We ran three textbook trading rules on 112 markets and combined them by majority vote. A model built from several others like this is called an ensemble. On 66 of the 112 markets, the vote beat the rule with the best past record.
The vote did not beat the best single rule. That rule, 12-month momentum, holds a market while its price is above where it was a year ago. It scored slightly higher on the median market. Here is how an ensemble works, what our test found and why this vote added so little.
What are ensemble models in trading? An ensemble combines several models or rules into one trading decision. In a majority vote, the position follows what most of the members say.
We picked the rule with the best record in the first half of each market's data. Over the second half, the vote had a higher Sharpe ratio, a score of return per unit of risk, on 66 of 112 markets.
The vote did not beat the best single rule, 12-month momentum. Their median Sharpe ratios were 0.55 and 0.56. Simply buying and holding scored 0.65.
A vote helps only when its members disagree. On the median market, the vote matched the 200-day trend rule on 96.7% of days. That rule holds while the price is above its 200-day average.
What is an ensemble model?
An ensemble is a group of models whose answers are combined into one. The simplest way to combine them is a vote. Each member says long or flat. Long means hold the market. Flat means hold cash. The majority decides.
The case for voting is old. Condorcet's jury theorem says a majority vote becomes more likely to be right as more members join. It needs two conditions. Each member must be right more than 1/2 of the time. Their errors must also be independent, so they do not all go wrong together. The second condition is the one to watch in markets.
Combining rules is one part of systematic investing, where every decision follows written rules.
The three rules, the vote and the data
We used three rules from the textbooks. Each is long or flat, decided at the close and acted on the next day:
200-day trend: hold while the price is above its 200-day average.
12-month momentum: hold while the price is above where it was 252 trading days ago, about a year.
50-day breakout: buy after a close above the highest close of the previous 50 days. Sell after a close below the lowest close of the previous 50 days.
The vote holds the market when at least two of the three rules do. We fixed all of this before running the test.
The data is YX Insights price data with dividends counted. It covers 81 shares, 27 exchange-traded funds (ETFs) and 4 cryptocurrencies. The test runs from mid-2017 to 24 September 2026. Markets with shorter histories start later, so the median test runs 9.1 years. Cash earns nothing. Results are before costs unless stated.
Median Sharpe ratio: each rule, the vote and buy-and-hold
To compare the rules, we use the Sharpe ratio. It is the mean daily return divided by the standard deviation of daily returns, scaled to a year. A higher score means more return for each unit of swing.
Source: YX Insights price data; YX Insights
Chart 1 gives the median Sharpe ratio across the 112 markets. The vote scored 0.55. That sits between 12-month momentum at 0.56 and the 200-day trend at 0.53. The 50-day breakout scored 0.49. Buying and holding scored 0.65, ahead of all four.
Does voting beat picking one rule?
Picking one rule sounds easy: choose the one with the best record. The problem is that the best rule changes. We split each market's history in half. The rule that scored best in the first half was also best in the second half on 29 of 112 markets. With three rules, chance alone would give a repeat on about 37.
Source: YX Insights price data; YX Insights
Chart 2 counts the markets where the vote had a higher Sharpe ratio than each alternative. Two bars are picked market by market over the full test. The worst rule is the one that scored lowest on that market. The best rule in hindsight is the one that scored highest.
The vote beat the worst rule on 94 markets. It beat the 50-day breakout on 72. It beat the rule picked on its first-half record on 66. That count uses the second half only. Over the second half, the vote's median Sharpe ratio was 0.51, while the picked rule's was 0.45.
The vote lost every other contest. It beat 12-month momentum and the 200-day trend on 51 markets each. It beat the best rule in hindsight on 21. It beat buying and holding on 30.
Our essay I Tested the Golden Cross Against a Coin-Flipping Monkey found the same with moving-average pairs. Choosing the past winner did no better than choosing at random.
Why the vote added so little: it mostly copied the 200-day rule
Source: YX Insights price data
Chart 3 shows SPY (the S&P 500 ETF). Blue marks the days each rule held it, while orange marks the vote. The vote row looks almost the same as the 200-day trend row. On SPY, the two matched on 99.8% of days.
Source: YX Insights price data; YX Insights
Chart 4 shows the same pattern across all 112 markets. On the median market, the vote took the same position as the 200-day trend rule on 96.7% of days. For momentum it was 85.2%. For the breakout it was 84.0%.
The reason is the jury theorem's second condition. These rules are not independent. All three agreed on 65.6% of days for the median market. Correlation measures how closely two series move together, from −1 to 1. The trend rule's daily positions had a median correlation of 0.56 with momentum. With the breakout it was 0.58. Momentum and the breakout correlated at 0.29. The rules split on 34.4% of days. On those days, the vote sided with the trend rule 90.5% of the time. So the vote mostly became the 200-day trend rule.
Costs, drawdowns and how often the vote trades
A drawdown is a fall from a peak to the next low. The table gives the median across the 112 markets.
Median across 112 markets | Buy-and-hold | 200-day trend | 12-month momentum | 50-day breakout | Majority vote |
|---|---|---|---|---|---|
Return a year | 17.3% | 10.5% | 11.8% | 9.5% | 11.4% |
Worst fall | −55.6% | −46.3% | −45.6% | −45.4% | −45.9% |
Share of days held | 100% | 66.9% | 71.5% | 60.5% | 67.3% |
Position changes a year | 0 | 8.0 | 5.3 | 3.1 | 6.8 |
Sharpe ratio, before costs | 0.65 | 0.53 | 0.56 | 0.49 | 0.55 |
Sharpe ratio, after 0.10% per change | 0.65 | 0.49 | 0.54 | 0.48 | 0.51 |
Source: YX Insights price data; YX Insights
The vote had a smaller worst fall than buying and holding on 83 of 112 markets. The trend and breakout rules each managed it on 90.
The vote changed position 6.8 times a year. Momentum changed 5.3 times, while the breakout changed 3.1 times. Only the trend rule traded more, at 8.0. Over the full test, a cost of 0.10% per change cut the vote's median Sharpe ratio from 0.55 to 0.51. Momentum's fell from 0.56 to 0.54.
How to judge an ensemble trading strategy
A few checks apply to any ensemble:
Measure how often the members disagree. If one member decides almost every vote, the ensemble is that member. Our three rules all follow trends, so they agreed most of the time.
Compare it with the best member, out of sample. Test it on data the rules were not chosen on. Our guide to backtesting explains why.
Count the trades. A vote can flip more often than most of its members.
Fix the rules first. Choosing members after seeing results is overfitting.
In this test, a majority vote of three textbook rules beat the rule picked on its past record. It did not beat the best single rule, 12-month momentum. An ensemble adds value only when its members make different mistakes.
Learn more with YX Insights
This explainer is part of the YX Insights Academy. Each one takes a single idea and checks it against real data.
The same approach runs through everything else we publish:
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DISCLAIMER: This article is strictly educational. Any information or analysis in this note is not an offer to sell or the solicitation of an offer to buy any securities. Nothing in this note is intended to be investment advice and nor should it be relied upon to make investment decisions. Any opinions, analyses, or probabilities expressed in this note are those of the author as of the note's date of publication and are subject to change without notice.