Alternative Equity Factor Portfolio Formation Method

The conventional approach to measuring equity factor returns is via hedge portfolios that are long (short) the equal-weighted or value-weighted extreme highest (lowest) fifth or tenth of stocks sorted by some firm/stock characteristic. Is there a better way? In their August 2023 paper entitled “Power Sorting”, Anastasios Kagkadis, Harald Lohre, Ingmar Nolte, Sandra Nolte and Nikolaos Vasilas construct equity factor portfolios based on power sorting, which: (1) models the firm characteristic-future stock return relationship using a power series; and, (2) uses the power series to set factor portfolio weights. This approach requires no arbitrary quantile break points, instead allocating some weight to all stocks and tilting toward/away stocks with extreme characteristics as a compromise between conventional sorts and machine learning methods. Power sorting employs separate parameters for the long and short sides of the factor portfolio. Higher parameter values generate portfolios that concentrate more in stocks with characteristic extremes, while lower values spread weights more evenly across stocks. Differences between the two parameters allow differently weighted long and short sides of a factor portfolio. Additionally, they set an upper limit on the allocation to any one stock (2% in their main analysis) to ensure factor portfolio diversification. Using monthly factor data and associated stock returns for 85 widely accepted factor characteristics during March 1980 through December 2021, they find that:

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