.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/asset_pricing/factors/plot_03_fama_french.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_asset_pricing_factors_plot_03_fama_french.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_asset_pricing_factors_plot_03_fama_french.py:


Fama-French three factors
=========================

The CAPM fails on portfolios sorted by size and book-to-market: small
stocks and value stocks earn more than their market betas justify.
Eugene Fama and Kenneth French (1993) added two long-short factors built
from the same sorts, SMB (small minus big) and HML (high minus low
book-to-market),

.. math::

   r^e_{it} = \alpha_i + b_i\,MKT_t + s_i\,SMB_t + h_i\,HML_t + \varepsilon_{it},

and found that the alphas of 25 size-value portfolios nearly vanish.
Here a synthetic market has stocks whose size and value characteristics
drive hidden factor loadings.

.. GENERATED FROM PYTHON SOURCE LINES 21-40

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.asset_pricing import grs_test, long_short_factor, sort_portfolios, time_series_regression
    from financialkit.asset_pricing.visualizers import plot_alphas

    rng = np.random.default_rng(1993)
    T, N = 360, 600
    size = rng.standard_normal(N)  # log market cap, standardized
    value = rng.standard_normal(N)  # book-to-market, standardized
    loadings = np.column_stack([rng.uniform(0.8, 1.2, N), -0.6 * size + 0.2 * rng.standard_normal(N), 0.6 * value + 0.2 * rng.standard_normal(N)])
    f_true = rng.multivariate_normal([0.006, 0.0025, 0.003], np.diag([0.045, 0.03, 0.03]) ** 2, T)
    R = f_true @ loadings.T + 0.08 * rng.standard_normal((T, N))

    mkt = R.mean(axis=1)
    smb = long_short_factor(-size, R)
    hml = long_short_factor(value, R)
    print(f"mean monthly SMB {smb.mean():.4f}, HML {hml.mean():.4f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    mean monthly SMB 0.0031, HML 0.0087




.. GENERATED FROM PYTHON SOURCE LINES 41-43

25 size-value portfolios
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 43-61

.. code-block:: Python


    size_q = np.digitize(size, np.quantile(size, [0.2, 0.4, 0.6, 0.8]))
    ports = np.column_stack([sort_portfolios(np.where(size_q == q, value, np.nan), R, 5) for q in range(5)])

    capm = time_series_regression(ports, mkt)
    ff3 = time_series_regression(ports, np.column_stack([mkt, smb, hml]))
    g1 = grs_test(ports, mkt)
    g3 = grs_test(ports, np.column_stack([mkt, smb, hml]))
    print(f"CAPM: GRS = {g1.statistic:.2f}, p = {g1.p_value:.3g}")
    print(f"FF3:  GRS = {g3.statistic:.2f}, p = {g3.p_value:.3g}")

    fig, ax = plt.subplots(figsize=(10, 4))
    plot_alphas(capm, ax=ax, label="CAPM", offset=-0.2, width=0.4)
    plot_alphas(ff3, ax=ax, label="Fama-French 3", offset=0.2, width=0.4)
    ax.set_xlabel("portfolio (size quintile x value quintile)")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/asset_pricing/factors/images/sphx_glr_plot_03_fama_french_001.png
   :alt: plot 03 fama french
   :srcset: /api/gallery/asset_pricing/factors/images/sphx_glr_plot_03_fama_french_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    CAPM: GRS = 1.64, p = 0.0297
    FF3:  GRS = 0.92, p = 0.577





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.080 seconds)


.. _sphx_glr_download_api_gallery_asset_pricing_factors_plot_03_fama_french.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/asset_pricing/factors/plot_03_fama_french.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_03_fama_french.ipynb <plot_03_fama_french.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_03_fama_french.py <plot_03_fama_french.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_03_fama_french.zip <plot_03_fama_french.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_