Calculate Jensen’s Alpha, a measure of an asset’s performance relative to its expected return based on the Capital Asset Pricing Model (CAPM).

Jensen’s Alpha is used to assess whether an investment has outperformed or underperformed its expected return given its systematic risk, as represented by the asset’s Beta.

The formula is as follows:

\[\text{Jensen's Alpha} = \text{Asset's Actual Return} - \left[\text{Risk-Free Rate} + \text{Beta} \cdot (\text{Benchmark Return} - \text{Risk-Free Rate})\right]\]

See definition: https://en.wikipedia.org/wiki/Jensen%27s_alpha

Also known as: Jensen alpha, risk-adjusted excess return.

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Calculate the Jensen’s Alpha in Python

The Jensen’s Alpha is available in the Performance module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_jensens_alpha as shown below.

from financetoolkit import Toolkit

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

toolkit.performance.get_jensens_alpha()

Which returns:

Date AAPL TSLA
2021 -0.0112 0.0062
2022 -0.0037 -0.2837
2023 0.2185 0.5267
2024 0.0741 0.1328
2025 -0.1082 -0.1999
2026 0.0531 -0.2615

Parameters

get_jensens_alpha 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.
Beta Capital Asset Pricing Model (CAPM) Factor Asset Correlations Factor Correlations Fama and French Model (FF) Alpha Treynor Ratio Sharpe Ratio Sortino Ratio Ulcer Performance Index (UPI) Calmar Ratio Sterling Ratio

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

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