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Different Moving Average Lengths for Up and Down Trends?

| | Posted in: Technical Trading

Should market timers use moving averages of different lengths for trading uptrends and downtrends? In his January 2017 paper entitled “Asymmetry between Uptrend and Downtrend Identification: A Tale of Moving Average Trading Strategy”, flagged by a subscriber, Carlin chun-fai Chu investigates whether the use of different (asymmetric) moving average lookback intervals for uptrends and downtrends outperforms using the same lookback interval for both. He considers three types of moving averages: Simple Moving Average, Exponential Moving Average and Triangular Moving Average. He calculates these moving averages separately for each of seven market indexes: S&P 500, FTSE 100, Nikkei 225, Deutscher Aktien, TSX Composite, ASX 200 and Hang Seng. The price series is in uptrend (downtrend) when above (below) a specified moving average. He takes a long (short) position in an index when it crosses above (below) the moving average used during downtrends (uptrends). Using the earliest daily data available from Yahoo!Finance for each of the seven indexes through October 2016, he finds that:

  • For all indexes, there are more days with positive than negative returns, but the average absolute daily return is larger for negative days.
  • Testing the S&P 500 Index as representative:
    • Combining downtrend (buy signal) EMAs with lookback intervals 60, 90, 120 or 150 trading days with an uptrend (sell signal) EMAs ranging from 5 to 200 trading days indicates that short uptrend EMA lookback intervals (5 to 7 trading days) beat longer ones for all four downtrend EMA lookback intervals.
    • Combining uptrend (sell signal) EMAs with lookback intervals 60, 90, 120 or 150 trading days with a downtrend (buy signal) EMAs ranging from 5 to 200 trading days generates no consistent pattern. Neither short nor long downtrend EMAs always work best.
    • Comparing symmetric and asymmetric EMAs:
      • During uptrends, potential performance of asymmetric EMAs is generally greater than that of symmetric EMAs, most strongly for lookback intervals in the range 90 to 120 trading days (average gross daily return as much as 2.6 times higher).
      • During downtrends, outperformance of asymmetric EMAs is consistent but generally smaller in magnitude.
    • Running the same tests on other stock indexes produces similar findings.
  • Across the seven stock indexes and a range of 5 to 200 trading days for both downtrend and uptrend moving averages, the optimal settings for asymmetric rules generate average gross daily returns that:
    • Beat buy-and-hold by 2.3 to 13.6 times and optimal symmetric rules by 1.6 to 4.3 times for SMAs.
    • Beat buy-and-hold by 2.5 to 15.4 times and optimal symmetric rules by 1.4 to 3.7 times for EMAs.
    • Beat buy-and-hold by 2.6 to 12.9 times and optimal symmetric rules by 1.4 to 5.9 times for TMAs.

In summary, evidence indicates that researchers can attain much higher optimal average gross daily returns when applying asymmetric moving averages rather than symmetric moving averages to take daily long or short positions in stock market indexes.

Cautions regarding findings include:

  • Use of indexes rather than tradable funds ignores costs of maintaining a liquid tracking fund, thereby overstating expected returns.
  • Return calculations are gross, not net, and frictions can be large when applying short moving averages to daily (noisy) data. Specifically:
  • Capturing index returns while short over a many-day shorting period may be problematic, as indicated by performances of -1X funds over extended holding periods.
  • Moreover, based on the data specifications, it appears that source data exclude dividends. Since short positions must pay dividends, results overstate performance while short.
  • In optimization tests, the very large number of combinations of moving average lookback intervals applied to noisy daily data indicates extreme snooping bias for best-performing combinations. In general, a strategy that allows snooping of values for two parameters can achieve higher backtested performance (and snooping bias) than a strategy that allows snooping of only one parameter value. In other words, findings may reflect differences in snooping biases and not any fundamental behaviors of stock indexes.
  • The paper does not present a trading strategy time series test showing the volatilities, compound annual growth rates, maximum drawdowns and Sharpe ratios of different moving average combinations.
  • The optimal moving average varies by asset type. See “Optimal Intrinsic Momentum and SMA Intervals Across Asset Classes”.

See also “Simple Tests of an Asymmetric SMA Strategy”.

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