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Simple Tests of an Asymmetric SMA Strategy

Posted in Technical Trading

A reader asked: “Should the moving average crossover threshold be symmetrical, or does it make sense to try getting back in close to the bottom?” In other words, should we perhaps use a 200-day simple moving average (SMA) to stick with the typical long bull market grind upward and then switch to a 50-day SMA signal after crossing under the 200-day SMA so that we re-enter closer to a V-shaped bear market bottom? Using daily closes for the S&P 500 Index commencing May 1959, the 3-month Treasury bill (T-bill) yield commencing January 1960 and S&P Depository Receipts (SPY), adjusted for dividends, commencing January 1993, all through September 2012, we find that:

We compare four strategies:

  1. Buy and hold.
  2. Enter when crossing over the 200-day SMA and exit when crossing under the 200-day SMA (200-200).
  3. Enter when crossing over the 50-day SMA and exit when crossing under the 50-day SMA (50-50).
  4. While over the 200-day SMA, exit when crossing under the 200-day SMA; while under the 200-day SMA, enter/exit on crossing over/under the 50-day SMA (200-50).

We apply the following assumptions in backtesting the strategies:

  • The start date for the S&P 500 Index analysis is based on availability of T-bill data.
  • The start date for the SPY analysis is based on availability of SPY data.
  • Enter/exit instantly at the close on the day of the crossover (in other words, slightly anticipate the crossover).
  • While out of the market, the SMA trading strategies earn the T-bill yield.
  • Apply constant trading frictions (transaction fee plus bid-ask spread) across the sample periods.
  • Ignore the capital gains tax implications of trading.

The following chart compares the terminal values of $1 initial investments in the S&P 500 Index over the available sample period for all four alternative strategies and one-way trading frictions ranging from 0.00% to 0.50% of portfolio value. Some observations are:

  • Both the 200-200 and 200-50 strategies appear potentially attractive compared to a buy-and-hold strategy.
  • For low trading frictions, the 200-50 strategy beats the 200-200 strategy.
  • The 50-50 strategy is ineffective compared to the 200-200 strategy.

The number of one-way trades for the 200-200, 50-50 and 200-50 strategies are 328, 818 and 440, respectively, corresponding to time in stocks of 67%, 62% and 76%.

For another perspective, we look at daily return statistics for the alternative strategies.

The next chart summarizes average S&P 500 Index daily net returns, and one standard deviation variability ranges, for each of the four alternative strategies with 0.1% one-way trading friction over the available sample period. Use of SMAs substantially reduces daily return volatility compared to buy-and-hold. The 200-200 and 200-50 strategies also increase average daily return.

Using the S&P 500 Index for testing ignores both the costs of maintaining a tradable fund and dividends. Moreover, actual trading frictions are likely much higher early in this sample period than late (e.g., decimalization and commoditization of brokerage services). For more realistic scenarios, we repeat tests using SPY data.

The next chart compares the terminal values of $1 initial investments in SPY over the available sample period for all four alternative strategies and one-way trading frictions ranging from 0.00% to 0.50% of portfolio value. Some observations are:

  • The buy-and-hold strategy dominates the timing alternatives.
  • The 50-50 strategy is again ineffective compared to the 200-200 strategy.
  • The 200-200 strategy beats the 50-200 strategy at all levels of trading friction.

The number of one-way trades for the 200-200, 50-50 and 200-50 strategies are 144, 336 and 184, respectively, corresponding to time in stocks of 71%, 65% and 79%.

Again, for another perspective, we look at daily return statistics for the alternative strategies.

The next chart summarizes average SPY daily net returns, and one standard deviation variability ranges, for each of the four alternative strategies with 0.1% one-way trading friction over the available sample period. Use of SMAs again substantially reduces daily return volatility compared to buy-and-hold, but there are also substantial decreases in average daily return. Daily return/risk ratios are 0.037, 0.018, 0.030 and 0.031, respectively for the 200-200, 50-50, 200-50 and buy-and-hold strategies.

For a third perspective, we look at cumulative performance.

The next chart compares the cumulative values of $1 initial investments in SPY for all four alternative strategies with one-way trading friction 0.1% over the available sample period. Some observations are:

  • There are a few times when the 200-200 strategy value is above buy-and-hold.
  • The 200-50 strategy mostly underperforms the 200-200 strategy.

This sample period (about 19 years) is modest for testing strategies using long-term SMA signals, such that results may be sensitive to the analysis start date. What if we start the test at the end of 1999?

The final chart compares the cumulative values of $1 initial investments in SPY for all four alternative strategies with one-way trading friction 0.1% starting at the end of 1999. Some observations for this subperiod are:

  • The 200-200 strategy mostly outperforms buy-and-hold.
  • The 200-50 strategy mostly underperforms buy-and-hold.

In summary, evidence from simple tests does not support a belief that investors should use shorter-term simple moving average crossovers during bear than bull markets in an attempt to get back in close to the bottom.

Cautions regarding findings include:

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