Why Mixing Factor-Sorted Equity Portfolios Can Improve Results
Summary
The post describes a historical S&P 500 simulation that forms annual portfolios from companies ranked by return on equity: a top group, a bottom group, and a portfolio combining both. Holdings that leave the index are sold and their value redistributed among the remaining holdings; the portfolios are rebuilt annually. In the reported simulation, the mixed portfolio performs better than either group, prompting the question of why it does not simply match their average.
The answer suggests that small groups of twenty stocks may produce noisy results and recommends examining broader groups, such as quintiles. It also points to diversification: combining firms selected on one characteristic can reduce the influence of idiosyncratic outcomes. Because ROE may not closely track absolute stock returns, the observed ranking may reflect noise or an anomaly rather than a robust effect. The post gives no detailed performance statistics or out-of-sample validation, so its explanation is plausible rather than demonstrated.
Key ideas
- A portfolio combining high- and low-ROE stocks can outperform either subset in a particular simulation.
- Results from small groups of stocks may be dominated by noise, so broader buckets can be more informative.
- Diversification may help a mixed portfolio when stocks are classified using a single characteristic.
- An apparent result based on ROE may be unstable because the ranking can capture noise rather than persistent return differences.
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Full text
# Does a combined Portfolio always performs like the average of the merged subportfolios? # Does a combined Portfolio always performs like the average of the merged subportfolios? I analyzed the historic data of the SP500 and tried a trading simulation on it. I picked the best 20 companies from SP500 for one year according to their ROE and put them in one portfolio. Let's call this TOP-Portfolio for now. I've also done this for the worst companies - BOTTOM-Portfolio and I've created a MIXED-Portfolio with the top 20, and bottom 20 companies. Then I simulated a 52 weeks to represent a whole year. If a company is no longer in the SP500, I 'sold' this company and distributed it's current value along all the other remaining companies. There are no companies bought during one year. If the year is over, I 'sell' all the companies and again create the 3 portfolios and distribute the whole money from the old portfolios on the new ones (money from old TOP-Porfolio will be distributed on the new TOP-Portfolio and so on). My mixed portfolio performs better than the bottom and the top portfolio. Is there a possibility that this outcome is still true? Since I thought the mixed portfolio would perform like the average of the TOP- and the BOTTOM-Portfolio, this outcome is rather strange for me. I'd appreciate any help from you. Here is a plot of my outcome: ## Answer by Chris (score 1) https://quant.stackexchange.com/a/46360 This is likely attributable to one of a couple things: (1) Your portfolio size for the top/bottom set are on the small side. If you broke the SP500 into quintiles by performance, made top (100) your top portfolio, bottom (100) your bottom portfolio, you're likely to see a more interesting result. (2) As an addendum to (1), your mixed portfolio probably performs better in large part due to diversification. Particularly bucketing based on a single attribute (not to mention one somewhat disconnected from absolute stock market return like ROE), your classification is much more likely the result of noise/anomaly, and as such your results lack robustness you'd hope to see.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.