Calculating moving average trading rule profits

2. Calculating moving average trading rule profits

The popularity of moving average trading rules is recognized in the literature Neftci, 1991; Lee and Mathur, 1996; Neely, 1997; Szakmary and Mathur, 1997; Neely, 1998. Moving average trading rules provide buy and sell signals at time t based on data that are available at time t. The process involves examining a time series to identify points in time where trends are expected to change or to be maintained. The decision to go long occurs when an upward trend is identified, while the decision to go short occurs when a downward trend is identified. This decision can be modeled as: LONG t = 1 if I i = 1 P t − i I ] J j = 1 P t − j J = 0 otherwise 1 where: P t = U.S. dollar price of the developing country currency on day t; I = length of short-term period in days with values of 1, 2, . . ., and 9; J = length of long-term period in days with values of 10, 15, 20, 25, and 30. Taking transaction costs into consideration, transaction cost-adjusted profits, TX, on day t can be calculated as: TX t = LONG t X t + LONG t − 1X t − T LONG t − LONG t − 1 2 where: X t = percent change in the US dollar price of the developing country currency on day t [P t − P t − 1 P t − 1 ]; T = transaction cost per trade; and LONG t is defined in Eq. 1. When the position changes from long to short or short to long, the return is reduced by the transaction cost. Transaction costs are typically represented by the bid-ask spread. For developed countries, the spread is oftentimes estimated at 0.05 e.g. Levich and Thomas, 1993; Bessembinder, 1994; Lee and Mathur, 1996; Neely, 1997. Since developing countries generally have less economic and political stability, greater spreads would be demanded. Data provided in the Financial Times support the presumption that the spreads are relatively large. From this source, it is determined that a 0.50 transaction cost one-way is a conservative approximation. 1 The 12 developing country currencies examined and associated exchange rate regimes are listed in Table 1. The countries represent various geographic regions and exchange rate regimes. Daily spot exchange rates from 1192 to 63095 as reported in the Wall Street Journal are used in this study. The examination period avoids the Latin American debt crisis and the recent Asian currency crisis. 2 Table 1 The bid-ask quotes are available for Argentina, Brazil, Malaysia, and Mexico in the Financial Times across the sample period. The bid-ask spreads are calculated on 71 for 1992 through 1995. The resulting mean values are 0.055, 0.036, 0.049, and .069, respectively. 2 The period in which the Mexican peso crisis occurred, December 1994, is included. The overall results of the study remain unchanged if the examination period for the Mexican peso is truncated at the onset of the crisis and even if the Mexican peso is dropped from the analysis altogether. 2 provides the mean, minimum, maximum and standard deviation of the 12 currencies over the examination period. Three basic steps are performed to generate an out-of-sample series of transac- tion cost-adjusted returns, TX t . First, in-sample moving average trading rule returns are estimated over the period from 1192 to 63092 to establish which combination of I and J, as specified in Eq. 1, maximizes TX, on average. Second, out-of-sample TX are calculated by applying the trading rule identified in the first Table 1 Exchange rate regimes a Country Regime Argentina Pegged Brazil Free float b Pegged Chile Colombia Managed float India Free float c Indonesia Managed float Crawling peg Israel Malaysia Free float Mexico Crawling peg d Pakistan Managed float Peru Free float Philippines Free float a These reported regimes are the predominant regime followed over the examination period, as described in the IMF annual reports on exchange rate arrangements and restrictions. b With the introduction of the real R on 7194, a floor of R1 per US1 was set. c Prior to 3193, the rupee was pegged to a basket of currencies. d The new peso was allowed to float on 122294. Table 2 Summary statistics over 1192–63095 a Country Mean return Minimum return Maximum return S.D. 3.0000 0.4088 0.0001 Argentina − 2.9125 1.9290 − 0.8323 − 12.6583 13.4612 Brazil 0.9120 0.0015 − 8.3621 Chile 10.9351 18.2421 1.5847 Colombia − 15.0313 − 0.0340 − 0.0204 − 8.6878 5.1837 0.4643 India 0.1222 − 0.0126 − 1.4799 0.8457 Indonesia 4.4888 1.0337 − 0.0248 Israel − 4.0995 1.4419 0.2584 0.0124 Malaysia − 2.3448 1.5196 18.2540 − 18.1416 Mexico − 0.0652 1.5432 0.2749 − 0.0250 Pakistan − 5.6022 14.1911 − 6.6740 − 0.0778 Peru 0.9252 0.0045 0.6186 Philippines 5.5210 − 6.2061 a Return is calculated as the percent change in the US dollar price of the developing country currency: P t − P t−1 P t−1 . 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