Uncovered interest parity and deviations from uncovered interest parity

1
Uncovered interest parity and deviations from
uncovered interest parity

• The Academy of Economic Studies,Doctoral School
  of Finance and Banking

MSc student,
Costescu Silvia
Mihaela
2
Dissertation paper outline

• The importance of uncovered interest parity
• The aims of the paper
• Literature review
• The model
• The data
• Empirical analysis
• Concluding remarks
• References

3
The importance of the uncovered interest parity

• UIP has an analytical importance and appears as a
  key behavioral relationship in virtually all of
  the prominent models of exchange rate
  determination.
• UIP is a key feature of linearized open-economy
  models, it reflects the markets expectations of
  exchange rate changes and represents the starting
  point for any analysis which depends on future
  exchange rate values.
• Because there are reasons to believe that UIP
  will not hold precisely, an investor must be able
  to identify the source of deviation and respond
  accordingly.

4
The aims of the paper

• I propose to test the UIP hypothesis for Czech
  Republic, Cyprus, Poland, Romania and in Panel
  over the sample period March 1999 November
  2007.
• If this hypothesis does not hold, I identify and
  calculate the deviations from uncovered interest
  parity.
• I identify which is the main component of UIP
  deviations for every country.
• I will try to explain why the deviations occur.

5
Literature review

• A lot of paper, back to Fama(1984) test for
  uncovered interest parity at distant horizons
  and evidence that interest rate differentials
  tends to be negatively, rather than positively,
  correlated with future currency movements,
  thereby wrongly predicting their direction.
• Flood and Rose(2001) find considerably
  heterogeneity across countries and detect signs
  that uncovered interest parity at the short
  horizon holds better in crisis countries, where
  both exchange and interest rates display high
  volatility.
• Cochrane(1999), Alexius(2001), Chinn and
  Meredith(2005), Chinn(2006) and Zhang(2006)
  suggest that uncovered interest parity tends to
  hold for financial instruments of longer
  maturities.
• For several industrialized countries, Gokey(1994)
  finds that movements in the real exchange rate
  are more important than those in the risk premium
  to explain the deviations from UIP.

6
The model

• In the condition of risk free arbitrage, the
  ratio of the forward to the spot exchange rate is
  equal the interest differential between two
  countries.
• Covered Interest Parity (CIP) can be expressed
  as
• (1)
• All variables are expressed in logarithms,
  where
• nominal spot exchange rate at
  time t expressed as the price, in home-country
  monetary units, of foreign exchange (EUR)
• forward rate of s for a
  contract expiring k periods in the future
• k period nominal interest
  rate in home country
• k period nominal interest
  rate in foreign country (EA)

7
The model

• If the investors are risk averse, the
  forward rate can differ from the expected future
  spot rate by a risk premium.
• Uncovered interest parity says that changes
  in the expected exchange rate equals the current
  interest differential, if the investors are
  risk-neutral
• (2)
• Where, is expected nominal spot
  exchange rate from period t to period tk,
  expressed in logarithm

8
The data

• The source of data is Eurostat, The National
  Bank of Czech Republic, The National Bank of
  Cyprus, The National Bank of Poland and The
  National Bank of Romania database. The periods
  covered are March 1999- November 2007. Empirical
  analysis has been made using monthly data for
• The average nominal exchange rate, of four
  European Union currencies against the euro,
  namely the Czech koruna (CZK), the Cyprus pound
  (CYP), the Polish zloty (PLN) and the Romanian
  new leu (RON). Each exchange rate is quoted as
  number of national currency units per euro.
• The average active money market interest rate
  used by banks for the Czech koruna (CZK), the
  Cyprus pound (CYP),the Polish zloty (PLN), the
  Romanian new leu (RON) and EUR operations using
  maturities of 3 and 6 month.

9
Empirical analysis

• I tested UIP equation, which is known as
  standard Fama(1984) regression for Czech
  Republic, Cyprus, Poland, Romania and in Panel,
  in the assumption of rational expectations
• I test the properties of the regression variable
  and perform unit root tests (ADF and PP).

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Unit-root test for exchange rate change (in log)

• Czech
• Republic
• Cyprus

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Unit-root test for exchange rate change (in log)
Poland
Romania
12
Unit-root test for nominal interest rate
differential (in log) - 3 month maturities
Czech Republic Cyprus
13
Unit-root test for nominal interest rate
differential (in log) - 3 month maturities
Poland
Romania
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Estimates of ß

• In line with Chinn and Meredith (2005) and
• Chinn (2006) I use GMM to correct the
  standard errors of the parameter estimates for MA
  serial correlation.

The coefficient is negative and the hypothesis
that ß equal unity is strongly rejected. A
negative ß coefficient suggests that interest
rates differentials explain future currency
movements systematically in the wrong
direction. This is a standard result in empirical
literature of international finance and
constitutes the forward discount puzzle.
15
Mean, variance and t-ratio for ex-post deviations
from UIP 3 month
I test the deviations from UIP to see if
it works. The ex-post deviations from UIP are
I perform unit root tests (ADF and PP) for
UIP deviation to see whether it fluctuates around
the mean or drifts boundlessly.
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Unit-root test for ex-post UIP deviation- 3 month
maturities
Czech Republic Cyprus
17
Unit-root test for ex-post UIP deviation- 3 month
maturities
Poland
Romania
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Ex-post deviations from UIP

• I can conclude that UIP works only for Czech
  Republic, because is the only one who has the
  mean of the UIP deviation not statistically
  different from zero, the t-ratio very low and
  less than unity and both ADF and PP tests suggest
  that ? is stationary.
• Similar results for 6 month horizon

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Deviations from UIP

• Fama(1984) suggest that deviations from UIP
  represent either a risk premium ( as measured by
  the real interest differentials) or an unexpected
  change in the real exchange rate
• The exchange rate growth can be written as
• Where, is the matrix of variables
  known at or before time t, including inflation
  rate differential, nominal exchange rate changes
  and nominal interest rate differential and
  is vector of corresponding coefficients.
• I first estimate the equation with all the
  predictable variable, then I eliminate the
  variable that are not statistically significant
  (nominal interest rate differential for all the
  countries and nominal exchange rate changes for
  Cyprus), and I obtained

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• The exchange rate growth equation
• Dependent Variable DQT_CZECH
• Method Least Squares
• Date 07/07/08 Time 2218
• Sample 1999M03 2007M11
• Included observations 105

21

• The exchange rate growth equation
• Dependent Variable DQT_CYPRUS
• Method Least Squares 
• Date 07/07/08
• Time 1311 
• Sample 1999M03 2007M11
•  Included observations 105 

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• The exchange rate growth equation
• Dependent Variable DQT_POLAND
• Method Least Squares 
• Date 07/07/08
• Time 2223 
• Sample 1999M03 2007M11 
• Included observations 105 

23

• The exchange rate growth equation
• Dependent Variable DQT_ROMANIA
• Method Least Squares Date 07/07/08
• Time 2224 
• Sample 1999M03 2007M11 
• Included observations 105 

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Deviations from UIP

• Tanner(1998) decomposes ex-post deviations
  from UIP into unanticipated and anticipated
  component of real exchange rate growth
• (resid series for
  every above equations),
• (the difference
  between real exchange rate growth and resid
  series)
• The deviation from UIP can be written ? ?
  e ?
• Nothing that cov(e,?)0, I can write the
  variance equation of ? as
• var(?) var(?) var (e) var (?) 2
  cov(?,e) cov(?,?)
• This equation tell us how much of the
  variance in ? is due to changes in the real
  interest rate differential, anticipated changes
  in the real exchange rate and unanticipated real
  exchange rate growth, or the covariance between
  interest rate differential and every component of
  exchange rate growth.

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Variance of deviations
Variance and covariance for 3 months
Variance and covariance as a fraction of var(?)
for 3 months
26
Variance of deviations
Variance and covariance for 6 months
Variance and covariance as a fraction of var(?)
for 6 months
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Concluding remarks

• In the covered period the results confirm the
  rejection of uncovered interest parity, for
  Czech Republic, Cyprus, Poland and Romania.
• I calculate UIP deviations and found that for
  analyzed countries real interest differential is
  the main component of UIP deviations.
• The interest rate differential accounts for
  nearly 64(Czech Republic), 77(Cyprus),
  85(Poland), 91(Romania) of deviations from UIP.
  
• These results are in line with developing
  countries, and one explanation can be the
  variability of inflation in these countries, and
  the fact that the prices rise rapidly.
• For Czech Republic and Cyprus I obtain the
  negative covariance between interest rate
  differential and unanticipated real exchange rate
  growth, implying that changes in the real
  interest differential will be offset to some
  degree by movements in real exchange rate growth,
  thus reducing the deviations from UIP.

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Selected References

• Alexius A(2001), Uncovered Interest Parity
  Revised, Review of International
  Economics,9(3).
• Cochrane, J (1999),New Facts in Finance,
  Economic Perspectives, Federal Reserve Bank of
  Chicago, XXIII(3).
• Chaboud, A and J Wright(2005), Uncovered
  Interest Parity It works, but not for Long,
  Journal of International Economics, 66
• Edison H. J. and Pauls B.D(1993) A Re-Assessment
  of the Relationship Between Real Exchange Rates
  and Retal Interest Rates 1974-1990, Journal of
  Monetary Economics 31,165-187
• Engel, Charles (2000), Comments on Obstfeld and
  Rogoffs The Six MajorPuzzles in International
  Macroeconomics Is There a Common Cause?, NBER
  working paper 7818
• Fama E. (1984), Forward and Spot Exchange
  RateS, Journal of Monetary Economics, 14.
• Flood R. and A. Rose(2001)-Uncovered Interest
  Parity in CrisisThe interest Rate Defense in the
  1990s, IMF Working Paper. No 01/207

29
Selected References

• Froot K. And R. Thaler(1990), Foreign exchange
  , Journal of Economic Perspectives, 4
• Gorkey T. C.(1994), What explains the risk
  premium in foreign exchange returns? Journal of
  International Money and Finance13,6
• McCallum, Bennett T. (1992), A Reconsideration
  of the Uncovered Interest ParityRelationship,
  NBER working paper 4113
• MacDonald R.(1997)What Determines Real Exchange
  Rates The Long and Short of It, IMF Working
  Paper 97/21(Washington International Monetary
  Fund)
• Marston R(1997), Tests of three parity
  conditions distinguishing risk premia and
  systematic forecast errors, Journal of
  International Money and Finance,16,2.
• Menzie D. Chinn, Guy Meredith(2005), Testing
  uncovered interest parity at short and long
  horizons during the post-breton woods era NBER
  working paper 11077.
• Meese R and Rogoff K (1988) What IS Real? The
  Exchange Rate-Interest Differential Relation Over
  the Modern Floating- Rate Period Journal of
  Finance, Vol XLIII, No. 4, pp 933-948
• Tanner, Evan (1998), Deviations From Uncovered
  Interest Parity A Global Guide to Where the
  Action Is, IMF working paper wp/98/117.