Fama Decomposition
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.
Fama Decomposition in Python
Install the Finance Toolkit 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
The function accepts the following parameters:
- period (str, optional): The period to use for the calculation. Defaults to “quarterly” if the Toolkit is initialized 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.