.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/market_microstructure/liquidity/plot_01_amihud.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_market_microstructure_liquidity_plot_01_amihud.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_market_microstructure_liquidity_plot_01_amihud.py:


Amihud's illiquidity ratio
==========================

Yakov Amihud (2002) proposed a liquidity measure that needs only daily
returns and dollar volume: the average of :math:`|r_d| / \mathrm{DVol}_d`,
the price move per dollar traded. It approximates Kyle's lambda, which
needs signed order flow, and Amihud found that stocks with a higher
ratio earn higher expected returns, an illiquidity premium.

.. GENERATED FROM PYTHON SOURCE LINES 13-21

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy import stats

    from financialkit.market_microstructure import amihud_illiquidity, kyle_lambda

    rng = np.random.default_rng(15)








.. GENERATED FROM PYTHON SOURCE LINES 22-28

A cross-section of stocks
-------------------------

Each stock's daily return is its Kyle lambda times its signed dollar
order flow plus public news. Lambdas span two orders of magnitude, and
less liquid stocks trade less.

.. GENERATED FROM PYTHON SOURCE LINES 28-52

.. code-block:: Python


    n_stocks, days = 80, 250
    lam = 10 ** rng.uniform(-9, -7, n_stocks)  # return per dollar of net order flow
    scale = 2e5 / np.sqrt(lam / 1e-9)  # typical net flow in dollars
    amihud, kyle = [], []
    for i in range(n_stocks):
        net = scale[i] * rng.standard_normal(days)
        dvol = np.abs(net) + scale[i] * rng.gamma(2.0, 1.0, days)
        r = lam[i] * net + 0.005 * rng.standard_normal(days)
        amihud.append(amihud_illiquidity(r, dvol))
        kyle.append(kyle_lambda(r, net).coef[1])

    rho = stats.spearmanr(lam, amihud).statistic
    print(f"rank correlation between Amihud's ratio and the true lambda: {rho:.2f}")

    fig, ax = plt.subplots(figsize=(6, 4.5))
    ax.loglog(lam, amihud, "o", color="C0", label="Amihud ratio (per $1M)")
    ax.loglog(lam, 1e6 * np.abs(kyle), "x", color="C1", label="regression lambda (per $1M)")
    ax.set_xlabel("true Kyle lambda")
    ax.set_ylabel("estimate")
    ax.legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/market_microstructure/liquidity/images/sphx_glr_plot_01_amihud_001.png
   :alt: plot 01 amihud
   :srcset: /api/gallery/market_microstructure/liquidity/images/sphx_glr_plot_01_amihud_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    rank correlation between Amihud's ratio and the true lambda: 0.99





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

   **Total running time of the script:** (0 minutes 0.066 seconds)


.. _sphx_glr_download_api_gallery_market_microstructure_liquidity_plot_01_amihud.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/market_microstructure/liquidity/plot_01_amihud.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_amihud.ipynb <plot_01_amihud.ipynb>`

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

      :download:`Download Python source code: plot_01_amihud.py <plot_01_amihud.py>`

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

      :download:`Download zipped: plot_01_amihud.zip <plot_01_amihud.zip>`


.. only:: html

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

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