Monkeys can throw darts at stock quote pages of newspapers. Is long-only momentum better than the monkeys?
In his best-selling book A Random Walk Down Wall Street, Burton Malkiel claimed that a monkey wearing blinders and throwing darts at a newspaper’s financial pages could choose a portfolio that would perform just as well as one put together by financial analysts.
Momentum promised a challenge to the random walk hypothesis. There have been many claims, for and against momentum, but most in favor of the existence of a momentum edge. Other studies have shown that, although this edge existed in the past, it has diminished.
Quants do not rely on claims or the work of others; instead, they strive to replicate the findings, as there may be hidden assumptions or even errors. This requires access to survivorship-free stock data. In this study, we utilize Norgate Data’s S&P 500 index series, which encompass both past and current constituents. Access to survivorship-free data is required for a sound analysis of stock market momentum.
The next challenge in studying momentum is the proliferation of models. Here we rely on falsification of a general hypothesis: if a few simple models fail to demonstrate an edge, we can reject the hypothesis in general.
A higher-level problem is that the past represents only a particular path in the time domain, and data mining bias can be an issue. To deal with this problem, we used randomization for both the ranking score and the entry signals measuring momentum. Therefore, we looked at a distribution of results to determine whether momentum had a significant effect.
All backtests started on January 4, 1988, and end on October 22, 2024. We did not include commissions at this stage because we wanted to measure the pure edge, not to decide whether a strategy was suitable to trade.
First Model: Daily timeframe
At the end of every month, rank stocks according to 120-day rate-of-change and select the top 10 stocks to invest in the next month. The 1988–1999 backtest performance is below.
Although the model did not outperform the buy-and-hold of the S&P 500 total return (red line on the equity growth chart), nevertheless the results were impressive, with a 17.4% annualized return and a 0.79 Sharpe ratio. Below are the results from the start of 2000 to October 22, 2024.
The model performed significantly better than buy-and-hold after the rebound from the dot-com bear market, but volatility in performance increased. The model outperformed buy and hold by a wide margin but at higher volatility and maximum drawdown, and the Sharpe ratio was only 0.35. In addition, the model has been flat after 2020, a phenomenon known as “momentum winter.”
Overall, from 1998 to 2024, the model underperformed in the 1990s but outperformed after the dot-com crash and subsequent financial crisis bear market, albeit with increased volatility. Based on summary statistics, this is how the model compares with the buy and hold strategy in the S&P 500 index.
| Momentum Model 1 | Buy and hold | |
| Annualized Return | 11.0% | 11.2% |
| Maximum Drawdown | -64.3% | -55.3% |
| Volatility | 25.3% | 17.9% |
| Sharpe Ratio | 0.43 | 0.63 |
In the best case scenario, momentum performance (annualized return) has been either statistically indistinguishable from buy and hold or worse than buy and hold. On a risk-adjusted basis (using the Sharpe ratio), momentum has underperformed.
However, we have selected a 120-day lookback period for the rank function and tried a specific model (Model 1). Additionally, the index reconstitution only represents a specific path in the time domain; it could have varied under different market conditions. For this reason, we will randomize both the entry signals and the ranking function and, in effect, test a large number of “momentum monkeys” throwing darts to select 10 stocks. Below is the distribution of the annualized return of 500 “momentum monkeys.”
About 61% of the “momentum monkeys” had higher annualized returns than Model 1, and the average performance was 11.5%. This confirms the theory that, on average, monkeys throwing darts have outperformed momentum. Also note that there have been no losing monkeys.
We only looked at one specific, long-only momentum model: Model 1. Model 2 is a monthly strategy that has an additional entry condition: the price of the stock must be above its 12-month moving average. This version of momentum, also known as price series momentum, has been a favorite among academics. The ranking function used to select the top 10 stocks is the 12-month rate-of-change of the price. Below are the backtest results, from 01/04/1998 to 10/22/2024.
The annualized return improved significantly after the introduction of the price series momentum rule, but the maximum drawdown did not improve much. The annualized return of Model 2 was lower than 11% of the “momentum monkeys,” also raising questions about its significance.
Furthermore, the selection of the 12-month period for the moving average and the lookback period of the ranking function was largely arbitrary, potentially due to data mining bias. Below is a table that shows the annualized return and maximum drawdown for values of the lookback period from 3 to 24 in increments of one month.
The annualized return does not exhibit a smooth relationship with the period. For example, the maximum value is 15.07% for a 3-month period, but for 4 months, it plunges to 11.05%. There may be a quasi-stable region between 7 and 12 months, but it could be regime-dependent. Regardless, the maximum drawdown levels are prohibitive for practical use, prompting some developers to introduce additional filters and conditions. Those increase the probability of overfitting to specific regimes.
Conclusion
In the 1980s and 1990s, momentum proved to be profitable at low maximum drawdown, which likely contributed to the false perception that it is a robust strategy. However, without additional filters that introduce biases and risk of overfitting, long-only momentum is not a robust strategy. As the two backtests in this article have shown, after the 2000 top, momentum volatility increased, the maximum drawdown surged, and there have been several “momentum winters.” This might have been the result of a crowding-out effect, a regime change, or other unknown factors or combinations of them.
Long-short momentum is a unique and intriguing strategy that could offer a portfolio hedge during periods of market stress. However, it is important to consider other factors, such as the availability of shares for shorting during rapid corrections and the associated costs. Therefore, this type of trading is only suitable for professional and hedge funds.
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Charting and backtesting program: Amibroker. Data provider: Norgate Data
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