Editor’s note: This is an extract of a paper written by Dr. LeBaron in July 1994 and revised in March 1996. It is as thought provoking today as when it was first published. Dr. LeBaron examines the impact Fed intervention had on technical signals in the foreign exchange market. With the Fed now routinely intervening in various markets, the research is perhaps more timely than when it was originally completed. The full paper can be found at SSRN. Dr, LeBaron will be making a presentation about his most recent work at the upcoming MTA Symposium.
Abstract
There is reliable evidence that simple rules used by traders have some predictive value over the future movement of foreign exchange prices. This paper will review some of this evidence and discuss the economic magnitude of this predictability. The profitability of these trading rules will then be analyzed in connection with central bank activity using intervention data from the Federal Reserve. The objective is to find out to what extent foreign exchange predictability can be confined to periods of central bank activity in the foreign exchange market. The results indicate that after removing periods in which the Federal Reserve is active, exchange rate predictability is dramatically reduced.
Introduction
One of the biggest controversies between academic and applied finance is the usefulness of technical trading strategies.
These rules, which intend to find patterns in past prices capable of giving some prediction of future price movements are
sold as easy ways to make money, and scoffed at as charlatanism. Since the publication of Fama & Blume (1966) most
academics have agreed that the usefulness of these ad hoc forecasting techniques was probably close to zero. However,
evidence in foreign exchange markets has been much more favorable toward the usefulness of technical indicators.[1]
This technical rule predictability is strengthened by other foreign exchange puzzles such as the forward bias and
deviations from uncovered interest parity.[2]
This paper looks at a possible explanation for some of the predictability found in foreign exchange markets. Using intervention series available from the Federal Reserve, predictability will be compared during periods with and without intervention.[3][4] The results of this paper are foreshadowed in the quotation from Dooley & Shafer (1983).
At worst, central bank intervention would introduce noticeable trends into the evolution of exchange rates and create opportunities for alert private market participants to profit from speculating against the central bank.
Studies of the profitability of intervention for central banks such as Taylor (1982) and Leahy (1989) are also related. However, the connection is probably not as strong as one might think initially. It depends critically on what positions the bank is taking as the foreign exchange price process moves through time. This will be discussed further in the conclusions. A related question is whether the central bank is operating to stabilize or destabilize exchange rate movements, which is indirectly related to the profitability of the central bank, or technical traders, and won’t be addressed here.[5]
Data Summary
This study uses both weekly and daily foreign exchange series from NatWest Bank provided by DRI.
The series represent the London close for the German Mark (DM) and Japanese Yen (JY) extending from January 2nd, 1979 through, December 31st, 1992. The weekly series use the Wednesday close from this daily series. The interest rate series are 1 week euro-rates (London close) for each currency from the London Financial Times and NatWest Bank covering the same period. Summary statistics for the log first differences of the two daily foreign exchange series are given in table 1. This table displays features that are fairly well known for relatively high frequency foreign exchange series. They are close to uncorrelated, not very skewed, showing large kurtosis.
The Federal Reserve intervention values were provided by the Federal Reserve Bank.
Trading Rule Evidence
This section repeats earlier statistical evidence on the forecasting properties of a simple technical trading rule. Many of these results are given in more detail in LeBaron (1991). Forecasts will be examined over 1 day and 1 week horizons. The rule used compares the current price to a moving average of past prices. Let Pt be the $/DM exchange rate at time t. Define mat as
where M is the length of the moving average. For the daily data M = 150 and for weekly M = 30.[6]
Define a buy or sell signal st as
This is an extremely trivial type of trading rule, but the strategy here is to look at the simplest versions of trading rules following common practices. This helps to reduce the impact of data snooping biases brought on by searching the entire space of trading rules for the best performers.
Table 3 examines these dynamic trading returns for both daily and weekly exchange rates. The t-statistics in the table test whether the mean returns are zero. It is clear from the table that the means from the dynamic strategies are statistically different from zero at any reasonable significance level. It also appears that adjusting for the interest differentials and changing from daily to weekly returns does not affect the results greatly. These t-tests may not be the proper way to test for significance because of the deviations from normality in the foreign exchange returns, so a second experiment is performed. A sample of bootstrapped random walk price series is generated using the log price differences of the original series. These differences are scrambled with replacement and a new price series is built.[7] Then the returns from the dynamic strategies, implemented on these simulated random walk series, are compared to the original. The column labeled P-Value presents the fraction of simulations generating a dynamic return larger than the original. The column agrees with the t-tests in indicating the significance of these means. The column labeled Sharpe estimates the Sharpe ratio over a one year horizon. This is approximated as,
where σr is the standard deviation over the short horizon. N is the number of short periods in a one year period. This approximation would be correct if the dynamic returns were independent over time. The values in table 3 show that, ignoring transactions costs, Sharpe ratios in the range of 0.6 – 0.9 are attained. This compares with Sharpe ratios of around 0.3 or 0.4 for buy and hold strategies on aggregate U.S. stock portfolios.8 Finally, the column labeled “Trade Fraction” shows the fraction of days on which an actual trade took place, or in other words the fraction of times the strategy had to switch currencies.
In summary, this section demonstrated significant forecastability from a simple moving average trading rule for two foreign exchange series. The results are unquestionably large statistically. Since they generate large Sharpe ratios, and their infrequent trading minimizes the impact of transactions costs, these returns appear to be economically significant as well.[9]
Removing Intervention Periods
This section looks at one possible explanation for the previously demonstrated puzzle in foreign exchange series, central bank intervention. Some of the previous tests are repeated with the foreign exchange intervention periods removed.
Direct evidence on the impact of intervention is presented in table 5 where the experiments from table 3 are repeated with intervention days removed. Returns to the dynamic trading strategy from t to t + 1 are examined conditional on the intervention series being zero on t + 1. For weekly series an intervention period is defined as a week in which intervention occurred on at least 1 day. The results suggest a dramatic change when intervention periods are removed. For the DM series all of the t-statistics are not significantly different from zero, and the Sharpe ratios are close to 0.1. For the JY the results are not as dramatic, but mean returns have gone into the range of only being marginally significant for two of the series, and showing simulated p-values of 0.146 and 0.198 for the other two.
These results are strong in suggesting that something different is going on when the Federal Reserve is active in terms of foreign exchange predictability.
The results in this section can be summarized graphically in figure 3. This picture clearly shows dramatic reduction in Sharpe ratios for the trading rules for each of the series. While conclusions about causality cannot be made, these results are very suggestive that Federal Reserve activity has something to do with the observed predictability. The next section explores the possibility that there is a common driving processes causing the correlation between technical predictability and intervention.
Conclusions
The fact that simple trading rules produce unusually large profits in foreign exchange series presents a serious challenge to the efficient market hypothesis. Further, the magnitude of these returns and their resiliency to the adjustment for transactions costs, makes it difficult to imagine a representative agent rational expectations model capable of explaining these results. However, foreign exchange markets differ from most other major asset markets in that there are several major players whose objectives may differ greatly from those of maximizing economic agents. The results in this paper show that this predictability puzzle is greatly reduced, if not eliminated, when days in which the Federal Reserve was actively intervening are eliminated.
Before quickly concluding a causal relationship between intervention and trading rule profitability there is a serious simultaneity problem that needs to be addressed. Interventions and profits may be driven by the same common factor and therefore the apparent causal relation might be spurious. This hidden factor can never be completely eliminated as a potential cause, but this paper explored several possible ways in which it might appear. The results of these experiments make it look unlikely that a common factor will be easy to find.
The policy recommendations are not as clear cut as they might seem. If the Federal Reserve is transferring money to traders, it may be worthwhile in that it has other variables in its objective function such as overall price stability. Stopping a potential trade war may far outweigh a few losses in the foreign exchange market. It is also interesting that other studies such as Leahy (1989) find that the Federal Reserve is making money on its foreign exchange intervention operations. This fact, while an interesting contrast to the results here, is not exactly a contradiction since the magnitudes of interventions or total bank positions have not been analyzed here.
Understanding the causes and structure of this apparent predictability in foreign exchange markets is important both from the standpoint of understanding the forces that drive exchange rate movements, but also for implementing appropriate policies. These results are still far from implicating the Federal Reserve in this puzzle but they make those biases are toward efficient markets a little more comfortable, while revealing a troubling lack of robustness for technical signal predictability.
[1] The earliest tests were in Dooley & Shafer (1983), and Sweeney (1986) which present results consistent with some trading rule predictability. More recent studies have included Taylor (1992), LeBaron (1991), and Levich & Thomas (1993). The latter two employed bootstrap techniques to further emphasize the magnitude of the forecastability. Other related evidence includes that ofTaylor & Allen (1992) which shows that a large fraction of traders continue to use technical analysis, and Frankel & Froot (1987) which shows that short term forecasts often extrapolate recent price moves.
[2] Hodrick (1987) and Engel (1995) provide surveys of the large literature in this area.
[3] Silber (1994) performs a similar test, but in a cross sectional context. He shows that technical rules have value in markets where governments are present as major players.
[4] For extensive surveys on the large literature on foreign exchange intervention see Edison (1993) and Almekinders (1995).
[5] This debate, which goes back to Friedman (1953), is a delicate one and depends critically the types of speculative trading going on along with many other variables. The debate on this subject began with Baumol (1957), and continues through papers such as Szpiro (1994), where an intervening central bank can actually introduce chaos into a foreign exchange rate. Hart & Kreps (1986) provide a modern treatment displaying the full delicacy of the problem of stabilizing or destabilizing speculation.
[6] Trading rule profitability is not overly sensitive to the actual length of the moving average. See LeBaron (1991) for some evidence on this. Also, these moving average lengths are very commonly used by traders.
[7] In the cases where interest rates are ignored this is a simple reconstruction of a random walk from the scrambled returns. In the interest rate cases, the returns less the interest rate differentials are scrambled, and rebuilt into a price series, adding the actual differentials back as the drift.
[8] See Hodrick (1987), or LeBaron (1991) for some further references and examples of Sharpe ratios on aggregate portfolios. Also, see Sharpe (1994) for a summary of related work. For connections between Sharpe ratios to variance bounds tests and more information on conditional Sharpe ratios for other portfolios, see Bekaert & Hodrick (1992).
[9] The judgment of economic significance would require more detailed testing of a specific model.
References
- Almekinders, G. J. 1995. Foreign Exchange Intervention: Theory and Evidence. E. Elgar, Brookfield, VT, US.
- Baumol, W. 1957. Speculation, profitability, and stability. Review of Economics and Statistics 39, 263-71.
- Bekaert, G. and R. J. Hodrick. 1992. Characterizing predictable components in excess returns on equity and foreign exchange markets. The Journal of Finance 47, 467-511. Dooley, M. P. and J. Shafer. 1983. Analysis of short-run exchange rate behavior: March 1973 to November 1981. In Exchange Rate and Trade Instability: Causes, Consequences, and Remedies, D. Bigman and T. Taya (eds). Ballinger, Cambridge, MA.
- Edison, H. J. 1993. The Effectiveness of Central-bank Intervention: A Survey of the Literature After 1982. Number 18 in Special Papers in International Economics. Department of Economics, Princeton University, Princeton, New Jersey.
- Engel, C. 1995. The forward discount anomaly and the risk premium: A survey of recent evidence. Technical Report 5312, National Bureau of Economic Research.
- Fama, E. F. and M. Blume. 1966. Filter rules and stock market trading profits. Journal of Business 39, 226-241. Frankel, J. A. and K. A. Froot. 1987. Using survey data to test standard propositions regarding exchange rate expectations. American Economic Review 77(1), 133-153.
- Friedman, M. 1953. The case for flexible exchange rates. In Essays in positive economics. University of Chicago Press, Chicago, IL.
- Hart, O. D. and D. M. Kreps. 1986. Price destabilizing speculation. Journal of Political Economy 94, 927-952. Hodrick, R. J. 1987. The Empirical Evidence on the Efficiency of Forward and Futures Foreign
- Exchange Markets. Harwood Academic Publishers, New York, NY. Leahy, M. 1989. The profitability of US intervention. Technical Report 343, Board of Governors, Federal Reserve Bank, Washington, DC.
- LeBaron, B. 1991. Technical trading rules and regime shifts in foreign exchange. Technical report,
- University of Wisconsin – Madison, Madison, WI.
- Levich, R. M. and L. R. Thomas. 1993. The significance of technical trading-rule profits in the foreign exchange market: A bootstrap approach. Journal of International Money and Finance 12, 451-474.
- Sharpe, W. A. Fall 1994. The Sharpe ratio. Journal of Portfolio Management , 49-58.
- Silber, W. L. 1994. Technical trading: When it works and when it doesn’t. The Journal of Derivatives 1(3).
- Sweeney, R. J. 1986. Beating the foreign exchange market. Journal of Finance 41, 163-182.
- Szpiro, G. G. 1994. Exchange rate speculation and chaos inducing intervention. Journal of Economic Behavior and Organization 24, 363-368.
- Taylor, M. and H. Allen. 1992. The use of technical analysis in the foreign exchange market. Journal of International Money and Finance 11(3), 304-14.
- Taylor, D. 1982. Official intervention in the foreign exchange market, or, bet against the central bank. Journal of Political Economy 90(2), 356-68.
- Taylor, S. J. 1992. Rewards available to currency futures speculators: Compensation for risk or evidence of inefficient pricing? Economic Record 68, 105-116.