitrage process and as a result, deviations from
IRP may exist.
Deviations from IRP (DIRP) can be calculated as follows:
DIRP = [S(1+irs)/ (1+i$) F] - 1
If IRP holds strictly, deviations from it would be randomly distributed, with expected value of
zero.
When IRP does not hold good, the situation gives rises to covered interest rate parity.Assume
that individuals are risk averse. Such anindividual would like to cover himself for any
unexpected currency fluctuationduring the tenure of the deal. Given the forward contract market,
he wouldpurchase a forward contract and use the exchange rate mentioned in the
contract.Then any difference in interest rate should be equated to forward premium. Any
deviation from CIP would suggest that the markets are inefficient,regulations like capital controls
exist and costs like sovereign risk, individualborrowing constraints are not accounted for.
MethodologyInterest rate parity connects the forward rates on a currency pair to the prevailing interest rates
in the respective countries and the existing spot exchange rate. In order to analyze the interest
rate parity relationship, the interest rates were obtained for both India and the US. The spot
exchange rate data between the US dollar and Indian Rupee was also obtained. Using this
data, the expected forward rate was calculated using the interest rate parity relationship which
specifies that higher Interest rates in India compared to the US should lead to the depreciation
of the Indian Rupee in the forward markets. This expected forward rate is compared to the
actual forward rates on currency forwards which are being traded in the market. The error was
calculated between the actual and expected rates and statistical analysis was done for the
same at 95% confidence level.
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
Data
Spot Exchange Rate Data:The spot exchange rate between Indian Rupee and US dollar (INR/USD) was obtained from
FEDAI (Foreign Exchange Dealers Association of India) website. The data was obtained on a
month end basis beginning September 2006 till July 2010.
Forward Rate Data:The forward rate data was also obtained from FEDAI website. On each date currency forwards
of different maturities are available. The currency forwards are available for different monthly
maturities ranging from 1 month to 9 months. 12 month currency forwards are also available.
Data related to currency forwards for 10 months and 11 months maturity was not available. For
each date, the
Interest Rate Data for India:Interest rate parity assumes default free investments in both the countries. The yield on 1 year
Government of India bonds was taken as a proxy for the default free rate in India. For different
maturities, the interest rates were calculated based on the one year bond yields. The data for
the interest rates was obtained from Fixed Income Money Market and Derivatives Association of
India (FIMMDA).
Interest Rate Data for US:The yields on one year treasury securities were taken as a proxy for the default free rate for the
US. The data for the yields on US treasury securities was obtained from the US Department of
Treasury website.
Analysis and Discussion
Deviations from Interest Rate Parity (DIRP):It measures the difference between the theoretical prediction of the forward rate and the actual
forward rate observed in the derivatives market. If interest rate parity holds, the deviations would
be randomly distributed with an expected value of zero.
DIRP = [(1 + i India) x Spot Rate / (1 + i US) x F ] - 1
The null and alternate hypothesis can be stated as follows:
Null:Expected (DIRP) = 0, Interest Rate parity holds
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
Alternate: Expected (DIRP) is non zero, Interest Rate Parity does not hold
The analysis was carried out for forwards of 1 month, 3 month, 6 month, 9 month and 12 month
duration. The expected value of DIRP was calculated for each of the forwards and the statistical
test was done at 5% significance level (95% confidence level)
One Month Forwards:The DIRP is plotted as follows. The horizontal axis indicates the number of observations for
which error has been calculated.
0 5 10 15 20 25 30 35 40 45 50
-0.4000
-0.3000
-0.2000
-0.1000
0.0000
0.1000
0.2000
Error (Actual - Expected)
Expected Value (Mean) of the Error Term: -0.0462
Standard Deviation of the Error Term: 0.082246844
t statistic = (Actual Value of Error – Expected Value of Error ) / Standard Deviation of Error
= ( -0.0462 – 0)/ 0.082246844
= -0.561512857
t critical at 95% confidence level for a 2 tailed test = 1.96 or -1.96
Since the calculated value of the t statistic is more than -1.96, the null hypothesis cannot be
rejected and IRP holds at 95% level of confidence.
Similar analysis can be carried out for forwards of other maturities which is as follows
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
3 Month Forwards:
0 5 10 15 20 25 30 35 40 45 50
-1.0000
-0.8000
-0.6000
-0.4000
-0.2000
0.0000
0.2000
0.4000
0.6000
Error (Actual - Expected)
Expected Value (Mean) of the Error Term: -0.1495
Standard Deviation of the Error Term: 0.199200692
t statistic = (Actual Value of Error – Expected Value of Error ) / Standard Deviation of Error
= ( -0.1495 – 0)/ 0.199200692
= -0.750568576
t critical at 95% confidence level for a 2 tailed test = 1.96 or -1.96
Since the calculated value of the t statistic is more than -1.96, the null hypothesis cannot be
rejected and IRP holds at 95% level of confidence.
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
6 Month Forwards:
0 5 10 15 20 25 30 35 40 45 50
-2.0000
-1.5000
-1.0000
-0.5000
0.0000
0.5000
1.0000
Error (Actual - Expected)
Expected Value (Mean) of the Error Term: -0.3559
Standard Deviation of the Error Term: 0.384524814
t statistic = (Actual Value of Error – Expected Value of Error ) / Standard Deviation of Error
= (-0.3559 – 0)/ 0.384524814
= -0.925596147
t critical at 95% confidence level for a 2 tailed test = 1.96 or -1.96
Since the calculated value of the t statistic is more than -1.96, the null hypothesis cannot be
rejected and IRP holds at 95% level of confidence.
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
9 Month Forwards:
0 5 10 15 20 25 30 35 40 45 50
-2.5000
-2.0000
-1.5000
-1.0000
-0.5000
0.0000
0.5000
1.0000
Error (Actual - Expected)
Expected Value (Mean) of the Error Term: -0.5879
Standard Deviation of the Error Term: 0.571277246
t statistic = (Actual Value of Error – Expected Value of Error ) / Standard Deviation of Error
= (-0.5879 – 0)/ 0.571277246
= -1.029028333
t critical at 95% confidence level for a 2 tailed test = 1.96 or -1.96
Since the calculated value of the t statistic is more than -1.96, the null hypothesis cannot be
rejected and IRP holds at 95% level of confidence.
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
12 Month Forwards
0 5 10 15 20 25 30 35 40 45 50
-3.5000
-3.0000
-2.5000
-2.0000
-1.5000
-1.0000
-0.5000
0.0000
0.5000
1.0000
1.5000
Error (Actual - Expected)
Expected Value (Mean) of the Error Term: -0.8329
Standard Deviation of the Error Term: 0.75560996
t statistic = (Actual Value of Error – Expected Value of Error ) / Standard Deviation of Error
= (-0.8329– 0)/ 0.75560996
= -1.102272763
t critical at 95% confidence level for a 2 tailed test = 1.96 or -1.96
Since the calculated value of the t statistic is more than -1.96, the null hypothesis cannot be
rejected and IRP holds at 95% level of confidence.
From the above analysis we can infer that Interest Rate Parity holds for maturities up to one
year at 95% level of confidence. For various maturities, the predicted forward rate could be
different from the actual rate, which is evident from the deviations from the horizontal axis in the
graphs, but on an average the differences are not statistically significant.
This is consistent with the literature related to IRP which states that covered interest rate parity
holds in the short run and deviations are observed from the relationship in the long run. Since
the data is available for short duration (having durations less than an year) forwards, we cannot
establish the relation for long term.
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
EconometricsIn order to find the variation in forward premium with respect to interest rate differential, we
perform the econometric analysis on the available data i.e forward rate, spot rate, interest rate in
India and Interest rate in US. As we know the interest parity relationship can also be rewritten as
(irs – i$)= [E(St+1) – St]/St
In order to find the relationship for forwards of different durations, we performed regression
analysis on interest rate differential (difference of interest rate in India and US) and forward
premium. Regression analysis gives the liner relationship as well as the explained variation in
the relationship. Explained variation analysis helped us in understanding the strength of
relationship and look for the reason of unexplained variation. Unexplained variation can be
attributed to various reasons i.e transactional costs, free capital mobility and other
macroeconomic events.
Before performing the regression model on a time series data, data needs to be validated for
stationary property. For time series data of interest rate differential and forward premium, we
performed unit test for validating the stationary property of data.In case of non-stationary times
series, the estimate of parameters of regression model would be spuriousand biased.
Unit testing for validating stationary dataTo validate the stationary property of time series data, we perform a regression analysis
between two variables, difference between Yt+1 and Ytwith Yt.as independent variable The
regression model can be written as
(Yt+1 - Yt ) = a + b* Yt + Et
After estimating the regression model we perform the hypothesis testing on slope parameter i.e.
Null Hypothesis: b equal to zero
Alternative Hypothesis: b not equal to zero
For validating this, we compare the p-value given by regression analysis for the independent
variable for 95% confidence interval. If the p-value is less than 0.05 we will reject the null
hypothesis otherwise we will accept the hypothesis. After validating the data for stationary
property, we proceed to regression model between forward premium and interest rate
differential.
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
Basic assumption in performing this analysis is that if the value of b=0 then data is not
dependent of previous time period data which implies time series data is stationary in nature.
Regression AnalysisRegression model for validating the relationship between interest rate differential and forward
premium can be estimated as
Forward premium = a + b * interest rate differential +error
After validating the time series data for various maturity of forwards, we performed the
regression analysis to estimate the relationship and also find the explained variation of forward
premium with respect to interest rate differential which is given by R-square parameter of the
regression analysis. We also plotted the forward premium and interest rate differential with
respect to time to find the variation with time and get the trend of both the variables with
time(Interest rate differential is multiplied by 10 to get clear trend)
Analysis
One-month forwardFor one month forward, the unit test for validating stationary time series data shows deviations from basic assumption.
CoefficientsStandard
Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.001325955 0.003536861 0.374896027 0.709538806-
0.005802119 0.008454029-
0.005802119 0.008454029Forward Premium
-0.714246068 0.143478264
-4.978078543 1.03655E-05
-1.003407506
-0.425084631
-1.003407506
-0.425084631
CoefficientsStandard
Error t Stat P-valueLower 95%
Upper 95% Lower 95.0% Upper 95.0%
Intercept0.00038898
2 0.0002081811.868476
40.068362
8-3.058E-
050.000808
5 -3.058E-050.00080854
4
Interest Rate
-0.08858624
5 0.056048638
-1.580524
50.121149
6
-0.201544
90.024372
4
-0.20154485
1 0.02437236
As shown in the above tables, p-value for forward premium is less than 0.05 where as it is more
for interest rate differential. Hence, data is not perfect stationary. As one series is stationary, we
proceed with the regression analysis as atleast one of the data series is stationary in nature.
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
Regression equation for one month forward is as follows:
forward premium = 0.0358 -9.392(Interest rate differential)
Regression Statistics
Multiple R 0.4575725
R Square 0.2093726
Adjusted R Square 0.1918031
Standard Error 0.02204885
Observations 47R-square value shows the explained variation as close to 21% only which is very low. The trend
can be shown as
OCT.2006
DEC.2006
FEB.2007
APR.2007
JUN.2007
AUG.2007
OCT.2007
DEC.2007
FEB.2008
APR.2008
JUN.2008
AUG.2008
OCT.2008
DEC.2008
FEB.2009
APR.2009
JUN.2009
AUG.2009
OCT.2009
DEC.2009
FEB.2010
APR.2010
JUN.2010
AUG.2010
-0.0800
-0.0600
-0.0400
-0.0200
0.0000
0.0200
0.0400
0.0600
0.0800
1M forward CIRP
Forward Premium Interest rate differential
As we can see in the trend analysis, that forward premium and interest rate differential shows a
opposite trend from mid of 2007 to the start of 2009. This can be attributed to economic
downturn when free capital mobility was hampered between India and US as US restored to
more conservative approach.
Three-month ForwardSimilar to one month forward, unit testing shows the same trend when forward premium data is
not stationary in nature where as interest rate differential data is stationary in nature.
Coefficient
sStandard
Error t Stat P-valueLower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept 0.0008066 0.0050935 0.158365 0.8749282
-0.009472
0.0110857
-0.009472
0.0110857
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Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
5 5
FORWARD PREMIUM
-0.2610094
0.10265673
-2.542544
90
.0147797 -0.468179
-0.053839
7 -0.468179 -0.0538397
CoefficientsStandard
Error t Stat P-valueLower 95%
Upper 95%
Lower 95.0% Upper 95.0%
Intercept 0.0012137 0.00061256 1.981294 0.0541299-2.253E-
05 0.0024499-2.253E-
05 0.0024499INTEREST RATE DIFF -0.0998457 0.05524714
-1.8072555
0.0778889
-0.211339 0.0116475
-0.211339 0.0116475
As shown in the above tables, p-value for forward premium is less than 0.05 where as it is more
for interest rate differential. Hence, data is not perfect stationary. As one series is stationary, we
proceed with the regression analysis as atleast one of the data series is stationary in nature.
Regression equation for three month forward is as follows:
forward premium = 0.112 -10.039(Interest rate differential)
Regression Statistics
Multiple R 0.73173712
R Square 0.53543921
Adjusted R Square 0.52463547
Standard Error 0.03392052
Observations 45The explained variation is good in this case which is close to 54%. This model shows a better
estimate than one month forward. The trend analysis is as follows
DEC.2006
FEB.2007
APR.2007
JUN.2007
AUG.2007
OCT.2007
DEC.2007
FEB.2008
APR.2008
JUN.2008
AUG.2008
OCT.2008
DEC.2008
FEB.2009
APR.2009
JUN.2009
AUG.2009
OCT.2009
DEC.2009
FEB.2010
APR.2010
JUN.2010
AUG.2010
-0.1500
-0.1000
-0.0500
0.0000
0.0500
0.1000
0.1500
0.2000
3M forward CIRP
Forward Premium Interest Rate Differential
ICF Group Project Page 18
Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
As we can see in the trend analysis, that forward premium and interest rate differential shows a
opposite trend from mid of 2007 to the start of 2009. This can be attributed to economic
downturn when free capital mobility was hampered between India and US as US restored to
more conservative approach.
Six Month ForwardUnit testing for time series data for 6 month forward shows that both the data series are
stationary in nature.
Coefficient
sStandard
Error t Stat P-valueLower 95%
Upper 95%
Lower 95.0% Upper 95.0%
Intercept-
0.00044060.005036
9 -0.087480.930737
6
-0.010628
60.009747
4
-0.010628
6 0.0097474
FORWARD PREMIUM
-0.0844871
0.0624442
-1.353002
30.183846
6
-0.210792
40.041818
2
-0.210792
4 0.0418182
CoefficientsStandard
Error t Stat P-valueLower 95%
Upper 95%
Lower 95.0% Upper 95.0%
Intercept 0.0024076 0.0012679 1.8988651 0.0649984 -0.000157 0.0049722 -0.000157 0.0049722INTEREST RATE DIFF -0.0973421 0.0575548
-1.6912952
0.0987579
-0.2137576 0.0190734
-0.2137576 0.0190734
As shown in the above tables, p-value for forward premium is more than 0.05 as well as for
interest rate differential. Hence, data is perfect stationary. As both series are stationary, we
proceed with the regression analysis.
The regression model for 6-month forward is as follows
forward premium = 0.1861 -8.334(Interest rate differential)
Regression Statistics
Multiple R 0.773163168
R Square 0.597781284
Adjusted R Square 0.587725816
Standard Error 0.051177283
Observations 42Explained variation in this case is close to 60% which shows a good relation. The trend analysis
is shown as follows
ICF Group Project Page 19
Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
MAR.2007
MAY.2007
JUL.2
007
SEP.2007
NOV.2007
JAN.2008
MAR.2008
MAY.2008
JUL.2
008
SEP.2008
NOV.2008
JAN.2009
MAR.2009
MAY.2009
JUL.2
009
SEP.2009
NOV.2009
JAN.2010
MAR.2010
MAY.2010
JUL.2
010
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
6M forward CIRP
Forward Premium Interest Rate Differential
As we can see in the trend analysis, that forward premium and interest rate differential shows a
opposite trend from mid of 2007 to the start of 2009. This can be attributed to economic
downturn when free capital mobility was hampered between India and US as US restored to
more conservative approach
Nine Month ForwardUnit testing for time series data for 9 month forward shows that both the data series are
stationary in nature.
Coefficient
sStandard
Error t Stat P-valueLower 95%
Upper 95%
Lower 95.0% Upper 95.0%
Intercept -0.0025426 0.005334
-0.476674
1 0.636475
-0.013360
40.008275
2
-0.013360
4 0.0082752
FORWARD PREMIUM -0.0654285
0.0494939
-1.321951
70.194523
1
-0.165806
80.034949
7
-0.165806
8 0.0349497
Coefficient
sStandard
Error t Stat P-valueLower 95%
Upper 95%
Lower 95.0% Upper 95.0%
Intercept 0.00350780.001934
31.813490
60.078099
8
-0.000415
10.007430
8
-0.000415
1 0.0074308
INTEREST RATE DIFF -0.0973005
0.0582829
-1.669452
20.103702
5
-0.215503
80.020902
7
-0.215503
8 0.0209027
ICF Group Project Page 20
Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
As shown in the above tables, p-value for forward premium is more than 0.05 as well as for
interest rate differential. Hence, data is perfect stationary. As both series are stationary, we
proceed with the regression analysis.
The regression model for 9-month forward is as follows
forward premium = 0.2068 -6.227(Interest rate differential)
Regression Statistics
Multiple R 0.671420292
R Square 0.450805208
Adjusted R Square 0.435962106
Standard Error 0.080495681
Observations 39
Explained variation in this case is close to 45% which shows a linear relation. The trend analysis
is shown as follows
JUN.2007
AUG.2007
OCT.2007
DEC.2007
FEB.2008
APR.2008
JUN.2008
AUG.2008
OCT.2008
DEC.2008
FEB.2009
APR.2009
JUN.2009
AUG.2009
OCT.2009
DEC.2009
FEB.2010
APR.2010
JUN.2010
AUG.2010
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
9M forward CIRP
Forward Premium Interest Rate Differential
As we can see in the trend analysis, that forward premium and interest rate differential shows a
opposite trend from mid of 2007 to the mid of 2009. This can be attributed to economic
downturn when free capital mobility was hampered between India and US as US restored to
more conservative approach
ICF Group Project Page 21
Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
Twelve Month ForwardUnit testing for time series data for 12 month forward shows that both the data series are
stationary in nature.
Coefficients Standard Error
t Stat P-value Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept -0.0025689 0.0071199 -0.3608029
0.7205463 -0.0170544
0.0119167 -0.0170544
0.0119167
FORWARD PREMIUM
-0.0737933 0.0556671 -1.3256185
0.1940702 -0.1870488
0.0394622 -0.1870488
0.0394622
Coefficient
sStandard
Error t Stat P-valueLower 95%
Upper 95%
Lower 95.0% Upper 95.0%
Intercept 0.004710.002696
61.746616
80.090007
1
-0.000776
40.010196
4
-0.000776
4 0.0101964
INTEREST RATE DIFF -0.0968552
0.0606361
-1.597317
90.119727
7
-0.220220
4 0.02651
-0.220220
4 0.02651
As shown in the above tables, p-value for forward premium is more than 0.05 as well as for
interest rate differential. Hence, data is perfect stationary. As both series are stationary, we
proceed with the regression analysis.
The regression model for 12-month forward is as follows
forward premium = 0.1744 -4.094(Interest rate differential)
Regression Statistics
Multiple R 0.508144918
R Square 0.258211257
Adjusted R Square 0.236393941
Standard Error 0.112197183
Observations 36
Explained variation in this case is close to 25% which shows a weak relation. The trend analysis
is shown as follows
ICF Group Project Page 22
Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
SEP.2007
NOV.2007
JAN.2008
MAR.2008
MAY.2008
JUL.2
008
SEP.2008
NOV.2008
JAN.2009
MAR.2009
MAY.2009
JUL.2
009
SEP.2009
NOV.2009
JAN.2010
MAR.2010
MAY.2010
JUL.2
010
-0.4000
-0.2000
0.0000
0.2000
0.4000
0.6000
0.8000
12M forward CIRP
Forward Premium Interest Rate Differential
As we can see in the trend analysis, that forward premium and interest rate differential shows a
opposite trend from mid of 2007 to the start of 2009. This can be attributed to economic
downturn when free capital mobility was hampered between India and US as US restored to
more conservative approach
As shown in the data analysis that IRP holds for 1-month to 12-month IRP, regression analysis
shows the liner variation in IRP. The trend analysis of all the forward premium and interest rate
differential shows the deviation for all period forwards which can be contributed to global
macroeconomic crisis which had its direct in free capital mobility between India and US. Even
before the crisis, as there was not perfect capital mobility in India, the low value of R-square can
be attributed to macroeconomic policy of both India and US.
Analysis using Capital InflowsThe deviations from Interest Rate Parity (DIRP) have been calculated for the years 2006 to
2010. The deviations are equal to the difference between the values of actual forward rates and
calculated value of forward rate using the IRP formula. If IRP holds, then the expected value of
DIRP should equal zero. The calculated deviations are as follows:
Year Average Deviation from IRP Standard Deviation of Errors2006 0.0475 0.1428536372007 -0.0788 0.415671665
ICF Group Project Page 23
Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
2008 -0.7533 0.5696893082009 -0.3131 0.2500066672010 -0.3734 0.255550415
The data indicates that the mean error (Expected value of DIRP) is highest for the year 2008-09
as compared to other years. Interest rate parity theory assumes free capital mobility between
two countries. Restriction on free capital mobility causes deviations from the IRP. During the
period 2008-09 the global economy witnessed a severe recession. This caused heavy capital
outflows from the Indian markets as foreign institutional investors (FII) withdrew the money
invested in Indian markets. Although the interest rates in India have always been higher
compared to the US, deviation from IRP could be observed due to the capital outflows from the
economy instead of capital inflows. The foreign investment flows are outlined as follows:
Year Direct Investment (USD million)
Portfolio Investment (USD Million)
Total (USD Million)
2006-07 22,826 7,003 29,829
2007-08 34,835 27,271 62,106
2008-09 35,180 –13,855 21,325
2009-10 37,182 32,375 69,557Foreign Investment Flows 2006-2010, (Source: RBI Website)
2006-07 2007-08 2008-09 2009-10
-20,000
-10,000
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
22,826
34,835 35,18037,182
7,003
27,271
-13,855
32,37529,829
62,106
21,325
69,557
Foreign Investment Inflows
Direct Inv.Portfolio Inv.Total
Foreign Investment flows witnessed a marked decrease during the period 2008-09. This is
consistent with the larger deviations observed from the interest rate parity.
ICF Group Project Page 24
Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
Conclusion
From the above analysis we can conclude that deviations from IRP are not statistically
significant in the short run. More comprehensive analysis can be carried out using bid-ask
prices of forward contracts as well as currency rates along with the incorporation of different
currency pairs to account for the macroeconomic policies of different countries related to capital
mobility.
ICF Group Project Page 25
Comparison of Interest rate differentials to exchange rate movement for Indian Rupee vis-a`-vis US Dollar
References
i. http://www.fimmda.org/Information_Center/Statistics/ASP/stats.asp
ii. http://www.fedai.org.in/
iii. http://www.ustreas.gov/
iv. http://www.rbi.org.in/
v. http://www.sebi.gov.in/
vi. http://www.indiastat.com/
vii. Vipul Bhatt and ArvindVirmani, 2005, “Global Integration of India’s Money Market:
Interest Rate Parity in India”, Indian Council for Research on International Economic
Relations, New Delhi Working Paper
viii. Menzie Chinn, 2007,”World Economy – Interest Rate Parity I”, Princeton Encyclopedia of
the World Economy
ix. O.Pipatchaipoom_and Stefan C. Norrbin, 2006, “Reexamining Real Interest Rate Parity”,
School of Business, Stanford University
x. DogaUnay, 2005, “A Note on Interest Rate Parity”
ICF Group Project Page 26
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