Hansen, Lars Peter, and Hodrick, Robert J. 1980. Forward exchange rates as optimal predictors of future spot rates: An econometric analysis. Journal of Political Economy 88 (October): 829 --53.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... each one quarter period, the initial growth or inflation estimate was a rational forecast of the final estimate and all revisions were independent by quarter, then the error term in the regression would be MA(I 1) where I is the number of quarters over which growth or inflation is computed ( Hansen and Hodrick 1980). 10 Of course, if these biases in the initial data could have been predicted when the initial data were released, then policymakers could have taken the biases into account when making their decisions. However, it is highly unlikely that policymakers can accurately estimate the changes that ....

Hansen, Lars Peter, and Hodrick, Robert J. 1980. Forward exchange rates as optimal predictors of future spot rates: An econometric analysis. Journal of Political Economy 88 (October): 829 --53.

....of the results presented (they turn out to be small relative to the measured risk premium) 4 Relevant theory includes Solnik (1974) Adler and Dumas (1976) Kouri (1977) and Dornbusch (1983) among many others. Evidence of serial correlation of excess returns includes Geweke and Feige (1979) Hansen and Hodrick (1980), and Cumby and Obstfeld (1981) among others. Hsieh (1984) shows that excess returns are correlated with beginning of period forward discounts. 4 The portfolio balance model of the risk premium explicitly links the premium to exchange rate second moments. Because the derivation of the model ....

Hansen, L. and R. Hodrick, "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, 88 (October 1980), 829-853.

.... if this strategy had been employed on information known to the market at time t, i.e. sf Zu tk tk t t = bb 0 (3) with the null hypothesis that b 0 =b=0, or simply b=0 (as b 0 non zero may be capturing the effects of the conditional variances and covariances above, see Hodrick (1987) See Hansen and Hodrick (1980), Cumby (1988) and Bekaert and Hodrick (1992) Such regressions are interesting as rejections of the null hypothesis would define a trading rule that could be more profitable than the naive rule. In particular, the following specification is frequently employed ss fsu tk t tk t t = gg 02 ....

Hansen, L.P. and R.J.Hodrick,1980, Forward Exchange Rates as Optimal Predictors of Future Spot rates: An Econometric Analysis, Journal of Political Economy, 88,829-853.

....However, we intuitively feel that adding overlapping intervals to the sampling scheme might increase the precision of the result. Is this intuitive feeling justified by theory The exact answerdependson the statistical properties of the analyzed variable. Theproblem has already been discussed in (Hansen and Hodrick, 1980), where a method of estimating parameters and their significance limits from overlapping observations has been developed and applied. In (Dunis and Keller, 1993a) and (Dunis and Keller, 1993b) a panel regression technique is presented and applied: the overlapping observations are grouped in ....

....using overlapping intervals (which just means a different aggregation scheme) cannot add any information. It is not clear whether the simple results of this paper have been published before, although the general problem of overlapping observations has found its first solution as early as 1980 (Hansen and Hodrick, 1980). A related problem is addressed by the literature on the jackknife method, for example (Yang and Robinson, 1986) This method is based on strongly overlapping resamples of the original sample. The beneficial effect of overlapping is probably lower than in the ideal example if there is already ....

Hansen L. P. and Hodrick R. J., 1980, Forward exchange rates as optimal predictors of future spot rates: an econometric analysis, Journal of Political Economy, 88(51), 829--853.

.... If the forecast error series 7 When the observation and forecast periods do not coincide, that is, when the time to maturity for t he forward contract exceeds the time interval between observations, the error term in the cointegrating regression in (4) is a noninvertible moving average process (Hansen and Hodrick (1980)) In that case, Moore (1992) shows that the Johansen cointegration methodology is inapplicable, as the Granger representation theorem breaks down in the presence of noninvertible moving average errors. Therefore, estimates and test results reported in previous empirical studies employing the ....

Hansen, L. P. and R. J. Hodrick (1980), Forward exchange rates as optimal predictors of future spot rates: An econometric analysis, Journal of Political Economy, 829-853.

....this value is distributed as # 2 (v) under the null hypothesis. 20 The use of overlapping observations in these moment conditions produces sample moments that exhibit serial correlation. Therefore the weighting matrix does not take the simple form of (23) I experimented with a variant of Hansen and Hodrick (1980) s weighting matrix, but in practice the matrix was typically not positive definite. I therefore adopted the approach of Newey and West (1987) To implement this test I set # = 1 2, so that six month ahead forecasts are examined. This horizon was chosen arbitrarily. A cursory investigation of ....

Hansen, Lars Peter, and Robert J. Hodrick, 1980, "Forward exchange rates as optimal predictors of future spot rates: An econometric analysis," Journal of Political Economy 88, 829-853.

....rate paths in the long run. For this reason it is important to investigate whether fi k 0. The dependent variable in model (5) can also be written as the sum of one period returns: Delta k e t k = Deltae t 1 : Deltae t k , with Deltae t i = e t i Gamma e t i Gamma1 . As is shown by Hansen and Hodrick (1980), if k 1 Delta k e t k has k Gamma 1 elements in common with Delta k e t k 1 and Delta k e t k Gamma1 respectively. Accordingly, there will be at least (k Gamma 1)th order autocorrelation in the disturbances t k s. This autocorrelation makes inference with regard to estimator fi k ....

Hansen, L. and R.J. Hodrick, 1980, Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis, Journal of Political Economy 88, 829-- 853.

....Since weinterpret the test of long horizon predictability as a test for cointegration, the regressor s t , f t is nonstationary under the null hypothesis, whichinvalidates the use of such estimators. 6 Uniform weights for the covariances, #i.e. w#j; l# = 1 for all j =1; lin #6##, cf. Hansen and Hodrick #1980#, are also commonly applied, see Fama and French #1988#, among others. To save space, we do not report results involving this estimator here, as they are very similar to the ones obtained with the Newey West estimator. These results are available upon request. 5 for l = 20 and l set according ....

Hansen, L.P. and R.J. Hodrick, 1980, Forward exchange rates as optimal predictors of future spot rates: an econometric analysis, Journal of Political Economy 88, 829#853.

....we interpret the test of long horizon predictability as a test for cointegration, the regressor s t Gamma f t is nonstationary under the null hypothesis, which invalidates the use of such estimators. 6 Uniform weights for the covariances, i.e. w(j; l) 1 for all j = 1; l in (6) cf. Hansen and Hodrick (1980), are also commonly applied, see Fama and French (1988) among others. To save space, we do not report results involving this estimator here, as they are very similar to the ones obtained with the Newey West estimator. These results are available upon request. 5 for l = 20 and l set according to ....

Hansen, L.P. and R.J. Hodrick, 1980, Forward exchange rates as optimal predictors of future spot rates: an econometric analysis, Journal of Political Economy 88, 829--853.

....separately or jointly. In step 1, since the constant is a strictly exogenous variable, generalized least squares or maximum likelihood estimation of Equation 3 will produce consistent estimates of d and the moving average coe#cients notwithstanding the property of v t stated earlier (c.f. Hansen and Hodrick, 1980). The specification of the higher order moving average alternative in step 2 might seem to be an arbitrary element of the proposed procedure. Suppose that the specified alternative moving average is u t v t #c # v t## #2#c j## v t#j # #c j v t#j #2#c r v t#r (4) so that we ....

Hansen, L. P. and Hodrick, R. J. (1980) Forward exchange rates as optimal predictors of future spot rates: an econometric analysis, Journal of Political Economy, 88, 829---53.

....CIP is given by the following relationship: Where i and i are domestic and foreign nominal interest rates, s is the spot tt t exchange rate and f is the forward exchange rate at time, t, for delivery at some t point in the future. All variables are expressed in logs. A number of authors such as Hansen and Hodrick (1980), Fama (1984) or Wolff (1987) provide a simple decomposition of the forward rate, f , into two components; t the expected future spot rate, s and an exchange rate risk premium , so that (1) e t 1 t becomes: If the risk premium is absent or agents are neutral with respect to exchange risk then ....

Hansen, L. and Hodrick, R. (1980) "Forward exchange rates as optimal predictors of future spot rates: An econometric approach." Journal of Political Economy, 88, 829-853.

....of the impliedvolatility forecast error. Within an option contractmonth the intervals represented by t; T and t 1;T overlap. So, if volatilityis forecast incorrectly 30 days from expiration, a substantial portion of thiserror willbereplicated by the forecast 29 days from expiration. Hansen and Hodrick(1980) outline a method for consistent GMM estimation in the contextofoverlapping forecast intervals; but, theirmethod is inappropriate for evaluating the impliedvolatilityhypothesis. Here, the forecast interval coincides with the option expiration cycle whichistelescoping rather than, as in Hansen and ....

Hansen, L.P.and R.J. Hodrick, 1980,Forward exchange rates as optimal predictors of future spot rates:Aneconometric analysis, Journal of Political Economy88, 829-- 853.

....forecasting ability of structural models compared to random walk models. We investigate additional economic forces acting on spot rates such as the expectations of 1 The author would like to thank Sam Ouliaris and Vance L. Martin for their kind guidance and generosity. 2 Cornell (1977) Hansen and Hodrick (1980), Fama (1984) and Kimbrough (1984) have focused on using forward rates as a predictor of future spot rates. However, Cornell (1977) indicated the unpredictability of exchange rate changes while Hansen and Hodrick (1980) states that: the forward rate is not the optimal predictor of the future ....

....and Vance L. Martin for their kind guidance and generosity. 2 Cornell (1977) Hansen and Hodrick (1980) Fama (1984) and Kimbrough (1984) have focused on using forward rates as a predictor of future spot rates. However, Cornell (1977) indicated the unpredictability of exchange rate changes while Hansen and Hodrick (1980) states that: the forward rate is not the optimal predictor of the future rate for some currencies. 252 Tan and Tan economic agents participating in financial markets as well as the risk aversity of individuals. The motivation for incorporating rational expectations into the model ....

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Hansen, L. P. and Hodrick, R. J. (1980): "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, 88, 829-852.

....difference in average monthly returns between R10 and R1 is significantly positive in all (J,K) combinations. The last five columns of Table I report the annual event time returns for each portfolio for five 12 month periods following the portfolio formation date, with t statistics based on the Hansen and Hodrick (1980) correction for autocorrelation up to lag 11. In Year 1, the R10 R1 portfolio yields a statistically significant return of between 10.62 percent and 12.70 percent per year. Consistent with Jegadeesh and Titman (1993) we observe a modest reversal to momentum profits in Years 2 and 3. Like their ....

....three volume portfolios (10 3) Year 1, Year 2, Year 3, Year 4, and Year 5 represent the annual returns of each portfolio in the five 12 month periods following the portfolio formation date. To correct for spurious autocorrelation from overlapping observations, we compute t statistics using the Hansen and Hodrick (1980) correction for autocorrelation up to lag 11. Panel A presents raw returns, Panel B reports industry adjusted returns, and Panel C reports size adjusted returns. The industry adjustment is based on 25 equal weighted industry portfolios formed by grouping two digit SIC codes (see Appendix) 16 ....

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Hansen, Lars P., and Robert J. Hodrick, 1980, Forward exchange rates as optimal predictors of future spot rates: An econometric analysis, Journal of Political Economy, 88, 829-853.

....most. 2. 1 The GMM Approach A very common approach for making inference on fi k in the context of dependent and possibly heteroskedastic observations is to correct the standard errors of regression coefficients estimates for serial correlation according to the generalized method of moments (GMM) by Hansen and Hodrick (1980) and Hansen (1982) Most papers that follow this idea base the correction on the additional hypothesis that log returns are uncorrelated, in which case the residuals of a k horizon regression follow a simple MA(k Gamma 1) process. The GMM method fares well in terms of asymptotic consistency. It ....

....GMM in the context of dependent observations, again a bandwidth parameter has to be selected in using a kernel for estimating the limiting covariance matrix. This problem sometimes seems to be swept under the rug in the applied literature. Fama and French (1988) and Campbell et al. 1997) use the Hansen and Hodrick (1980) kernel, weighting autocovariances up to lag k Gamma 1 with weight one and autocovariances beyond lag k with weight zero. This will produce a consistent estimator of the limiting covariance matrix only under the null hypothesis of fi k = 0 and under the additional assumptions that the log returns ....

Hansen, L. and Hodrick, R. (1980). Forward exchange rates as optimal predictors of future spot rates. Journal of Political Economy, 88, 829--853.

....independent observations. Although the parameter estimates from Ordinary Least Squares are unbiased, the OLS parameter estimates of variance covariance matrix are inconsistent. This paper resolves the presence of serial correlation by employing the Generalized Method of Moments estimator (GMM) of Hansen and Hodrick (1980) and Hansen (1982) along with the Newey and West (1987) approach to estimate the variance covariance matrix. In practice, the variance covariance matrix S T is not necessarily positive semi definite, kernel estimators are then applied S T = Omega 0 m X j=1 w(j; m) Omega j Omega ....

Hansen, L.P., and R.J. Hodrick, 1980, "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis" Journal of Political Economy, 88, 829-853.

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Hansen, L.P., and Hodrick, R. J. (1980) Forward exchange rates as optimal predictors of future exchange rates: An econometric analysis. Journal of Political Economy, 88, 829-53.

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Hansen, L.P., and R. J. Hodrick, (1980), Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis, Journal of Political Economy, 829-853.

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Hansen, L.P. and R.J. Hodrick(1980): "Forward exchange rates as optimal predictors of future spot rates: An econometric analysis," Journal of Political Economy 88, 829-853.

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Hansen, L.P and R. Hodrick, 1980, Forward exchange rates as optimal predictors of future spot rates, Journal of Political Economy 88, 829853.

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Hanson, L.P. and R.J. Hodrick(1980): "Forward exchange rates as optimal predictors of future spot rates: An econometric analysis," Journal of Political Economy 88, 829-853.

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