A Factor Model Based on Purified Past Returns and No Fundamentals

Does alignment of return-based factors with informed traders and against noise traders produce a superior model of stock returns? In his August 2025 paper entitled “An Auto-Residual Factor Model”, Malek Alkshaik introduces and tests a 5-factor Auto-Residual Factor Model of stock returns comprised of: market excess return; market capitalization (size); residual short-term reversal (last month); residual momentum (measured from 12 months ago to one month ago): and, residual long-term reversion (measured from 24 months ago to 13 months ago). This model uses no firm fundamental data. He postulates that the latter three factors occur due to interactions between noise traders and informed traders. He calculates (purifies) residuals via regressions against five principal components derived from the last 24 months of returns for all stocks, thereby aligning residuals with informed traders and against noise traders (purifying). He emphasizes maximum squared Sharpe ratio (based on mean-variance optimal factor allocations) to compare the new model to seven widely used alternatives. Using a main sample of U.S. listed common stocks during 1972 through 2022, plus a 1932 through 1971 U.S. sample and a 1992 through 2022 global sample for robustness tests, he finds that:

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