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Momentum or Trend-following? Removing the Bias

We remove data-mining bias, increase samples and compare the performance of momentum and trend-following.

Many articles on momentum and trend-following select some lookback period for the indicators that is known to result in good performance without taking into account data-mining bias. As a result, the performance metrics are affected by the multiple comparisons problem and suffer from bias.

For example, the table below shows the performance of momentum and trend-following with 12-months lookback period in SPY ETF. Backtest period is from SPY inception to 11/19/2019.

Parameter MOM12* TF12**
CAGR 9.9% 8.8%
Max. Drawdown -16.2% -19.8%
Sharpe 0.87 0.83

   *Buy if ROC(12) > 0, exit if ROC(12) <0
** Buy if price > SMA(12), exit if price < SMA(12)

From the above table it appears that momentum outperforms trend-following. However, the performance metrics are biased due to selection of the lookback period. Unfortunately, this is a misunderstood or not understood problem.

Increasing the samples size

The sample for SPY is small. We will use DJIA from 01/02/1914 to 11/18/2019 to increase the sample.

Removing selection bias

We will vary the lookback period n for momentum from 1 to 24 and for TF from 2 to 24 (n=1 is price) Then we will average performance. The results are shown below.

Parameter MOMn TFn
avg. CAGR 4.9% 5.0%
avg. Max. Drawdown -50.2% -52.0%
avg. Sharpe 0.36 0.37

As it turns out then, when bias is removed as much as possible, momentum and trend-following have statistically indistinguishable performance. This should be expected.

More importantly

The average maximum drawdown of about -50% is an estimator of the future drawdown. Some people get the impression that about -20% is the expected drawdown from these timing strategies. But future drawdown will depend on speed of corrections and in fast markets these momentum and trend-following indicators have significant lag. Therefore, large drawdown levels can be realized in the future.

In addition, an annualized return of about 5% should be expected in the next 20 to 50 years, rather than the optimistic 8% or more. People should not confuse expectation with realized values. Expectations help in risk management and portfolio allocation, they are not point forecasts.

I f you have any question do not hesitate to contact me.

Charting and backtesting program: Amibroker

Data provider: Norgate Data

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