Calculate the Appraisal Ratio, i.e. Jensen’s Alpha divided by the idiosyncratic (residual, unsystematic) standard deviation left over from the CAPM regression that produced that Alpha.

Jensen’s Alpha (see get_jensens_alpha) measures how much return a manager generated above what CAPM would predict given the asset’s Beta. However, a large Alpha achieved with wildly noisy, unpredictable residual returns is far less attractive than the same Alpha achieved consistently. The Appraisal Ratio normalizes Alpha by that noise (the “specific risk” not explained by market exposure), giving a Sharpe-ratio-like measure of stock-picking or timing skill per unit of idiosyncratic risk taken.

The formula is as follows:

\[\text{Appraisal Ratio} = \text{Jensen's Alpha} / \text{Residual Standard Deviation}\]

Where the residual standard deviation is the standard deviation of the pointwise CAPM regression residuals (Asset Excess Return − Beta * Benchmark Excess Return), reusing the exact same CAPM regression formula as get_jensens_alpha.

See definition: https://en.wikipedia.org/wiki/Information_ratio

Also known as: Treynor-Black Appraisal Ratio.

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Calculate the Appraisal Ratio in Python

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

pip install financetoolkit -U

Then call get_appraisal_ratio as shown below.

from financetoolkit import Toolkit

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

toolkit.performance.get_appraisal_ratio()

Which returns:

Date AAPL TSLA
2022 -0.0946 -0.5928
2023 1.4422 1.0563
2024 0.3371 0.1716
2025 -0.5687 -0.5019
2026 0.1411 -1.8633

Parameters

get_appraisal_ratio 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 Rachev Ratio STARR Ratio Treynor-Mazuy Model Henriksson-Merton Model Fama Decomposition

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

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