Lessons from the Evolution of Foreign Exchange Trading Strategies

Abstract

The adaptive markets hypothesis posits that trading strategies evolve as traders adapt their behavior to changing circumstances. This paper studies the evolution of trading strategies for a hypothetical trader who chooses portfolios from forex technical rules in major and emerging markets, the carry trade and U.S. equities. The results show that forex trading alone dramatically outperforms the S&P 500. But there is little gain to coordinating forex and equity strategies, which explains why practitioners consider these tools separately. In addition, a backtesting procedure to choose optimal portfolios does not select carry trade strategies until well into the 1990s, which helps to explain the relatively recent surge in interest in this strategy. Forex trading returns dip significantly in the 1990s but recover by the end of the decade and have greatly outperformed an equity position since 1998. Overall, trading rule returns still exist in forex markets – with substantial stability in the types of rules – though they have migrated to emerging markets to a considerable degree.

Full text

Research Division
Federal Reserve Bank of St. Louis
Working Paper Series
Lessons from the Evolution of Foreign
Exchange Trading Strategies
Christopher J. Neely
and
Paul A. Weller
Working Paper 2011-021D
http://research.stlouisfed.org/wp/2011/2011-021.pdf
September 2011
Revised April 2013
FEDERAL RESERVE BANK OF ST. LOUIS
Research Division
P.O. Box 442
St. Louis, MO 63166
______________________________________________________________________________________
The views expressed are those of the individual authors and do not necessarily reflect official positions of
the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors.
Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulate
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cleared with the author or authors.

Lessons from the Evolution of Foreign Exchange Trading Strategies
Christopher J. Neely a,*, Paul A. Weller b
a Federal Reserve Bank of St. Louis, St. Louis, MO, USA
b University of Iowa, Iowa City, IA, USA
This version: April 9, 2013
Abstract
The adaptive markets hypothesis posits that trading strategies evolve as traders adapt their
behavior to changing circumstances. This paper studies the evolution of trading strategies for a
hypothetical trader who chooses portfolios from foreign exchange (forex) technical rules in
major and emerging markets, the carry trade, and U.S. equities. The results show that a
backtesting procedure to choose optimal portfolios improves upon the performance of
nonadaptive rules. We also find that forex trading alone dramatically outperforms the S&P 500,
with much larger Sharpe ratios over the whole sample, but there is little gain to coordinating
forex and equity strategies, which explains why practitioners consider these tools separately.
Forex trading returns dip significantly in the 1990s but recover by the end of the decade and have
been markedly superior to an equity position since 1998. Overall, trading rule returns still exist
in forex markets—with substantial stability in the types of rules—though they have migrated to
emerging markets to a considerable degree.
JEL classification: F31; G14; G11; G15
Keywords: Exchange rate; Technical analysis; Technical trading; Carry trade; Efficient markets
hypothesis; Adaptive markets hypothesis
*Corresponding author. Send correspondence to Chris Neely, Box 442, Federal Reserve Bank of St. Louis, St. Louis,
MO 63166-0442; e-mail: neely@stls.frb.org; phone: +1-314-444-8568; fax: +1-314-444-8731. Paul Weller’s email:
Paul-Weller@uiowa.edu; phone: +1-319-335-0948. Christopher J. Neely is an assistant vice president and economist
at the Federal Reserve Bank of St. Louis. Paul A. Weller is the John F. Murray Professor of Finance Emeritus at the
University of Iowa. The views expressed in this paper are those of the authors and do not necessarily reflect those of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks.

1
1. Introduction
The literature on technical analysis has established that simple technical trading rules on
dollar exchange rates provided 15 years of positive, risk-adjusted returns during the 1970s and
1980s before those returns were extinguished (Levich and Thomas, 1993; LeBaron, 2002; Olson,
2004).1 More recently, more complex and less studied rules have produced more modest returns
for a similar length of time (Neely et al., 2009). Researchers have extensively investigated
explanations that rely on risk adjustment and/or central bank intervention but found that these do
not plausibly justify the observed excess returns produced by simple technical trading rules, nor
can data mining explain the apparent profitability of technical analysis (Neely et al., 2009).
Andrew Lo’s (2004) adaptive markets hypothesis (AMH) offers a plausible explanation for
this technical trading puzzle, however. The AMH posits that profit opportunities will generally
exist in financial markets but that learning and competition will gradually erode these
opportunities as they become known. A core principle of the AMH is that traders learn over time,
adapting their behavior to changing circumstances. This suggests that one should expect to see
an evolution of strategies and desired investment currencies. In the context of technical trading in
the foreign exchange market, a number of studies have confirmed the prediction that profits
associated with particular rules will gradually decline as more traders learn about them.
But another important prediction of the AMH, that adaptive trading strategies will show
superior performance to simple fixed rules, has been largely ignored. The present paper focuses
on examining this prediction. Ideally, one might like to examine the evolution of technical
trading strategies by directly looking at the trading records of technicians. As these data are not
1 Menkhoff and Taylor (2007) and Neely and Weller (2012) review the literature on technical analysis in the foreign
exchange market from different perspectives.

2
available, an alternative approach is to consider how a hypothetical trader would have adapted to
changing market conditions using simple rules of thumb. Traders face a number of practical
problems as they choose strategies to maximize their welfare. How to choose rules, individually
or as part of a portfolio? How to combine technical rules in foreign exchange (forex) with carry
trade or equity strategies? In practice, traders must make these choices by backtesting rules on
existing data. In this paper we model adaptive behavior in terms of a simple backtesting
procedure applied to a group of commonly studied technical and carry-trade rules in tradable
currencies.2 Although these rules are not necessarily the most effective or popular rules today,
we prefer to consider families of commonly studied rules to maintain continuity with the
previous literature and ensure that all rules would be known to traders throughout the sample.
Specifically, we investigate whether a hypothetical trader could use past performance of
trading rule-currency pairs—i.e., combinations of a specific trading rule applied to a particular
exchange rate—to predict future performance and construct a dynamic trading strategy superior
to individual trading rules. To mimic the decision process of a forex trader, we construct a
dynamic strategy as follows: We start with a pool of rule-currency pairs (including carry trades)
and rank them at month t according to the Sharpe ratio over some past time window.3 We then
2 Researchers have independently examined both technical trading rules and the carry trade (Brunnermeier et al.,
2009; Jordà and Taylor, 2009; Farhi et al., 2009; Burnside et al., 2011a,b; Menkhoff et al., 2012a,b) and
practitioners widely use both sorts of trading strategies, but researchers have done little comparison between them
(Menkhoff et al., 2012b).
3 Given that none of the returns appear to have systematic risk, the Sharpe ratios allow one to easily compare
performance from strategies with differing volatility. Ingersoll et al. (2007) demonstrate how a clever fund manager
can dynamically manipulate his portfolio to maximize his Sharpe ratio. The manager essentially reduces (increases)
the size of his investments after a successful (unsuccessful) investment run to increase the relative weight of more

3
form portfolios of the highest-ranked N rules and measure the return to the portfolio over month t
+ 1. Each month individual rule-currency pairs are re-ranked and the results of the ex ante
ranking are allowed to determine the composition of the portfolio for the next month.
In addition, we investigate whether such a trader would benefit from an adaptive approach to
diversification. Given the well-documented fact that currency trading rule returns typically
display very low correlation with stock market returns, one would expect that combining equity
with a dynamic currency trading strategy would substantially improve over the latter.
What does our trader learn? Backtesting works well. Past performance clearly does predict
the future: Rule-currency pairs that are more highly ranked in backtesting have higher ex post
Sharpe ratios. Indeed, the Sharpe ratio of the dynamic trading strategy is much superior to that of
the S&P 500. The success of backtesting supports the prediction that an adaptive trading strategy
fares better than using fixed rules. It also suggests that the positive results in the literature are not
due to data mining. The backtesting methodology is fairly robust to the selection window. Both
ex ante optimal and 1/N portfolios produce very good Sharpe ratios in every subsample, well
exceeding the average of their constituent strategies. The ex ante optimal and 1/N forex
combinations are similarly profitable over the entire sample, with no statistically significant
differences in profitability when other portfolio characteristics —i.e., number of strategies,
weighting—are held constant.
The research does, however, confirm a dip in the profitability of major investment currencies
in the 1990s and a switch to emerging market currencies in the 1990s. In contrast, the types of
positive outcomes. The dynamic strategies studied in this paper do not change leverage over time and so the Sharpe
ratios calculated here are not subject to this problem. Therefore, we focus on Sharpe ratios as our metric for
rule/strategy performance.

4
rules chosen show few noticeable time trends, with the following exceptions: the channel rules
become somewhat less frequently used over the sample and the carry trade becomes much more
frequently used after the mid-1990s.
There is almost no payoff to diversifying across equities and currencies. We show that this
finding is consistent with the observed levels of excess return and volatility in currency and
equity markets. Given the substantially higher Sharpe ratio of the dynamic currency strategy, the
equity allocation in the optimally diversified portfolio is rather small and so equity’s impact on
performance is also very small, even ignoring parameter uncertainty and sampling error. This
lack of benefit to active diversification is consistent with the prevalence of the previously
puzzling “compartmentalization” of forex and equity trading activities by practitioners.
We also find that the selection strategies do not select the bilateral carry trades in the top-
ranked rules until the mid-1990s. The fact that carry trade strategies did not measure up well to
the best-ranked technical rules might in part explain the almost complete lack of academic
interest in the carry trade before 2006. For example, Google Scholar reports only 5 articles with
the phrase “carry trade” in the title from 1990 through 2005 but 98 since 2005. We surmise that a
combination of time to accumulate data, time to write articles and time to publish them explains
the delay between the initial success of the carry trade and publication of articles on the topic.
In studying how a trader would have learned about the properties of adaptive rules, our paper
differs from the vast majority of research on technical trading. Early papers considered the
profitability of simple nonadaptive (static) technical rules (e.g., Sweeney, 1986), or the statistical
significance of this profitability (e.g., Levich and Thomas, 1993). Later papers evaluated more
complex nonadaptive rules (Osler, 2003, 2005) or considered explanations for the profitability of
nonadaptive rules, such as central bank intervention (LeBaron, 1999; Neely, 2002) or data

5
mining (Neely et al., 2009). Neely et al. (2009), for example, ruled out data mining as an
explanation for technical rule success by examining the true, ex post out-of-sample profitability
of several sets of fixed, nonadaptive rules from previous papers. Several papers have looked at
time variation in the profitability of nonadaptive rules (Levich and Thomas, 1993; Neely et al.,
2009).
We wish to emphasize, however, that this paper does not test the AMH. We believe that
existing evidence suggests that the AMH is the most plausible explanation for the changing
patterns of profitability in forex markets but we recognize that this remains a hypothesis. Rather,
we examine the actions of a hypothetical trader to discover what such a trader would have
learned and whether those lessons are consistent with observed patterns in the forex market.
Two studies examine trading strategies with adaptive features, although they differ from our
approach in important respects. Olson (2004) dynamically selects the best moving average rule
for each of 18 developed market currencies in successive 5-year periods from 1971–2000 and
then tests these in successive 5-year out-of-sample periods. He finds that returns declined from
the 1970s to about zero in the 1990s. Okunev and White (2003) construct momentum strategies
by using moving averages to identify the strongest and weakest momentum currencies. The
strategies thus switch between different currencies over time. The authors find that the returns
generated by these momentum strategies appear to have been more persistent, at least until the
end of their sample in 2000.
2. Methodology
We examine the performance of portfolios of technical trading rules that are rebalanced
monthly by applying a performance criterion. We use a standard pool of rules that we consider
representative of those that the academic literature has investigated: 7 filter rules, 3 moving

6
average rules, 3 momentum rules, 3 channel rules, and 1 type of carry trade rule.4 Although these
rules are not necessarily the most sophisticated and popular rules in current use, we believe that
they are appropriate for several reasons: 1) traders had knowledge of these rules over the whole
sample; 2) their use allows comparisons with the previous literature; and 3) using commonly
known and tested rules insulates us from the danger of rule snooping.
A filter rule generates a buy signal for a foreign currency when the exchange rate (domestic
price of foreign currency) has risen by more than y percent above its most recent low. It
generates a sell signal when the exchange rate has fallen by more than the same percentage from
its most recent high. Thus,
where  is an indicator variable that takes the value +1 for a long position and –1 for a short
position. We denote the exchange rate at date t (domestic currency per unit of foreign currency)
by ; nt is the most recent local minimum and xt the most recent local maximum. The seven
filter rules have filter sizes (y) of 0.005, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.1.
A moving average rule generates a buy signal when a short-horizon moving average of past
exchange rates crosses a long-horizon moving average from below. It generates a sell signal
when the short moving average crosses the long moving average from above. We denote these
rules by vma(S, L), where S and L are the number of days in the short and long moving averages,
respectively. The moving average rules are vma(1, 5), vma(5, 20), and vma(1, 200). Thus,
4 Dooley and Shafer (1984) and Sweeney (1986) look at filter rules; Levich and Thomas (1993) look at both filter
and moving average rules; Jegadeesh and Titman (1993) consider momentum rules in equities, citing Bernard
(1984) on the topic; and Taylor (1994) tests channel rules, for example.
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7
vma(1, 5) compares the current exchange rate with its 5-day moving average and records a buy
(sell) signal if the exchange rate is currently above (below) its 5-day moving average.
Our momentum rules imply a long (short) position in an exchange rate when the n-day
cumulative return is positive (negative). We consider windows of 5, 20 and 60 days for the
momentum rules.
A channel rule counsels to buy (sell) if the price exceeds (is less than) the maximum
(minimum) over the previous n days plus (minus) the band of inaction (x).5 Thus,
We set n to be 5, 10, and 20, and x to be 0.001 for all rules.
Finally, we consider a bilateral carry trade rule applied to each exchange rate, as in Burnside
et al. (2011a). For each currency pair, these rules take a long position in the currency with the
higher overnight interest rate and a short position in the other currency.
We thus generate a pool of 17 bilateral rules applied to 21 dollar exchange rates and 19
cross-rates, which Table 1 lists. The series for the DEM was spliced with that for the EUR after
January 1, 1999. For simplicity we refer to this series throughout as the EUR. The exchange rate
series are added to the sample as data become available and the respective series can be
realistically traded. The next Section of the paper discusses the data more fully.
5 We define the channel rule following Taylor (1994). Sullivan et al. (1999) instead call this rule a “support-and-
resistance” rule. Sullivan et al.’s (1999) definition of the channel rule is similar to Taylor’s (1994), but the rule is
conditioned on a formed channel—that is, the minimum and maximum over the last n days must be within a certain
distance of each other.
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8
We sort all currency-rule pairs with at least 250 days of data (since the beginning of the
respective samples) by Sharpe ratio. There is a maximum of (17*40=) 680 rules on any given
day, but missing data for some exchange rates often leave fewer than half that number of
currency-rule pairs. The ranking and rebalancing procedures are performed every 20 business
days. Thus, the top-ranked portfolio’s returns will be generated by a given trading rule applied to
a particular currency for a minimum of 20 days, at which point it may (or may not) be replaced
by another rule applied to the same or a different currency.
In any study of trading performance—especially when using exotic currencies—it is
important to pay close attention to transaction costs. Rules and strategies that may appear to be
profitable when such costs are ignored turn out not to be attractive once the appropriate
adjustments have been made. The impact of transaction costs depends both on their magnitude
and on the frequency with which positions are changed. For example, in research on intraday
technical trading strategies Neely and Weller (2003) found that realistic transaction costs
eliminated very high gross excess returns in the case of four highly liquid currencies, the German
mark, the Japanese yen, the British pound and the Swiss franc. This result was driven by the high
trading frequencies for the rules considered. The size of the spread plays a particularly important
role for emerging market currencies. Burnside et al. (2007) found that bid-ask spreads for
emerging market currencies over the period 1997 to 2006 were between two and four times as
large as those for developed market currencies. Thus using the same transaction cost for all
currencies will exaggerate the relative profitability of trading in emerging market currencies.
In order to account for variation in transaction costs both over currencies and over time we
used Bloomberg data on one-month forward bid-ask spreads as the basis for estimating
transaction costs. Correspondence with several foreign exchange traders and with the head of the

9
foreign exchange department of a commercial bank led us to believe, however, that the quoted
spreads appear to substantially overestimate the spreads actually available to traders. After
comparing spreads from Bloomberg with those on actual trader’s screens and then discussing the
size of spreads with traders, we concluded that actual spreads were roughly one third of the
quoted spreads. Therefore, we calculated transaction costs as follows. Before the spread data
from Bloomberg were available (December 1995) the cost of a one-way trade for advanced
countries (UK, Germany, Switzerland, Australia, Canada, Sweden, Norway, New Zealand and
Japan) was set at 5 basis points in the 1970s, 4 basis points in the 1980s and 3 basis points in the
1990s. For all other countries it was set at one third of the average of the first 500 bid-ask
observations.6 Once Bloomberg data become available, we use the figure of one third of the
quoted one-month forward spread. Deliverable forwards are available for all countries but
Russia, Brazil, Peru, Chile and Taiwan, for which we have only non-deliverable forwards. For
cross-rate transaction costs, we use the maximum of the two transaction costs against the dollar.
We use a minimum of one basis point transaction cost for all currencies. Figure 1 shows the
estimated transaction costs for each currency over time. The greater magnitude and volatility of
these costs for emerging market currencies is readily apparent.
3. Data
Table 1 shows the complete set of exchange rates that were used, as well as the starting and
ending dates for which they were available to trade in our sample. All exchange rates are from
the Haver daily or intdaily databases. The original source for most of the exchange rates is the
Board of Governors of the Federal Reserve System statistical release H.10 (Foreign Exchange
6 The costs during the 1970s and 1980s are consistent with triangular arbitrage estimates originally done by Frenkel
and Levich (1975, 1977) and McCormick (1979), and used by Sweeney (1986) and Levich and Thomas (1993).

10
Rates), but some emerging market exchange rates are from the Wall Street Journal.7 The
HUF/CHF and ILS/EUR rates are originally sourced from the National Bank of Hungary and
Financial Times, respectively. The DEM/USD return series was spliced with the EUR/USD
return series at the date of the introduction of the euro, January 1, 1999.
We take a conservative view of the periods in which emerging markets currencies can be
traded. To avoid periods in which capital controls or market disruption would have prevented
actual trading, we restricted the start of simulated trading for a number of currencies: the South
African rand (April 1, 1995), Brazilian real (May 1, 1999), Mexican peso (January 1, 1996),
New Zealand dollar (August 1, 1987), Turkish lira (January 1, 2002), Peruvian nuevo sol (April
1, 1996), Israeli shekel (January 1, 1995) and Taiwanese dollar (January 1, 1998).8 The Bank for
International Settlements (BIS) provided most of the interest rate data, which were mostly
overnight money market rates. For several countries, overnight interbank or money market
interest rate series were obtained from their central banks: Australia, Europe, Russia, the United
States, and the United Kingdom. Japan’s interest rate was constructed by splicing three series:
one from the Bank of Japan and two from the BIS. Swiss and Japanese interest rate data
exhibited a few (small) negative values early in the data and in the most recent period. We set
these interest rate observations to zero for return calculations.
4. The performance criterion
We now turn to the measure of excess return, which is the performance criterion we use in
7 Exchange rates in the H.10 release are quoted at noon ET, while the Wall Street Journal reports prices at New York
close.
8 A dual exchange rate system was in operation for the rand until March 1995 (Farrell and Todani, 2004). De Zwart
et al. (2009) provide information on the tradability of these currencies.

11
conjunction with the Sharpe ratio for both technical trading rules and the carry trade. We first
distinguish between technical trading “rules” and technical trading “strategies.” Examples of a
technical trading rule are a 1% filter applied to the Japanese yen or a moving average rule vma(5,
20) applied to the Swiss franc. A technical trading strategy uses some selection criterion to
switch between individual rule-currency pairs.
The rules/strategies we consider switch between long and short positions in the domestic and
foreign currencies. If a trading rule signals a long position in the foreign currency at date t, the
trader borrows the domestic currency at the domestic interest rate, converts it to foreign currency
at the exchange rate for date t and earns the foreign overnight rate. We denote the domestic
(foreign) overnight interest rate by ( ). Then the excess return, , to a long position in
foreign currency is given by
. (1)
We denote the continuously compounded (log) excess return by ztrt+1, where zt is an indicator
variable taking the value +1 for a long position and –1 for a short position, and rt+1 is defined as
. (2)
The cumulative excess return from a single round-trip trade (go long at date t, go short at date
t + k), with one-way proportional transaction cost c, is
, ∑

 ln
1
ln1
 (3)
Note that a trading strategy may incur transaction costs even when individual trading rules do
not, and conversely. This will happen if a strategy requires a switch between two rules holding
different positions but the rules themselves signal no change of position. In this case, the strategy
incurs a transaction cost but the individual rules do not. If, on the other hand, a strategy dictates a
itit*Rt1
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12
switch from a rule requiring—let us say, a long position at time t to a different rule requiring a
long position in the same currency at time 1—then no transaction cost is incurred, even
though one or both individual rules may have signaled a change of position from time t to 1.
5. Results
5.1. Average rule performance
As a benchmark for comparison, Table 2 presents the average performance of all rules by
individual currency. That is, for each exchange rate, we construct an equally weighted portfolio
consisting of the 17 bilateral rules over the available data. For most currencies the net annual
returns are modestly positive—in the range of 0 to 5%—but eight are negative. About a quarter
of the exchange rates produce statistically significant positive net returns. The mean Sharpe ratio
over all rules and exchange rates is 0.17.9 Average trading frequency is modest, ranging from
about 11 to 21 trades per year.
5.2. Ex ante strategy performance
Of course, choosing an almost-random group of trading rules and currencies would not be a
sensible trading strategy. Some rules may consistently outperform others or the level of
performance may vary, with certain rules doing well for a while and then declining. In practice,
traders seek to exploit such patterns by choosing rules that “backtest” well. In other words,
traders choose rules on the basis of past performance. To emulate this behavior, we construct ex
ante portfolios with the simple procedure described in Section 1. After an initial period of 500
business days, we commence the following selection procedure each month (20-day period). We
rank all rules according to Sharpe ratio over a selection window at the current date. We then
9 The statistical significance of this mean Sharpe ratio cannot directly be tested with the mean standard error of the
Sharpe ratios in the next column. Table 4 displays standard errors for Sharpe ratios for various portfolios.

13
measure the performance of N ranked strategies over the next month in an out-of-sample test. To
investigate the impact of time variation on rule profitability, we investigated three lengths of
selection windows: the full available sample and the 1000- and 500-observation periods prior to
the portfolio construction date. In the interests of brevity, we will only present results from the
selection window using all ex ante data but will discuss differences with the shorter selection
windows when appropriate. We emphasize that all portfolios are constructed with only ex ante
information, thus ensuring that traders could have implemented the strategies. Having measured
and ranked the N rules by their past performance each month, we then label portfolio strategies
according to the rank, n, of the rule. Thus the strategy corresponding to n = 1 selects the top-
ranked rule every 20 days. The strategy corresponding to n = 2 selects the second-ranked rule
every 20 days, and so on. Thus, strategies with small values of n will switch between rules that
have had relatively high Sharpe ratios over previous data. The composition of these ex ante
strategies will vary with the profitability of rule-exchange rate pairs over time, as markets
gradually adapt and agents arbitrage away previously profitable trading opportunities.
Table 3 details the performance of the top 10 ex ante strategies. Thus, portfolio 1 describes
the performance of the strategy for which trades are determined each period by the signals of the
top-ranked rule. Portfolio 2 describes the performance of the strategy using the signals of the
second-ranked rule, and so on. Over the full out-of-sample sample period (April 1975–December
2012), the best ex ante strategy earns a gross annual excess return of 10.08%. Since the strategy
trades 13.76 times a year, transaction costs lower the gross return to a net return of 9.40%. The
associated Sharpe ratio is a very healthy 0.78. Figure 2, which plots the Sharpe ratios for the top
662 ranked strategies, reveals that higher-ranked strategies tend to have better net excess returns
and Sharpe ratios. A graph of net excess returns by portfolio rank is almost identical. As rank

14
declines, return also declines and becomes more volatile across ranks; this supports the
hypothesis that the ranking and selection procedures do indeed improve performance.
Figure 3 illustrates a striking pattern of trade frequency across rank. The top-ranked
strategies have the lowest trade frequency, with portfolio 1 trading only 13.76 times a year.
Trade frequency rises to reach a local plateau of almost 35 trades for strategies 100 to 230 and
then declines to a lower plateau until about strategy 600, when it rises sharply again. Note that
the trading strategies almost always trade more than individual rules (see Table 2) because of
changes made at rebalancing periods when the strategy often switches rules/positions. The use of
filter rules probably influences the peaked pattern in trade frequency. As in Neely et al. (2009),
filter rules of intermediate size generate the highest excess returns. These rules trade less
frequently than small filters and more frequently than large ones. In addition small filter rules
outperform large ones. These facts partially explain the pattern in Figure 3.
We next consider the performance of the strategies over time. Figure 4 shows the net annual
excess return over time for the top 5 strategies and for the corresponding 1/N portfolio. The
consistent profitability until the early 1990s emerges clearly, as does the more recent
improvement in performance. The first conclusion we can draw from these results is that
although a strategy of switching between rules and currencies may mitigate the 1980-1995
decline in profitability of individual rules, it does not eliminate it. The second conclusion is that
profitability returns in the late 1990s. The portfolio of the top 5 ranked strategies has positive
Sharpe ratios in 12 of the 16 years from 1997 through 2012 and its average during that period is
a very respectable 0.78. Third, the portfolio provides clear diversification benefits. The annual
standard deviations of the top 5 individual strategies over the whole sample ranged from 9.79 to
11.42 percent but the annual standard deviation of the portfolio was only 6.91 percent.

15
5.3. Currency portfolios and diversification
A stylized fact in the literature on technical trading in currency markets is that returns to
individual rules and portfolios of rules are uncorrelated with stock returns (e.g., Neely et al.,
1997; Neely and Weller, 1999). Therefore, one would expect significant diversification benefits
from combining the returns from a technical trading strategy and a stock market index. One
possible approach is to consider the performance of an ex ante optimally weighted portfolio for a
mean-variance investor. However, DeMiguel et al. (2009) argue that the naïve 1/N allocation rule
is more robust and outperforms the optimally weighted portfolio in the context of stock
portfolios because means and covariances of returns are imprecisely estimated. This issue has not
been investigated in the context of forex rates, however. It is therefore of interest to be able to
compare the performance of naïve and optimal portfolios of rules.
We form ex ante optimal portfolios as follows. At each date t, we choose the ex ante best N
(N = 10 and N = 50) individual rules according to their Sharpe ratios. We calculate the mean
annual excess return and the covariance matrix of the returns to these forex rules and the S&P
500 long position over the previous 500 observations. (Note that this is not the same as the
covariance matrix of the trading strategy returns because the identities of the rules making up the
strategy change over time.) So, for example, if N = 2 and the best 2 rules according to the
selection criterion at time t are “GBP filter 0.005” and “CHF vma(1,5),” then we calculate the
mean and covariance matrix for those 2 rule-currency pairs and the buy-and-hold equity position
over the previous 500 observations. Denoting the covariance matrix by  and the mean return by
, we obtain portfolio weights

. (4)

16
We set negative weights to zero and scale the weight vector to sum to 1. If the non-negativity
constraint is not binding, then these weights maximize the Sharpe ratio of a portfolio consisting
of the N rules and the buy-and-hold equity position. Next we compute the return to a portfolio
consisting of the N forex rules and the equity position with optimal weights over period t + 1. We
also construct a naïve portfolio consisting of equal weights attached to each of the N rules and
the equity position. We also consider treating the equity position separately from the forex
strategies in two ways: We consider a 50-50 split between the 1/N portfolio of forex strategies
and the equity position; and we consider a 50-50 split between ex ante optimal portfolio of forex
strategies and the equity position.
We construct 12 different portfolios that vary according to (1) whether they use the top 10 or
50 trading strategies; (2) how the forex strategies are combined with each other and with equity.
Table 4 displays the results for these 12 portfolios. For ease of reference, we label the various
portfolios as follows:
 1/(N+1) (naïve) weights on each of N currency strategies and S&P 500 NE
 1/(2N) weights on each of N currency strategies and ½ weight on the S&P 500 NH
 1/N weights on each of N currency strategies and zero weight on the S&P 500 NZ
 Optimal weights on each of N currency strategies and the S&P 500 OE
 ½ optimal weights on each of N currency strategies and ½ weight on the S&P 500 OH
 Optimal weights on each of N currency strategies and zero weight on the S&P 500 OZ
To distinguish between portfolios with 10 and 50 foreign exchange strategies, we write, for
example, NE-10 or NE-50.
Both the portfolios with N = 10 and N = 50 perform very well in almost all subsamples.
Table 4 shows that the portfolios NE and OE have Sharpe ratios ranging from 0.72 to 0.94 over

17
the whole sample period (1975–2012). The OE-10 and OE-50 portfolios typically have fairly
similar performances for both the full sample and for the three subsamples. Over the full sample,
OE-10 has a Sharpe ratio of 0.72 compared with a value of 0.89 for OE-50. However, there is no
evidence of significant diversification benefit from combining the currency portfolio strategies
with equity. The overall performance of OZ and NZ portfolios is not markedly different from
that of the OE and NE portfolios, though the differences between like combinations, e.g., OZ-10
vs. OE-10, are sometimes significant because the series are highly positively correlated. These
facts strongly indicate that the high Sharpe ratios are attributable entirely to the currency
portfolio strategies. The largest difference in OE/OZ or NE/NZ Sharpe ratios occurs during the
bull market subsample of 1988–99, when the OE-10 portfolio, with a Sharpe ratio of 0.28,
significantly outperformed the OZ-10 portfolio, which had a Sharpe ratio of 0.10.
The absence of any marked diversification benefit from combining the currency portfolios
with equity might appear surprising in light of the fact that they show slightly negative
correlations. The top 10 forex strategies have daily correlations between -0.04 and 0.01 with the
S&P 500 total return series over the full sample and 7 of these 10 correlations are negative.
Nonetheless the lack of diversification benefit is perfectly consistent with the measured levels of
return and volatility. Over the full sample, the net returns to equity and the dynamic trading
strategy OZ-10 are 6.04 and 4.20 percent respectively, but the Sharpe ratios are 0.37 and 0.66
because the forex returns are much less volatile.10 The standard deviation of annualized net
returns of the S&P 500 is 17.43 percent, whereas for OZ-10 it is only 6.05 percent.
To illustrate how such numbers translate into portfolio weights, consider an example in
10 Serban (2010) notes the superiority of Sharpe ratios from a forex strategy that combines momentum and mean-
reversion elements with an equity position.

18
which equity and the dynamic strategy earn the same annual return of 5%, and the annual
standard deviations of the equity portfolio and dynamic strategy are 15% and 5%, respectively. If
the two return series are uncorrelated, then the optimal equity portfolio weight is 0.1. However,
the Sharpe ratio of the optimally diversified portfolio is only 5.4% higher than that of the low-
volatility dynamic strategy return. If we were to adopt a Bayesian perspective to account for
parameter uncertainty, the improvement from diversification would be even smaller. The
intuition for the very marginal benefit from diversification is as follows: Excess returns for the
two investment strategies are fairly similar, whereas Sharpe ratios are dramatically different
because equity returns are much more volatile than currency returns. This means that there are
only very modest benefits to diversification even when the two return series are uncorrelated.
Whether or not one finds benefits to diversification depends on the choice of baseline
portfolio. Levich and Pojarliev (2011) report that investors with a global equity exposure gain
significant diversification by adding returns generated by currency managers. This is certainly
what we find for a baseline S&P 500 portfolio. Our result is stronger in that it says that there is
no advantage to adding equity exposure to our adaptive forex trading strategies.
Another result of interest is that the OZ and NZ portfolios substantially outperform equity
alone. The last panel of Table 4 shows that the Sharpe ratio of the S&P 500 over the full sample
is 0.37, whereas OZ-10, OZ-50, NZ-10 and NZ-50 have Sharpe ratios of 0.66, 0.89, 0.80 and
0.92. The latter three Sharpe ratios are significantly higher than that of the S&P 500. Only over
the strong (mostly) bull market of 1988–99 does equity outperform the OZ and NZ portfolios. In
the other two samples, the currency portfolios clearly outperform equity. For example, over the
last 13 years (2000–2012) the OZ-10 (50) Sharpe ratio is 0.54 (0.81) but the ratio for the S&P
500 is only 0.09. The differences in the first subsample are statistically significant but those in

19
the latter two subsamples are generally not. Consistent with the fact that the currency strategies
outperform equity, optimal and 1/N combinations of the forex strategies with equity (OE and
NE) produce significantly higher Sharpe ratios, at the 10 percent level, than the 50-50 portfolios
(OH and NH).
In contrast to results in equity markets, there is little evidence to suggest that naïve (1/N)
portfolios of forex trading strategies outperform optimal portfolios in terms of Sharpe ratios.
That is, the average Sharpe ratio produced by the NE, NH, and NZ portfolios is only modestly
higher than the average Sharpe ratio produced by the OE, OH, and OZ portfolios. The average
full sample improvements in Sharpe ratios for naïve portfolios over the optimal portfolios are
only about 0.1 and 0.03 for the 10- and 50-strategy portfolios, respectively, and none of these
differences are statistically significant.
Figure 5 shows the time series of rolling Sharpe ratios for several of the top 10 strategy
portfolios, both with and without equity, as well as the rolling Sharpe ratio to a buy-and-hold
position in the S&P 500. The top (center) panel displays 1-year rolling Sharpe ratios from the
OE-10 and OZ-10 (NE-10 and NZ-10) strategy portfolios from 1976 to 2012. Contrary to the
general perception in the literature, forex technical trading rules tend to perform at least as well
from 2000–12 as from 1990–1999, although the differences are not statistically significant. The
bottom panel of Figure 5 displays the 1-year rolling Sharpe ratios to the S&P 500. The ratios are
quite variable and show no obvious trend.
To investigate the effect of emerging market currencies on the recovery in profitability after
1997, we redid the strategy selection exercise with only currencies from developed countries.
Table 5 shows that when only non-emerging market currencies are used, about half of the 10-
strategy and 50-strategy portfolios earn negative excess returns in the final sample (2000-2012)

20
and none of the portfolios earn statistically significant positive Sharpe ratios. This result is
consistent with the literature and the results of Pukthuanthong-Le et al. (2007) and
Pukthuanthong-Le and Thomas (2008), who find that emerging market currencies appear to
provide profit opportunities to technical rules.
5.4. Currency portfolio composition
Our findings support the view that traders could have used backtesting to improve on the
performance of individual trading rules by switching rule/currency compositions. In other words,
rules can be reliably ranked according to expected future performance, and these rankings
change over time (see Figure 2). How does the composition of the portfolio strategy vary over
time? Table 6 presents the frequency with which different rules appeared in the top 5 ranked
portfolios. The carry trade applied to the TRY was the overall “winner” in that it was used 14.3%
of the time in the top-ranked portfolio. This is a striking illustration of the importance of the
carry trade, since the TRY did not start trading in our sample until 2002. The CLP carry trade
was the next most frequently used rule in the top portfolio, with a frequency of 11.2%.
Moving average, filter, momentum, channel rules, and the carry trade all appear among the
most-used rules in the top portfolio, and both developed and emerging market currencies are
represented. However, the analysis for the full sample masks substantial variation across
subsamples. Some of this variation is driven mechanically by the fact that data for some
emerging markets are either not available or cannot be used for certain (earlier) periods because
of the presence of capital controls or other restrictions on market activity. Table 7 reproduces the
information for the top-ranked portfolio divided into four distinct subperiods. The GBP ch(10)
rule during the first subperiod (1973-82) was dominant; it was used 45.9% of the time. The next
most frequently used rules were the CAD/GBP mom(20) and EUR ch(10), which were used 18.4

21
and 15.3% of the time, respectively. The EUR ch(10) rule continued to be frequently used in the
second subperiod (1983-92), where it was used 24.8% of the time. It is not until the third
subperiod (1993–2002) that emerging market currencies start to acquire a more prominent role.
The CLP carry trade and CLP 0.02 filter are used 41.2% and 10.7% of the time respectively.
Over the most recent subperiod (2003 – 2012) rules applied to emerging market currencies
become completely dominant.
Figure 6 shows the frequency with which various rule classes appeared in the top-ranked
portfolios. The top panel depicts the proportion of appearances in the top 10 ex ante trading
strategies of rules from each group k:
∑∑
∈ 


∗ (5)
where  is the number of days rule i was the top jth strategy and N is the total number of days
in the given sample. The should sum to one. The bottom panel adjusts for the fact that larger
rule groups would have a better chance of being represented in the top 10 trading strategies. The
adjusted rule score (̃) controls for the size of the groups by dividing  by the number of rules
in each group ( and then normalizing the results to sum to one.
̃

/∑

 (6)

Over the whole sample, channel rules dominate, whereas from the mid-1990s the carry trade
takes the top spot until near the end of the sample when there is a striking decline in its use. This
suggests that the effects of learning and competition might have already come into play.
The rule group prevalence seems to be reasonably stable over time with a few caveats. First,
the channel rules, momentum rules and MA rules tend to decline in importance toward the end of
the 1990s, recovering more recently. Second, the small filter rules and the large filter rules each

22
have a brief upsurge of frequency—peaking in 1990 and 2002, respectively—before declining
again. Third, and most remarkably, the carry trade is unimportant until the mid-1990s.
How frequently were different types of exchange rates used in the best 10 strategies over
time? To summarize the prevalence of exchange rates in the best strategies over time, we divide
the currencies into 5 currency groups, shown in Table 1. The advanced market exchange rates
consist of the AUD, CAD, CHF, EUR, GBP, JPY, NOK, NZD, and SEK; developing Europe
consists of the CZK, HUF, PLN, RUB, TRY and HUF/CHF; the Latin American group consists
of the BRL, CLP, MXN, PEN and the JPY/MXN; the Other group consists of ILS, TWD, ZAR
and ILS/EUR; and the Advanced cross rates consist of non-emerging cross rates. Figure 7 shows
the prevalence of exchange rate groups in the top 10 trading strategies. The lower panel of Figure
7 adjusts the frequency of each group’s representation by dividing by the number of exchange
rates in the group and then normalizing the frequencies to sum to 1. It is constructed similarly to
the lower pane of Figure 6, as described in (6).
Exchange rates from advanced economies dominate the top 10 ex ante trading strategies in
the early part of the sample because there were no developing currencies in our data sample
before the early to mid-1990s. Consistent with Lee and Mathur (1996), cross rates tend to be
used with lower frequency in the top trading strategies throughout the whole sample. In the late
1990s, currencies from Latin America began to dominate the top 10 ex ante strategies and have
maintained that position until very recently.11
11 Lee, Gleason and Mathur (2001) discern mixed results for MA and channel rules for 13 Latin American exchange
rates using an earlier sample.

23
6. Discussion and conclusion
The “efficient markets hypothesis” holds that no trading strategy should be able to generate
unusual profits based on publicly available information—such as past prices—except by bearing
unusual risk. Previous research has established that the standard approach to risk adjustment
using the CAPM cannot explain the observed positive excess returns to technical trading in
currency markets. This is a consequence of the very low and sometimes negative correlation
between returns to technical trading rules and stock market returns. The long-term profitability of
technical strategies in the forex market suggests that the adaptive markets hypothesis would
better describe market functioning. Adaptive behavior allows for the possibility that profit
opportunities persist for considerable periods of time. Eventually, however, traders learn about
these opportunities and compete them away. A number of studies of the forex market have
confirmed this prediction. However, researchers have paid little attention to the distinct question
of whether an adaptive trading strategy can outperform a nonadaptive strategy. Previous research
has very largely focused on nonadaptive strategies, namely fixed trading rules or fixed portfolios
of these rules. The contribution of this paper is to examine the performance of explicitly adaptive
trading strategies and to compare them to nonadaptive strategies.
We draw several conclusions from our analysis. First, a portfolio trading strategy that
switches between different rule-currency pairs according to past Sharpe ratios improves
substantially on the average performance of the rule-currency pairs (Figure 2). That is,
backtesting is an effective adaptive strategy because rule-currency performance is persistent.
Second, there are benefits to diversifying among forex trading strategies: The optimal and 1/N
currency portfolio strategies (OZ-10, OZ-50, NZ-10 and NZ-50) clearly outperform almost all
strategies based on using a single currency rule at a time. They also turn out to be very

24
significantly superior to a pure equity portfolio (S&P 500) in terms of Sharpe ratios (Table 4).
But the portfolio strategy optimally combined with equity generally does not markedly improve
on the portfolio strategy on its own. The naïve strategies that combine portfolios split evenly
between equity and a currency strategy (OH and NH) are generally inferior to the currency-only
portfolio strategies (OZ and NZ) and the results are statistically significant for the 50-rule
portfolios. The lack of a diversification benefit may help to explain why firms typically treat
their forex and equity positions separately. There is little or no advantage to be gained from
coordinating them.
Although the performance of the currency portfolio strategies has fluctuated, with a
noticeable dip in the 1990s, Sharpe ratios have rebounded over the most recent decade (Figures 4
and 5). This observation sharply contrasts with the evidence from other studies that the
profitability of individual technical trading rules had disappeared by the early 1990s. It lends
support to the prediction of the Adaptive Markets Hypothesis that adaptive strategies will
outperform nonadaptive strategies. The rebound in optimal rule profitability since 1998 coincides
with a strong shift in the optimal strategies away from major currencies to emerging markets,
first in Latin America in the late 1990s and then recently to developing Europe (Figure 7).
The types of rules used by the optimal rule portfolios are fairly stable over time (Figure 6).
Channel rules, momentum rules and MA rules decline somewhat in importance after the mid-
1980s and small and large filter rules each become more important for a time before declining
again. The most interesting change, however, is that the carry trade becomes prominent only
after 1995. This shortly predates a surge in academic and practitioner interest in carry-trade rules.
The relatively poor performance of the carry trade compared with the best technical strategies
prior to 1999 might explain the dearth of interest in the carry trade until recently. 

25
Acknowledgements
The authors thank an anonymous referee and participants at presentations at the Federal
Reserve Bank of St. Louis, Colorado State University Department of Finance, the Midwest
Finance Association, Rutgers University Department of Economics, the SNDE meetings and the
Society for Quantitative Finance for helpful comments and Brett Fawley for excellent research
assistance. The authors are responsible for any errors.
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Table 1
Data description
Notes: The table depicts the 21 exchange rates versus the USD and 19 non-USD cross rates used
in our sample along with the starting and ending dates of the samples, number of trading dates,
average transaction cost, and standard deviation of annualized log returns.
Currency Group Country Currency abbreviation
versus the USD # of trading
obs Trading start
date Trading end
date Mean TC STD of Annualized
FX Return
Advanced Australia AUD 9008 4/7/1976 12/31/2012 3.1 11.6
Advanced Canada CAD 9344 1/2/1975 12/31/2012 2.9 6.7
Advanced Euro Area EUR 9717 4/3/1973 12/31/2012 3.0 10.6
Advanced Japan JPY 9599 4/3/1973 12/28/2012 3.0 10.5
Advanced New Zealand NZD 6027 8/3/1987 12/31/2012 3.9 12.4
Advanced Norway NOK 6515 1/2/1986 12/31/2012 3.4 11.6
Advanced Sweden SEK 7278 1/3/1983 12/28/2012 3.3 11.4
Advanced Switzerland CHF 9697 4/3/1973 12/31/2012 3.1 12.0
Advanced UK GBP 9338 1/2/1975 12/31/2012 2.9 9.9
Dev. Europe Czech Republic CZK 5049 1/5/1993 12/31/2012 5.2 12.4
Dev. Europe Hungary HUF 4466 1/2/1995 12/28/2012 10.3 14.3
Dev. Europe Hungary/Switzerland HUF_CHF 4165 1/3/1996 12/28/2012 10.5 12.0
Dev. Europe Poland PLN 3918 2/24/1997 12/31/2012 7.1 14.6
Dev. Europe Russia RUB 3055 8/1/2000 12/28/2012 3.6 7.4
Dev. Europe Turkey TRY 2769 1/2/2002 12/31/2012 12.9 15.4
Latin America Brazil BRL 3330 5/3/1999 12/31/2012 6.0 16.8
Latin America Chile CLP 4359 6/1/1995 12/28/2012 5.9 9.5
Latin America Japan/Mexico JPY_MXN 3887 1/4/1996 12/28/2012 4.6 16.9
Latin America Mexico MXN 4220 1/4/1996 12/31/2012 4.6 10.5
Latin America Peru PEN 4252 4/1/1996 12/31/2012 5.3 5.0
Other Israel ILS 3750 7/20/1998 12/31/2012 8.1 7.8
Other Israel/Euro Area ILS_EUR 2552 1/2/2003 12/31/2012 8.5 10.2
Other South Africa ZAR 4394 4/3/1995 12/31/2012 8.7 16.4
Other Taiwan TWD 3605 1/5/1998 12/28/2012 5.0 5.3
Adv. Cross Rates Switzerland/UK CHF_GBP 9169 1/3/1975 12/31/2012 3.0 9.8
Adv. Cross Rates Australia/UK AUD_GBP 8920 4/7/1976 12/31/2012 3.2 12.4
Adv. Cross Rates Canada/UK CAD_GBP 9217 1/2/1975 12/31/2012 3.0 10.3
Adv. Cross Rates Japan/UK JPY_GBP 8982 1/2/1975 12/28/2012 3.0 12.2
Adv. Cross Rates Euro Area/UK EUR_GBP 9187 1/2/1975 12/31/2012 3.0 8.1
Adv. Cross Rates Australia/Switzerland AUD_CHF 8848 4/7/1976 12/31/2012 3.2 14.4
Adv. Cross Rates Canada/Switzerland CAD_CHF 9150 1/3/1975 12/31/2012 3.1 12.4
Adv. Cross Rates Japan/Switzerland JPY_CHF 9338 4/3/1973 12/28/2012 3.2 11.7
Adv. Cross Rates Euro Area/Switzerland EUR_CHF 9602 4/3/1973 12/31/2012 3.2 5.9
Adv. Cross Rates Canada/Australia CAD_AUD 8894 4/7/1976 12/31/2012 3.2 10.3
Adv. Cross Rates Japan/Australia JPY_AUD 8633 4/7/1976 12/28/2012 3.2 15.3
Adv. Cross Rates Euro Area/Australia EUR_AUD 8861 4/7/1976 12/31/2012 3.2 12.8
Adv. Cross Rates Japan/Canada JPY_CAD 8968 1/2/1975 12/28/2012 3.1 12.7
Adv. Cross Rates Euro Area/Canada EUR_CAD 9158 1/2/1975 12/31/2012 3.1 10.7
Adv. Cross Rates Japan/Euro Area JPY_EUR 9347 4/3/1973 12/28/2012 3.1 11.3
Adv. Cross Rates New Zealand/Australia NZD_AUD 5943 8/3/1987 12/31/2012 3.9 8.7

31
Table 2
Average trading rule statistics by foreign exchange rate
Notes: The table presents the annual gross and net (of transaction costs) excess return and Sharpe
ratio averaged across all 17 trading rules for each currency over the full data sample. Sample
periods differ by currency.
Currency Gross AR Net AR Net AR t-statistic Sharpe Sharpe (s.e.) Trades per year per rule Observations
GBP 2.36 1.91 2.18 0.34 0.16 16.79 9337
CHF 3.50 2.95 2.81 0.46 0.16 18.09 9696
AUD 2.01 1.50 1.42 0.25 0.16 16.73 9007
CAD 0.59 0.18 0.32 0.05 0.16 14.68 9343
SEK 1.71 1.13 0.99 0.19 0.18 17.88 7277
JPY 3.53 3.07 3.46 0.53 0.15 15.98 9598
ZAR 2.27 0.42 0.19 0.05 0.25 19.89 4393
CZK 2.69 1.71 1.15 0.27 0.23 18.02 5048
RUB 3.78 3.26 2.86 0.64 0.22 12.96 3054
EUR 4.21 3.73 4.12 0.64 0.15 16.53 9716
BRL 5.25 4.03 1.44 0.42 0.26 19.48 3329
HUF -0.28 -1.48 -1.21 -0.29 0.25 12 4465
MXN -0.52 -1.37 -0.98 -0.25 0.27 17.72 4219
NZD 1.28 0.57 0.41 0.09 0.21 18.42 6026
NOK 0.73 0.10 0.08 0.02 0.20 18.20 6514
PLN 1.72 0.24 0.12 0.03 0.26 19.30 3917
TRY 1.75 -0.80 -0.29 -0.10 0.33 19.79 2768
PEN 0.37 -0.23 -0.36 -0.09 0.25 11.20 4251
CLP 6.07 5.14 3.97 0.90 0.21 15.27 4358
ILS 3.13 1.96 1.80 0.45 0.25 14.11 3749
TWD 1.40 0.77 1.14 0.27 0.26 12.58 3604
CHF_GBP 1.53 1.02 1.19 0.19 0.16 16.94 9168
AUD_GBP 1.43 0.86 0.79 0.13 0.16 18.28 8919
CAD_GBP 2.13 1.62 1.78 0.28 0.16 17.66 9216
JPY_GBP 2.63 2.11 1.84 0.30 0.16 17.97 8981
EUR_GBP 1.86 1.40 1.96 0.32 0.16 15.62 9186
AUD_CHF 1.59 0.98 0.73 0.12 0.17 19.11 8847
CAD_CHF 2.64 2.08 1.83 0.30 0.16 18.55 9149
JPY_CHF 2.66 2.10 2.00 0.33 0.16 17.83 9337
EUR_CHF 0.83 0.39 0.80 0.12 0.16 13.93 9601
CAD_AUD -0.10 -0.64 -0.67 -0.12 0.18 17.43 8893
JPY_AUD 3.21 2.62 1.73 0.30 0.16 18.81 8632
EUR_AUD 2.35 1.79 1.51 0.25 0.16 17.81 8860
JPY_CAD 3.35 2.83 2.42 0.40 0.16 17.71 8967
EUR_CAD 3.41 2.90 3.09 0.51 0.16 17.23 9157
JPY_EUR 3.75 3.24 3.16 0.53 0.16 16.99 9346
NZD_AUD -0.89 -1.59 -1.75 -0.37 0.21 17.31 5942
HUF_CHF -2.49 -4.43 -2.95 -0.82 0.29 17.83 4164
ILS_EUR -2.91 -4.55 -2.80 -0.94 0.34 18.70 2551
JPY_MXN 1.57 0.59 0.24 0.06 0.26 20.67 3886
Mean 1.90 1.10 1.06 0.17 0.20 17.04 6912

32
Table 3
Top 10 ex ante portfolio results

Notes: The table presents the gross annual excess return (Gross AR) and annual excess return net of transaction costs (Net AR) for the
top 10 ranked ex ante portfolio strategies. The sample for the ex ante portfolios is April 1975 to December 2012.
Portfolio # Gross AR Net AR Net AR t-statistic Sharpe Sharpe (s.e.) Trades per year
1 10.08 9.40 4.81 0.78 0.17 13.76
2 3.31 2.41 1.33 0.21 0.16 19.10
3 5.68 4.79 2.61 0.44 0.17 19.25
4 5.58 4.66 2.69 0.44 0.16 19.74
5 8.90 8.00 4.79 0.78 0.17 20.36
6 5.45 4.43 2.62 0.40 0.16 22.96
7 6.18 5.06 3.05 0.50 0.17 25.77
8 5.87 4.77 2.77 0.46 0.17 24.77
9 6.73 5.65 3.12 0.52 0.17 25.30
10 6.24 5.19 2.91 0.49 0.17 24.70
Mean 6.40 5.44 3.07 0.50 0.17 21.57

33
Table 4
Portfolios of technical trading strategies and equity: Sharpe ratios
Notes: The table reports Sharpe ratios with standard errors in parentheses. The trading rule portfolios consist of the top 10 and top 50
ranked strategies, respectively, in the left-hand and right-hand panels. The rows provide Sharpe ratios and their standard errors on
portfolios constructed from the 10- and 50- rule currency trading strategies and a long position in the S&P 500. The six types of
portfolios are constructed as follows: 1/(N+1) weights on N currency strategies and S&P the 500 (NE); 1/(2N) weights on N currency
strategies and ½ weight on the S&P 500 (NH); 1/N weights on N currency strategies and 0 weight on the S&P 500 (NZ); optimal
weights on N currency strategies and the S&P 500 (OE); ½ optimal weights on N currency strategies and ½ weight on the S&P 500
(OH); optimal weights on N currency strategies and 0 weight on the S&P 500 (OZ). The bottom panel displays the Sharpe ratio to a
buy-and-hold position in the S&P 500 over various samples.
Weight on each
of N FX rules Weight on
equity Name 1975-2012 1975-1987 1988-1999 2000-2012 1975-2012 1975-1987 1988-1999 2000-2012
1/(2N+1) 1/(2N+1) NE 0.86 1.37 0.40 0.79 0.94 1.47 0.55 0.77
(0.16) (0.27) (0.28) (0.27) (0.16) (0.28) (0.28) (0.27)
1/(2N) 1/2 NH 0.62 0.76 0.90 0.30 0.61 0.68 1.03 0.24
(0.17) (0.31) (0.30) (0.29) (0.17) (0.31) (0.30) (0.29)
1/N zero NZ 0.80 1.36 0.23 0.79 0.92 1.46 0.49 0.75
(0.16) (0.27) (0.28) (0.26) (0.16) (0.28) (0.28) (0.26)
optimal optimal OE 0.72 1.28 0.28 0.56 0.89 1.29 0.56 0.81
(0.16) (0.26) (0.28) (0.25) (0.15) (0.27) (0.28) (0.25)
1/2 optimal 1/2 OH 0.59 0.75 0.84 0.24 0.60 0.63 1.05 0.27
(0.17) (0.31) (0.30) (0.29) (0.17) (0.31) (0.30) (0.29)
optimal zero OZ 0.66 1.32 0.10 0.54 0.89 1.31 0.54 0.81
(0.16) (0.26) (0.28) (0.25) (0.15) (0.27) (0.28) (0.24)
S&P 500 0.37 0.27 0.94 0.09
(0.17) (0.30) (0.32) (0.29)
Top 10 ex ante rules Top 50 ex ante rules

34
Table 5
Portfolios of technical trading strategies and equity using only non-emerging exchange rates: Sharpe ratios
Notes: See the notes to Table 4.
Weight on each
of N FX rules Weight on
equity Name 1975-2012 1975-1987 1988-1999 2000-2012 1975-2012 1975-1987 1988-1999 2000-2012
1/(2N+1) 1/(2N+1) NE 0.67 1.37 0.45 0.13 0.56 1.47 0.41 -0.30
(0.16) (0.27) (0.28) (0.28) (0.16) (0.28) (0.28) (0.29)
1/(2N) 1/2 NH 0.58 0.76 0.95 0.13 0.52 0.68 1.00 0.02
(0.17) (0.31) (0.30) (0.29) (0.17) (0.31) (0.30) (0.29)
1/N zero NZ 0.59 1.36 0.28 0.09 0.53 1.46 0.36 -0.31
(0.16) (0.27) (0.29) (0.27) (0.16) (0.28) (0.28) (0.29)
optimal optimal OE 0.55 1.28 0.41 -0.03 0.51 1.29 0.53 -0.27
(0.16) (0.26) (0.28) (0.27) (0.16) (0.27) (0.28) (0.29)
1/2 optimal 1/2 OH 0.55 0.75 0.91 0.09 0.52 0.63 1.07 0.03
(0.17) (0.31) (0.30) (0.29) (0.17) (0.31) (0.31) (0.29)
optimal zero OZ 0.50 1.32 0.22 0.00 0.52 1.31 0.52 -0.24
(0.16) (0.26) (0.28) (0.27) (0.16) (0.27) (0.28) (0.29)
S&P 500 0.37 0.27 0.94 0.09
(0.17) (0.30) (0.32) (0.29)
Top 10 ex ante rules Top 50 ex ante rules

35
Table 6
Rule prevalence over the full sample
Notes: The table reports the largest 10 trading rule frequencies for the top 5 ranked ex ante portfolios over the full sample, 1975-2012.
Thus the left-most columns indicate that for the strategy using the top ranked rule, carry trade applied to TRY appeared 14.3 percent
of the time, the carry trade applied to the CLP appeared 11.2 percent of the time, and so on.
12345
FX rate rule % us ed FX rate rule % us ed FX rate rule % use d FX rate rule % us ed FX rate rule % us ed
TRY Carry Trade 14.3 EUR ch(10) 14.3 CLP ch(20) 15.7 EUR vma(5,20) 10.4 EUR vma(5,20) 7.0
CLP Carry Trade 11.2 CLP Carry Trade 12.6 EUR ch(10) 9.1 CLP ch(20) 5.8 JPY_CAD ch(5) 5.6
EUR ch(10) 9.5 CLP ch(20) 7.5 EUR mom(20) 6.4 EUR mom(20) 4.6 EUR mom(20) 5.4
GBP ch(10) 9.3 CLP filter .03 5.8 EUR vma(5,20) 5.6 CLP mom(20) 4.3 CLP mom(20) 4.8
EUR vma(5,20) 7.0 EUR vma(5,20) 5.4 EUR_CAD ch(10) 5.4 JPY vma(5,20) 4.3 JPY_CAD mom(5) 4.1
RUB filter .005 6.8 GBP ch(10) 4.6 CLP Carry Trade 4.6 JPY_CAD ch(5) 4.3 HUF_CHF Carry Trade 3.5
CAD_GBP ch(20) 6.8 JPY vma(5,20) 3.9 CLP ch(5) 3.7 CLP filter .02 3.7 JPY vma(5,20) 3.3
EUR_CAD ch(10) 4.3 CLP ch(5) 3.9 JPY_CAD ch(5) 3.7 HUF_CHF Carry Trade 3.1 EUR ch(10) 3.1
CAD_GBP mom(20) 3.7 RUB vma(1,5) 3.9 CLP filter .03 3.1 EUR_CAD ch(10) 3.1 EUR ch(5) 3.1
JPY vma(5,20) 3.1 CAD_GBP ch(20) 3.1 JPY vma(5,20) 3.1 TWD vma(5,20) 2.7 TRY Carry Trade 2.9

36
Table 7
Rule prevalence over subsamples


Notes: The table reports the largest 5 trading rule frequencies for the top ranked portfolio over different sample subperiods. Thus the
top row entry in the left panel indicates that for the strategy using the top ranked ex ante rule in the 1973-1982 subsample, the ch(10)
applied to the GBP appeared 45.9 percent of the time in the top rule and so on.
1973-1982 1983-1992 1993-2002 2003-2012
FX rate rule % used FX rate rule % used FX rate rule % used FX rate rule % use d
GBP ch(10) 45.9 CAD_GBP ch(20) 26.4 CLP Carry Trade 41.2 TRY Carry Trade 53.5
CAD_GBP mom(20) 18.4 EUR ch(10) 24.8 EUR_CAD ch(10) 14.5 RUB filter .005 25.6
EUR ch(10) 15.3 EUR vma(5,20) 24.0 CLP filter .02 10.7 RUB vma(1,5) 4.7
EUR mom(20) 7.1 NOK vma(1,200) 6.4 JPY vma(5,20) 10.7 CLP ch(20) 4.7
CAD_GBP ch(10) 3.1 NOK Carry Trade 4.8 MXN Carry Trade 5.3 RUB mom(20) 3.1

37
Figure 1
Transaction costs

2000
0
2
4
6
GBP
2000
0
2
4
6
CHF
2000
0
2
4
6
8AUD
2000
0
2
4
6
CAD
2000
0
5
10
SEK
2000
0
2
4
6
JPY
2000
0
20
40
ZAR
2000
0
10
20
CZK
2000
0
10
20
RUB
2000
0
2
4
EUR
2000
0
10
20
BRL
2000
0
20
40
60
HUF
2000
0
10
20
30
MXN
2000
0
5
10
NZD
2000
0
5
10
15
NOK
2000
0
20
40
PLN
2000
0
50
100
150
TRY
2000
0
10
20
30
PEN
2000
0
50
100 CLP
2000
0
10
20
30
ILS

38
Notes: The figure displays the time series of transaction costs used for each exchange rate in
basis points.
2000
0
10
20
TWD
2000
0
2
4
6
CHF/GBP
2000
0
2
4
6
8AUD/GBP
2000
0
2
4
6
CAD/GBP
2000
0
2
4
6
JPY/GBP
2000
0
2
4
6
EUR/GBP
2000
0
2
4
6
8AUD/CHF
2000
0
2
4
6
CAD/ CHF
2000
0
2
4
6
JPY/CHF
2000
0
2
4
6
EUR/ CHF
2000
0
2
4
6
8CAD/AUD
2000
0
2
4
6
8JPY/AUD
2000
0
2
4
6
8EUR/AUD
2000
0
2
4
6
JPY/CAD
2000
0
2
4
6
EUR/CAD
2000
0
2
4
6
JPY/EUR
2000
0
5
10
NZD/AUD
2000
0
20
40
60
HUF/ CHF
2000
0
10
20
30
ILS/EUR
2000
0
10
20
30
JPY/MXN

39
Figure 2
Sharpe ratios from the top 662 strategies
Notes: The figure displays the Sharpe ratios for the top 662 ex ante portfolio strategies along
with a trendline.
-1.5
-1.0
-0.5
0.0
0.5
1.0
1
21
41
61
81
101
121
141
161
181
201
221
241
261
281
301
321
341
361
381
401
421
441
461
481
501
521
541
561
581
601
621
641
661
Rank of Ex Ante Portfolio
Sharpe ratio

40
Figure 3
Trades per year
Notes: The panel displays the average number of annual trades for the top 662 ex ante portfolio
strategies.
10
15
20
25
30
35
40
45
50
55
60
65
70
1
20
39
58
77
96
115
134
153
172
191
210
229
248
267
286
305
324
343
362
381
400
419
438
457
476
495
514
533
552
571
590
609
628
647
Trades per year
Rank of Ex Ante Portfolio

41
Figure 4
Net returns for the top 5 ranked strategies
Notes: The top panel displays the net annual returns for the top 5 ex ante portfolio strategies,
along with the net annual return of the corresponding 1/N portfolio. The bottom panel displays
the net annual return of the 1/N portfolio from the top 5 strategies for clarity.
-40
-30
-20
-10
0
10
20
30
40
50
1973 1978 1983 1988 1993 1998 2003 2008
12345Portfolio
Annualized Percent Net Return
-15
-10
-5
0
5
10
15
20
1973 1978 1983 1988 1993 1998 2003 2008
Portfolio
Annualized Percent Return

42
Figure 5
1-year Rolling Sharpe ratios from 1976 for the top 10 strategy portfolios and the S&P 500
Notes: The top (center) panel displays 1-year rolling Sharpe ratios from the OZ-10 and OE-10
(NZ-10 and NE-10) portfolios, from 1976 to 2012. The bottom panel displays the 1-year rolling
Sharpe ratios to the S&P 500.
-3
-2
-1
0
1
2
3
4
1976 1981 1986 1991 1996 2001 2006 2011
Optimally weighted without equity (OZ-10)
Optimally weighted with equity (OE-10)
-3
-2
-1
0
1
2
3
4
1976 1981 1986 1991 1996 2001 2006 2011
naively weighted without equity (NZ-10)
naively weighted with equity (NE-10)
-3
-2
-1
0
1
2
3
4
1976 1981 1986 1991 1996 2001 2006 2011
S&P 500 rolling Sharpe ratio

43
Figure 6
Trading rule prevalence over time
Notes: The panels denote the 3-year moving average prevalence of types of trading rules in the
top10 ex ante trading rule strategies. The panel on the top denotes the raw frequency of the rule
groups, whereas those on the bottom adjust for group size (see equation (6)). Small filters are
those less than or equal to 0.02; large filters are those greater than 0.02.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1975 1980 1985 1990 1995 2000 2005 2010
Raw fraction of top 10 ex ante rules by rule type
Sm. Filter Lg. Filter Channel
MA Momentum Carry
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1975 1980 1985 1990 1995 2000 2005 2010
Adjusted fraction of top 10 ex ante rules by rule type
Sm. Filter Lg. Filter Channel
MA Momentum Carry

44
Figure 7
Exchange rate prevalence over time in the top 10 trading strategies
Notes: The panels denote the 3-year moving average prevalence of currency groups in the best
10 ex ante trading rule strategies. The top panel illustrates the raw prevalence of each group,
whereas those on the bottom adjust for group size (see equation (6)). The advanced market
exchange rates consist of the AUD, CAD, CHF, EUR, GBP, JPY, NOK, NZD, and SEK;
developing Europe consists of the CZK, HUF, PLN and RUB, TRY and HUF/CHF; the Latin
American group consists of BRL, CLP, MXN, PEN and JPY/MXN; the Other group consists of
ILS, TWD, ZAR and ILS/EUR; and the advanced cross rates group consists of all cross rates
between two advanced countries.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1975 1980 1985 1990 1995 2000 2005 2010
Raw fraction of top 10 ex ante rules by currency groups
Advanced Dev. Europe Latin America Other Adv. Cross Rates
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1975 1980 1985 1990 1995 2000 2005 2010
Adjusted fraction of top 10 ex ante rules by currency groups
Advanced Dev. Europe Latin America Other Adv. Cross Rates