_CIP_ hypothesis at Russian money market using actual interbank by jianghongl


									                   Covered Interest Parity: Evidence from Russian Money Market

        Purpose of the project is to estimate presence, scale and sources of deviations from covered
interest parity (CIP) at Russian money market using actual interbank credit rates.
        Domestic (as well as international) money market provides information necessary to develop and
conduct monetary policy. Choosing an adequate indicators and interpreting them in a proper way is
crucial for decision making in this sphere. For example, it is important for Russian banks to have an
access to world capital market. Instability at the financial markets could deteriorate credit conditions for
the banks quickly. In these circumstances central bank may find it reasonable to provide additional
liquidity or introduce additional credit facilities etc. Thus, link between national and world market of
capital is of monetary authority's interest. Deviations from CIP are a sign of looser link with the world
capital market. However, improper choice of indicators may be disguiding.
        It is typical to use offered rates as indicative rates of money market conditions. However, it
turned out during the recent financial crisis that offered rates may be confusing even if related to most
developed markets. Dollar LIBOR is a good example. That is why central banks start to switch to the
actual rates. Use of these rates in lesser developed money markets is complicated as the data has irregular
frequency arisen from an absence of deals in some days.
        Central bank of Russia pays special attention to actual rates (MIACR family), while practitioners
often prefer Mosprime. However, basic MIACR is noisy due to heterogeneity of banks. Recently, Central
bank introduced MIACR-IG rate which takes into account only interbank credit to investment grade
banks. These banks borrow at the Russian money market infrequently, and a number of deals per day
decreases as maturity grows. That is why it is typical to use monthly averages of these rates (for example,
Коваленко (2010)). In an open economy during the financial turmoil it is desirable to use higher
frequency data to capture an actual state of money market.
        In the research we are going to discuss properties of main money market rates and to use daily
data including the MIACR-IG to test CIP and to explain deviations from parity in Russia.
        Basic hypothesis we are going to test is covered interest parity. In case of CIP, return on
comparable assets in domestic and foreign currency is equal.
        There is kind of disagreement in literature concerning the speed of convergence to parity. Usually
profitable opportunities of arbitrage at financial markets disappears almost immediately and would not be
observable in daily data.
        Typically, small, but significant, deviations from the parity are observed. These deviations could
be explained by transaction costs at least partially. As far as we have no data on transaction costs, we’re
going to use TAR models to estimate them.
        Some researchers (Baba at al. (2009)) note that deviations from CIP are higher during the periods
of turbulence.
        Finally, Baba and Packer (2009a), Baba et al. (2009) find that higher deviations from parity
could be explained by counterparty risk.
         Covered interest rate parity hypothesis is not new in economics. Developing FX forward market
in the end of the XIX century put covered interest rate arbitrage into textbooks for practitioners (e.g. Dent
(1920)). Keynes (1924) discussed both parity condition and sources of deviation from it. Basic model of
CIP is very simple. Parity relation could be written as:
                                       Ft                                                                 (1)
               1  i t  1  i *t       ,

         where it is an interest rate at domestic currency market, i*t is a foreign currency market interest
rate, St is a spot FX rate and Ft is a forward FX rate. It is assumed, that forward and credit maturities are
                                                        1 it
                                                                 1  i t  i *t
                                                       1  i *t
the same and interest rates are not annualised.                                    is an interest rate differential and
    1  ln Ft   ln S t 
                                is a forward premium. Thus, in words CIP means equality of interest rate
differential to forward premium.
         There are several approaches to test CIP empirically had been applied by researchers. First one is
based on checking if actual deviation from parity, that is interest rate differential minus forward premium,
differs from zero (Taylor and Tchernykh-Branson (2004), Takezawa (1994), Taylor (1989), Fletcher and
         Second approach for testing CIP based on regression of interest differential on forward premium
or, alternatively, on regression of returns on assets in domestic currency on the returns in foreign currency
corrected for forward premium. Thus, we have basic regression (2)

                1 it          F                                                                          (2)
                            t t
               1  i *t        St


               1  i t     1  i *t        t

         If CIP holds,  and  should be equal to zero and unity respectively in both cases. Equation (2)
had been analyzed by many authors for various data and time horizons. Older studies (Branson (1969),
Popper (1994)) does not pay attention to time-series nature of data. Maenning and Tease (1999) allow for
autocorrelation, but not test for cointegration. Moosa and Bhatti (1996) and Гурвич и др. (2009) found
cointegration between the returns on domestic and foreign assets, but restricted model was rejected in the
first paper and while in the latter one the test was not reported.
         Al-Loughani and Moosa (2000) suggested third approach of testing for CIP. They test variances
of differently hedged portfolios for equality instead of testing means. Authors report of holding CIP and
agreement between latter and cointegration based approaches.
        Most of empirical research found significant deviations from CIP. Some of such works suggested
to take transaction costs into account (Clinton(1988), Frenkel and Levich (1977) Fletcher and Taylor
(1996), Maening and Tease (1999), Bhar et al. (2004)).
        Nature of transaction costs during a covered interest rate arbitrage was considered in Frenkel and
Levich (1977). After Demsetz (1968) they derived the costs from either bid-ask spread or brokerage fee.
According to Frenkel and Levich (1977) transaction costs captured at least 85 percent of the apparent
profit opportunities originated in the deviation from CIP depending on currency pair.
        Clinton (1988) estimated no-arbitrage band due to transaction costs for U.S. dollar and five most
traded currencies as ±0.06 per cent per annum and showed that profitable arbitrage opportunities are not
infrequent. Similar conclusion made in Fletcher and Taylor (1996) that used data on long-term contracts.
        There are heated discussions among researchers concerning a quality of financial data. According
to Taylor (1989) differences in maturities, no simultaneity and incomparability due to calculation method
may lead to incorrect results. Using high-quality, high-frequency data for spot/forward dollar-sterling,
dollar-mark exchanges rates and Eurodeposit interest rates for various maturities Taylor tested CIP
adjusted for bid-ask spread and came to conclusion there was a few profit opportunities and all of them
were very small. Deviations from CIP during turbulence periods were greater compared with calm period.
Maasoumi and Pippenger (1989) demonstrated that seemingly harmless slight asynchronism and
incomparability in data may lead to a dangerously biased conclusions.
        One more important question concerns of the persistence of the profitable opportunities. While
earlier papers such as Fletcher and Taylor (1996) report of the more or less longlasts profitable
opportunities, recent studies demonstrate using high frequency data clearly the opposite. For example,
Akram et al. (2008) investigated the properties of potential departures from CIP conditions. Data were
collected from the Reuters trading system and includes three major exchange rates (USD/EUR, UD/GBD,
JPY/USD) quotations, FX swap and Eurocurrency deposit rates for currencies involved. Akram et al.
(2008) concludes that duration of CIP deviation didn't seem to last more than a few minutes. In most
cases, average duration was between 20 seconds and 4 minutes.
        There is some evidence that deviations of CIP are conditional on turbulence in financial markets.
Branson (1969) and Taylor (1989) noted that deviations from parity grow eith turbulence. Taylor and
Tchernykh-Branson (2004) focused on deviations from CIP during the financial crisis of 1998 in Russia
and attributed deviations to risk premium. Counterparty risk is could be captured by LIBOR-OIS spread
as it became eveident that LIBOR rates are far not riskless. Baba and Packer (2009a) and Hui et al.
(2011) studied recent deviations from CIP during the recent financial crisis and stressed strong effect of
the spread on deviations from CIP. Latter paper argues that the spread explained 75-80 percent of
deviation for major currency pairs. Additional measures of turmoil were used in these papers as well as in
Skinner and Mason (2011). They include TED spread, CDS spreads, VIX, equity premium and others.
        Aliber (1973) stressed political risk as a reason of CIP disparity. Assets available in money
market differ in two way – first is in currency in which they are denominated, second is in the political
jurisdiction in which they are issued. This differences lead to exchange and political risks, first of them
can be eliminated by purchasing forward contract. Consequently, existence of political risk can
potentially influence CIP conditions. Empirical analysis indicated that deviation from CIP are smaller
among deposits in different currencies within one jurisdiction than among deposits in different currencies
in different jurisdiction.
        It is interesting to consider empirical works related to CIP testing for Russian money market.
They includes Skinner and Mason(2011), Taylor and Tschernyh-Branson (2004), Коваленко (2010),
Гурвичидр. (2009). Taylor and Tschernyh-Branson (2004) estimated TAR model for Russian and U.S.
treasury bills for the period from December 1996 to August 1998. Deviation from CIP was observed and
explained by risk premium. Opposite results were obtained by Skinner and Mason(2011). Using daily
data for period from January 2003 to October 2006, they didn't rejected CIP hypothesis for five years and
three months maturities. In fact, they found that average deviation from CIP was less than one basis point
for three month maturity. However, this deviation substantially higher for 5 year maturity (about 35 bp)
and could be fully explained by credit risk measured as CDS rate. Гурвич и др. (2009) also tested CIP
hypothesis. They used daily NDF forward, Libor and Mosibor money market rates for 2001 to 2008 in
order to investigate an effect of the exchange rate policy of the Central Bank of Russia on deviations from
CIP. By conducting cointegration analysis Гурвич и др (2009) tested sensitivity of Russian interest rate
to NDF implied return. While they found long-run relationship between the rates and argued in favor of
CIP, they didn't provide any tests for coefficient restrictions. Published estimates show CIP violation for
at least two of three subperiods. Another empirical work was conducted by Коваленко (2010). To test
CIP hypothesis basic model was applied (eq. (2)). Mibor, Miacr, Mibid in rubles with 1 month maturities
were taken as domestic rates and Mibor, Miacr, Mibid, Libor in dollars used as foreign ones. Коваленко
(2010) used monthly average data for period of 2001 to 2010. Implied rates were regressed on domestic
rates which is in odd with practices. The results of estimation were presented, but, unfortunately, there
was no opportunity to test for deviations of α from zero and β from unity respectively as there were no
standard errors reported. Коваленко (2010) concludes that relationship between rates was very closed to
        Data, we are going to use, is, generally, published at Central Bank of Russia site. Main time-
series listed as follows
        Interbank ruble interest rates:
                MIACR
                MIACR-IG
                Mosprime
                MIBOR
                MIBID
        Interbank money market turnover volumes:
        FX swap implied rate of return
                dollar
                euro
        All the data is published on a daily basis. Our sample includes daily observations since April 1,
2010 since there is no earlier data on FX swap implied rate.
        Central bank publishes rates for a different credit terms. Our primary interest is concerned with
credits of week-to-month terms. This choice is directed by a compromise between liquidity of market and
transaction costs compared to interest income.
        As a basic model we use (1). A more complicated model takes into account transaction costs of
interbank borrowing and foreign exchange. As far as these transaction costs presented by bid and ask
spreads, we expect, that internal interest rate should be bounded as follows.
              Fb                                                                                     (3)
                 1  i *b   1  ia  1  ib  Fa 1  i *b ,
              Sa                                 Sb

        where b and a subscripts denote bid and ask quotations respectively. Cf. Bhar et al. (2004),
inequalities (2) and (3).
        To test for CIP we use equation (1). Ruble interbank rate it is presented by MIACR, MIACR-IG,
                                                                               1  i *t   1.
Mosprime, MIBOR or MIBID. FX swap implied rate of return is just a                                Thus, two tests
follow from equation (1) immediately. Firstly, it is natural to run simple linear cointegration model. As
far as basic CIP holds, we expect to have zero intercept and unit slope. Alternatively, we propose to test
deviation between ruble interbank rate and FX swap implied rate for equality to zero. In most interest
cases of MIACR and MIACR-IG as ruble interest rates we have a lot of missings due to absence of deals.
        Error-correction (ECM) model let us to estimate for how long deviations from parity survive. We
expect zero autocorrelation of deviations as it takes seconds, not days, to use profitable opportunities in
FX and interest markets. However, the problem may arise due to incomparability of data. For example,
while FX swap implied rate is calculated and published at 12:30 p.m. MSK, MIACR interest rates are
daily averages.
        The deviation from CIP may have place due to transaction costs. In the case linear model is
inadequate. Equation (3) implies use of three-regime threshold autoregression (TAR) model with outer
regimes correspondent to cases of capital outflow and inflow due to interest rate differential and inner
regime describing a case of arbitrage-prohibitive transaction costs. We expect unit slopes in both outer
regimes. However, difference between intercepts reflects transaction costs. The TAR model of
cointegration may be accompanied with TAR ECM model to focus on deviations persistence in the outer
regimes. TAR model is a direction for future research.
                                                Some preliminary results
        We use domestic rates with one month maturity such as Mibor, Mibid, Miacr, Miacr-IG, Mosibor
and implied rates (NFEA FX Swap Euro/Dollar) in dollars and Euro provided by CBR over the period
from April 1, 2010 to February 14, 2012. All data is for one month terms. To test for CIP we use basic
regression model (eq. 2 in the Proposal). CIP implies   0;   1. All estimations were made in
statistical package Eviews.
           Mibor, Mibid, Miacr, Miacr-IG and NFEA FX Swap Doll/Euro were considered as a time series.
To avoid spurious regression, we test first of all for integration and cointegration. Results presented in the
table 1.
                                            Table 1. Dickey-Fuller test
     Variable              t-Statistic        Prob.       Variable           t-Statistic         Prob.
     MIBID                  0.009820         0.9581      ∆ MIBID             -18.49151          0.0000
     MIBOR                 -0.247412         0.9295      ∆ MIBOR             -21.05273          0.0000
                                                        ∆ NFEA FX
                           -1.344364         0.6100        SWAP              -19.47506          0.0000
NFEA FX SWAP                                           ∆ NFEA FX
                           -1.413459          0.5764                         -20.56479          0.0000
   EURO                                                SWAP EURO

      Mosibor              -1.344364          0.6100     ∆ Mosibor           -19.47506          0.0000

critical values:          1% level                 3.444311
                          5% level                 2.867590
                          10% level                2.570055

           Thus, we conclude that Mibor, Mibid, Miacr, Miacr-IG and NFEA FX Swap Doll/Euro are I(1).
Now we apply Granger causality test. Results are in the table 2.

                                          Table 2. Granger casualty test
                                         Null Hypothesis                                          Prob.
                   NFEA FX Rate USD does not Granger Cause MIBOR                                 1.E-12
                   MIBOR does not Granger Cause NFEA FX Rate USD                                 0.7092
                 NFEA FX Rate EURO does not Granger Cause MIBOR                                  7.E-12
                 MIBOR does not Granger Cause NFEA FX Rate EURO                                  0.7014
                   NFEA FX Rate USD does not Granger Cause MIBID                                 3.E-16
                   MIBID does not Granger Cause NFEA FX Rate USD                                 0.3682
                  NFEA FX Rate EURO does not Granger Cause MIBID                                 2.E-15
                  MIBID does not Granger Cause NFEA FX Rate EURO                                 0.2125
                 NFEA FX Rate USD does not Granger Cause MOSIBOR                                 0.0005
                 MOSIBOR does not Granger Cause NFEA FX Rate USD                                 0.0009
                NFEA FX Rate EURO does not Granger Cause MOSIBOR                                 0.0005
                MOSIBOR does not Granger Cause NFEA FX Rate EURO                                 0.0009

           We observe that external interest rates determines internal ones and not vice versa (with
MOSIBOR is an exception with bidirectional link).
           CIP regressions are presented in the table 3. We observe significant deviations from CIP. Alphas
are significantly positive while betas are far lower than unity. Note, that MOSIBOR's  is far closer to 1
compared to other rates, but still significantly less than unity.
        Table 4 provides results of Engle-Granger test. Hypothesis of cointegration relationship between
MIBID and FX dollar, Mosibor and FX euro and, also, Mosibor and FX dollar can not be rejected at 5
percent significance level.
                                            Table 3. Regression analysis.
MIBID = 1.167 + 0.671 *NFEA FX Rate USD

 st.er.          (0.065) (0,018)             n = 464

 t-St.       [18.0] [37.49]                        = 0.876

MIBID =1.299 + 0.585* NFEA FX Rate EURO

 st.er.      (0.033) (0.009)                 n= 459

 t-St.       [39.84] [64.35]                      = 0.907

MIBOR = 2.25 + 0.637 *NFEA FX Rate USD

 st.er.      (0.066) (0.018)                 n = 464

 t-St.       [34.05] [35.33]                        = 0.814

MIBOR =2.368 + 0.557* NFEA FX Rate EURO

 st.er.          (0.039) (0.01)                n = 459

 t-St. [60.82] [54.89]              = 0.847
MOSIBOR = 0.902+ 0.872*NFEA FX Rate USD

         st.er.     (0.049) (0.012)               n = 463

         t-St.      [18.53] [71.86]                      =0.918

MOSIBOR =1.197+ 0.733 NFEA FX Rate EURO

    st.er.        (0.043491) (0.009914)                n = 461

  t-St.          [27.54480] [73.90949]                 = 0.847

                                   Table 4. Dickey-Fuller test of regressions resids
                                     Variable                                    t-Statistic   Prob.

           Residual (MIBID on NFEA FX SW RATE DOLL)                                -3.457      0.009

           Residual (MIBID on NFEA FX SW RATE EURO)                                  -2.8      0.059

           Residual (MIBOR on NFEA FX SW RATE DOLL)                                -1.968      0.301

           Residual (MIBOR on NFEA FX SW RATE EURO)                                 -1.93      0.316

         Residual (MOSIBOR on NFEA FX SW RATE DOLL)                               -4.739728    0.0001

         Residual (MOSIBOR on NFEA FX SW RATE EURO)                               -3.048842    0.0313
           It is impossible to analyse MIACR rates in the same way as we proceed with offered and bid rates
as they have lot of missings. At the table 5 we report robust least squares and weighted least squares
estimates. In latter case we use turnover as a weight. By using Wald test linear restriction (α=0 and β=1)
was checked for each regression. Null hypotheses were rejected at 5 percent significance level in each
                             Table 5. Regression analysis with White procedure.
                  unweighted regressions                             weighted regressions

  MIACR= 2.65 + 0.594 *NFEA FX Rate USD                     MIACR = 0.408 + 0.946 *NFEA FX Rate USD

        st.er.    (0.267) (0.057)        n = 393               st.er.    (0.176) (0.042)      n = 393

        t-St.     [9.933] [10.466] R2 = 0.216                  t-St.     [2.31]   [22.5]   R2 = 0.897

 MIACR =2.78 + 0.516* NFEA FX Rate EURO                     MIACR =0.88 + 0.777* NFEA FX Rate EURO

        st.er.    (0.238) (0.045)         n= 389                st.er.   (0.148) (0.028)       n= 389
        t-St.     [11.697] [11.488] R2 = 0.226                 t-St.     [5.95] [27.855]    R2 = 0.91
  MIACR-IG = 0.251 + 1.004 *NFEA FX Rate
                                                          MIACR –IG= 1.469+ 0.767 *NFEA FX Rate USD
        st.er.    (0.217) (0.061)         n = 76                st.er.   (0.714) (0.129)       n = 76

        t-St.     [1.158] [16.326] R2 = 0.817                   t-St.    [2.056] [5.934]   R2 = 0.488

   MIACR-IG=0.627 + 0.828* NFEA FX Rate
                                                          MIACR-IG=1.778 + 0.64* NFEA FX Rate EURO
         st.er.   (0.147) (0.04)          n = 76                st.er.   (0.46) (0.075)        n = 76

        t-St.     [4.25] [20.6]      R2 =0.831                  t-St.    [3.827] [8.476]   R2 = 0.535

             Unfortunately, OLS estimations ignore time-series nature of the data. Special structure of Miacr
and Miacr- IG (in term of missings and autocorrelation) required a more flexible approach of estimation.
One of such methods is maximum likelihood estimation. First of all, it was necessary to test series for
stationarity. In previous analysis FX dollar and FX euro swap rates were found to be I(1). To test MIACR
and MIACR-IF for I(1) we express missing values in term of observable values and errors. Miacr and
Miacr-IG are similar in structure. All calculations below were valid for both series.
             Test for stationarity means that |β| <1 in equation (A1):
X t     * X t 1   t                                                                         (А1)

 ~ N0;  2 
t  0,...,T .
          The problem is while we could observe X t , X t 1 is generally not observable. Suppose, that we

observe X at moment (t-z) and X at moment t and we can not observe X between these moments.
Now write observable Xs in chronological order and construct correspondent time-serie of Zs indicating
number of missings (plus 1) between the current and previous observations of X (see Fig. 1).

                                         Figure 1. Constructing Z

          Now draw probability density function

                                                                    , if i>1                         (A2)

                                                                , if i=1 (first observation)         (A3)

          MLE estimates of (A1) are at the table 6 for MIACR and at the table 7 for MIACR-IG. As we
can see hypothesis that MIACR is I(1) was rejected. AS FX dollar/euro swap rates and Miacr have
different orders of integration, Miacr is eliminated from analysis. Instead,  in MIACR-IG regression is
very close to unity and insighnificantly differs from it.

                                Table 6. Regression of Miacr on Miacr(-1)

                                  Coefficients         Std. Errors             z-Statistic     Probability

           σ2                        1.638                  0.076               21.489           0.0000
                ρ                          0.446                  0.035      12.553          0.0000

                α                          2.702                  0.204      13.218          0.0000

                                  Table 7. Regression Miacr-IG on Miacr-IG (-1).

                                     Coefficients             Std. Errors.   z-Statistic   Probability

                                         0.182                   0.024         7.678         0.0000

                ρ                        0.975                   0.012        83.115         0.0000

               α                         0.096                   0.046         2.096         0.0361

              To test CIP we used model which was described  equation 2, where y i  was Miacr-IG and

x i was FX Dollar (FX Euro) swap rates. We supposed, that long-term relationship could be described as
Yt     * X t   t                                                                           (A4)

 t   *  t 1   t

           2 
 t ~ 0;       
         1  

 ~ 0; 2 

t  1; T 

Then ECM could be written:

Yt  Yt 1   * ( X t  X t 1 )   (Yt 1     * X t 1 )   t                            (A5)


Yt   * X t  (Yt 1   * X t 1 )   ( t 1 )   t                                         (A6)


 t   t 1   *  t 1   t                                                                  (A7)

If (1+γ)=ρ, then
 t   *  t 1   t

           Thus, errors are distributed as AR(1).
           Probability density function is constructed for equation in levels (A4):

                                                                            , if i>1         (A8)


                                                                           , if i=1          (A9)

The MLE estimations presented at the tables 8 and 9.

                                      Table 8. Miacr-IG on FX Dollar

                                  Coefficients         Std. Errors       z-Statistic   Probability

              σ2                     0.254               0.042             6.015         0.0000

              ρ                      0.664               0.062            10.692         0.0000

              α                      0.414               0.755             0.548         0.584

              β                      0.962                0.13              7.4          0.0000

                                      Table 9. Miacr-IG on FX Euro

                                  Coefficients         Std. Errors       z-Statistic   Probability

              σ2                     0.275               0.042             6.607         0.0000

              ρ                      0.591               0.060             9.874         0.0000

              α                      0.713               0.670             1.064         0.2871

              β                      0.813               0.104             7.784         0.0000
          If series were cointagrated, then residuals of regression Miacr – FX Dollar (Miacr – FX Dollar)
had to be stationary. Residuals had the similar unobservable values as Miacr-IG. In order to test residuals
for stationarity we apllied the similar procedure as in case of Miacr and Miacr-ig (see eq.A1-A3). Results
presented at the tables 10 and 11.
       Table 10. Regression ressidual of regression (Miacr-IG on FX Dollar) on residuals (-1).

                                     Coefficients      Std. Errors      z-Statistic         Probability

             σ2                          0.284           0.039             7.312              0.0000

             ρ                           -0.512          0.090             -5.661             0.0000

             α                           -0.028          0.093             -0.298             0.7656

        Table 10. Regression residual of regression (Miacr-IG on FX Euro) on residuals (-1).

                                     Coefficients      Std. Errors      z-Statistic         Probability

             σ2                          0.261           0.039             6.728              0.0000

             ρ                           -0.553          0.089             -6.196             0.0000

             α                           -0.072          0.087             -0.825             0.4092

          By comparing ρ with unity in each cases we conclude that long-term relationships between
Miacr-ig –Dollar and Miacr-ig – Euro exist.
          Note, that slopes in the cointegration regressions are not far from 1. To test for CIP we use LR
test of restricted vs unrestricted models.
                                      Table 11. LR test
  Log Likelihood (Miacr-IG on NFEA FX Swap       Log Likelihood (Miacr-IG on NFEA FX Swap
                  Dollar unrestricted)                                 Euro unrestricted)
                        -68.538                                              -68.65
Log Likelihood (Miacr-IG on NFEA FX Swap Log Likelihood (Miacr-IG on NFEA FX Swap
Dollar unrestricted)                                  Euro unrestricted)
                       -71,16149                                           -74,81094
          By comparing LR with critical values we found that CIP was rejected for ruble-euro and CIP
couldn't be rejected for ruble-dollar.

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