.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/market_microstructure/spreads/plot_01_demsetz_spreads.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_spreads_plot_01_demsetz_spreads.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_spreads_plot_01_demsetz_spreads.py:


Demsetz: the bid-ask spread as the price of immediacy
=====================================================

Harold Demsetz (1968) argued that a trader who wants to trade *now*
pays the dealer the spread for standing ready, and that the spread
shrinks as trading activity grows, because a busy dealer turns over
inventory faster. Today the spread is measured three ways: the
*quoted* spread on the screen, the *effective* spread actually paid
relative to the midquote, and the *realized* spread the liquidity
provider keeps once the price has moved; the difference is the *price
impact*, lost to better-informed traders.

.. GENERATED FROM PYTHON SOURCE LINES 16-24

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.market_microstructure import effective_spread, price_impact, quoted_spread, realized_spread
    from financialkit.market_microstructure.visualizers import plot_quotes

    rng = np.random.default_rng(0)








.. GENERATED FROM PYTHON SOURCE LINES 25-31

Quoted, effective and realized spreads
--------------------------------------

A dealer quotes 10 cents wide around the efficient price. Trades fill at
the quotes or, sometimes, inside them; each trade then moves the
efficient price by a cent in its own direction (information) plus noise.

.. GENERATED FROM PYTHON SOURCE LINES 31-50

.. code-block:: Python


    n, half, impact = 2000, 0.05, 0.01
    side = rng.choice([-1.0, 1.0], n)
    m = 100 + np.cumsum(impact * side + 0.01 * rng.standard_normal(n))
    mid = np.concatenate([[100.0], m[:-1]])  # the quote before each trade
    bid, ask = mid - half, mid + half
    price = mid + side * np.where(rng.random(n) < 0.3, rng.uniform(0, half, n), half)
    later = np.concatenate([m[5:], np.full(5, m[-1])])  # midquote five trades later

    for name, x in [
        ("quoted", quoted_spread(bid, ask)),
        ("effective", effective_spread(price, bid, ask, side)),
        ("realized", realized_spread(price, later, side)),
        ("price impact", price_impact(bid, ask, later, side)),
    ]:
        print(f"{name:13s} {x.mean():.4f}")

    plot_quotes(price[:40], bid[:40], ask[:40], side=side[:40])




.. image-sg:: /api/gallery/market_microstructure/spreads/images/sphx_glr_plot_01_demsetz_spreads_001.png
   :alt: plot 01 demsetz spreads
   :srcset: /api/gallery/market_microstructure/spreads/images/sphx_glr_plot_01_demsetz_spreads_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    quoted        0.1000
    effective     0.0843
    realized      0.0649
    price impact  0.0194

    <Axes: xlabel='trade', ylabel='price'>



.. GENERATED FROM PYTHON SOURCE LINES 51-57

Demsetz's cross-section
-----------------------

Demsetz regressed the spreads of 192 NYSE stocks on their number of
transactions and found a strongly negative slope. Here a synthetic
cross-section with an elasticity of -0.4 is recovered by a log-log fit.

.. GENERATED FROM PYTHON SOURCE LINES 57-71

.. code-block:: Python


    trades_per_day = 10 ** rng.uniform(1, 4, 150)
    rel_spread = 0.02 * trades_per_day**-0.4 * np.exp(0.25 * rng.standard_normal(150))
    slope, intercept = np.polyfit(np.log(trades_per_day), np.log(rel_spread), 1)
    fig, ax = plt.subplots(figsize=(6, 4))
    ax.loglog(trades_per_day, 1e4 * rel_spread, ".", color="0.5")
    grid = np.logspace(1, 4, 50)
    ax.loglog(grid, 1e4 * np.exp(intercept) * grid**slope, "C3", label=f"elasticity {slope:.2f}")
    ax.set_xlabel("transactions per day")
    ax.set_ylabel("relative spread (bp)")
    ax.legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/market_microstructure/spreads/images/sphx_glr_plot_01_demsetz_spreads_002.png
   :alt: plot 01 demsetz spreads
   :srcset: /api/gallery/market_microstructure/spreads/images/sphx_glr_plot_01_demsetz_spreads_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.071 seconds)


.. _sphx_glr_download_api_gallery_market_microstructure_spreads_plot_01_demsetz_spreads.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/spreads/plot_01_demsetz_spreads.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_demsetz_spreads.ipynb <plot_01_demsetz_spreads.ipynb>`

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

      :download:`Download Python source code: plot_01_demsetz_spreads.py <plot_01_demsetz_spreads.py>`

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

      :download:`Download zipped: plot_01_demsetz_spreads.zip <plot_01_demsetz_spreads.zip>`


.. only:: html

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

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