.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fixed_income/duration/plot_05_ho_key_rate_durations.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_fixed_income_duration_plot_05_ho_key_rate_durations.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_fixed_income_duration_plot_05_ho_key_rate_durations.py:


Ho's key rate durations
=======================

A single duration assumes the whole curve moves in parallel. Thomas Ho
(1992) shocked the curve one *key rate* at a time, with triangular shapes
that sum to a parallel shift, so a bond's risk becomes a vector whose
entries add up to its effective duration. Two portfolios with the same
duration can have very different key rate profiles.

.. GENERATED FROM PYTHON SOURCE LINES 13-22

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.fixed_income import NelsonSiegelCurve, bond_cash_flows, key_rate_durations, key_rate_weights, redington_immunize
    from financialkit.fixed_income.visualizers import plot_key_rate_durations

    keys = np.array([0.5, 1, 2, 5, 10, 20, 30])
    curve = NelsonSiegelCurve(0.045, -0.02, 0.01, 2.0)








.. GENERATED FROM PYTHON SOURCE LINES 23-25

The key-rate shock shapes
-------------------------

.. GENERATED FROM PYTHON SOURCE LINES 25-34

.. code-block:: Python


    t = np.linspace(0, 35, 400)
    fig, ax = plt.subplots()
    for k, w in zip(keys, key_rate_weights(t, keys), strict=True):
        ax.plot(t, w, label=f"{k:g}y")
    ax.set_xlabel("maturity (years)")
    ax.set_ylabel("shock weight")
    ax.legend(ncol=4)




.. image-sg:: /api/gallery/fixed_income/duration/images/sphx_glr_plot_05_ho_key_rate_durations_001.png
   :alt: plot 05 ho key rate durations
   :srcset: /api/gallery/fixed_income/duration/images/sphx_glr_plot_05_ho_key_rate_durations_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x117062ba0>



.. GENERATED FROM PYTHON SOURCE LINES 35-37

Bullet and barbell with equal duration
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 37-47

.. code-block:: Python


    bullet = bond_cash_flows(100.0, 0.045, 10.0)
    target = bullet.scaled(1.0)
    barbell = redington_immunize(target, [bond_cash_flows(1.0, 0.04, 2.0), bond_cash_flows(1.0, 0.05, 30.0)], curve).portfolio
    fig, axes = plt.subplots(1, 2, figsize=(10, 4), sharey=True)
    for ax, (name, cf) in zip(axes, (("bullet 10y", bullet), ("2y/30y barbell", barbell)), strict=True):
        res = key_rate_durations(cf, curve, keys)
        plot_key_rate_durations(res, ax=ax)
        ax.set_title(f"{name}: sum {res.durations.sum():.2f}")
    plt.show()



.. image-sg:: /api/gallery/fixed_income/duration/images/sphx_glr_plot_05_ho_key_rate_durations_002.png
   :alt: bullet 10y: sum 8.16, 2y/30y barbell: sum 8.16
   :srcset: /api/gallery/fixed_income/duration/images/sphx_glr_plot_05_ho_key_rate_durations_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.061 seconds)


.. _sphx_glr_download_api_gallery_fixed_income_duration_plot_05_ho_key_rate_durations.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/fixed_income/duration/plot_05_ho_key_rate_durations.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_05_ho_key_rate_durations.ipynb <plot_05_ho_key_rate_durations.ipynb>`

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

      :download:`Download Python source code: plot_05_ho_key_rate_durations.py <plot_05_ho_key_rate_durations.py>`

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

      :download:`Download zipped: plot_05_ho_key_rate_durations.zip <plot_05_ho_key_rate_durations.zip>`


.. only:: html

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

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