Calculate the Fama (1972) decomposition of total excess return into Selectivity and Diversification.

Jensen’s Alpha alone conflates two very different sources of excess return: genuine stock/timing selection skill, and simply carrying more total risk than the market by holding an under-diversified portfolio (which, in a CAPM world, should be compensated with extra return even absent any skill). Fama’s decomposition separates the two by comparing the portfolio’s actual return against two different CAPM-implied return benchmarks: one using the portfolio’s actual Beta (systematic risk only), and one using the portfolio’s actual total risk ratio (Sigma_Portfolio / Sigma_Market) in place of Beta.

The formulas are as follows:

\[\text{Selectivity} = (\text{Asset Return} - \text{Risk-Free Rate}) - (\text{Sigma\_Portfolio} / \text{Sigma\_Market}) \cdot (\text{Benchmark Return} - \text{Risk-Free Rate})\] \[\text{Diversification} = \left[\text{Risk-Free Rate} + (\text{Sigma\_Portfolio} / \text{Sigma\_Market}) \cdot (\text{Benchmark Return} - \text{Risk-Free Rate})\right] - \left[\text{Risk-Free Rate} + \text{Beta} \cdot (\text{Benchmark Return} - \text{Risk-Free Rate})\right]\]

Selectivity is the return earned above what would be required for a fully diversified portfolio carrying the same total risk, i.e. genuine security selection or timing skill. Diversification is the extra return the manager left on the table (if positive, it is a cost) by taking on unsystematic risk that a fully diversified portfolio of the same total risk would not have. Selectivity plus Diversification equals Jensen’s Alpha (see get_jensens_alpha).

Also known as: Fama’s Net Selectivity, Fama performance decomposition.

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Calculate the Fama Decomposition in Python

The Fama Decomposition is available in the Performance module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_fama_decomposition as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(["AAPL", "TSLA"], api_key="FINANCIAL_MODELING_PREP_KEY")

toolkit.performance.get_fama_decomposition().xs("AAPL", level=0, axis=1)

Which returns:

Date Selectivity Diversification
2021 0.0113 -0.0084
2022 0.022 -0.0375
2023 0.1048 0.0979
2024 -0.1053 0.1698
2025 -0.1774 0.056
2026 -0.0958 0.1246

Parameters

get_fama_decomposition accepts the following parameters:

  • period (str, optional): The period to use for the calculation. Defaults to “quarterly” if the Toolkit is initialised with quarterly=True, otherwise “yearly”.
  • rolling (int, optional): The rolling window size to use for the Beta component of the calculation. If set, Beta is estimated over a rolling window of this many periods across the full return history instead of per period. Defaults to None.
  • rounding (int, optional): The number of decimals to round the results to. Defaults to 4.
  • growth (bool, optional): Whether to calculate the growth of the ratios. Defaults to False.
  • lag (int | str, optional): The lag to use for the growth calculation. Defaults to 1.
  • standardize (bool, optional): Whether to standardize (Z-Score) the result. When combined with growth=True, standardizes the growth values instead of the raw values. Defaults to False.
Gain-to-Pain Ratio Compound Growth Rate Returns Excess Return Correlation Matrix Covariance Matrix Carhart Four-Factor Model Appraisal Ratio Rachev Ratio STARR Ratio Treynor-Mazuy Model Henriksson-Merton Model

The Performance module page introduces the module, and the sidebar lists all of its functions.

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