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An Example of Survivorship Bias in Trend-following

We estimate the survivorship bias in backtesting a simple but popular trading strategy for trend-following large cap stocks. We compare the results with survivorship bias to those that account for desisted stocks.

Strategy

Buy at the open of next month if monthly close > 12-month moving average
Sell  at the open of next month if monthly close < 12-month moving average

We used Norgate data for Dow 30 and S&P 100 indexes that include current and past constituents to backtest the above simple but popular trading strategy in monthly timeframe from 01/3/2000 to 10/30/2019. Note that more articles will follow with more advanced strategies including mean-reversion.

Norgate Data offers a comprehensive solution for backtesting current and past constituents and removing survivorship bias from backtests. We highly recommend their data service (we do not have a referral arrangement with the company.) I downloaded their software and in about 30 minutes I was running backtests in Amibroker. They provide everything, even the Amibroker code to handle delistings.

Backtest details

Maximum open positions: For Dow 30 we use 30, for S&P 100 we use 100
Position size: For Dow 30: equity/30, for S&P 100: equity/100, equity is fully invested
Commissions: none  (just for analysis purposes, no strategy development)

Results

Dow 30 (survivorship bias with only current constituents)

Dow 30 (survivorship bias removal with past and current constituents)

Comparison of results for Dow 30.

Parameter No Survivorship bias Survivorship bias
CAGR 5.6% 7.7%
Max. DD -23.7% -20.9%
Sharpe 0.64 0.84
MAR (CAGR/Max. DD) 0.24 0.37

The survivorship bias due to accounting for only current constituents results is overstating CAGR by about 2%. This is substantial bias.

Below is the comparison for S&P 100.

Parameter No Survivorship bias Survivorship bias
CAGR 6.5% 8.4%
Max. DD -18.4% -18.3%
Sharpe 0.75 0.95
MAR (CAGR/Max. DD) 0.34 0.46

The survivorship bias due to accounting for only current constituents results is overstating CAGR by about 2% also in this case.

Note that the bias decreases as a function of time and number of constituent changes. For example, in Dow 30, after 2014 it is negligible.

Dow 30 – Test period: 01/2015 – 10/2019

Parameter No Survivorship bias Survivorship bias
CAGR 7.2% 7.4%
Max. DD -8.3% -8.4%
Sharpe 0.85 0.87
MAR (CAGR/Max. DD) 0.87 0.89

The survivorship bias due to accounting for only current constituents results in overstating CAGR is non-existent after 2014 due to minimal constituent changes.

Thanks to companies like Norgate Data, trading strategy developers can estimate survivorship bias of trading strategies with minimal effort and without resorting to complicated methods.

In future articles we will repeat the analysis for more advanced strategies, including our own PSI5.


Charting and backtesting program: Amibroker

Data provider: Norgate Data

Technical and quantitative analysis of major stock indexes and 34 popular ETFs are included in our Weekly Premium Reports. Market signals for position traders are offered by our premium Market Signals service

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