With the advent of portfolio backtesting software and platforms, in the last few years there has been a proliferation of equities momentum strategies with very attractive backtesting metrics. In this article, we focus on some of the issues and present the results of a randomization study of the position score of a popular strategy.
Backtesting portfolio strategies is challenging because, when sampling from stock indexes, there are usually more signals than allowed positions. We handle this by ranking the alternatives, then selecting those that meet user-defined criteria at each rebalancing step.
Ranking alternatives introduces additional parameters and increases the risk of overfitting. Although some strategy developers view the position score as an “innocent step” that enables selection, as it turns out, it is often the most crucial step that determines profitability.
Let us look at a simple, long-only strategy for S&P 500 index stocks:
1. At the end of each month, exit all open positions.
2. Check if the S&P 500 index price is above the 200-day moving average. If so, then buy the five stocks with the highest 120-day rate of change.
3. The stock must be in the index at the time of purchase, with more than two days to delist.
4. Sell delisted stocks after the delisting.
For the S&P 500 current and past constituents, we used data from Norgate. The backtest results are shown below, from January 2, 2003, to October 3, 2024.
The annualized return is 13.4%; the maximum drawdown is 37.7%; and the Sharpe ratio is 0.62. This simple momentum strategy has outperformed the S&P 500 total return in the same period: the annualized return of SPY ETF is 10.4%, the maximum drawdown is 55.2%, and the Sharpe ratio is 0.56.
However, we notice that after 2017, performance has been flat. Is it possible that the proliferation of momentum strategies has caused a performance deterioration? We cannot know for sure, but what we do know is that the position score has a significant impact on performance.
Assume that at the end of each month, we only know the score’s sign, forcing the strategy to randomly select between the signals. We repeat the experiment 500 times and plot a histogram of annualized returns, as follows.
The mean performance is 8.7%, with a 1.6% standard deviation. A 13.5% CAGR lies at the end of the right tail. Could it be that applying a suitable score overfitted those strategies before they gained popularity?
All we can say is that overfitting is highly likely. Consider a scenario where we did not select a stock after scoring, but it significantly rallied the next month while the performance of the selected stock declined. This could be a scenario in the future because of a shift in market dynamics. As a result, the performance of a strategy that uses the rate of change to score alternatives will revert toward the mean of about 8.7% for the annualized return, on average. In fact, I argue that a CAGR of 8.7% is the expectation over a sufficiently large sample. In other words, momentum could deliver better risk-adjusted returns but not outperform buy and hold.
We believe these randomizations are useful to determine what a reasonable expectation is from momentum strategies that select from a universe of alternatives. One time-domain path and a metric selected via data snooping cannot yield a reliable predictor of the future.
We are not fans of momentum strategies for stocks, especially from large indexes, such as the S&P 500, Nasdaq-100, or worse, from the Russell 3000. The Dow-30 is a more manageable index, but momentum has not performed well in backtests. The main reason is the small number of alternatives, the much lower number of high beta stocks, and the high correlation, especially during down markets. Below, we display the results for Dow-30 stocks.
The annualized return is 5.8%, while Sharpe is only 0.51.
This limited study concludes that we should not expect momentum to outperform buy and hold in an out-of-sample scenario. Some strategies might be luckier than others, but the ensemble will always underperform.
Disclaimer: No part of the analysis in this blog constitutes a trade recommendation. The past performance of any trading system or methodology is not necessarily indicative of future results. Read the full disclaimer here.
Charting and backtesting program: Amibroker. Data provider: Norgate Data
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