step over 7192 to 63093. Third, this process is repeated to allow for the possibility of different trading rules to be followed in subsequent time periods. For
example, in-sample TX are re-estimated over 1192 to 63093 to re-establish which combination of I and J maximizes TX on average. Again, out-of-sample TX are
calculated by applying these trading rules over 7193 to 63094. Ultimately, an out-of-sample series of transaction cost-adjusted returns is generated for each of the
twelve countries from 7192 to 63095.
3. Results
Table 3 displays the in-sample and out-of-sample mean daily returns as well as the break-even transaction costs. The first data column of Table 3 identifies the I,
J trading rules that maximize the transaction cost-adjusted returns over the in-sample period of 1192 to 63092. For Brazil, Indonesia, and Pakistan, there
are several I, J combinations that result in the same mean return. For these particular countries, it appears the trading rule is somewhat robust to the length of
the short-term horizon, I. Consider Brazil, the mean transaction cost-adjusted return is maximized when I is equal to 1, 2, 3, . . ., or 8 and J equals 10. Although
somewhat arbitrary, in these cases, the shortest short-term horizon is used to select the I, J trading rule.
None of the countries reveal negative in-sample mean returns. The mean daily return ranges from 0.0000 Mexico to 0.8802 Brazil. The in-sample mean return
is shown to be greater than 0.20 daily or approximately 50.0 annually assuming 250 trading days per year for six out of 12 of the countries. The mean return is
shown to be greater than 0.14 daily or approximately 35 annually for eight out of 12 of the countries. Considering the large number of I, J combinations explored,
high levels of in-sample returns are not altogether surprising.
As expected, the out-of-sample returns are not as favorable as the in-sample returns. In nine out of 12 cases, the mean TX is lower than the in-sample mean TX.
Only the Mexican peso produces a substantially improved mean return. Further- more, only three of the 12 now reveal mean returns greater than 0.20 daily, and
five of the 12 reveal the returns to be greater than 0.14 daily. Brazil, Colombia, and Israel exhibit the highest out-of-sample mean TX, while India and Indonesia
reveal negative mean TX.
The P-values for t-tests and sign-rank tests of a zero mean are reported in Table 3. The null hypothesis of a zero mean using the parametric t-test is not rejected for
Argentina, India, Indonesia, and Malaysia. The null hypothesis of a zero mean using the non-parametric sign-rank test is not rejected for Argentina and Malaysia.
Thus, the negative returns generated by India and Indonesia may be considered to be significantly different from zero.
3
3
The negative returns may also be explained if the assumed 0.50 transaction cost is too high for India and Indonesia.
A .D
. Martin
J .
of Multi
. Fin
. Manag
.
11 2001
59 –
68
64
Table 3 Moving average trading rule returns and break-even transaction costs
a
I, J Trading t-Test P-value
Country Sign-rank test
In-sample mean daily Out-of-sample mean daily
Break-even return
transaction costs rule
P-value return
Argentina 0.52
1, 15 0.4125
0.0003 0.9034
0.8652 0.0001
0.0001 22.27
Brazil 0.8802
1–8, 10 0.8897
1.10 1, 15
0.0001 Chile
0.6086 0.0001
0.0871 0.0001
1, 15 3.19
0.4535 0.2469
0.0001 Colombia
0.5369 0.0005
0.40 1, 30
India 0.1516
− 0.0090
0.1149 0.0021
0.36 6–9, 30
Indonesia 0.0141
− 0.0077
1.62 0.2483
0.0001 0.0001
0.4516 Israel
1, 10 0.9442
1, 10 0.54
0.0538 0.0058
0.5417 Malaysia
0.0110 0.0003
2.64 1, 25
Mexico 0.0000
0.1475 1.35
Pakistan 1–9, 20
0.0111 0.0314
0.0011 0.0001
1.46 Peru
0.0001 1, 10
0.0001 0.3340
0.1421 1.79
Philippines 1, 30
0.1564 0.0659
0.0025 0.0010
a
These I, J trading rules maximize the mean daily returns over 1192–63092. The mean daily returns are adjusted for transaction costs of 0.50. The in–sample period is 1192–63092 and the out-of-sample period is 7192–63095. The t-tests and sign-rank tests assess whether the out-of-sample returns
differ from zero. The break-even transaction costs are estimated as those that force the out-of-sample mean daily returns to equal zero.
The transaction costs that result in exactly zero profits are calculated for each country and are displayed in the last column of Table 3. These break-even
transaction costs are found to range from 0.36 to 22.27. Brazil, Colombia, and Mexico exhibit the largest break-even transaction costs. Argentina, India, Indone-
sia, and Malaysia all reveal break-even transaction costs around 0.50 or less.
4
If actual transaction costs were higher than these break-even costs, then the profitabil-
ity of these trading rules would be eliminated. There is not an obvious relationship between the profitability of moving average
trading rules and the stated exchange rate regimes. Countries that supposedly embrace freely floating systems e.g. Brazil, Peru, and Philippines are not expected
to intervene, yet significant out-of-sample returns are revealed. Argentina pegs their currency and as such is expected to frequently intervene, yet the out-of-sample
returns are not significant.
Another way of capturing the relationship between intervention and trading rule profitability is to examine the correlation between foreign currency reserves and the
out-of-sample TX. In order to intervene successfully, central banks need sufficient reserves to affect the market prices of their currencies.
5
Greater reserves may be more indicative of central banks’ ability to defend their currencies than their stated
exchange rate regimes. The US dollar value of foreign currency reserves over 1992 – 1995 from International Financial Statistics are collected to conduct the
analysis. A correlation analysis between the average reserve balance and the out-of-sample TX shows a statistically significantly positive relationship r =
0.5578 at the five percent level. Thus, there is evidence of a relationship between the profitability of moving average trading rules and the potential for intervention.
It may be argued that higher trading profits are due to higher levels of risk. The Sharpe ratio for measuring performance is adopted to estimate the excess returns
per unit of risk Neely, 1997, 1998. This performance measurement is defined as following:
SHARPE = TX − X
s
TX
3 where SHARPE = excess return performance measurement; TX = mean daily trans-
action cost-adjusted return over 7192 – 63095; X = mean daily return of either the short-selling or risk-free strategy over 7192 – 63095; s
TX
= S.D. of the
transaction cost-adjusted returns over 7192 – 63095. Using this excess return performance measurement, two comparisons are made.
First, the moving average trading rule returns are compared to the returns from a simple short-selling SS strategy. Since it is commonly believed the currencies of
developing countries are frequently devalued, a short-selling strategy may be a good baseline for comparison. Second, the moving average trading rule returns are
4
Recall the out-of-sample mean returns for these same four countries are not found to differ significantly from zero using t-tests.
5
Or they need to coordinate the efforts of multiple central banks.
Table 4 Moving average trading rules performance comparisons
a
Excess return over Sharpe ratio for
Country Excess return over
Sharpe ratio for short-selling
risk-free strategy short-selling
risk-free strategy strategy
strategy −
0.01 Argentina
− 0.0000
– –
0.41 −
17887.01 Brazil
− 331.9998
0.0076 –
0.13 –
Chile 0.0008
0.13 Colombia
0.0020 0.0009
0.06 −
0.05 −
0.15 India
− 0.0006
− 0.0002
– Indonesia
− 0.0002
– −
0.14 –
0.27 Israel
– 0.0022
0.03 Malaysia
0.0001 –
– 0.05
Mexico 0.0008
0.0009 0.05
0.03 –
Pakistan –
0.0001 −
0.03 Peru
0.0008 −
0.0002 0.12
0.05 Philippines
0.0006 0.0003
0.10
a
Excess return is defined as the difference between the mean daily returns of the moving average trading rules and the returns from either the short-selling strategy or the risk-free strategy. The Sharpe
ratio is defined as the excess return divided by the S.D. of the moving average daily returns. The mean daily returns are adjusted for transaction costs of 0.50.
compared to the risk-free RF returns as a way to judge the risk-adjusted performance. The central bank discount rate is used to represent the risk-free rate.
These rates are collected from International Financial Statistics, but are available for only six of the 12 countries.
6
Table 4 provides the excess returns and Sharpe ratios. The first comparison indicates that the technical trading rules generate greater returns than the short-sell-
ing strategy in nine of 12 cases. Although, the Sharpe ratios indicate they are not significantly greater. The second comparison indicates that on a risk-adjusted basis,
the technical trading rules do not provide superior returns.
7
For Brazil, the Sharpe ratio indicates that the technical trading rules significantly underperform the
risk-free strategy.
4. Conclusion
