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We examine the in- and out-of-sample behavior of two popular trading systems, Alexander and Double MA filters, for 14 developed-country currencies using daily data with bid-ask spreads. We find significant in-sample returns in the early periods. But out-of-sample returns are lower and only occasionally significant. We show that a currency risk factor proposed in the literature is systematically related to these returns. We find no support for the hypotheses that falling transactions costs are responsible for declining trading profits or for the Adaptive Market hypothesis. Importantly, we show that algorithms that simulate out-of-sample returns have serious instability difficulties.

Examining the profitability of technical trading systems has been the subject of much research, because it can reveal market inefficiencies and possible disequilibria in the FX market. These systems – sets of mechanical rules that generate buy, sell or hold signals based on historical data – are designed to take advantage of time-dependencies in price changes. Under the Efficient Markets Hypothesis (EMH), price changes should not be time-dependent; in particular, there should be no systematic profits, after adjusting for returns to risk-bearing and transactions costs. Under the Adaptive Market Hypothesis (AMH; see Lo, 2004), price changes may be time-dependent, and the resulting profits are expected to dissipate only slowly. The results in the literature to-date as to whether trading profits exist are inconclusive. The following four items summarize the findings in the literature on trading systems: (1) Almost all the studies find statistically and economically significant trading (system) profits when profits are computed in-sample, that is, when all the sample data are used to identify winning strategies. (2) Out-of-sample evidence is more mixed, particularly in the most recent papers we review below. Some studies find smaller, declining, and often insignificant out-of-sample returns from trading systems. “Out-of-sample” evaluations simulate trading using historical data but they use information available only at each decision date in the selection of strategies. (3) A “filter” is the minimum change required in the benchmark variable for the trading system to trigger action; the filter can be set to a variety of values. The general conclusion is that, ignoring transactions costs, small filters – triggered by small changes in the benchmark variable– produce higher returns than large filters. But because small filters imply very frequent trading, unaccounted-for transactions costs are high and trader profits are dissipated. (4) At least the in-sample profits documented for trading systems are often judged to be too large to represent likely returns to risk-bearing.1 The existence of trading system profits, if reliable, raises troubling questions about the efficiency of the FX markets. In this paper we investigate the main issue in FX market efficiency: do excess trading profits still exist? We address this question by re-examining the profitability of two popular trading systems, a variant of the Alexander filter, and the Double Moving Average (Double MA) filter, from January 1986 to August 2009. We use daily data for 14 developed-country currencies, for which bid-ask spreads are available for both FX rates and Eurocurrency deposit and loan rates. The bid-ask spreads allow us to take into account explicitly the direct transactions costs of trading, rather than ignoring, estimating, or assuming them, as in the literature to-date. We find that, consistent with the literature, these two trading systems often generate significant and positive returns (profits) when applied in-sample. When we take into account the bid-ask spreads, profits and their statistical significance is lower; however, with a few exceptions they retain significance at a lower confidence level. We confirm that in-sample trading profits are considerably lower in the second half of the sample; their statistical significance is much reduced or is nonexistent. Also consistent with the literature, we find that trading system profits are economically smaller and generally statistically insignificant when the systems are simulated out-of-sample, and losses are much more frequent. We do find some evidence of significant out-of-sample excess returns in the beginning of our sample period (1989–1991). However, the level and significance of trading returns in the subsequent periods is very uncertain, and there are only a few instances in later subperiods where we find significant returns. We use regression analysis to more formally test several hypotheses: (i) the risk premium hypothesis, which suggests that the exposure of the trading returns to market-wide risk factors is responsible for any measured profits, (ii) the hypothesis that lower transactions costs reduce profits by making it more attractive for less efficient traders to trade, and (iii) the AMH. We find that the FX risk factor proposed by Lustig et al. (2008) is statistically significant for most currencies. In contrast, of the Fama-French risk factors only the market risk is occasionally significant, while the other two almost never are; this is true for both the in-sample and out-of-sample trading returns. Jensen's alphas are almost never statistically significant in the out-of-sample returns, consistent with Lustig et al. (2008) and contrary to Neely et al. (2009); they are frequently significant for the in-sample returns. All the loadings on the FX and market factors are negative but small. This suggests that the speculative positions we examine provide a small level of hedging against FX and market risks. Our results do not provide support for the hypothesis that lower transactions costs are responsible for declining trading returns. We also show that a time trend does not fit trading returns. Though lower second-period returns is consistent with the AMH, our inability to document a declining pattern in returns over time with this more specific test casts doubt on the hypothesis. However, since the AMH is not precisely articulated, this type of test cannot be said to reject it. A very important finding is that the out-of-sample returns are extremely sensitive to the parameters of the simulations that create them. We investigate the effect of two parameters of the trading algorithms: the starting date and the training period of the algorithm. For example, when we start the Double MA algorithm for the Deutsche Mark (DM) on 5/13/86, the 23-year out-of-sample return is 1.3% and not statistically significant. But start the algorithm four months later, on 9/5/86, and the average return is 5.2% and statistically significant at the 5% level. Our findings on out-of-sample returns and the very high sensitivity of the returns to the initial conditions of the algorithms, lead us to conclude that there are no reliable profits to be had with these two trading systems. Furthermore, our finding that simulation results are excessively dependent on initial conditions makes any past or future reports of out-of-sample success extremely suspect. It means that researchers or practitioners may examine the same data and trading systems and yet reach different conclusions about the profitability of a system because of small differences in the algorithm parameters. The remainder of the paper is organized as follows. Section 2 provides a brief review of the relevant literature. Section 3 discusses the calculation of trading returns, the trading systems we study, and the procedures we use to evaluate the returns from both statistical and economic perspectives. Section 4 describes the data sources and the statistical properties of the FX rates we use. Section 5 reports the in-sample and out-of-sample results, as well as tests of the risk exposure, the transactions costs, and the AMH explanations of trading returns. Importantly, it also describes a new source of instability related to the algorithms used to simulate out-of-sample returns. Section 6 offers concluding remarks.

We examine the profitability of “Alexander” and “Double MA” technical trading systems for 14 developed-country currencies, from 1986 to 2009, to assess whether technical trading still makes excess returns in the FX markets. A positive return to a zero-net-investment portfolio governed by such a trading system is either a return to risk-bearing or an “excess” return or profit, once transactions costs have been taken into account. Our bid-ask spread data for FX and interest rates allow us to take into account explicitly an important component of transactions costs, which previously were only estimated or imputed. Our main result is that we find no reliable out-of-sample trading profits. We also show that results from the standard methodology used to simulate out-of-sample trading are very sensitive to the algorithms’ starting conditions. Thus, researchers or practitioners may examine the same data and the same trading systems and still reach different conclusions about the profitability of a system because of small differences in the parameters of their simulations. Consistent with the literature, we find substantial and statistically significant in-sample returns over the whole sample, mainly in the first subperiod, for both trading systems. Significant positive returns are much harder to come by in the second subperiod, which is also consistent with the literature. The bid-ask spreads reduce both the magnitude and statistical significance of profits but eliminate neither, except in isolated instances. When we simulate our trading systems out-of-sample we find that overall trading returns are low, rarely significant at the 5% level, and never at the 1% level. We show that there appear to be substantial and significant out-of-sample returns for the 1988–1991 period but only isolated significant returns thereafter; many of the returns are negative. Using daily returns, we report tests of various explanations for trading returns: payment for risk, falling transactions costs, and the AMH. We find that the FX risk factor, introduced by Lustig et al. (2008), is highly significant but negative for most of the in- and out-of-sample trading returns. The Fama-French risk factors are generally insignificant, with except for the market factor in some instances; its coefficients are negative as well. The Jensen's alphas are generally highly significant for the in-sample returns but almost uniformly insignificant for the out-of-sample returns. Expected returns for these hedging portfolios would be slightly negative, and they provide a small degree of hedging against FX and market risks. Our measures of transactions costs and a time variable are also not significant. Thus, neither the proposition that declining transactions costs result in lower trading profits nor the AMH finds support in our results, in contrast to Neely et al. (2009). We show that small variations in the parameters of the out-of-sample simulations produce substantial differences in the returns obtained and in the inferences of significance. This has not been reported in the literature. It implies that traders operating the same trading system but with slightly different “training parameters” for their algorithms are likely to realize very different speculative returns. This finding casts further doubt on the existence of reliable profit opportunities from trading systems or any single simulated out-of-sample documentation of such profits. We must leave to future research how to incorporate this additional source of instability in drawing proper inferences.