Is there a reliable way to improve the performance of conventional moving average signals? In the October 2011 and November 2011 versions of their papers entitled “An Improved Moving Average Technical Trading Rule” and “An Improved Moving Average Technical Trading Rule II”, Fotis Papailias and Dimitrios Thomakos investigate a modification of the conventional moving average crossover trading strategy that add a dynamic trailing stop (long-only variation) or a dynamic trailing stop-and-reverse (long-short variation). In order to stay long after a moving average buy signal, the modification requires that the asset price must remain at least as high as the entry price. Specifically:

- Price crossing above a moving average, or a short-interval moving average crossing above a long-interval moving average, signals initial entry.
- After going long, switching to cash or a short position occurs only if the price falls below the reference entry price (ignoring conventional moving average sell signals).
- While long, the reference entry price changes when the crossover signals a sell/switch and then a subsequent buy/re-switch.

Entry and exit/switching times for the modified strategy therefore differ over time from those of a conventional moving average crossover strategy. In comparing modified and conventional strategy performance characteristics, they consider: simple, exponential and weighted moving averages; price crossovers of 5, 20, 50, 100 and 200-day moving averages; and, (5,20), (10,20), (20,50), (20,100) and (50,200) pairs of short-interval and long-interval moving average crossovers. They conservatively assume a delay of one trading day in signal implementation. Using daily prices for broad stock indexes, a variety of exchange-traded funds (ETF) and several currency exchange rates as available, *they find that:*

For the long-only variation, they test the strategy modification on nine price series: the DJIA (1928 through 2/9/2011); the S&P 500 Index (1950 through 2/9/2011); SPY, QQQQ, XLF, XLE and EJW equity ETFs (1/4/99 through 12/11/2010); the IYR U.S. real estate ETF (2000 through 12/11/2010); and, the EUR/USD exchange rate (1/3/2000 through 4/13/2011). *Findings include:*

- The modified strategy generally increases gross terminal return and gross Sharpe ratio, while exhibiting smaller maximum drawdown and smaller drawdown duration:
- For all three types of moving average.
- For both price-moving average and moving average-moving average crossovers.
- Across moving average measurement intervals.
- For example, based on gross results over entire sample periods:
- For DJIA, the modiﬁed strategy beats the conventional strategy for 89% of combinations, with an average terminal value advantage of 2900%. The modified strategy has higher Sharpe ratios than the conventional strategy for 74% of combinations, with average improvement 8%.
- For the S&P 500 Index, the modiﬁed strategy beats the conventional strategy for 70% of combinations, with an average terminal value advantage of 1600%.
- For SPY, the modiﬁed strategy beats the conventional strategy for 74% of combinations, with an average terminal value advantage of 38%.
- For the two stock indexes (six ETFs), moving average-moving average crossovers generate higher terminal values than price-moving average crossovers for 78% (46%) of combinations.
- For the two stock indexes, the exponential moving average works best most of the time. While results for other assets is mixed, exponential and weighted moving averages appear to be safer bets than the simple moving average.
- The modified strategy mostly, but not always, generates extra trades (and trading frictions) compared to conventional strategy.

For the long-short variation, they test the strategy modification on six equity ETFs (SPY, QQQQ, XLE and EWJ during 1/4/1999 through 12/11/2010) and seven currency exchange rates (EUR/USD, USD/JPY, USD/CHF, GBP/USD, EUR/GBP, EUR/JPY and EUR/CHF during 1/3/2000 through 04/13/2011). *Findings include:*

- For the four ETFs, the long-short modiﬁed strategy variation generally beats the conventional strategy based on gross terminal value, with higher average gross outperformance but lower percentage of outperforming combinations than the long-only variation (riskier than long-only in terms of combination selection).
- For example, for SPY on a gross basis over the entire sample period, the long-short (long-only) modified strategy variation beats the conventional strategy for 67% (74%) of combinations, with an average terminal value advantage of 33% (24%). However, the long-short variation generates more trades (and trading frictions, including shorting costs) than the long-only variation.
- For the seven currency exchange rates, the long-short modiﬁed strategy variation is inferior to the long-only variation based on both percentage of wins and average margin of gross terminal value wins over the conventional strategy.
- In aggregate, based on gross performance, the authors recommend:
- For equity ETFs, if limiting maximum drawdown is the principal consideration, use the long-only variation.
- For equity ETFs, if average return is the principal consideration, use the long-only variation.
- For equity ETFs, if cumulative return is the principal consideration, use the long-only (long-short) variation as the conservative (aggressive, riskier) alternative.
- For currency exchange rates, use only a carefully backtested combination of the long-short variation.

In summary, *evidence from tests on many combinations of moving average rules and target assets indicates that adding a dynamic stop-loss or stop-and-reverse signal based on* *conventional moving average rule **entry prices generally enhances gross performance of conventional moving average timing rules.*

The papers include many tables with detailed results. The authors offer a step-by-step example for their modified moving average strategy as “MA Guidelines” and the code for implementing the strategy as “IMA R Code” on their web site.

Cautions regarding findings include:

- In the first paper, the authors state: “The eﬀect of these extra trades on total return is, of course, negative but it should not aﬀect our results considerably – the ﬁnal eﬀect depends on the strategy and its performance and rests with the investor’s trade-oﬀ with respect to increased gains & lower drawdowns vs. increased number of trades.” Explicit tests of the sensitivity of findings to estimated trading frictions (including shorting costs for the long-short variation) would lend confidence to this assertion. (For example, see “Simple Tests of an Asymmetric SMA Strategy”.)
- Sample periods for ETF and currency exchange rate tests are short with respect to the longer moving average measurement intervals, limiting confidence in findings.
- Subperiod analyses are overlapping (different start dates but same end dates), limiting confidence in consistencies found across them.
- Given the large number of rule combinations considered, data snooping bias may be material in discriminating among moving average types, moving average measurement intervals and target assets. Reported statistics for “winning combinations” impound data snooping bias. The recommendation regarding currency trading appears seriously dependent on data snooping.
- The authors do not address effects of dividends on moving average calculations or rule performance.