The long memory of the forward premium during the 1920s’ float: evidence from the European foreign exchange market

Abstract

This paper investigates the fractional dynamics of the foreign exchange forward premium during the floating period of the 1920s. We apply weekly exchange rates of the currencies from Belgium, France, Germany, Holland, Italy and the USA against the British pound from February 1921 to May 1925 and employ two different definitions of the forward premium. The German data are for the period ranging from February 1921 to December 1922. This period includes the German hyperinflation era. The empirical investigation is conducted by means of two different fractional integration methods: the Geweke and Porter-Hudak and the Robinson tests. The results provide some evidence of long memory, mostly in the case of Belgium, Holland and Italy. Many of the forward premiums during the 1920s may have become non-stationary as markets began to anticipate the UK's return to gold at its pre-war parity. In the case of Germany, it may have been due to market failure. The varying results presented could be due to the wide differences in the microeconomic and macroeconomic fundamentals and political setups of the countries during the 1920s.

Keywords:

• GPH test
• Robinson test
• ARFIMA
• forward premium
• long memory

JEL Classification:

• F3
• F31

Notes

1. Detailed theoretical and mathematical outlines of the unbiased forward hypothesis are available in several books and articles, such as in those of Baillie and McMahon (1989) and Gibson (1996). Therefore, in order to save space, we do not include a detailed analysis here.

2. If the forward market is not efficient, there are policy prescriptions that could be used to reduce exchange rate volatility. One such proposal is the Tobin tax, which is a uniform international tax payable on all spot transactions involving the conversions of one currency into another, in both domestic security markets and foreign exchange markets. Other policy options may be a tax on domestic stock of foreign assets, tax on capital outflows or inflows, and sliding-scale capital gains tax that would be higher for short-term capital gains (Spahn 1996).

3. Goodhart, McMahon, and Ngama (1992) showed that the rejection of the unbiased hypothesis may not be due to the risk premium but due to the domination of the forward exchange market by covered interest arbitrageurs. If the forward rate only reflects that the difference between the domestic and foreign interest rates and the spot rate is (approximately) a random walk, then the unbiased hypothesis will not hold.

4. Maynard and Phillips (2001) proposed a new limit theory for the forward premium anomaly. Their theory has non-standard limiting distributions with long left tails and proposes to explain the forward premium anomaly as a statistical artefact.

5. Choi and Zivot (2007) found evidence of long memory in forward premiums with and without adjusting for structural breaks. According to Li (2009), low-frequency data (monthly) tend to overstate the importance of structure breaks. In higher frequency data (both daily and weekly), long memory bears the primary responsibility for the forward premium anomaly. Coakley, Kellard, and Snaith (2009) concluded that the forward anomaly vanishes over the horizon. They claimed that this anomaly is a short-term phenomenon that should be resolved at medium horizons. Ding (2008) claimed that Thursday consistently appears to be a special day on which the anomaly disappears, while it is present on other weekdays. Furthermore, according to Bond et al. (2006), forward premium may be time-wise nonlinearity. This result was further confirmed by Amri (2008).

6. See Aliber (1962) and Baillie, Bollerslev, and Redfearn (1993) for an analysis of the 1920s’ floating exchange rate period.

7. They did not investigate the stochastic structure of the forward premium.

8. Baillie and Han (2002) using daily data found the spot exchange rate returns during the 1920s to have a long-memory property. They did not study the forward premium.

9. The length of the German data was determined by the availability of the data. The rest of the data ends when Britain returned to gold in 1925.

10. According to Booth and Tse (1995), the main advantage of the GPH method is that it permits the estimation of d without knowledge of p and q in . Furthermore, this method is robust for short-term dependence, conditional heteroscedastic effects and variance shift. However, possible biases of the spectral regression against the null hypothesis may be caused by infrequent shifts in the mean of the process and large AR parameters.

11. Using 1920s’ daily data, Phillips, McFarland, and McMahon (1996) found stationary forward premiums using the Belgian franc and the Italian lira. They did not apply the fractional integration tests but fully modified least square deviations regression procedure.

12. Graphs of both the definitions for all forward premiums failed to show any shift in the mean of the series. An AR model was fitted to each of the series according to the Schwarz information criterion. AR(3) and AR(4) models adequately describe dependence in the conditional mean of the series in question. Most of the AR coefficients were found to be small in value, suggesting the absence of strong short-term dependencies. Therefore, neither a shift in the mean nor strong short-term dynamics appears to be responsible for finding long memory in the forward premiums during the 1920s. The graphs and the AR test results are not presented in order to save space but are available on request.

13. Keynes (1972) stated that market speculation regarding the return of the pound to the gold began with the election of a conservative government in October 1924.

14. Ignoring data from September 1924 onwards, Rossiter (2002) reported stationary forward premiums for the pound–Belgium franc, the pound–Holland guilder and the pound–dollar. Rossiter (2002) did not apply the fractional integration test but cointegration test with log-likelihood test.

15. One of the referees pointed this out to us.

16. Investigating the effects of the microstructure is beyond the scope of this paper, but provides incentive for future research.