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Academy of Economic Studies Bucharest Doctoral School of Finance and Banking DOFIN. FORWARD DISCOUNT PUZZLE AN APPLICATION FOR THE USD/GBP EXCHANGE RATE. Supervisor: Professor Moisa ALTAR MSc student: Anca-Ioana SIRBU. Bucharest, June 2004. CONTENTS. THE UNCOVERED INTEREST RATE PARITY

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Academy of Economic Studies BucharestDoctoral School of Finance and BankingDOFIN

FORWARD DISCOUNT PUZZLEAN APPLICATION FOR THE USD/GBP EXCHANGE RATE

Supervisor: Professor Moisa ALTARMSc student: Anca-Ioana SIRBU

Bucharest, June 2004

contents
CONTENTS
  • THE UNCOVERED INTEREST RATE PARITY
  • FORWARD RATE UNBIASEDNESS HYPOTHESIS
  • AN EMPIRICAL ANALYSIS
uncovered interest rate parity uip
UNCOVERED INTEREST RATE PARITY(UIP)
  • UIP is the cornerstone of international finance (it appears as a key behavioral relationship in almost all models of exchange rate determination)
  • UIP states that if risk-neutral market hypothesis holds, then the expected foreign exchange gain from holding one currency rather than another must be offset by the opportunity cost of holding funds in this currency rather than the other-the interest rate differential
  • Since UIP reflects the market’s expectations of exchange rate changes, it represents the starting point for any analysis which depends on future exchange rate values.
  • That is why, if there are reasons to believe UIP will not hold precisely, an investor must be able to identify the source of deviation and respond accordingly.
notations used
Notations used
  • St – nominal spot exchange rate at time t expressed as the price, in “home-country” monetary units, of foreign exchange (USD against GBP);
  • Ste – expected nominal spot exchange rate at time t;
  • Ft – forward rate at time t;
  • it, it*, nominal interest rate at time t in home country, respectively in the foreign country.
  • E(.) - expectation conditional on information available at time t.
  • Small letters denote the nominal logarithm of the variable
covered interest rate parity
COVERED INTEREST RATE PARITY
  • In the absence of arbitrage barriers across international financial markets, the arbitrage should ensure that the interest rate differential on two assets, identical in any relevant aspect, except currency of denomination, adjust to cover the movement of currencies at the maturity of the underlying assets in the forward market

or, a logarithmic approximation

  • If

then

covered interest rate parity1
COVERED INTEREST RATE PARITY
  • Testing for CIP

1. Computing actual deviations from interest parity

2. Regression analysis

Assuming rationale expectations and risk neutrality, we get

In logs, this relationship is approximately

FRUH:

forward rate unbiasedness hypothesis
FORWARD RATE UNBIASEDNESS HYPOTHESIS
  • FRUH stipulates that under the joint hypothesis of risk neutrality and rational expectations, the current forward rate is an unbiased predictor of the future spot rate
  • Bilson(1981) and Fama(1984)

FRUH: α = 0, β = 1, and Et(εt+1) = 0

  • Typical finding:

forward discount anomaly

forward rate unbiasedness hypothesis1
FORWARD RATE UNBIASEDNESS HYPOTHESIS

ENGEL(1996)

  • the existence of a foreign exchange risk premium;
  • a peso problem;
  • irrational expectations;
  • international financial market inefficiency from various frictions.

Fama(1984): omitted variables

which leads to the following decomposition

forward rate unbiasedness hypothesis2
FORWARD RATE UNBIASEDNESS HYPOTHESIS
  • Frankel and Froot (1987):excess returns are due to systematic forecast errors – participants form expectations in an irrational manner

* irrational agents earn higher expected returns because they

bear higher risk;

* rational agents, being more risk-averse, are not necessarily

able to drive the first group out of the market by

aggressively betting against them.

  • Baillie and Bollerslev (1994,2000): time series statistical properties, that is the long memory behavior exhibited by the forward discount, which results in an unbalanced regression.
  • Granger (1999): structural changes or regime switches can generate spurious long memory behavior in an observed series
techniques for analyzing fruh
Techniques for analyzing FRUH

1.OLS regression

2.Cointegration techniques:

*long-run relation (cointegration between st+1 and ft)

*short-run relation (cointegration between st and ft)

Zivot(2000), Guerra(2002)

3.Fractional integration

Structural changes (Bai and Perron (2001))

long memory processes
Long Memory Processes
  • time domain

{Yt} a covariance stationary processexhibits long memory in the time domainif its autocorrelations ( ρ(k)) exhibit slow decay and persistence

  • frequencies’ domain

{Yt} exhibits long memory properties if the spectral density function f(w) has the following property

  • In our analysis we use: GPH estimator, MLP estimator and HURST exponent
the bai and perron methodology for estimating structural breaks
The Bai and Perron Methodology for estimating structural breaks
  • estimation of single and multiple structural breaks in dynamic linear regression models
  • estimates the unknown break points given T observations by the least squares principle
  • provide general consistency and asymptotic distribution results under fairly weak conditions

*serial correlation

*heteroskedasticity

  • considers the simple structural change in mean model
  • pure and partial structural change models
models of cointegration between s t 1 and f t eg methodology step 1
MODELS OF COINTEGRATION BETWEEN st+1 AND ft – EG Methodology: Step 1
  • st+1 = 0.02395420+ 0.951353*ft + et

(0.899071) (0.019174)

[2.664328] [49.61727]

models of cointegration between s t 1 and f t johansen methodology
MODELS OF COINTEGRATION BETWEEN st+1 AND ft – Johansen Methodology

st+1 =-0.008327+1.022440ft + et+1

(0.00296) (0.00634)

models of cointegration between s t 1 and f t johansen methodology1
MODELS OF COINTEGRATION BETWEEN st+1 AND ft – Johansen Methodology

The cointegrating relation (stationary residuals:ADF and PP)

models of cointegration between s t and f t johansen methodology
MODELS OF COINTEGRATION BETWEEN st AND ft – Johansen Methodology

st =- 0.821933+1.022254ft + et

(0.00637) (0.29862)

models of cointegration between s t and f t johansen methodology2
MODELS OF COINTEGRATION BETWEEN st AND ft – Johansen Methodology

The cointegrating relation (stationary residuals:ADF and PP)

forward discount
FORWARD DISCOUNT

Classic testing of FRUH

Forward discount – AR(1) process

α = -0.398245 and β = -1.96552

(0.262959) (0.977023)

FWD_DISC = -0.21546 + 0.96085*FWD_DISC(-1) + RESID

(0.079487) (0.022346)

[-2.710614] [42.99797]

long memory in forward discount
Long memory in FORWARD DISCOUNT
  • GPH estimator
  • MLP estimator
  • HURST exponent = 0.979207261
conclusions
CONCLUSIONS
  • We find evidence of a negative β for 1982/01:2004/05, which suggests that the risk premium is negatively correlated with the expected depreciation, which may explain the negative slope coefficient and can therefore explain the puzzle.
  • Using cointegration techniques, we find that in the long run there is mixed evidence regarding the FRUH, as we can accept the unbiasedness, finding that the coefficients are close to their theoretical values, even though by imposing a priori restrictions, we reject the unbiasedness assumption.
  • The short-run investigation clearly rejects the FRUH
  • A possible explanation for the FRUH not to hold may be that the forward discount is a fractionally integrated process, so it exhibits long memory, which makes the classical regression unbalanced
  • Part of the long-memory behavior turns out to be due to structural breaks. We identify four such structural break points for the analyzed period.
  • Further analysis should identify how much of the long memory behavior may be explained by the existence of structural breaks
bibliography
BIBLIOGRAPHY
  • Bai, J. and P. Perron (2001): “Computation and Analysis of Multiple Structural Change
  • Models”, Journal of Applied Econometrics
  • Baillie, T. R. and T. Bollerslev, (1994): “Cointegration, Fractional Cointegration and
  • Exchange Rate Dynamics”, The Journal of Finance,vol. 49, no 2, 737-745.
  • Baillie, T. R. and T. Bollerslev, (2000), “The Forward Premium Anomaly is not as Bad
  • as you Think,” Journal of International Money and Finance, 19, 471-488.
  • Bilson, John F.0. (1981): “The ‘speculative efficiency’ hypothesis,” Journal of Business,
  • 54, 435-51.
  • Enders,W. (2000), “Applied Econometric Time Series”, in John Wiley & Sons.
  • Engel, C., (1996): The forward discount anomaly and the risk premium: A survey of
  • Recent Evidence Journal of Empirical Finance 3, 123–192
  • Engle, R.F. and C.W Granger., (1987): Cointegration and error correction: representation,
  • estimation and testing Econometrica 55, 251–276.
  • Evans, Martin D.D. and Karen Lewis (1995): “Do long-term swings in the dollar affect
  • estimates of the risk premia?” Review of Financial Studies, Vol. 8, No. 3,
  • 709-742.
  • Fama, E., (1984): Forward and spot exchange rates. Journal of Monetary Economics 14,
  • estimation and testing Econometrica 55, 251–276
  • Froot, Kenneth A. and Jeffrey A. Frankel(1987): “Using Survey Data to Test Standard
  • Propositions Regarding Exchange Rate Expectations”, The American Economic
  • Review 77, no. 1, 133-153.
  • Froot, Kenneth A. and Jeffrey A. Frankel (1989): “Forward discount bias: is it an
  • exchange risk premium?” Quarterly Journal of Economics, 104, 139-61
bibliography1
BIBLIOGRAPHY
  • Guerra, Roger (2002): “Forward Premium Unbiasedness Hypothesis: Old Puzzle,
  • New Results”, University of Geneva, Department of Economics, working
  • paper no. 02.02.
  • Hamilton, J., 1993. Time Series Analysis. Princeton University Press, Princeton (NJ).
  • Maynard A., Phillips P.C.B. 2001. Rethinking an old empirical puzzle: econometric
  • evidence on the forward discount anomaly. Journal of Applied Econometrics
  • 16: 671-708.
  • Sakoulis G., Zivot E. 2001. Time variation and structural change in the forward discount:
  • Implications for the forward rate unbiasedness hypothesis. Working Paper,
  • Department of Economics, University of Washington
  • Sarno, L. and M.Taylor(2000): “The Economics of Exchange Rates”, Cambridge
  • University Press.
  • Zivot, E., 1999. The power of single equation tests for cointegration when the
  • cointegrating vector is prespecified. Econometric Theory (in press) Department of
  • Economics, University of Washington, Seattle.
  • Zivot E. 2000. Cointegration and forward and spot exchange rates. Journal of
  • International Money and Finance 19: 785-812
  • Zivot E, J. Wang(2003), Modeling Financial Time Series with S-Plus, Springer