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Currency Risk in Brazil during the Real Plan

Currency Risk in Brazil during the Real Plan. Márcio Garcia Gino Olivares Dept. of Economics, PUC-Rio. Conference “One Year of Inflation Targeting” Central Bank of Brazil Rio de Janeiro - July 10-11, 2000. Motivation. Why is the currency risk relevant?

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Currency Risk in Brazil during the Real Plan

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  1. Currency Risk in Brazil during the Real Plan Márcio Garcia Gino Olivares Dept. of Economics, PUC-Rio Conference “One Year of Inflation Targeting” Central Bank of Brazil Rio de Janeiro - July 10-11, 2000

  2. Motivation Why is the currency risk relevant? • Uncovered Interest Parity (UIP) / Covered Interest Parity (CIP); • Capital Flows; • Domestic interest rate calibration (Central Bank); • Inflation Targeting.

  3. Covered Interest Parity Differential (up to the devaluation) 25% 0.60 0.50 20% 0.40 15% Ln 0.30 10% 0.20 5% 0.10 0% 0.00 Jul-95 Jul-96 Jul-97 Jul-98 Mai-95 Mai-96 Mai-97 Mai-98 Mar-95 Mar-96 Mar-97 Mar-98 Set-95 Set-96 Set-97 Set-98 Jan-95 Jan-96 Jan-97 Jan-98 Nov-95 Nov-96 Nov-97 Nov-98 Libor Forward Premium Covered Interest Parity Differential Covered Interest Parity Differential

  4. 25% 0.50 20% 0.40 15% 0.30 10% 0.20 5% 0.10 0% 0.00 Jul-99 Fev-99 Mar-99 Abr-99 Fev-00 Mar-00 Abr-00 Mai-99 Out-99 Set-99 Dez-99 Jan-99 Jun-99 Jan-00 Ago-99 Nov-99 Covered Interest Parity Differential (post devaluation) 0.60 Ln Libor Forward Premium Covered Interest Parity Differential Covered Interest Parity Differential

  5. Objectives of this research: • To measure and analyze the Currency Risk in Brazil during the Real Plan; • To identify some of the relations between the currency risk and the fundamentals of the Brazilian economy; • To obtain policy lessons about the management of monetary and exchange rate policy.

  6. Main questions: • How can we measure the currency risk ? • What are the determinants of the currency risk?

  7. Outline • Introduction; • Futures price bias: theory and intuition; • Fama’s methodology: theory and results; • Currency Risk estimation using the Kalman Filter; • Interest rate parity conditions; • Conclusions.

  8. Definitions • Forward Premium ft - st • Forward Discount ft - st+1 • Currency Risk (Insurance Premium) ft - Et(st+1) • Covered Interest Rate Parity 1 + it = (1 + it*)Ft/St

  9. Fama’s methodology: Theory and results (1) • Fama (JME,1984): “Forward and Spot Exchange Rates”. Attempt to rationalize the existence of a time-varying risk premium using a simples framework. • The model is as follows: Rational Expectations:

  10. Fama’s methodology: Theory and results (2) • Efficiency hypothesis: H0: 2=0, 2=1 • Fama used data of nine international currencies from the period 1973:08 - 1982:12 and rejected H0 in all the cases. • He found that his estimates of 2 were not just different from 1, but also negative. • This seemingly counter-intuitive result became known as the Forward Premium Puzzle. • Based on his results, Fama formulated his two “fundamental” conclusions.

  11. Fama’s methodology: Theory and results (3) • First conclusion: The exchange rate risk premium (currency risk) and the expected depreciation rate are negatively correlated. • He obtained this conclusion form his negative estimates of 2. Implying:

  12. Metodologia de Fama: Teoria e resultados (4) • Second conclusion: The variance of the currency risk is greater than the variance of the expected depreciation rate. • He obtained this conclusion from the fact that his estimates of 2 were all less than 1/2. Implying:

  13. Fama’s methodology: Theory and results (5) Case Var(p) and Var(d) Cov(d,p) I Uncovered =1 Var(d) > Var(p) = 0 Cov(d,p)=0 interest rate parity or or Var(p) = |Cov(d,p)| Cov(d,p)<0 II Forward premium <0 Var(p) > |Cov(d,p)| > Var(d) Cov(d,p) <0 puzzle III >1 Var(d) > |Cov(d,p)| > Var(p) Cov(d,p) <0 IV =0.5 Var(d) = Var(p) Indeterminate

  14. Spot Exchange Rate and Exchange Rate Futures 1.30 1.25 1.20 1.15 1.10 R$ / US$ 1.05 1.00 0.95 0.90 0.85 05/Jul/95 09/Jul/96 14/Jul/97 16/Jul/98 11/Abr/95 22/Set/95 18/Abr/96 25/Set/96 22/Abr/97 30/Set/97 24/Abr/98 25/Jan/96 27/Jan/97 03/Jun/97 29/Jan/98 04/Jun/98 05/Out/98 25/Mai/95 29/Mai/96 02/Mar/95 07/Mar/96 10/Mar/97 12/Mar/98 03/Nov/95 05/Nov/96 07/Nov/97 16/Nov/98 14/Ago/95 14/Dez/95 16/Ago/96 16/Dez/96 21/Ago/97 17/Dez/97 25/Ago/98 24/Dez/98 Fama’ s methodology: Theory and results (6)

  15. 3.0 2.5 2.0 1.5 Percentage per month 1.0 0.5 0.0 -0.5 -1.0 1995:04 1995:06 1995:08 1995:10 1995:12 1996:02 1996:04 1996:06 1996:08 1996:10 1996:12 1997:02 1997:04 1997:06 1997:08 1997:10 1997:12 1998:02 1998:04 1998:06 1998:08 1998:10 1998:12 ft - st+1 ft - st st+1 - st Fama’s methodology: Theory and results (7)

  16. Results from the OLS Estimation of Fama's regresssions using brazilian data Period 1995:04 - 1998:12 Coefficients estimated and standard deviations Autocorr. and Partial Autocorr. of w t f - s = s - s = Lag AC ACP t t+1 t+1 t a + b (f - s ) + w a + b (f - s ) + w 1 1 t t 1,t 2 2 t t 2,t a -0,3579 a 0,3579 1 -0,09 -0,09 1 2 s(a ) 0,1370 s(a ) 0,1370 2 -0,19 -0, 20 1 2 b 0,7050 b 0,2950 3 -0,25 -0,30 1 2 s(b ) 0,1789 s(b ) 0,1789 4 0,06 -0,06 1 2 2 2 R 0,5308 R 0,1653 5 -0.02 -0,15 4 5 s(w ) 0,3295 s(w ) 0,3295 6 0,08 -0,02 1,t 2,t Note: All the standard deviations are "White Heteroskedasticity-Consistent" . Fama’s methodology: Theory and results (8) • Ous results using Brazilian monthly data from the period 1995:04 - 1998.12 were not consistent with Fama’s first “fundamental” conclusion.

  17. Fama’s methodology: Theory and results (9) • Froot e Thaler (1989) report that the majority of empirical papers using the Fama methodology obtains negative estimates of 2. • In the case of Brazil we obtained a positive estimate of 2, but the null-hypothesis H0: 2 = 1 was rejected. • Why do we obtain a different result? • Bansal and Dahlquist (1999). “The Forward Premium Puzzle: Different Tales from Developed and Emerging Economies”.

  18. Fama’s methodology: Theory and results (10) B&D (1999): There is a negative relation between the estimates 2 in the Fama equation and per capita GDP. Estimates of 2 1,0 0,0 -1,0 Per capita GDP (as a proportion of US per capita GDP) -2,0 0,4 0,6 0,8 1,0

  19. Fama’s methodology: Theory and results (11) B&D (1999): There is a positive relation between the estimates of 2 in the Fama equation and the inflation rate. Estimates of 2 1,0 0,0 -1,0 Log of inflation (compared with the US inflation) -2,0 -1,0 -0,5 0,0 0,5 1,0 1,5

  20. Fama’s methodology: Theory and results (12)

  21. Fama’s methodology: Theory and results (13) Case Var(p) and Var(d) Cov(d,p) I Uncovered =1 Var(d) > Var(p) = 0 Cov(d,p)=0 interest rate parity or or Var(p) = |Cov(d,p)| Cov(d,p)<0 II Forward premium <0 Var(p) > |Cov(d,p)| > Var(d) Cov(d,p) <0 puzzle III >1 Var(d) > |Cov(d,p)| > Var(p) Cov(d,p) <0 IV =0.5 Var(d) = Var(p) Indeterminate

  22. Currency Risk estimation (1) • How to measure the risk premium? Two possibilities: • Structural models of the risk premium • Signal-extraction models • Structural models: The ideia is modelling the determinants of the risk premium. The main problem with this type of models is that we need to identify the determinants of the risk premium and their relationships (functional form) with it.

  23. Currency Risk estimation (2) • Signal-extraction models: They do not need the hypothesis the structural models need. But, on the other side, they do not give us information about the relationships between the risk premium and other economic variables. In this sense, the signal-extraction models and the structural models would be complementary. • Examples of this type of models: • Wolff (JF,1987). “Forward Foreign Exchange Rates, Expected Spot Rates, and Premia: A Signal-Extraction Approach”. • Cheung (JIMF,1993).”Exchange Rate Risk Premium”.

  24. Currency Risk estimation (3) • Wolff presents the following model:

  25. Currency Risk estimation (4) • Estimation using Brazilian monthly data from the period 1995:04 - 1998:12. • We use a AR(1) specification for pt. • The results show a currency risk with a higher degree of persistence. • The ADF test reject the null-hypothesis of existence of a unit root in the estimated risk premium series.

  26. Currency Risk estimation (5) Currency Risk estimated using the Kalman filter 35% Currency Risk Premium Forward discount 30% 25% 20% Percentage per year 15% 10% 5% 0% -5% 1995:04 1995:06 1995:08 1995:10 1995:12 1996:10 1996:12 1997:02 1997:04 1997:06 1998:04 1998:06 1998:08 1996:02 1996:04 1996:06 1996:08 1997:08 1997:10 1997:12 1998:02 1998:10 1998:12

  27. Forward Premium decomposition Expected depreciation Currency risk Interest rate parity conditions (1) 50% 45% 40% 35% 30% Percentage per year 25% 20% 15% 10% 5% 0% 1995:06 1995:08 1995:10 1996:02 1996:10 1996:12 1997:02 1997:04 1998:02 1998:04 1998:06 1998:08 1998:10 1995:04 1995:12 1996:04 1996:06 1996:08 1997:06 1997:08 1997:10 1997:12 1998:12

  28. Interest rate parity conditions (3) Currency Risk Expected Actual Estimated series statistics (1995:04 - 1998:12): depreciation depreciation Average 4,33% 8,27% 8,34% Standard 4,96% 3,33% 4,78% deviation

  29. Interest rate parity conditions (4) Hull (2000): The relationship between the futures price and the spot price is: This formula must be adapted to take into account the country risk. Country risk = Convenience yield = Covered interest rate parity differential.

  30. Interest rate parity conditions (5) Thus: Foreign interest rate + Expected depreciation + Currency risk + Country risk Domestic interest rate

  31. US interest rate Expected depreciation Currency risk Country risk Interest rate parity conditions (6) Domestic interest rate decomposition 80% 70% 60% 50% Percentage per year 40% 30% 20% 10% 0% 1996:02 1996:06 1996:08 1996:10 1996:12 1997:02 1997:04 1998:06 1998:10 1998:12 1995:04 1995:06 1995:08 1995:10 1995:12 1996:04 1997:06 1997:08 1997:10 1997:12 1998:02 1998:04 1998:08

  32. Interest rate parity conditions (8) Correlations between the estimated series

  33. Conclusions (1) • Our estimates for Brasil were not consistent the Fama’s first “fundamental” conclusion, but they were consistent with the results obtained for other emerging market economies (Bansal and Dahlquist (1999)): * The currency risk has a higher volatility than the expected depreciation, but the correlation between them is positive; * After the change of regime in January 1999, the expected depreciation turned to be more volatile than the currency risk. • Using the methodology of Wolff (1987) it was possible to obtain an estimated series of the currency risk.

  34. Conclusions (2) • Using our estimated series of the risk premium it was possible separate it from the expected depreciation. • The estimates were consistent with the results obtained with the Fama’s methodology. • We use our estimated currency risk and expected depreciation series to decompose the domestic interest rate. • It was shown that the covered interest parity does not hold in the brazilian case during the period analyzed. In other words, it was shown that the covered interest parity differential (country risk) is a significant component of the domestic interest rate.

  35. Conclusions (3) • The country risk shows a higher correlation with the currency risk (0,50) than with the expected depreciation (0,07). We interpret this fact as an evidence that both risks had a common source during the period analyzed. • With no econometric evidence, we argue this common source would be the higher degree of uncertainty about the fundamentals of the brazilian economy (fiscal desequilibrium, basically).

  36. Conclusions (4) • If our hypothesis is correct, it would help to explain that fact that, eighteen months after the change of the regime, the real interest rates in the brazilian economy continue being extremely higher for international standards. • On the other side, the continuation of a series of good news about fiscal efforts, jointly with the perception that the fiscal equilibrium as a long-lasting event, could generate significant interest rate reductions, by reducing both the currency risk and the country risk.

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